Chiral magnetism: a geometric perspective
arXiv:2008.08681 · doi:10.21468/SciPostPhys.10.3.078
Abstract
We discuss a geometric perspective on chiral ferromagnetism. Much like gravity becomes the effect of spacetime curvature in theory of relativity, the Dzyaloshinski-Moriya interaction arises in a Heisenberg model with nontrivial spin parallel transport. The Dzyaloshinskii-Moriya vectors serve as a background SO(3) gauge field. In 2 spatial dimensions, the model is partly solvable when an applied magnetic field matches the gauge curvature. At this special point, solutions to the Bogomolny equation are exact excited states of the model. We construct a variational ground state in the form of a skyrmion crystal and confirm its viability by Monte Carlo simulations. The geometric perspective offers insights into important problems in magnetism, e.g., conservation of spin current in the presence of chiral interactions.
5 pages, 2 figures. Minor edits in response to referee reports
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Cited by in corpus (17)
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- Magnetization dynamics with time-dependent spin-density functional theory: significance of exchange-correlation torques
- Curvilinear manipulation of polarized spin wave
- Gauge theory applied to magnetic lattices
- Gravitational wave analogues in spin nematics and cold atoms
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- Mode splitting of spin waves in magnetic nanotubes with discrete symmetries
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- Disentangling electric field effect on spin waves in ferromagnetic insulators