Gauge-Field-Mediated Symmetry Breaking of Matters Under Electromagnetic Fields and Its Impact on Spin Dynamics

TL;DR

This paper reveals that gauge-field contributions are crucial for understanding symmetry breaking and spin dynamics in materials under electromagnetic fields, challenging the common neglect of these terms.

Contribution

It demonstrates that gauge-field terms govern symmetry breaking and spin dynamics, using real-time density functional theory to show their importance in nonequilibrium conditions.

Findings

Gauge-field terms induce symmetry breaking in spin dynamics.

Spin states evolve beyond symmetry constraints when gauge fields perturb canonical SOC.

Gauge-invariant SOC formulation is essential for accurate nonequilibrium spin dynamics.

Abstract

When a condensed-matter system is subjected to external electromagnetic fields, the gauge-invariant formulation of physical operators must explicitly incorporate the gauge-field contribution. However, in the context of spin-orbit coupling (SOC), this gauge-field term is often regarded as negligible or merely additive compared to the canonical SOC, which is typically localized near atomic cores. Here, we demonstrate that the symmetry breaking and consequent spin dynamics are governed by the gauge-field term, without which the spins remain symmetry-constrained. We perform real-time time-dependent density functional theory calculations to investigate spin-orbit dynamics, focusing on representative cases with mirror, glide, and screw-rotational symmetry. We demonstrate that when the gauge-field term in the time-dependent Hamiltonian perturbs the symmetry of the canonical term, a dynamical spin state gradually develops during the time evolution, beyond the symmetry-frozen states. We suggest that, for nonequilibrium spin-orbit dynamics, the gauge-invariant formulation of SOC is not only formally required but also quantitatively essential, even for a weak external field.