Spin-orbit magnetism in altermagnets

Abstract

While the anomalous Hall effect was proposed as a transport fingerprint of altermagnets, it originates from the spin-orbit coupling-induced net magnetization, corresponding to a distinct magnetic phase termed spin-orbit magnetism. However, the microscopic mechanism enabling spin-orbit magnets to yield a prominent anomalous Hall response despite a vanishingly small net magnetization remains elusive. Here, by employing oriented spin group theory and spin-orbit-coupling tensor expansion, we systematically disentangle the perturbative behaviors of orbital and spin magnetizations with respect to spin-orbit coupling in altermagnets. Remarkably, we find that only if the opposite-spin sublattices are connected through a fourfold rotation, the orbital and spin magnetizations exhibit distinct perturbative orders. In these altermagnets, we further discover a coaxial Hall effect characterized by the induced spin and orbital magnetizations aligning parallel to the Néel vector, which we further demonstrate by first-principles calculations in the altermagnet KV${}_2$Se${}_2$O. This effect holds great promise for achieving deterministic switching of the Néel order under weak external fields. Our work provides a systematic symmetry approach to identify potential altermagnetic candidates combining a large anomalous Hall effect with minimal net magnetization, paving the way for high-performance, stray-field-free spintronic applications.

6 pages, 3 figurs, 1 table