Magnon-mediated analog to the Edelstein effect in an antiferromagnet

In metallic and semiconducting materials, the Edelstein effect produces a non-zero average non-equilibrium spatially homogeneous spin polarization by applied external electric field due to the imbalance of spin relaxation time of system with spin degeneracy lift by spin-orbital coupling (SOC). For magnons, the Dzyaloshiniskii-Moriya interaction (DMI) can play similar role to the SOC in a semiconductor and it can result in a non-equilibrium spatially homogeneous spin polarization in collinear and noncollinear insulating antiferromagnets under a temperature gradient. Using the linear response theory, we theoretically predict that by applying a temperature gradient to insulating antiferromagnet with spin non-conserving Hamiltonian, one can produce homogeneous spin accumulation mediated by magnons. We applied our theory to honeycomb, kagome, and pyrochlore collinear and noncollinear antiferromagnets. This prediction can be applied as a new way to generate spin currents in antiferromagnetic spintronic devices.