Equivariant Space Group and Hamiltonian for Collinear Magnetic Systems

TL;DR

This paper introduces a symmetry-based framework called equivariant magnetic Hamiltonians (EMHs) for modeling collinear magnetic systems with explicit dependence on the magnetic order parameter orientation, enabling new topological and dynamical studies.

Contribution

The authors develop a general, symmetry-based method to construct EMHs that incorporate the magnetic order parameter, applicable to both model and real materials, and extendable to non-collinear systems.

Findings

Demonstrated magnetic-dynamics-driven topological pumping in model systems.

Constructed ab-initio EMHs capturing n-dependent band structures.

Revealed unconventional symmetry actions and topological features in EMHs.

Abstract

Condensed matter physics increasingly focuses on exploiting the magnetic order parameter orientation n as a tuning knob for properties of collinear magnetic materials, but a general method for constructing effective Hamiltonians with explicit n-dependence has been lacking. Here, we develop a symmetry-based framework, built on the equivariant space group, for constructing such Hamiltonians, termed equivariant magnetic Hamiltonians (EMHs). The resulting EMH lives in a higher-dimensional k-n space and exhibits unconventional symmetry actions and topological features. Using a 1D ferromagnetic chain and a 3D antiferromagnet as examples, we demonstrate that explicit n-dependence in EMHs enables the study of magnetic-dynamics-driven topological pumping, including even-integer charge pumping and a second-Chern-number-induced quantized pumping of surface anomalous Hall conductivity. Beyond model systems, we incorporate the framework into first-principles calculations to construct ab-initio EMHs that accurately capture the n-dependent band structures of real materials. The approach can also be generalized to non-collinear magnetic systems. Our work establishes a general framework for constructing EMHs and for exploring the rich physics arising from magnetic anisotropy and magnetic dynamics.