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

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