Magnon-mediated Neel torques and magnonic responses to Neel order dynamics

Using the Neel ground state, we formulate a microscopic linear response theory of magnon-mediated Neel torques generated by the thermal gradient in collinear antiferromagnets. We also describe the inverse effects in which spin and heat currents are induced by the Neel order dynamics. We obtain the extrinsic and intrinsic contributions where the intrinsic contributions are related to the mixed space Berry curvature. We derive a closed equation of motion of Neel dynamics in antiferromagnets related to thermal Neel torque from linearized LLG equation. We confirm that the Neel torque effect is related to the inverse effect by the Onsager relations. We apply our theory to honeycomb antiferromagnet and confirm that a net magnon-mediated heat current can be induced by the Neel order precession.