Linear and nonlinear spin-current generation in polar collinear antiferromagnets without relativistic spin-orbit coupling

We investigate spin-current generation in polar collinear antiferromagnets without relying on the relativistic spin-orbit coupling. The symmetry and microscopic model analyses indicate that both linear and nonlinear spin conductivities are induced; the linear spin conductivity is characterized by the non-Hall-type transverse tensor component, while the nonlinear spin conductivity is characterized by the Hall-type tensor component. We show that the emergence of the linear and nonlinear spin currents is caused by the quadrupole and dipole components of the magnetic toroidal multipoles in the collinear antiferromagnetic structure, respectively. We demonstrate the important conditions to enhance and/or suppress the spin conductivity in each component by analyzing a fundamental tight-binding model. The experimental separation between their contributions is also discussed.