Topological spin torque emerging in classical-spin systems with different time scales

Abstract

In classical spin systems with two largely different inherent time scales, the configuration of the fast spins almost instantaneously follows the slow-spin dynamics. We develop the emergent effective theory for the slow-spin degrees of freedom and demonstrate that this generally includes a topological spin torque. This torque gives rise to anomalous real-time dynamics. It derives from the holonomic constraints defining the fast-spin configuration space and is given in terms of a topological charge density which becomes a quantized homotopy invariant when integrated.

5+ pages, 2 figures, supplemental material (4 pages), v2 with minor modifications

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• Dynamical torques from Shiba states in $s$-wave superconductors
• Nonequilibrium dynamics in a spin valve with noncollinear magnetization
• Prethermalization in periodically-driven nonreciprocal many-body spin systems
• Unsupervised Machine Learning Phase Classification for Falicov-Kimball Model
• Non-Hamiltonian dynamics of indirectly coupled classical impurity spins
• Geometrical torque on magnetic moments coupled to a correlated antiferromagnet
• Suppression of scattering from slow to fast subsystems and application to resonantly Floquet-driven impurities in strongly interacting systems