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From confinement to deconfinement of magnetic monopoles in artificial rectangular spin ices

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Logo of Institute of Physics (IOP)Institute of Physics (IOP)
Logo of Deutsche Physikalische Gesellschaft (DPG)Deutsche Physikalische Gesellschaft (DPG)
 Nascimento, F. S. Mól, L. A. S. Moura-Melo, W. A. Pereira, A. R.

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From confinement to deconfinement of magnetic monopoles in artificial rectangular spin ices
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15
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We study a frustrated two-dimensional array of dipoles forming an artificial rectangular spin ice with horizontal and vertical lattice parameters given by a and b respectively. We show that the ice regime could be stabilized by appropriate choices for the ratio γ ≡ a/b. Our results show that for , i.e. when the centers of the islands form a triangular lattice, the ground state becomes degenerate. Therefore, while the magnetic charges (monopoles) are excitations connected by an energetic string for general rectangular lattices (including the particular case of a square lattice), they are practically free to move for a special rectangular lattice with . Besides that, our results show that for the system is highly anisotropic in such a way that, even for this range out of the ice regime, the string tension almost vanishes along a particular direction of the array. We also discuss the ground state transition and some thermodynamic properties of the system.
New Journal of Physics, Volume 14, 20126 / 15
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Transcript: English(auto-generated)
00:04
From confinement to the confinement of magnetic monopoles, an artificial rectangular spin ice. In 2006, a group from Penn State University built an artificial version of the spin ice materials by using elongated magnetic nano-islands organized in square legs.
00:20
Each nano-island contains a net magnetic moment, spin, that has an easy-like behavior. Therefore, in each vertex, there are 4 spins and the energy is minimized when the ice rule is obeyed. Two spins point in and the other two point out, or two in, two out. However, differently from the natural spin ice, the ice rule is not degenerate for the square only.
00:44
Indeed, from the 4 possible topologies, topologies 1 and 2 obey the ice rule, but topology 2 has more energy than topology 1. Then, the ground state obeys the ice rule with all-verses in topology 1. The first question is, may the excitations exhibit the phenomena of fractionalization as a car with natural spin ice,
01:07
in which apparently invisible microscope degree of freedom falls to pieces? I mean, may magnetic monopoles be present in these systems? The first excited state arises when, in a particular vertex, the ice rule is violated.
01:22
It creates two adjacent vertex, in which one has 3 spins point in and one out, while the other has 3 out, one in, both in topology 3. This excitation is a peculiar pair of neighbor repulsive magnetic charges separated by magnetic spacing. If one tries to separate the charges more and more without further violation of the ice rule,
01:46
an energetic string arises in the separation pathway. Due to the energetic string, this larger excitation is more similar to a pair of number monopoles in contrast to giraffe monopoles. In this work, we show that the deformation of the square lattes can solve this difficulty.
02:03
Thus, we suggest that the fabrication of samples with an intentional change in the lattes space on the original square ice, A and B respectively, may take the system to the ice regime depending on how the lattes is compressing or stretching. Ratio A over B.
02:21
Different from the square lattes, which has 4 topologies, in the rectangular ice, there are in general 5 topologies, T0, T1, T2, T3 and T4. Other extra characteristics of the rectangular lattes is the presence of residual magnetic charges, even for lattes obeying the ice rule, which also depends on the ratio A over B.
02:43
Only topology T1 does not have residual charge, but it has residual magnetic moment. Considering A over B bigger than 1, the ground state of the rectangular lattes will exhibit residual charge in all vertices if A over B is smaller than square root of 3.
03:02
This charge alternates from north to south in edges at rest in such a way that the total charge of the system is zero. On the other hand, if A over B is bigger than square root of 3, is still a charge, the ground state has residual magnetic moment in the vertices. Again, the total magnetic moment of the system is zero.
03:23
There is therefore a ground state transition which occurs at A over B equal to square root of 3. In this case, the space around the vertex becomes equidistant and the topologies T0 and T1 have the same energy. Then, the magnetic monopoles are not connected by energetic strings anymore.
03:43
The string tensor vanishes and the poles become deconfined. In summary, we have shown that the lattes geometry in two dimensions can be modified in such a way that the artificial rectangular spin ice finds the ice regime or stays very near it for A over B equal to square root of 3.