Chiral ferromagnets have spatially modulated magnetic order exemplified by helices, spirals, and more complex patterns such as skyrmion crystals. The theoretical understanding of these states is based on a competition of a strong Heisenberg exchange interaction favoring uniform magnetization and a weaker Dzyaloshinskii-Moriya (DM) interaction promoting twists in magnetization. In this seminar, we consider a geometric approach, in which chiral forces are treated as a manifestation of curvature in spin parallel transport. The resulting theory is a gauged version of the Heisenberg model, with the DM vectors serving as background SO(3) gauge fields. This geometrization of chiral magnetism is akin to the treatment of gravity in general relativity, where gravitational interactions are reduced to a curvature of spacetime. The geometric perspective provides a simple way to define a conserved spin current in the presence of spin-orbit interaction. We show that the gauged Heisenberg model in d=2 is partly solvable when an applied magnetic field matches the gauge curvature. This model is shown to have a skyrmion-crystal ground state in the presence of a sufficiently small magnetic field.
Reference: Daniel Hill, Valeriy Slastikov, Oleg Tchernyshyov, SciPost Phys. 10, 078 (2021)