B-type Quadratic Planar Hall Effect as a Probe of Altermagnetic Order

Abstract

Conventional transport and optical responses, such as the Hall effect, can only distinguish material phases with substantially different symmetries. However, many quantum materials, such as candidate altermagnetic materials, host competing phases with similar structures, making it difficult to differentiate them using conventional transport or optical measurements. Here, guided by symmetry principles, we introduce a B-type quadratic planar Hall effect (B2-PHE) as a sensitive probe of magnetic structures. B2-PHE features a planar Hall current that scales quadratically with the applied magnetic field. This response originates from the interplay among external magnetic fields, intrinsic magnetic order, and quantum geometric properties of the electronic bands. We investigate B2-PHE in two altermagnetic candidates, KV2Se2O and RuO2, whose ground-state magnetic orders are under intense debate. Remarkably, B2-PHE emerges in their altermagnetic phases but is symmetry-forbidden in their antiferromagnetic (nonmagnetic) phases. We also show that B2-PHE should be detectable under a moderate magnetic field on the order of 1 Tesla. These findings establish B2-PHE as an experimentally convenient and potentially unambiguous probe of altermagnetic order, which is otherwise difficult to realize.