# Hidden ferromagnetism of centrosymmetric antiferromagnets

## TL;DR

This paper demonstrates that certain centrosymmetric antiferromagnets can be represented as ferromagnets within a minimal unit cell due to special spin-orbit interactions, explaining phenomena like the anomalous Hall effect.

## Contribution

It reveals how symmetry constraints in centrosymmetric antiferromagnets enable a simplified ferromagnetic description and explains emergent properties such as orbital magnetization and piezomagnetic response.

## Key findings

- Centrosymmetric antiferromagnets can be modeled as ferromagnets in a minimal unit cell.
- The special form of spin-orbit interaction explains the anomalous Hall effect in these materials.
- Theoretical models match first-principles calculations for various materials.

## Abstract

The time-reversal symmetry ($\mathcal{T}$) breaking is a signature of ferromagnetism, giving rise to such phenomena as the anomalous Hall effect (AHE) and orbital magnetism. Nevertheless, $\mathcal{T}$ can be also broken in certain classes of antiferromagnets, such as weak ferromagnets or altermagnets, which remain invariant under the spatial inversion. In the light of this similarity with the ferromagnetism, it is tempting to ask whether such unconventional antiferromagnetic (AFM) state can be represented as the simplest ferromagnetic one, i.e. within the minimal unit cell containing only one magnetic site. We show that such representation is possible due to special form of the spin-orbit (SO) interaction in an antipolar lattice hosting this AFM state. The inversion symmetry constrains the form of the SO interaction, which becomes invariant under the symmetry operation $\{ \mathcal{S}| {\bf t} \}$, combining the $180^{\circ}$ rotation of spins ($\mathcal{S}$) with the lattice shift ${\bf t}$, connecting two antiferromagnetically coupled sublattices. This is the fundamental symmetry property of centrosymmetric antiferromagnets, which justifies the use of the generalized Bloch theorem and transformation to the local coordinate frame with one magnetic site per cell. It naturally explains the emergence of AHE and net orbital magnetization, and provide transparent expressions for these properties in terms of the electron hoppings and SO interaction operating between AFM sublattices, as well as the orthorhombic strain, controlling the piezomagnetic response. The idea is illustrated on a number of examples including two-dimensional square lattice, monoclinic VF$_4$ and CuF$_2$, and RuO$_2$-type materials with the rutile structure, using for these purposes realistic models derived from first-principles calculations.