Spin–Orbit Coupling Free Nonlinear Spin Hall Effect in a Triangle-Unit Collinear Antiferromagnet with Magnetic Toroidal Dipole

We investigate emergent conductive phenomena triggered by collinear antiferromagnetic orderings. We show that an up-down-zero spin configuration in a triangle cluster leads to linear and nonlinear spin conductivities even without the relativistic spin–orbit coupling; the linear spin conductivity is Drude-type, while the nonlinear spin conductivity has Hall-type characterization. We demonstrate the emergence of both spin conductivities in a breathing kagome system consisting of a triangle cluster. The nonlinear spin conductivity becomes larger than the linear one when the Fermi level lies near the region where a small partial band gap opens. Our results indicate that collinear antiferromagnets with triangular geometry give rise to rich spin conductive phenomena.