| Summary: | 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.
|
|---|