Geometrical torque on magnetic moments coupled to a correlated antiferromagnet

The geometrical spin torque mediates an indirect interaction of magnetic moments, which are weakly exchange coupled to a system of itinerant electrons. It originates from a finite spin-Berry curvature and leads to a non-Hamiltonian magnetic-moment dynamics. We demonstrate that there is an unprecedentedly strong geometrical spin torque in the case of an electron system, where correlations cause antiferromagnetic long-range order. The key observation is that the anomalous torque is strongly boosted by low-energy magnon modes emerging in the two-electron spin-excitation spectrum due to spontaneous breaking of SU(2) spin-rotation symmetry. As long as single-electron excitations are gapped out, the effect is largely universal, i.e., essentially independent of the details of the electronic structure, but decisively dependent on the lattice dimension and spatial and spin anisotropies. Analogous to the reasoning that leads to the Mermin-Wagner theorem, there is a lower critical dimension at and below which the spin-Berry curvature diverges.