Topological Spin Torque Emerging in Classical Spin Systems with Different Timescales.

In classical spin systems with two largely different inherent timescales, 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.