Master class with Andreas Heinrich

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Master class with Andreas Heinrich
The quantum mechanics of spins on surfaces
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We all learn in quantum mechanics lectures how to treat the spin of an electron using the Pauli matrices of an S=1/2 system. However, the magnetic properties of atoms in gas and in particular those in a solid-state environment or in molecules are often much more complex and interesting. We will begin by trying to understand what happens when the spin of a quantum system is larger than S=1/2 at which point ligand fields (crystal fields in solids) become important and lead to important effects such as magnetic anisotropy. We will then move from the treatment of a single spin system to coupled spins. How do you set up spin matrices for such a situation and how do you find solutions to those problems? We will discuss some experimental findings about spin chains on surfaces as studied by STM. If time permits we will try to apply the concepts of coupled spin systems to quantum computation.
Keywords Spin Quantum
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but it Hi everybody my name is Andrea and I'd like to tell you the votes some of all work on spins on surfaces as you probably know I also have a talk tomorrow nite when going talk about something quite different so you won't hear the same thing again so that's that's good I guess but it also something which I've never done before which is to try to teach you that the spin matrices is Polly matrices that you probably hated in quantum mechanics just as much as I hated them at the time that they are actually pretty useful To calculate things that you can actually measure with a scanning tunneling microscope so that's basically the goal I have and that might be little boring sometimes because I wish want to use the word to show you that they can actually do Real calculations with them and so that's too boring to let me know and so I don't really have a detailed agenda I put something together and you have a copy of that that's not exactly what I'll be using so you'll see some differences all be happy to provide the exact slides them using if you guys want to have those 4 4 for later that's fine before we get started the word like to take maybe 5 minutes or so and have each 1 of you tell me you know in a few sentences or what your background is To so have a bit of an idea know what what to expect so they would start over here just just you name any couple sentences on on what you're looking at a senior from the state and the Internet and you cannot just have thank you I'm just saying was In this my name on lost in the mail but I like to think in the language of and some 1 of the men and women who traveled on the 2 men were not the kind of people that actually reinforces this morning so long as the sum of money and from the and the quality of gasses and and and the like and work on you just you and me and my working and as you on a roll you know what you and I miss you know the been transport is not meant as a set in the time of the year in view of the world In the were all going to be this something when you have a problem you know it's almost like a little leeway to my mind I don't even want to know what the President of the United States and use I want you to know that the people of the world and I'm going to stick in the eye and said to him What do you want and if you look at the man who led to the end of the course 33 Tests of at end to the ban on and on and on and on and on and on and on but you know what you and you have have much to learn he had and what we great so some of you will be really bored if you working on Spain Cuba's you probably know more about spin operators and I do and so you really be bored and the rest of you know I see some of you will actually learned something today which which is what we want to achieve OK so so let me get going on I was making the little bit of fun off the magnetism was suspended right but it's actually is actually a very very serious serious distinction that thing between the 2 and the distinction really lies in whether you think of them as quantum-mechanical as classical objects a classical here I mean and this folly what you also Mendes use something like a lender should kill words equation or just the direction of democratization as the as the magnetic moment and you can determine that the mechanization direction to any position that's in contrast of course of the quantum-mechanical description where you spin operators and you have quantum computing and all these applications in life so maybe that's the distinction that you have this is something that I'm actually very interested in is you know if you take a single atom for example he put that on a surface like I'll be using in this in this discussion today then we mostly use quantum-mechanical concept I won't be telling you anything the boldface coherent and quantum mechanics such such as you would need for for quantum computation but we trying to get there but we don't have that with our systems so it's all going to be but the energy I'd states essentially of such systems on the other hand if you want to do data storage then no you don't really want to do squander mechanical systems you want to have something that a compass needle it's points north of up South that's magnetic state that you want to use for data storage and so quantum mechanics is a bad thing for those kind of spin systems and so it's interesting question how go-between so the million items that you haven't these things you too the few items we use quantum mechanics and you can ask yourself how the transition region works which is really what I mostly working on now since his election and I don't really wanna talk the whole time I really need you guys to 2 break this upright and ask questions and give me your your thoughts on things OK so what do you want to learn from from such a quantum system and in the end we want to do this the quantum computation that those so and in the really far future I'd like to put items on surfaces that let users scanning incoming microscope as a tool to interact with those guys and you fall coherent quantum mechanics like some of you were doing if you do Cubans in in semiconductors for example now we don't have to sit for this you need to know a lot of things and
a lot of what further detail about the interaction between this Adam cured spin and for example that the environment that is that is in there no we will talk about today to quite some extent is the energy landscape that these spin states here will have so here on sketching has been that is larger than it's been 1 have which you probably accusing perfume that's so here spin too which is 16 iron and in all cases and the silent Adam has 5 spin states those spin states and not be generated 0 magnetic field and we will talk about this in quite some detail I want to show you how we can calculate the so-called 0 fewer splitting from some knowledge about the spin operators that's 1 of the girls I have for this talk and also how he can then learn something about the dependence of his energy states as a function of say an external magnetic if we have time then we can also talk about how we can measure relaxation time so if you take 1 of those states and you put it into an excited state than you might also want to know how long does this does disconnection living this excited state how fast a real expert down next a T-1 relaxation time for those of you walking quantum computing somewhat to 2 might not faced were here just energy relaxation time and those we can measure but with the time resolution down to approximately 1 nanosecond if we have time we can talk about this and they it in a pair of using his spring excitation spectroscopy with STM so using scanning tunneling microscopy to be sensitive to the magnetic states of those of those single acts OK now I've promised for someone who would do quantum computing and this is going to be trivial so you have to be quiet everybody else this is sort of the introduction to what is the difference between classical classical spins classical monetization descriptions and quantum mechanics so you've probably all learnt that electrons have a spin and you can measure the speed with which to Angalich experiment the Sangatte experiment to take a of Adams that have a simple magnetic state just a single electron essentially even think of this as a single electrons flying through space if you want and you put this single electrons in this apparatus which is based in measuring its monetization indices direction among particular spatial directions I call 0 here and because this is a quantum mechanical thing and it has 2 states we see too deflections of those being deflects into 2 I'm states with equal opportunities please use it as a signal here which recall as the and a single down here which is a C-minus In practice this is done with it in homogeneous magnetic field that deflects the spins depending on the monetization of the spin and gives you gives rise to this but no more about the details because when it's not going to do this we just good was conceptually here OK but that's not that difficult like what you learned from this is that there is such a thing called the spin and that the spring has 2 levels but they can obtain now this becomes more interesting if you then use a similar apparatus that you've wrote now rotated by 90 so now he measuring the monetization of this beam of atoms in the direction he and blocking out one-half of those Adams so I know but all of these guys guys the SE plus stadium and now I'm sending them for the standout experiment here In the x-direction 90 degrees rotated and they 2 means coming out I can repeat this now I blocked the Essex is due the x-direction here so block out the 6 miners and so now I have received and as 6 blasts and so the question then is what comes out of this operators we have already measure that is a C-plus Of already measured its SX blast surfer dude is the measurement again would work it out the local quantum computing that is what you get up half and half and you probably learned why this is but I would like to take a moment and then maybe take some time with and show you why this actually works so that we do this number so you have to slide actually in Europe In your hand out there from so really what the I mean the answer for why this is 1 half of 1 house of course because this staying lf experiment in x-direction has destroyed the information From the Stengel experiment into is the direction is among commuting operators saying quantum mechanics but let's look at this little bit more in detail so I'll be very sloppy today the SX operators defined as age would too 0 1 1 0 and we're just going to make the same plot by using using just the thing nepali matrices his on leaving this 1 half year and I'm also not worry about age Barclay the sisters just don't use this for detailed computations at home was up my from now also what you need to know the 2 states that we have the upstate here is defined as 1 0 and the downstate is defined as 0 1 and so you can just for example you can apply Sigma X the upstate it is 0 1 1 0 France 1 0 he do this the little 1 and that is 0 . just misses island state that can't be right so seem too fast Valentine's Day so what comes out 0 1 but some new paying attention at school so basically applying the Sigma X operator on the upstage gives us the downstate .period I will be doing in this experiment here it is within walking out the Essex minus component right blocking out the assets minus component but basically preparing this guy in the S X fighting state witches with Estonia the sex I'm saying something like later but I don't know what's the proper terminology the Sigma X upstate or something like that something like 1 1 end now we are seeing this last experiment was the probability of finding this guy in the upstate and downstate and this is just the 1 was good to hear this is 1 of a square with 2 times 1 0 was 1 of was square with too I'm still 1 and this is the 1 half but you get the legal possibilities now then we can also do something maybe a little bit more interesting here witches that's what I just told you here so
you can ask of what happened in this experiment here basically have already given the answer here I think quite so the only difference is we're not locking out the Essex miners here and so the question is what comes out here is it's still 50 cent right so we're preparing the system in the SE plus state roh operating on this with the standout experiment in the next election we're not locking out 1 of the 2 being and then we were asking the question What is your stayed in the same direction 50 50 but what a quantum computing yeah but I don't think it's 50 50 because the 50 50 came about because you prepared here than Essex plus state by blocking out the Essex state that's what we do and now is we're doing something that is more akin to actual quantum computation will operating on a well-prepared stayed here With this operator which gives us exactly this year and then we are asking the state what is your decomposition in plus as C-minus which is 100 per cent as the mines but it's not magic that's really in a nutshell what this whole talk about this is probably the only thing but you really gonna learn that you can use these matrices if you apply them halfway reasonably 2 learn something about what this kind of system so we can take your time here we you know you seriously the difference between these 2 experiments it's just the
facts whether you blocking out
this 6 here where so this experiment you don't have to do this at all this doesn't give you anything dozens those mechanism and essentially invited just leave this up they will be exactly the same outcome this just means that you preparing system in the Essex plastic and then you asking if you are the Essex busted How much probability have to be in the S plus India C-minus which is what this guy In the
other hand if I do this experiment here then this 1
really matters but I'm preparing the system in the SE plus state and now I'm doing something that you would call a quantum computation if you if you on this field you operating under state With this operator here and you keeping the full ways of it and then asking them what is the result was the outcome of but yeah this year with is back in the year walk all those having all the losses at the at all it does because the outcome of this this is the standout flip spent the last year of the the the and settling in if made experiment with Essex class and Essex miners yeah but of equal weight silicon and see if this stadium if you express this guy the fastest way musician of his explosiveness it's minus that's 1 have equal weight of Of those 2 the but this is what it's all about I mean there's no need to not answer your question I was going to to be more of a role look at what I mean by those boxes as it is in the end some way to make these matrices bring those medicines to life but so so this is sort of I mean I didn't make these apparatuses does is standard textbooks and of some of them suck rise is my favorite 1 that actually starts the quantum mechanics with this experiment to show you that classically with that for the 1st 1 that classically Of course the
outcome is if this is a classical sprint mother quantum-mechanical spin like you can measure is the component and you can measure the that's fine classically you can determine the memorization to any precision in all 3 spatial directions at the same time that's what we mean by classical spin this and so the outcome here is that you get a plus plastic what sort of used as an example of why quantum mechanics is different from classical
I really like your question of what makes you shouldn't I don't come across as not liking question OK so now
I want to take maybe 10 15 minutes to introduce the basic measurement techniques that I'm using witches an STM scanning Tommy microscopy technique based on inelastic electron tunneling spectroscopy which tells us something about the images separations between the ground state and the excited states Of dispenses this is going to be a little more like like a like a regular talk but again I'd like you to interrupt me and then ask questions as we go along so the experiment would do doing some of you are doing transport in they're feeling the other plane at junctions in some senses related we run electric current through a tunnel junction well we have a single magnetic Adams in the beginning or chain of atoms on the surface and the but taking the current from and in the 1st place among magnetic tip to a moment that example but running it through all magnetic Adam in the middle 1 that he was working on on no 1 that could us like a structures I to so with the break junction what was there "quotation mark and how do you measure the states that on the other side the Net electrical transport going through several molecules at once so this is this is in some sense the need to single molecule equivalent if you want but if you had 1 of these molecules in between I break junction experiments for example can do this to some degree looking so I am in the simplest case if we just have a spin one-half like these guys over here he applied magnetic field to spend 1 half of 0 magnetic field is to generate at finite magnetic field you have an energy separation that's a managing zuma energy is proportional to the external magnetic field but in the property that you can learn here is the so-called G value which tells you something about overdoing momentum and spinning lamented of of the structure that you have no I'm going to be using only 1 material here which is a thin layer of copper nitrate which is prepared on copper and this is a scanning tunneling microscopy image approximately 192 by 109 large or small and what you see here is in green the beer surface of copper the particular spatial direction of 1 0 0 0 1 0 0 direction and you can see that that's basically atomically flat and and beautiful then we prepare on these these patches of blue here which are a single atomic layer often insulated copper nitrate that's an area of approximately 10 nominators but 10 nominee does here and that's 1 atomic layer thick or thin and then we put magnetic Adamson on there and here says Maine and manganese copper and iron yes the only this is the right it does so what they're doing duty operating mode here is to keep a constant tunnel current and so then and I'm showing you hear the height of the tipped as a function of medal position under the assumption that all under the condition that won constant kind of say 1 and so if you have an inflated their than the tip passed brought in closer over the insulated to keep that 1 9 ramp of current required all of the couple I tried here physically physically actually this is more likely or more that more like this so you have your copper here and then the nitrogen is almost sitting inside the car so you can think of and if there's if there is an end to the to the problem I tried so there's no matter use my passion student that's basically playing structure the soaking the 1st approximation was not sitting on top sitting inside the top layer and it appears here but it appears likely to step down because of this requirement to keep a constant this we only know from calculations density functional theory calculations the precise but the measurement of the candidates strictly here was about 30 times that's currently the cheapest same high over the cup when I tried them on the McCain and so then we can take OST entered and we can pocket on 1 of these items and can vinyl currently that as a function now Of the voltage shall
be applied between the tip and the sample and this is the connectivity DID the here as a function of the soldiers you are so so what we have as we have a low-temperature scanning tunneling microscope and attached to that we have room-temperature essentially a simple indeed a chambermaid would beam epitaxy chamber in the case of nitrogen so the 1st step is to prepare a clean copy so that the many recipes that that other people develop a long time ago you sputtering to to blast off some of the dog the news heating to bring out you know make the clean flat copper surface so that's relatively easy to do and then the nitrogen we have to crack the nitrogen boss but if you just let gas and vacuum chamber you will not make up when I tried because much of what is very strong chemical so you need to break and we do it very simply by using that same spot accelerates selection to something like the kilovolt that stiffening of energy but that kilovolt of flight then hits the surface and gets implanted somewhere in the material and if we then heated up to public temperatures like 300 degrees C than this legend comes out and South limits to only single layoffs complementary so we're using recipes developed by other people mostly to do this but we can do other materials as well like NGO magnesium oxide is 1 that we're working on right now so yeah the 2 men had disagreements not use that word force but they do so you can see that this is really a fairly fairly regular kind of looking structure where they really want to be a circumcised but and they also keep if you see here they keep only 1 layer of missing nitrogen here there's 1 layer of missing nitrogen there's 1 there's 1 seeking at a fairly regular patten national pattern if you want to call it that time and so some people interested in just using this as a template to grow something else wanted in a regular pattern for example the price that's not that important because you can always find an area where we have a couple nitrite or not but this is this is limited by the strain the copper nitrate has a slightly different lattice constant the copper and so wants to relax strength and so that has space it will keep some copper in between if it doesn't have the space it will leave just 1 layer 1 roll of missing copper and if even forced more nitrogen in there you can make a continuous film but they will also have some defects in to get some strangled it's a lot of things that we can learn about the growth of the debt he those single atoms we put there so every 1 of these mountains is a single atom and in this case these amendments copper and iron atoms defects are these guys here so there's some defects in the but again the beauty of a local program if you have a defect nearby just don't look at that could use a different 1 so so that and sometimes that's why like this technique because it allows us to make measurements of extremely well characterized I know exactly but this is for example a manganese item on the sofa so I can tell you 50 people this is a structure that I have calculate food for me not hold what does look like atomic arrangement look like that I can't see him in detail right so you can do this kind of experiments or discuss comparisons relatively I mean if you guys have a
bit more for technical questions about how this technique works we can do that too so I have no agenda in which direction you guys want to take OK now so the basic measurement then we we have are STM took part in this case on manganese Adam 1 cup tried on copper and we measure the conductance conductivity yes so so here you actually see that that's not so easy to tell right I mean if you look at these 4 guys they've basically look the same so without prior knowledge you know they might have a very slight difference in height meaning how much current flows through there but if you don't know what a priori who was higher and not you will not be able to tell to what we do is we of course before we do something this complicated like this we only use 1 metal atoms so a manganese and we look at the surface and we look at the Spectrum which showing the next slide for all the different bumps like a hundred different ones and of those maybe 95 will look the same and 5 of them are close enough to defects they will look different so we just say I most slightly this spectrum belongs to manganese and then you repeat the same thing with another species and then you can different tell them apart but this is actually not a trivia question at all you have to do a lot of work to do that OK so
Back to all manganese said and we run current of this and we measured the conductance that flows through this Adam here as a function of the voltage to be applied this is now the the the basic measurement of inelastic tunneling spectroscopy that I want to explain to you what you see here is 0 is no voltage applied and corresponds basically too from the from the energies of tape and sample being at the same same energy level saying similar them the same energy so that's this point here we have a constant conductance around the Fermi energy and then we get a stepwise the increase in the conductors to hire current Ohio conductance at a voltage of approximately 1 million poultry yeah well you have to make I would say it's pretty symmetric what we can cover whether it's in and it's a difficult question the fact government and people in the world In this in this case here but not very much I'll show you an example where it matters very dramatically which direction you play magnetic field but to give you a quick answer to 2 years to your 1st question is the really the difference is that there seems to be peaking up right if you ignore the stepwise increased if you basically subtract the step from this negative side you see that there is a peak year right there's also the slope here and there is this so it actually has a peek at the same energy and this is to my knowledge not fully understood yet why sometimes a peaks and sometimes only steps it has something to do with with higher-order correlations something like a Kondo effect happening if you know what to factors so higher correlations often so this is a single were and what I'm going to tell you and the next slide holders if she works is a single electron picture and you need more than the same electrons to describe this kind of thing but I cannot tell you why it happens on this side and not on this so that's actually putting on trivial questions but that the other questions are trivial but that only means that I don't know the answer look now how do we know that this is a magnetic excitation while that's that's also nontrivial question right now and we really do this by changing this external magnetic field and you can see that this energy orders voltage would step across goes too long energies low voltages as we decrease the magnetic field really have a low magnetic field scanning tunneling microscope Soviet 33 Tesla you would make you step somewhere way out there actually this is well-matched or to the measurement temperature off 0 . 5 degrees Kelvin so we need the combination of relatively high field and low-temperature connectors visible if few 33 count Tesla you could do this at 4 Calvin and you get similar information desk yeah the enactment of these 2 of them in the amplitude height on the door opening and then yes yes assured next line so I am so the basic
information is what is the location of the step as a function of the external magnetic field so this is what actually hear the magnetic field and here's the the splitting Christie from 0 To this energy and so what you see from this Is that a linear increase corresponding to the Zeman energy between the 2 spin states of ground state and excited spin state With the slope that you can learn something about this she values it's 1 . 9 0 in this particular case for manganese on this couple binding site on copper nitrate that's very specific to the Adams and to the local binding site as well but it does tell you that is less than 2 . 0 0 which is what you would expect for free electron but this is a money that's not the same NSG value for free electron basically so significantly less than that and that tells you something also in a way that I don't fully understand the boat orbital Mendham and spinning element if you go into atomic physics if you look up but what is that you value of certain certain state in Adams then this Chevalier will tell you something about orbital moment and spend In a not very trivial way and that is it is flawed because it actually sits on this copper binding site here it's it's like the 704 have of the DFT calculation in here so it replaces 1 of the copper atoms that used to be there in the scope tried and so it has these nitrogen atoms nearby and these medicines are negatively charged and so it sets up something that recall the crystal field local electric fields so this environment here matters very dramatically for these effects it's not an adamant free space OK so but I still haven't explained to you really why we get a step and what we can learn about the width of the say yes I really like the fact that you're asking a lot of questions this but on the way yes sir should go to 0 but if you if you get in the late 80 s what is splitting at 0 magnetic field call that 0 feels splitting that's something that's well known from electron spin resonance which is basically the other techniques that can measure some demagogy value right this is so residents experiment usually in in gigahertz range and microwave fields and this year well-established technical 30 40 years isn't like that and they can measure G is much more precisely than we can but it needs like tended the 10 spinster get enough signal to do this them and so they coined the term 0 fuel splitting In their measurements and and I will explain to you in quite some detail how this comes about 4 irony on the same binding site is due to the direction dependence of the spin so if the spinners pointing in the horizontal direction like here what called isn't copper I was going to call this amended soil this was supposed to be 97 so if this many spend is pointing in the perpendicular directions it has a certain energy if it's pointing in thing direction it might have a different energy and that's set up by the local symmetry of your binding site and that difference in energy recall of magnetic anisotropy that is something that gives rise to these finite energy offsets but and then I wanna take quite a bit of time actually to explain how this comes about using something like this spin operators in interviews lights OK sometimes what do in talks as I say the was hit by the body always I 1 questions and then nobody asks questions so what I do quite frequently is I stopped talking as they only gotta talk for 5 minutes and then you know you have to ask questions fortunately uncovered that with you guys have to keep up the question OK so that offsets is due to magnetic anisotropy not before we go any further I wanted to explain to you How this is spectroscopy actually works and so he had made a slight where have 4 different cartoons they all cartoons based in our reality right all cartoons are trying to motivate why we see the symmetric stepwise increase in the conduct and so here I have to fill states on the tip of the fills states on the sample sample my terminology I mean the copper the couple underneath the spin basically and he I show you that energy off the electrons that we have here In relation to the energy splitting between the ground state and the 1st excited states of emergency started so if we increase the voltage between 2 and sample that shifts the energies that's what we mean by applying a voltage between these 2 electrodes on and nothing interesting happens we get a constant conductance India as we increase the voltage untill this situation is reached where the maximum energy available is equal to the energy difference between the ground state and 1st excited state when this case is reached then this electron up here sometimes will give of energy during the timing passes and come as a cold electrons on the other side and somebody has to be available to take that energy because obviously we have conservation of energy and this is actually possible by this local Spaniard manganese Adam switching from the ground state to an excited state yes I know is that you have this is what you would like more over news In the end that's a very good question I mean of course we do this experiment also on the bare copper nitrate we don't see anything we do it with same copper Adam instead and in place of demand is out and the proper under happens to be my magnetic in this case which is also monitoring statement we don't see anything so we do this kind of control experiments and then in the end I will not this is again a simplified picture but I can't really tell you that's all I can tell you is that this cluster whatever it is that might be the manganese together with the much here but that together behaves like this so it's not atomic physics all this really this guy together with local environment that is doing this OK
so when we have enough energy we can make the this guy can conflict and now what you see is that we have 2 ways to make it across where we can't handle elastically and we can tell inelastic tilt without any proved you would say that it's much not much it's easier for a select from the tunnel benefit cannot make this excitation but it changes the conductance is all I'm trying to say and increase the conductance usually not always and then if I further increase the voltage all the additional electrons can makers excitation and this guy gets kicked more and more often from the ground state to the 1st excited state so it's not a peak In the conductance effective better the voltage corresponding to the same energy but it's a stepwise increases yeah right so this only works if there is a sufficiently fast relaxation mechanism from the excited state back to the Boston so I'm basically at this only works if this relaxation mechanism is faster the average time between timing we usually use To this experiment at time of occurrence on the order of 1 people and to 1 analyst 1 9 0 and corresponds attended the 10 electrons per which is 1 electron 1 is that every every 100 people seconds so you need to have relaxation that is on that ought to make this possible but I don't have this in the stack of slides but we can actually get to regime would relaxation is not fast enough anymore and then display Exxon and becomes a bit more interesting OK so it's symmetric because you can reverse this process you can be applied voltage the other direction the same things that happened to 1st approximation and so use you should see a stepwise increase on the other side this by the way is a hallmark of inelastic excitation right that is really the difference between 0 and a finite voltage or energy that medicine is not the absolute value of this energy that's 1 way you can distinguish between so-called lasted expectations and inelastic what plastic handling process changes in the in the density of states for example and this is not too dissimilar to superconductor coming spectroscopy pretty similar in that respect but now your question was earlier what's the width of the sky here the with set by the by the width of 2 Fermi energy and the sample and the width of the Fermi energy on the tip but at 0 disappears from the shot at finite we actually get a broadening that corresponds to 5 . 5 times Katie because we have 2 from the functions of the get that broadened here and there that also explains the wise experiment is experimentally difficult because most people have magnetic fields only on the range of a few Tesla very few people have 33 Tesla available and so you need to make sure that this energy here is bigger than you stumble broadening so readers of 0 . 5 Calvin and magnetic fields up to 7 when I started IBM my 1st task was to build 1 of his machines there was no commercial machines available at the time it took about 10 years or so for commercial machines to become available now they are available if you have a million dollars that OK self what can we do with this and we can do the timing might need a resistance I'll tell you what this is and in a moment we can measure magnetic anisotropy which is a 0 splitting I wanna spend a lot of time and that we can measure spin spin coupling but to Spain's next to each other and learn something about how the compliance system works I wanna spend little time on this and if you guys keep up the questions with hope and that's going to be the end of all the have time for them we can learn something about strong interactions between the spin and the substrate giving rise to these peaks which should give you something about a condo effect I definitely will not talk about this we can drive the system part of thermal equilibrium which is basically if the relaxation time is not fast enough we can learn something about the relaxation time and then we can also measure this relaxation time directly at the 1 show you this at the very end below but because it's kind of fun technique not so will spend most of our time on these 1st 3 issues here OK so telling Oneida resistance so the Nobel Prize in physics it was given to 2 gentlemen Albert feared endeavor clean background was 1st named Peter did agree that a few years ago many 4 years ago some make that 5 years ago no way old people always tell you it's amazing how time flies in the area but so was given for development office transport in solids that is dependent on demand position on the spin direction of metallic materials so-called Mobutu resistance but as was done at 1st by growing magnetic layers thin films stacks of Eastern fields and seeing that if you changed about the orientation of these films you can get a change in the conductance but this is actually what's use I still have a computer that has a hard drive here that's used as the rate mechanism in every hard disk drive read if you time-limit need resistance so we put a insulating barrier between his magnetic materials and that's how you read the state of your magnetic bits and in your hottest right now we want something similar here on the atomic scale and let me show you a few experiments how we can do this is also answers little bigger question how we know who's who in this case so now we have a smaller which she has 6 points 590 meters I of copper nitrite that's the blue area bare copper that's the queen here and for Adams on the surface which have already labeled here as copper iron and to manganese so we can't take this step we can pocket on the maintenance will do the spectrum that I just explained to you but we get a stepwise increase at find that magnetic field it's again 7 Tesla here at approximately 1 the label now what we actually
learned by doing a lot of experiments actually this that we can bring this tip into point-contact bringing very close and applying a fairly high voltage at the same time and if we do this right we can transfer this Adam from the Cup when I tried to the tip but this is actually very simple in this cartoon but in reality that's a very difficult experiment to do because when we do this if I go back when we do this at this point here we apply to volts and approximately 10 microns of current running so a single so it's not surprising that you change something man if you do that to vaults and 10 migrants to a single out should change things the only thing that surprising about this is that sometimes you can actually make this a reproducible process now how do we know this again on a very very nontrivial question 1 thing we know is we
can take this step now and we can take an image of the same area and of course 1 thing you notice is that this Adams missing so we can conclude from this fine we can make Adams disappear only 1 only has to work that's a difficult instrument on a probably just similar things so I I'm going to they they had out failed we my answer to so we can easily spend 2 days where doesn't work ever we can always make the Adamses appear they can always disappeared it's easy but to make it go to the end of the tip and then could get it back off that's a difficult expert are sure you on the next flight very similar process the book so 1st thing in the state's missing the 2nd thing you also see that these Adams the remaining items look better look look more round so this is the mall .period like STM because in the end PST an image is always a convolution of the shape of your With the shape of the surface that nature doesn't distinguish between the and service so if you have a very sharp Adam on the surface and really what you've seen is the shape of tip the shape of last year items of YouTube went so that's what this 1 is not a very nice image you see this Adams slightly deformed because of what it has to Adams said a close to the variant instead of 1 but he's the it's better so maybe 2 points for this mechanism at the Adams gone and the other in which looks sharper them but then we can also take this tip now and measures spectrum on the remaining manganese and what you see
that is the following so he sees that inelastic timing spectra measured on the same manganese iron but now with a modified tips and what you have here again at minus 1 million vote you have a step and at last won the league you have a step at the height of the steps is different where this step is about half as tall as the step over here so the amplitude has changed the energy has stayed the same OK so they're holding to the reverse weekend we take this step and we bring it back down to the surface .period contact several my grams of current and now we applied the polarity difference opposite polarity and then sometimes this works this is a difficult process actually to get the speckle and you know I work for a company so we actually do not spend a lot of time trying to understand why this works we we don't have time for that in the end because I can't go a house on a small group we always have to focus on the highlights basically we can focus on this 1 because in the end who cares when it works it works my bosses don't care but can guarantee that OK and so then we can take this empty tip image again and you can see we can go back to exactly the same shape of step without the manganese Adam on it but this man is Adam has moved from here to here so we can move this manganese Adam by few lattice sites if 2 with me in this case by using this this manipulation pass right now if you have a tip that works the biggest structure we've built with total position was 96 With the same we could do this 96 Adams 6 times a role without messing up this so if it works it works OK so go back to the same out and we can measure spectrum again of course we go back to exactly the same spectrum that we have to begin with because we have exactly the same tips and exactly the same thing on the surface and that's again the beauty of this if you know at this precision what you have everything has to be exactly the same we can pick up a copper atom which was the guy up here I'm so we now have a copper at the end you see that the spectrum is essentially exactly the same as what I call the entity it's not 100 per cent the same if you look very carefully he conceded slight differences on a the conceded Branca of underneath a dusty old 1 right because the density of states changes a little bit between having to cooperate in there and not having copper but the 1st approximation the height of the steps is again identical and go back to the empty 1 that amenities we can do this again you know many many times OK
so How does this work 1 problem that we have all won complication that I haven't mentioned to you yet is that the manganese Adam is not spin one-half particle manganese if you look at the periodic table is in the middle of the day shells of the 3 D shall so if you just look up at at the at the at the Adams periodic table you have 5 electrons in addition giving rise to a span of 5 half into 0 already the momentum that's what they wanted .period cable tells you this so if you have a 5 have Adam you should have 6 education was 6 6 other energy levels and 1 energy diagram but we only see 1 excitation it's kind of weird right so we have some selection rules at play here and I want explained that to you I now this election will stems from the fact that we actually using electrons for this excitation mechanism and this action not so difficult to understand so the electrons of course has been one-half particles electron is a single electron spin 1 house and we have to conserve not only energy but we also have to conserve space endowment was a tool I mean what's been but England and has to be conserved unless you produce all were delaying momentum the spin has to be conserved basically in the stomach ulcers so really what we can do here is we can exchange spin between the manganese Adam and the tunneling electron and so really this is an exchange interaction between the spins and so that means that we can only go from the ground state to this 1st excited state the electron here at the time the electron just does not have enough over the moment to get you from 5 have to 1 this you was yes yes so if we don't give it enough time to relax back down from the state to the ground state before the next election comes about then we can drive it from the state to this excited states so sequential electrons will do this and that Will yes yes yes and all don't think we will have time but but that we did this experiment a couple years ago and this will tout the houses something about how fast as workstation based on the grounds it because we can make this same measurement as a function of the tip sample distance but so she said had 1 million bold you know at some height I have 1 9 and of current if you bring tip closer and 1 merely you have more current or put to back at 1 of bold you have less so that's something that the people that are doing transport in say playing a tunnel junctions they can do that you basically have a tunnel junction it has a certain resistance given by the thickness of insulator and so that's it so it at 1 voltage you always have the same current we can have this freedom by changing the justice OK so why does this give rise to this this asymmetric spectrum here it's not so difficult to understand if you allow me to make a simple simplification him if you think that this manganese Adam together with an external magnetic on this trip no it's sitting on the medal here so let me make the simpler that ignore quantum mechanics here and then use quantum mechanics here they both Adams that's nontrivial statement this pretty drastic approximation but if you think about how what you learned about spin polarized times usually in solid-state physics then what you mean by having a spin polarized material like Cobol for example what you learn is that you have a different number of electrons of one's been flavor at the Fermi energy than the others been but usually city of war majorities Princeton minority students at the Fermi energy and transport will be spin it's been dependent spin bowlers now if we say that this step behaves like this so I have fewer minus-1 have electrons and more less 1 have electrons then you can understand why the spectrum becomes a symmetric now we have the 6 current going from tip to sample In this window here we have lost current going in the opposite direction and just changing the polarity here of the bias voltage more interesting if I go In the inelastic window here I have to start as a minus one-half electrons because I want to transferring the momentum you have to start as a minus-1 have electron books and they want to end up as a plus one-half have electric so in this direction I can do this with a certain ability in this direction I can do this with few electrons because I have less initial states available and the beauty of this is that this allows us to measure this degree of spin polarization usually defined as as the density of class voltage and miners voltage minus this divided by the the average of the 2 so we can assign spin polarization directly to this asymmetric spectrum but the degree of asymmetry tells us what the spin polarization is giving this simple formula here and in this case this comes out to be approximately 0 . 3 it's been polarization 0 . 3 means that you have twice as many electrons of one's been flavor the been flavor Justice using this form this is interesting because it it tells us that the know it agrees well that that we put a magnetic Adam on this understood and be applied magnetic field to monetize this out basically that makes spin bowlers sanctions and it allows us to quantitatively measure what the spin globalization is but this is very difficult in practice in other materials if you ask somebody somebody somewhere you do being transport right they How do you know what the polarization of fuel use cobalt electrodes Audina Witherspoon polarization is a vehicle all of them it's very difficult to measure right is very difficult to measure minister people have died by measuring the 18 year using a superconductor and pushing magnetic material into the superconductor using those kind of devices but it's very difficult to measure but so here we have a way to measure this for the simple yeah he and his wife and mother of 2 . 1 per cent because it was because this
election will is basically that we start with the patterns in the ground state and we need to transfer certain direction of any element of this well if you were transfer the opposite amounted go from this state down in 1 state but you don't have a stake below that your 1st year in it is the only 1 it's somewhat typical but not reproducible in the sense that every time you pick up a manganese and you will get exactly that's been polarization Of course it depends on magnetic field over temperature but at 0 magnetic field you will not get any spin polarization to 1st approximation of but you need to polarized you need to magnetized quote-unquote the single atoms to revise law it's right just be which he so in the saturated reaching selected if you play more than 1 Tesla said 0 . 5 Calvin during the saturated regime and then I would say it's typically in that range if you become warmer getting items you can make it bigger or smaller and it does not depend very dramatically and whether it's Manganese Ore it is the just going to have a lot of was known the have requested to be used of the not in the ground state based on the ground state they will be aligned and you get a certain calm right so so the answer to that is really in the sense of having a steady state another tunnel junction where you can do this this will experiment with change 1 orientation of steel we can do a time-dependent when a free kick this guy out of the ground state then this will be rotated if you think about a classically and you can't will change for short while untill relax suspect onto the grounds so you be China you on this In practice the answer is no it in all but what other people have done is built structures of say 5 or 10 atoms on the surface the big blob of iron atoms for example and then those will be it will be a steady magnetic state in a certain direction affirming ended couple to each other and then then you could have this if you could transfer that to the kids and the answer would be yes but that doesn't actually work that depends extremely heavily on the local environment around it's very very very different guaranteed to be yes and we don't know it right winger told you so you know the word that we know everything about the structure on the surface we don't really know much about the structure of the 2 so the tip is always a black box for us the honeymoon when exercising a review of the so I don't have the time to do this it will ultimately be it was what this energy difference if yeah arrives this is supposed to be the picture I agree to this not not categories specialists this so if you think about what happens when you play magnetic field to a normal metal you have your your parabola of states basically right energy was skate for example what 1 of case and now in this a been up and this has been done you take a normal metal not affirmative but normal metal and you apply a magnetic field we get is a minor G of the electrons in the middle of the city and in some sense what you do the 1st approximation just shift 1 of these problems down and keep the other 1 and the same at the same place and you could do this change the potential for managers or you can change the bottom of this space right now what happens of course is that the firm energy will stay constant because you when get spin the spin gone in the from the energies maybe the same basically going build up the voltage come across in inside you material by applying a magnet to annulment and applying magnetic field to right so I just brought basically as a shift in this in this problem search of 1 of these problems here by the semantics so this shift there would be the same on energy but so this distance here would be the same energy In the end the man in the middle this afforded for the for of cause particles don't take it too seriously and this is really meant to be a total cartoons if you don't like this problem I'm perfectly OK with this but just say that you have a difference of the number of electrons at the Fermi energy offered 2 different spins but that's really all that supposed to mean maybe that's taken the Khartoum to 4 I was going to go
along my work yes you imaging attempt to some degree so we learn something about it and you could in principle do sort of D convolutions and take the image that you get maybe different Adams but if you have 1 out of this very tall 1 and this looks very short you know you could learn something we haven't done this in practice not anybody down there probably not only the people of the 2 region you so hand waving U.S. and failing you know you learn something about our distant might work just because it looks like this and then it works half the time them in so it's not it's not really scientific not that could I'm sure there are many it in the end it is but we haven't got the time and effort now I think we already went through this but as I said in the beginning I do want to spend a bit of time on this on this operators trying to explain to you now how we can understand these experiments a little bit more you know from the theory .period now what I'm going be tell you sort of in the next few sections is not something interference would actually tell you because it's not really theory this is trivial for theorist but it's just a little bit beyond what normal experimentalists learned the ball been operators and so I think that's why it might be worthwhile for for someone OK so 1st step here is how can we model this year so we start with our spin manganese being in the ground state and equals plus 5 half and we ask if I have the timing electron that starts as a spend on electrons but what can do it can flip and become a span electron but we have to conserve and momentum and that means that the manganese has to go to an excited spinster but that is the inelastic timely but you can also do the following passes you can keep the star electron as a delicate and the manganese of course stays as a M equals plus 5 half and remains in Eagle Pass 5 that's a perfectly allowed transport process as well you could take up electrons and start in the ground state and keeping up electron and still be in the grounds said of the manganese and the 4th channel you strike as an up electron I think you are that somebody asked the question them and we stopped in the end it was classified half we flip this to adorn electron and go to an M equals plus 7 have that state doesn't exist for this probability is 0 this year so we have 3 different probabilities and can we learn something about what happens spaces can we did some modeling it and improved quite a bit of work will be actually learned is that it's actually not that difficult so the timing electron which is the state that is either up or down and I'm not using full quantum mechanics here so there's no no coherent manipulation or something like that this is either up or down the town electrons in the copper off the tip or Armenian the tip and the copper and the metal wire so this is this is slated to appear and this is this is in the middle underneath and so that's the timing electron operators and then the operators corresponding to local Adam the manganese with its local environment here so that's and if for those of you familiar with this this is an exchange action S 1 . es 2 times usually parameter like Jay that's called highs were exchange actions and tells you something about the exchange of electrons interactions between electric and I want to spend a lot of time understanding what these operators actually mean now Have you something a little bit more complicated than we have in additional potential scattering trip and I can't explain to you why this comes about the arrests will explain to you why this comes about it but I know that we need this parameter to do good modeling right so I'll just use it here you can grill me later if you want on why this works I guess so we fit there isn't this disk holds that any magnetic field and we basically fitted with know for example is you parameter is a single parameter 1 number basin is a real number and we fit this to a certain set of measurements for example as a function of magnetic fields but we want this parameter to be constant independent should be a prominent only depends on having manganese in this particular configuration book this means you his expertise and then everything else should come out of the race OK so this time you're Sigma .period S is actually pretty difficult animal if you look at the slow but more carefully because the start s what that really means this is just a definition of what in blood s means it means Sigma X SpaceX plus signal y s wipers Sigma XE SE all of these operators in this sense that's a pretty non-trivial trivial charm if you really want calculator but when
missing I think I have this written down here in a little bit slower 1 takes some time here and can bring this to life a little bit closer where's so OK so what we have there is In the end you know I let just like the stumps where 4 cases you decide about and this is in this light much but give those to you I still think the half-dozen likely the look at my my hand written notes or if you care about this report have to write the down so the signal initial offer timing electron the signal final so it can be from up to up from up to down on down 2 up and from down 2 . like those of the 4 cases that we sort of evaluate as we do simulations and again I'm ignoring quantum coherent enough states here the electron ended in the chip could be admissible position of states but I'm not dealing with this at all he just just sort of classical memorization state come the firm what such a stake example here 1 of these probabilities here is up electron this final signal plus as minus signal ministers plus signals SEE plus you after his initial all right civil War I calculate what support ability of this process happening namely the electron starts as an Appalachian and ends up electric but this is just 1 of the 4 cases that I have to couple it basically I'm so that's this case over here then you see that what happens with you guys apology Emilia was minus right that's Sigma X signal why those erasing already operates just like you learned in basic quantum mechanics so but you know that if I operate Sigma miners on the upstate I get the downstate and then multiply all I checked the downstate overlap with enough state is 0 if I operate signaled last on upstate did 0 for that tells you that these 2 terms don't play any role in this particular case so I can I can simplify are saying this is Sigma Zeta Psi bless you but this initiative that's a square so you can do some of these simple terms and so we learned that if you don't change the spin of the timing electrons the plus and minus terms don't play a role on the other hand if I do the opposite way you if I do change to spin 2 down this final signal plus as minors it was in the city this by the way is the part where you can yell at me and say This is too slow if you want I can do worse handwriting but not much time if you do if you want a cabinet this 1 here now you have to find the term with the AP electron changes to a dollar election by applying the signals and that is which 1 but so now I have it's final Signal minus after its initial after going square so if you want a capillary basically what are the occupations of these of these 6 and states a have from my manganese but in the final magnetic field you have to keep track of these processes and do something like a bookkeeping of which state and maybe you start on the ground state he 1 electron Phil it certain volatility goes in the 1st excited state maybe now you do a relaxation mechanism or not but and then you keep track of this and you calculate what is to come on as a function of the occupation of the states following these rules here on the other hand I can simplify this even further was a noted signal minus operated on up and down excluding age flowers implied that only age was have written down here that is as final "quotation mark this plus its initial right but they
applied the Sigma -minus here To this upstate I get is not excluding factors of 2 or something like that I don't have all these factors would nominate each part probably right you get the downstate here and then you can evaluate this and you get a certain value out and so you are left with this With this process you so basically what this tells you this by doing some bookkeeping you can you can keep track of the time and led what upon electron is doing and you left with some operators that depend upon the manganese Adam that is sitting on the sofa and that that's why in this in this description here I call this the elastic tunneling that space timely where this where the wooded pounding electron does not change if it is stances adopted ends as enough if it starts as a down ends as a down and the inelastic 1 where does she does a flip this but to the inelastic one-half the Texas the X and Y which is the same as pleasant operators and the other 1 has this symposium I don't have this written down any better than that by them and I think you get the idea of how you can do this ,comma modeling this is the end of we really don't make any yeah we treat this in a very funny way if you think about you quantum dot a person in a quantum dots you actually think about the electron hopping on the door and hopping back off but he I'm not doing this because the electron is zapping through there and it leaves behind an excitation or not and I'm asking this is more like a scattering process in that sense I don't urged that all will tell you that the electron lives on this on this album here for 10 from seconds or something I have no idea what I can tell you if the election goes through and makes an excitation in the spin how long the suspended I can measure that but I can't tell you how long this electron that if you went through there this on this album I can't even tell you this is not allowed question to ask I know this is a good hand waving really don't know the answer to that question it bugs me I don't really know you know how does this transport process really works but we do know that it actually looks like it does this exchange index that's really what is happening from experimental measurements and that it you yeah that's in the end is somehow what is you parameter that it's the ratio office exchange interaction to a potential scattering it's only 1 parameter that matters is not to parameters I was the on the strength of the telecom nor does not the I think that's I think the answer to that is that the timing passes always slow in comparison to the to the transition time of this electron quite a while ago just before the before you guys were born almost button before you go started physics basically people wondering how fast as an electron tunnel was the time corresponding to a tunneling process and I don't really know what came out of this discussion but that's you know at least 15 20 years ago there was an unsettled problem I don't know if this is settled by no 1 can you actually assigned a time to such a timing process I don't know anybody know In this and this that was the only that's how we can that so we can calculate basically you know how much current will flow that's the overlap of the wave functions but it doesn't tell you anything about the time that takes the top now it's virtually nontrivial question but so you know this 2 excluding the effect of of one-half wasn't like that "quotation mark you can actually be Quaid said Max Essex with Sigma plus as minors and so on true to effect of one-half or but that's the same thing OK so I'll tell you a couple flights how we can measure this because you basically and then I want to go into the sea off fields but so With announced and polar tip you know we get our manganese spectrum that we talked about quite a bit now and here we have elastic tunneling and elastic tunneling and inelastic Thailand's because we have announced in Boston if we take a spin
bowlers we have become more here in Lhasa current in this channel than in this channel but that's just the polarity of the bias voltage and sometimes letting someone you asks Can we make different tips but picking up more Adams yes we can and sometimes we can even make into a spin polarized it's that big of a lot Adams may rulemaking and that on the table knows we don't know but sometimes we actually see that the opposite argument holds and soul we that the base what this means is that the and Adam on the tips this entered aligned to the external magnetic field maybe that was the question can we make this sometimes we can but we can't do this we produce but I can't say I different pick up 10 manganese items I will make this just happens to be sometimes it's OK now this I'm not from this measurement but from something similar I don't let me just skip that part ,comma we can calculate this you parameter the quantity but that this belongs to for the manganese out of that the dashed line here he is the value we get the maximum time limit to resist and that I will show you in in in the compilation the couple's flights but so for manganese the Magnuson looks like it wants to be fully spin polarized where is an iron added that line here is 1 . 0 in all parameters but he has 1 . 2 5 that's just because the IRA has not spend 5 half it's been too right so we didn't use a proper not that I mean the difference between 1 and 1 . 2 5 it's just the magnitude office been that's just a way another theorist would do this better and this would be it's always 1 but you can see that the iron atom this is not correspond to this maximum value of you and so you really have some physical Maine it tells you something about how this tournament process works I think but what it tells me I don't know so we be treated as if it were measured parameters but only 1 parameter but if you take manganese on this binding said uncover nitrite you have you of 1 . 2 5 to take Ireland the same binding site you have you of 1 so we can determine all you can learn from this we can determine this has value and the histogram years taking different Adams measuring this you you know about 100 times with different Adams doing all this the procedure and you can see that it does very little who knows why L but on average this is what comes up I want to spend a moment
on on these to both of them some still have to have to figure out how to do this but but OK so
magnetic anisotropy we talked a little bit about that 0 fewer splitting for the iron hadn't had 0 magnetic fields there seemed to be some energy required to make an excitation and I want to tell you think a little bit more detail how this works and I'm going to use different adding where this is much more dramatic than the iron now what this all comes down to is of course if you have only the Zaman Hambletonian at 0 magnetic field all the states have to be general this is proportional to be sorted at 0 field use 0 if you take the spin and you break the rotational symmetry of space and you can do this the right by putting this this being on a surface like I'm doing here all by putting to spin in the molecule we're doing anything else that breaks the rotational symmetry of space than in general the energy of the island states will depend on the direction that the spinners pointing it is allowed to depend on this direction this because the local environment His making the directions different and and this gives rise to 2 affects 1 it gives rise to the CEO Phil splitting and then I will use this kind of picture to describe the Sufis putting this is based again on his on his quantum models and is called spin Hambletonian which is used all the time and electron spin resonance this is how people describe electron spin resonance around but it's not so well used in normal solid-state physics I would say that I'm so molecular magnets people chemistry people they uses all the time as the picture now he was the 1st time that plays any role in this d SE square so now disease not the direction of the magnetic field consideration given by for example the stood to suffer perpendicular to the surface the manganese case I applied the magnetic field perpendicular to the surface because that's the easiest case because the spin ones too .period parallel to the perpendicular to the surface now what happens here it's an AC square charm so you see that if I apply magnetic field along the Seine spatial direction then this is a term that is being times staff z it and S square their commuting operator that means that the energy just add up that's what this picture over here so you have a certain energy a 0 fields and on top of that you add the linear terms of Zeman splitting if I apply this magnetic field in a different direction the C X but now I have a Xia and square here not as X Estes credit not commute and then the world is more complicated so as I increases this term he had as a mantra you know get some complicated dependence of the energy levels on the magnitude of this direction of this magnetic field in this direction so having magnetic anisotropy in my pictures gives rise to 0 fewer splitting and it gives rise to a direction dependence offline admitted field and they very closely related to each other now let's this experiment we take an iron atoms on the same binding site on copper nitrate so all I've really done is every place the manganese With an Eye and and I take the spectrum here at 0 magnetic field and at low temperature and you see something quite dramatically different remember the manganese Adam had just a tiny little feature it's it's your magnetic field but that basically this guy and this is plus minus 10 enables so this is 10 times bigger energy scale the city and has to be excitation at 0 magnetic field 1 and 0 . 2 million Poles 1 it formerly bolts and 1 of 6 new labels my so in some sense 0 fierce bidding here is dramatically bigger than manganese about 500 times bigger to be precise and so this is just because we using a different items so definitely this guy has 0 fused with that please 3 I'm in why those guys why do I know why those days while the other 3 d transition metals those I use magnetism all the time that's not really good answer but that's why we did this city and there so we've looked at that most of the 3 d transition metals and I'm just showing you those 2 cases here today but if you use f electrons you should be able to see something similar but the f electrons are much closer confined to the to the to the to the core of the and so it's not clear to me if you can actually see this current on Oct . 1 so it's lot of experiments besieged but for us it's just that's the way we chose to be for no particular reason OK so we definitely have 0 few splitting what about direction
depends so that supply the magnetic field in plain here along this particular direction in vain and what you see here is 0 test that fielded spectrum just showed me that before and now 1 test at 3 Tesla 5 and 7 tests and what you see it is that the formerly bold as your field mold goes up and energy as increase magnetic field and the 6 movie also was up and energy but and also the middle guy you disappears pretty rapidly as we increase the magnetic field along the spatial direction if I apply the magnetic field and perpendicular directions also in the magnetic field but 90 degrees rotated With respect to the cyanide and and this particular special direction here you see of course is your test under the same have to be the same and increase the field well the former labeled mold stays roughly constant the 6 million votes old goes down in energy and the central role seems to be sticking around much longer so quite different dependency yes you look all of this 1 with the model I'm showing you in the next couple slides this would be the location of this excitation at 7 Tesla so we should be seeing something there if it was visible the transition amplitudes is 0 basically we just don't see also this In some quantitative detail extinguishers 1 of the golds out OK and a 3rd direction out of play magnetic field is yet another defense OK so by now you know what I do I plucked the center of this step by that's here as a function of the external magnetic field that's basically extracting information from the society as measurement in Lhasa ,comma spectroscopy measurements and then I can get a very good fit to the With a simple Hambletonian that has only a few parameters so that's them fit that I get when I use this Hambletonian so I have Azima energy not shown here then I have this DAC squared terms so that's a certain special direction that I have the so-called easy access magnetic anisotropy here that's this term here and then I have the transverse magnetic anisotropy now if you look at these terms again you have a C & S X and his wife so again we have none commuting operators so you have to do the calculation you can just simply see what this stuff space but that's kind of the the outline of my talk in the end you can actually do this by using the spin operators in a fairly simple way that you can all do without you know going to quantum mechanics 2 or 3 courses now the parameters that we measure from this this fit we get by getting the equals minus 1 . 5 million volts and iii of 0 . 3 million votes just take those as the parameters this yet because of something yes I yes so this this Deke was minus 1 . 5 together with the fact that this is the the year simple directions meaning the direction will be all their energies just adding up together but this is much more complicated than this in some sense tells you that this is the preferred direction office spin so this band wants to point in plain where's the manganese spin that we talked about before I wanted to point out of playing a very weakly it has very weak preference to point out flame With this parameter for manganese it's 50 times smaller but so that the the magnitude of this parameter tells you how much does it want to point below a certain spatial direction and 1 . 5 is very very big the cobalt Adam in the bulk of cobalt for example would have the energy equivalent that is about 500 times smaller than so because it has this net disasters local nitrogen atoms nearby these guys here date said all the energy scales for this magnetic induction they played a very important role OK but for the next 20 minutes or so I want to take time to show you how this kind of model actually works this is a good thing it directions to yes yes or it's completely set by the local environment minister the yes manganese very different from mine very different from Cold missing the way you do that's why I chose the manganese to begin with so if you exclude that tiny little rebel it 0 magnetic field where there was a small fraction of the Zeman energy but and this year here this year European building is a large fraction of the same as you so this manganese is the closest I have to freeze them this because you know it's wisest because manganese isn't as equals 5 have system and that's a half-filled the shelf In a half-filled the shell 2 very good approximations spherically symmetric just like a fully fueled shelf and so that's why half-filled shelves all are very nearly less susceptible to those influences OK so How can we understand how this stuff works so Of course you know
that that if I just have to see my energy and I have 0 magnetic field applied I don't get any excitation might have only your energy excitation nothing to learn from that time forward put it so and I have I have 5 energy states right all degenerate here and so if all generate I can label them any anyway 1 ignore this White Nile doesn't make much sense if I look at finite magnetic field this is something you learned in quantum mechanics what you learned in quantum mechanics is that the magnetic field sets the conversation exits but that's what's typically talk and so that's what you see here so if you apply a magnetic field along a certain direction that SE but doesn't really matter which direction it is then this direction is a good basis to use and so all we do is we use the the MIT value off the SC operator along that particular spatial direction which is set by the operator choosing a certain direction of the magnetic field and so that's what about what the what these are here so any was plus 2 plus 1 0 minus 1 and minus 2 and also a very good there's a good buying states but so the island-state state corresponding to the ground state is 100 per cent and was cluster the ground state corresponding to the 1st excited state of 0 . 9 million is 100 per cent and plus 1 this is just repeating the basic quantum mechanics just written nominated the different but you'll notice but but now let's take a moment and look at this time DST square it is a wonder that I wanted to buy the stock will bid for you come to not go too fast here so 1st of we have in S equals to systems which I haven't proven to you work let's assume that that's the case here so do right the SC operator but remember fallen as was 1 half of was just just minus 1 and 1 basically all mines 1 haven't 1 1 plus one-half if you want the precise so here the SCO operator is 2 0 1 0 minus 1 minus 2 with everything else being 0 and if you want to know what St squares what you can do the matrix product if you want to put another matrix next to the makers modification and what you see is that this is for 1 0 1 4 Everything else is but as happens to be the case because as a diagonal matrix this up I just wish it singles What if we want to use this and we want to know what's the energy this square d St square if I'm in the past to state we have to convert this 2 vector because I'm using a matrix here the vector that corresponds to the past 2 that's written up here that's 1 0 that's a 1st line appeal but that's 1 0 0 0 0 multiplying the remake that simply here a St square off plus 2 once we get plenty here and this is Christmas matrix and I have to say plus 2 1 0 0 right to the majors modification here and you get 4 times 1 0 0 0 0 so this is hiding vector of this operator With item value for I do the same for the for the miners and it was minus 2 state you also get for the other 2 fold the generous of the state's nothing magic about this just simple matrix multiplication please yes yes now let me take this 1 step further wouldn't you OK so this is really simple now let's yourselves for example what is the current but I get foreign up electron if I don't change suspended in comparison to the current I get for down electrons will do the same thing what this is something like I'm not looking at the inelastic components I'm just looking at the last 2 components right of the timing processes that we have to worry about if you want to calculate the current year done now we can do this by operated on gives us to at times plus 2 let me make this slowly the last 2 years tool signals no but tricky lab to you and that can't quite do that so slowly let me operate both of them so far operate the SC on the upstate agreed to attend the upstate before operators Sigma zeal and one-half hence the upstate and one-half times too one-half times to bless you plenty of less 2 absolute value square but nothing magic is just metres modifications or basic quantum mechanics and now so deep that this was the gives you you if you do 1 step further here gives you something like this is not just numbers they can take those numbers out and this operated on this is 1 so I get out of this 1 class you In brackets square To same over here right now I have a C 1 trust to disclose to signal the on the dollar is minus one-half so I get here minus 1 plus you square so and remember I told you higher the EU was 0 . 7 5 In these arbitrary units which I'm using here consistently for this year and I said that the maximum value for spin polarization for is 1 and what this means is that if you had the you off 1 that means that if you haven't up electron that's tumbling that a certain current if he ever done electronics tumbling minus 1 plus 1 0 you have won 100 percent spin bowlers track but this channel is exactly 0 if you have the maximum value of now it's not exactly because 0 . 7 5 but you can see it as quite a dramatic dramatic difference between an up electron tunneling through design and and the dollar contaminants but and unlocked and again I'm not using any magic is just simple matrix those expenses OK so that's what we learn from this but going back to to all measurement but we only get 1 excitation and 0 magnetic field and not 3 so this is not the full story when we had 1 excitation at 1 million votes still point to also wanted for Wilson 1 of 6 million and so on that's what
we just did what transitions are allowed to that OK now if we
include this this transfers magnetic anisotropy term then what you see is that you get the much more rich picture of what the quantum states are here the ground state it is now the mixture of and it was plus 2 and Emmett was minus 2 that means that this Adam in the ground state is pointing it's been a long 1 particular spatial direction equally up and dull Quantum coherence of opposition of these 2 states but if you pointing at the same time up and down you have no net magnetic moment but they can slow so in other words this pattern it's 0 magnetic field as it's canceling that's only possible because you doing the quantum-mechanical classically 11 .period this way or that way this comes out if we believe this Hambletonian just from analyzing if you look at the 1st excited state here at 0 . 1 7 the electron volts that's also the superposition of plaster when minus 2 but with a different face here with a minus 1 just comes out of the matrix that's just what comes out of the diagnosis matrix basis and so on and so this is this is so again we are not not too difficult but if you believe in this kind of matrix stuck in on this kind of quantum mechanics now see what I was gonna show you here let me not like this down because I do want to show you the 2nd part to of now I showed you the SC operator like that's the 2 1 0 minus 1 minus 2 you can also look up what the SX and here's why operators like those have 0 on the diagonal and have some fun and values on the 1 off diagonal this is just looking up in the textbook basically what is SX and that's why I'm for these guys now you can make a small today which I actually did down the paper and pencil ,comma guided I am you can't just multiplied by itself and you get this matrix salt for X square and this major source for his wise square they're not diagonal so it's not trivial you can just just square these components and a matrix of my because what we have to actually matrix multiplication then we can look at this time is actually times S X where miners as white square so we look as excrement is as widespread as only 6 components in that nature here and so then our full Hambletonian excluding magnetic field is DSC square must be as excrement is as widespread and this time he accuses diagonal elements and this guy here his city's off diagonal elements he finished but that's not difficult but we can just happened at this and then you can but analyzes majors that I did not do myself like this beyond my powers of matrix algebra also meant that but you get out but this is the ground state if you take this and put in the DNC value that we measure this city and this is the 1st excited states profits when so this is suspect this is again not particularly difficult but what I want to do now now for a 2nd year is I want to show you what happens when I operate the S-Class operating here on this guy remember that 1 of the terms that we have is S-Class operated on the ground state and then we can ask what that gets so as plus operated on the ground state ground state now the S-Class operator is related to the S X right and here's why it's a simple operator really feel 0 0 0 0 square which 6 0 0 0 0 0 0 square with 6 0 0 0 0 0 2 0 0 0 0 0 this is just began looking up what is the operator for its sequels to look like and now want to operators on the ground state them but now the ground state has some components of class to similar 0 and some minus 2 so that's the place to component here so that's just 0 . 6 9 something rather 0 . 7 0 0 minus 0 . 1 7 0 0 . 7 0 right this it's just another way for writing this exactly the same thing this is just how you translate the slang to matrix and then but I mean you don't do this right you go this 1 and this 1 dentist from insist on that this 1 is 0 in the 1st 1 but this 1 comes this 1 times this 1 gives you find value this 1 this 1 gives you find value off minus 0 . 4 2 the next 1 and ending do and so on just basic matrix multiplication and you get 0 1 . 4 0 0 but nothing magic about it and what this another way to write that is that is basically times minus 0 . 4 2 hands plus 1 plus 1 . 4 0 times minus 1 it's just the same thing now the next day that a half-year 1 higher than this
go back to this in the 2nd so
the next highest state good that it is I don't have written
down you go back the go back to
this 1 year the so this is the ground state 1st excited that the 2nd excited state that is a state that has just 1 and minus 1 component right the remember for all over that we always have final then the initial absolute value square and so you can project this 1 is we just calculated this we can project on the final stage and you see that that has a lot of overlap with the final status has plus 1 and minus 1 yeah what's word why is it not because I'm very sloppy and very sloppy when it comes to page bars and normalization and so on what is this right this 1 probably has effect of square with something missing in the normalization I just sort of trying to highlight 1 of the ways that this works pretty hard not to be used for actual computation no this is what we get out of this and if you want to do this overlap here you just get there the plus 1 component overlaps with this plus 1 here 0 . 7 1 of this and this 1 over here and you get find value coming up so that means with the operator s plus we can go from the ground state to the 2nd excited state we can also go To this excited states With these operators also a mixture of plus 1 minus 1 and the last 1 has only a component of M equals 0 and we can reach that at all was always with or injection Hamilton we don't have a way to make it to and was plus 2 was only 1 S class from the provinces so in a nutshell we can calculate what these
what these transition and intensities are tender and so you can see that for what so from the ground state to this 1 we have a large over that if we operate with the SEC operator the elastic fiber called elastic but it's not lasting because changing the energy but it is not spin flip recently and we can also get to this 1st excites the 2nd excited state here because here we have a Delta amount plus 1 In minus 1 on the other way around sorry for that and that we can get equally this guy here now they have a different amplitude why is the 1 in blue smaller than the 1 in angry if we had a little bit more time I could just write this down it's just a fact that here we have a certain combination of these numbers and you get this together with this face you multiply this and you'll see that 1 is small and the other 1 by a factor of 3 when so all of this detail all of this you can get from this From this Spamalot Hambletonian which has a few parameters the TNT and the direction of the easy access and the sick modeled as but which has 1 all of this the height of these things and the energy falls out of this what does not fall out is the fact that there is a peak here somewhere but it's not just a step it's a peak also and that perspective this maybe Kondo effect kind of thing which I don't fully understand what I don't understand what fully committed I don't understand what even halfway so they're not shell using relatively simple matrix stuff you can look up In a simple textbook basically you can get this full understanding relatively easily
OK then skip this part here
because what 1 of you as Esterly hardly noted differences but I showed you the manganese and the iron I mean they're very different you can deftly tell them apart the call was Adam also very different so once you know who was who you can actually tell them apart relatively easily in a copper atoms just flat because spin 0 in this case so I saw going tidbit faster here because it's it's 20 minutes to To be a time and I don't want it but I do want to tell you the little bit about what you do when you have more than 1 state and then then the caller quits OK so single manganese Adam you know how this works by
To manganese Adams completely different like this guy this spectrum he really has nothing to do with the suspect yes will it doesn't matter if you think about the trip here hero in the middle of this and that is still localized because the items fairly close together and we really can't individually tell only 1 they would look like a cigar when you have an image of a mail Avenue much later you see it's cigar so we don't really if we built them with the spacing then we can actually tell which out the tumbling into and then it can depend on which other murders which is what outspoken In Delft not mail looking 3 items very different again well sort of has little future in the middle similar to the single 1 that has some big energy stuff maybe similar to the to the diner and for
Adams different again but so spectroscopic if we know what we're talking about their very different if individual experiment carefully we know exactly that is for Adams and not to be but that's an experiment if you try to do this with other techniques other than STM is very difficult but if you wanna make a spin chain and you want to know the some materials that behave like sprinting but that Dechaine has a certain length and if you wanna make that length 1 vessel 1 more you know you have to talk very hard you chemistry friends all materials friends to make that material is very difficult to do it so we can do this year because of this combination of Adam manipulation and local spectroscopy you think so what can we understand about this I'm going back to the dimer here at their 1st observation is that this is 0 field four-Test 7 Tesla 1st observation around
the energy with a single manganese and does all of its physics all of its been physics namely no plus minus 1 million bowl nothing happens in the diamond what looks like a small magnetic and like the on this come and see that the facilities now if we look at the higher energy higher magnetic fields it just 7 slide looks like we have actually 3 steps you know this 1 here at 5 million bolsters wanted 6 and this 1 at 6 . 5 maybe but just observation Manoel interpretation of this at this point and so we can plot what is the center of this step and this step and this step as a function of magnetic field and we can do this maybe down to 3 Tesla and you can see that we have 1 step that stays constant once the pickles up with magnetic field and 1 that goes but that again should look familiar to you that looks like an S equals 1 system but as equals 1 has quantum numbers chemicals plus 1 0 and minus 1 and they would behave exactly like that so what's happening here was not too surprising India we have 2 very strongly coupled but very items here they happened a couple accounted for a such that you make spin a spin singlet is really a long magnetic state been and state where you have a total spending of 0 that doesn't mean that the manganese itself not this spin 0 you can take to electrons 1st lecture on up said 1 is down minus certain match-winners Don 1st one is up that's a single state for 2 electrodes and that has no nets and known expert total spin of the status 0 so that's what the ground state is like it's a spin 0 state and then the 1st excited state isn't as total equals made out of 2 basic was 5 have manganese items by making magic combinations of spin states basically and then you can get 3 quantum numbers and they all have allowed transitions according to always been direction ,comma .period the simple and so on we use the Heisenberg interactions J S 1 as too as a way to tomorrow this kind of system this is simple Heisenberg directions as total is as 1 plus too why does just definition of its total operator His total square is as 1 square Plaza as to square was 2 times as 1 as tool because the 2 hour commute with each other and that's your highs work these guys are constant and so you really can't say that the s total operator as the same as the above interaction for 2 spins excluding effect of 2 so this as 1 that is to was the same as story city yeah for 2 spins and so we have and the femininity coupling ground status as total equals 0 1st excited states as total equals 1 With an energy difference of J and so this is a way to measure this J 6 enables so we can quantitatively determine the strength of this interaction again by just making this in inelastic tunneling spectroscopy and so was that I'd like to very briefly show you how we can actually calculate things when you have 1 and once because that's probably something that everybody in this room doesn't do quantum computation has never seen White House writes a matrix for spin that is composed of 2 Spence but I mean the quantum people him short seeing this but the other guys you probably haven't seen so many go back to the Knicks operators Sigma X for single spin-one have particle is 0 0 1 1 now how do you do this if you have to spins what you write this down how do you even know the bookkeeping basically I'm not talking science he you know that's all the highs and interaction has to offer but how do you like the sound you diagnose a matrix that has more than 1 spinning under the bookkeeping already makes set up this matrix so if we take to spins right if we take to spins potatoes beans small ones been sorry we have to states that we keep track of up and down but we call the other 1 1 0 McCullough down 1 0 1 In this picture if we take 2 spinsters once 2 expense How do we do this To spends all states are basically first one is up 2nd 1 is about that's no 1 0 0 0 but the right expressed down 0 1 0 0 don't up 0 0 1 0 down down 0 0 0 1 right so with 2 spends you have 4 basis states that you have to keep track of them in general the number of the states is to to the power of right which is why quantum computation works exponential in the number of students legal what's this becomes big very fast but you know 2 we can still write the matrices astounded simple so ripen SX operator and this the 1st of what we know what we want in the north of the year the year I was like a solution the couple minutes I'm so if I want to flip the first one and I don't want to flip the 2nd 1 but I can write this as a signal operate on the 1st guy and identity of the 2nd guy and I know that my outcome of this should the first one flip 2nd 1 month because the Sigma axis of flipped operator but how do I might make this matrix and that's actually not that difficult if you keep this this definition based status is not Sciences just definition bookkeeping so how do you make this operator here so the basically what you wanted the Sigma X this guy here so you set up your matrix 0 identity identity 0 and by this I mean that you get your four-dimensional matrix here by saying this is 0 0 0 0 this guy 0 0 0 0 and then I have identity matrix here the identity matrix there just bookkeeping science and this just avoided that quantum computing people basically do the bookkeeping and that's how you calculate expansion if you want to set up the Hill as explosive as the 6 square pass is why square Plaza square for change of 2 spins of spin one-half OK that's just take a quick look at what the stars operate on 1 1 but 1 1 is 1 0 0 writes a 1 0 0 1st line 0 2nd line is 0 3rd line I get this 1 times this 1 is 1 4th line is 0 look at this again that's just down but final think What if you want to operate on the other guy but we want to flip the stood the 2nd 1 than I do identity times Books times Sigma X and my matrix looks 1st to the identity so I get Sigma Sigma X 0 and then I feel this into my full dimensions Sigma acts it is 0 1 1 0 this is 0 0 0 0 this is 0 and then a good mother Sigma next year 0 1 1 0 but that's different than this matrix here because somehow the major says the bookkeeping for you which operator you actually operating of which which Spacey operating on those at work well let's do the same thing we operate on 1 1 1 but 1 of them by which is 1 0 0 0 and we get this guy is 0 this 1 is 1 this 1 0 this 1 is 0 if you looked at them that is the 2nd 1 there which is up don't but but that's not really tiny Sciences just tell you how the bookkeeping works end of "quotation mark but I'm almost finished so I brought this town and you use lights here so you can
look at this look with more I was going to
have you do a few exercises to what that's not going to work we do the
and and actions of OK so finally we do this Of course with mathematical meth lab wasn't my set up these matrices 4 a spin chained up to lengths 6 of magnitude you this equals 5 House you get a very big matrix very quickly like a million by millions also matrix some animals very big matrices there Creek but we noted from the diner From the China we can actually determined that the magnitude of the spin of the individual 5 House but he using the J from the diner we can look at all like the best agreement is with as equals 5 half and that's it that's all the parameters of the rock the bondage and the for individual be using the simplest Norman nearest neighbor highs connection and then for the event's you can see that this fits very well before the arching also fits with so if you want to do this you know you have to know how you translate this into matrices and how diagonal matrices with this is sort of the beginning of party set up these matrices and with that I think I would like to stop and just just in the summary am I guess I tried to teach you 2 things 1 this but you can learn something about this quantum mechanical systems of spins on services using scanning tunneling microscopy where can we particularly USA inelastic tunneling spectroscopy to learn something here and 2nd that you can if you model the sings with fairly simple basic physical some models if you're not afraid to use the spin operators it's been matrices ,comma 2 messages so thank you very very much for coming and I promise tomorrow will be completely different been fixed so I think we have about 10 minutes or so 65 minutes so feel this should so what are you going to Europe we agree that this was the only 1 so if you wanted to face coherent measurements that's 1 of the many parts that didn't have time a lot more stuff in there in the slides you have so
what he needed to face coherences you need something that keeps the clock for you when you need usually you use timeless leading magnetic field wartime oscillating electric field something that oscillates and in sync with the energy spacing of the energy levels of the system and that can give you coherent oscillations between the ground state and the 1st excited states so what we need is 2 things 1 we need to make a system where the relaxation times long enough that you would have any chance of doing that if he doesn't come I tried to relaxation times T 1 looks Asian times on the order of a nanosecond way too fast for anything face for hearing to work with and so that's what make them lower the remake them microsecond or something like that In the 2nd 1 is include something like a time-dependent feel that sort of sets the clock is so we are trying to do both of these forces both of these steps what we want to the T 1 is currently limited by the fact that this couple nitrate is so thin so we have for example the iron in here and the relaxation times of I put the Adam into an excited state this will accession is completely dominated by an electron from the copper coming in and going back out so we need to make this insignificant so that's that's how we think we can get rid of this relaxation mechanism but then you will have other relaxation mechanisms but you have anatomically small systems of nuclear spins will not be as bad as they are for sampling gallium arsenide quantum dots but we don't know if this works we have never seen anything that is G 2 phase him the picture well you know what good kind of good theorists I am now a so I'm I'm not going to get a good answer from me for that I don't know nobody knows I mean you know there's so many examples were point defects in the material can have very long relaxation like the fashionable 1 2 days is the envy center diamond that has relaxation times and can be held up to Ms a longer T 2 and T 1 them phosphorus in silicon is another 1 workstation fans can be very long so I don't think there is a very general reason to expect them to be long or not you have to really work hard on local symmetry and so on the beauty that we have as you select the feeling for we have quite a bit of flexibility quite so we can build different Adams different surfaces different structures so that the phase space of possible experiments is we don't but we have a problem with these conduction electrons which we have to solve social so 1 step at a time was things become more difficult right but through so you need to find a balance of course we want to maybe able to tunnel through this so we need to find a balance where we can still get enough current to do all measurement but where this process here becomes long enough that it doesn't really matter and so what we're doing is on copper nitrate we can make this anything just south limiting to 1 and the neck but that's when the nature works in this case and so for other materials like magnesium oxide we can make them 1 2 3 4 5 layers thick and then we're in the process basically of measuring these things that I told you here as a function of the thickness Of these materials so the the space of experiments that showed was maybe 5 years of work for this is not fast with the the all this in always certainly will change everything like minute I think you had a feeling Ford at the local environment plays a very important role by age of produce probably hexagonal Vermont mistaken so that's very interesting because you can set up you frustrated spin systems and what not but I haven't done it so I don't know if that would actually work From the magnetic anisotropy will also be different because the symmetries of different you probably don't get charges nearby the nitrogen atoms so magnetic anisotropy apology much less so you can see I can make speculations but but 1 has tried we can make a ship which is Stephanie conductive enough that 1 can work with this with St should work on the word some of the things we arrived at the end of the involved with all of the provisions of the House there is a vast amount of stuff known about the boat spin polarized STM by them in the most prominent open that respect this is in Germany and humble um we've done quite a bit of work with spin polarized as well so we know that another layer of spin bowlers stuff on top of this column to actually see this being the also busy Wannamaker playing junction and then there was the the latest version the new year .period is and agrees with me so the problem will be that you don't have to eclipse so if you use your tip for the injections you can't measure away from the tips what is it yes we'd have to do that so you have to make a lateral structure and that has not been done as far as but any time you go for you know this level of more complexity it becomes very difficult this experiments worked beautifully in UHV clean samples No . at all that's what we can do with this team as soon as you do lithography or any stuff like that the world becomes much more difficult for us this is probably the best answer we will find 1 slide further and see how he had this 1 year this was this is the original IBM that was built by Don love the guy handed left from that was the 1st Adam manipulation 1989 1990 tomorrow I'll talk exclusively about Adam manipulation and how we can build structures and have fun with that no spectra Knoll in last atomic spectroscopy at all just pictures well just pretty pictures I was in year science papers and even more important than that New York Times articles or mentioning of IBM as a leader in our sites if we can portray the academic community and even more importantly to the general to the shareholders basically that IBM is the leader in Nablus science and that this stuff might have applications to to the future of IBM's business then we went so tomorrow I'll show you 2 examples will be used at manipulation of computation and reuse manipulation to the data storage them and that I think you know that's why IBM Francisco work that's also why we can focus on figuring out exactly what happens in this manipulation process by the end of secure about I have to be careful after the stuff that is interesting to the company sold even tho I don't look at anything that is product-related nobody IBM expects any of the stuff I do to make actual product I still have to be able to to demonstrate faithfully that the work I do has net benefit to the company some of the more yes yes I often say that I feel the marketing Of course the marketing Bob doesn't pay for the I never saw you saw the movie that we made the boy and his added that was actually paid by the marketing department that was approximately a million dollars kind of budget to promote this and producers and all that stuff because it's a marketing from the 2 more often than they have won it's not IBM's this know we use a commercial marketing firm in Manhattan and the and I don't know how much I don't know the number of based about but it's definitely more than 100 thousand dollars they were involved in this for what half-year was probably in a 5 to 10 people and that's a lot of money a set of all the all the PR that went with it and come up with the idea design that would have on the way he system basically for people in the lab 10 days but we money for sports we get paid that's the money we OK thank you very very much beer on tomorrow and on Wednesday so the rise of more questions feel free to to approach me and that's Symbios Thank You few


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