Adiabatic spin dynamics and effective exchange interactions from constrained tight-binding electronic structure theory: Beyond the Heisenberg regime

TL;DR

This paper develops a method for adiabatic spin dynamics within tight-binding electronic structure theory, enabling the extraction of effective exchange interactions and analyzing limitations beyond the Heisenberg model in non-collinear magnetic systems.

Contribution

It introduces a novel approach to simulate adiabatic spin dynamics and extract effective exchange interactions from non-collinear states, extending beyond traditional Heisenberg models.

Findings

Adiabatic spin dynamics conserve energy but not total spin angular momentum when magnetic moments change length.

Effective exchange interactions can be derived from energy curvature tensors during simulations.

Non-collinearity significantly affects exchange interactions, highlighting multi-spin effects beyond the Heisenberg regime.

Abstract

We consider an implementation of the adiabatic spin dynamics approach in a tight-binding description of the electronic structure. The adiabatic approximation for spin-degrees of freedom assumes that the faster electronic degrees of freedom are always in a quasi-equilibrium state, which significantly reduces the numerical complexity in comparison to the full electron dynamics. Non-collinear magnetic configurations are stabilized by a constraining field, which allows to directly obtain the effective magnetic field from the negative of the constraining field. While the dynamics are shown to conserve energy, we demonstrate that adiabatic spin dynamics does not conserve the total spin angular momentum when the lengths of the magnetic moments are allowed to change, which is confirmed by numerical simulations. Furthermore, we develop a method to extract an effective two-spin exchange interaction from the energy curvature tensor of non-collinear states, which we calculate at each time step of the numerical simulations. We demonstrate the effect of non-collinearity on this effective exchange and limitations due to multi-spin interactions in strongly non-collinear configurations beyond the regime where the Heisenberg model is valid. The relevance of the results are discussed with respect to experimental pump-probe experiments that follow the ultra-fast dynamics of magnetism.