Topological Spin Torque Emerging in Classical Spin Systems with Different Timescales

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Theoretical Physics

Background:

• Classical spin systems often exhibit dynamics across vastly different timescales.
• Understanding emergent phenomena in such multi-timescale systems is crucial.
• The instantaneous following of fast spins by slow spins simplifies some models.

Purpose of the Study:

• To develop an effective theory for slow-spin degrees of freedom in classical spin systems.
• To identify and characterize emergent phenomena, specifically topological spin torques.
• To explain the origin of anomalous real-time dynamics in these systems.

Main Methods:

• Formulation of an emergent effective theory focusing on slow-spin dynamics.
• Derivation of a topological spin torque from holonomic constraints.
• Analysis of the topological charge density and its properties.

Main Results:

• The effective theory successfully describes the slow-spin dynamics.
• A novel topological spin torque is identified as a general feature.
• This torque leads to anomalous real-time dynamics not predicted by simpler models.
• The torque is linked to a topological charge density, a quantized homotopy invariant.

Conclusions:

• The emergent effective theory provides a powerful framework for multi-timescale spin systems.
• Topological spin torques are a key mechanism driving anomalous dynamics.
• The quantization of the topological charge highlights fundamental topological properties.