📝 SummarXiv

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 (OM). 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 anomalous antiferromagnetic (AFM) state can be presented as a simplest ferromagnetic one, i.e. within a minimal unit cell containing only one magnetic cite. We show that such presentation is possible due to the special form of the spin-orbit (SO) interaction in an antiferroelectrically distorted lattice hosting this AFM state. The inversion symmetry, combined with the lattice translations, imposes a severe constraint on 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 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 cite per cell. It naturally explains the emergence of AHE and OM, and provides transparent expressions for these properties in terms of the electron hoppings and SO interaction operating between nearest neighbors as well as the orthorhombic strain of the next-nearest-neighbor hoppings. The idea is illustrated on a number of examples, using realistic models derived from first-principles calculations. These examples include two-dimensional square lattice, monoclinic VF$_4$ and CuF$_2$, and RuO$_2$-type materials with the tetragonal symmetry.