Altermagnet is a class of antiferromagnets showing a staggered spin ordering with wave vector q = 0, while its net magnetization is cancelled out in the limit of zero relativistic spin-orbit coupling. The simplest case is when the up and down spins are ordered on two sublattice sites within the unit cell which are not connected by either translation or inversion. Consequently, the system breaks the macroscopic time-reversal symmetry and exhibits non-relativistic spin splitting in the energy band and characteristic cross-correlation phenomena.

In this talk, I will introduce our theoretical studies based on effective models for correlated electrons in k-type organic compounds [1] and perovskite-type transition metal compounds [2]. In these systems, the dimeric molecular arrangements and the GdFeO₃-type lattice distortions, respectively, play the role of the crystallographic setting for altermagnetism. We show that antiferromagnetic orderings give rise to the non-relativistic spin splitting, owing to anisotropic sublattice dependent (and thus spin dependent) electron hoppings, and its consequent spin current generation, and the anomalous Hall effect in the presence of the spin-orbit coupling. Recent developments will also be discussed.