Altermagnetic Perovskites

Altermagnet is a class of antiferromagnets, which shows a staggered spin ordering with wave vector ${\bm q}=0$, while its net magnetization is canceled out in the limit of zero relativistic spin-orbit coupling. The simplest case is when the up and down spins are ordered on two crystallographically equivalent sublattice sites within the unit cell that are not connected by translation, and consequently, the system breaks the macroscopic time-reversal symmetry. Accordingly, it exhibits non-relativistic spin splitting in the energy band and characteristic cross-correlation phenomena between spin, charge, and lattice (orbital) degrees of freedom. This is in contrast to conventional N\'{e}el-type antiferromagnets with ${\bm q} \neq 0$ conserving the macroscopic time-reversal symmetry, where the time-reversal operation flipping of spins combined with translation can make the system identical to the original state. Altermagneticsm is universally latent in various magnetic materials that have been considered as simple collinear-type antiferromagnets. In this article, we focus on perovskites with chemical formula {\it ABX}$_3$, which are typical playgrounds for strongly correlated electron systems, and overview their altermagnetic aspects that have been overlooked in the past researches, based on microscopic model studies revealing the mechanisms of their properties. We display that a combination of a variety of antiferromagnetic ordering and the commonly-seen lattice distortions in perovskites gives rise to a non-relativistic spin splitting whose mechanism does not rely on the spin-orbit coupling and its consequent spin current generation, and the anomalous Hall effect in the presence of the spin-orbit coupling.