Phenomenological model of magnon spin transport in polar antiferromagnets*

Thermally excited magnons in an antiferromagnetic insulator can give rise to a non-local inverse spin Hall voltage in a detector wire in a planar device structure. Recently, the multiferroic bismuth ferrite (BFO) has been demonstrated to exhibit electric field controlled magnon transport, offering tantalizing opportunities for electrically controllable spintronic devices. The magnetic order of BFO, however, is complex, hosting a spin cycloid tied to the ferroelectric polarization, and the physics of spin transport in BFO remains a significant question. Here, we present a phenomenological model for magnon spin transport in polar antiferromagnets, inspired by the symmetries associated with the material and the device geometry. The model summarizes the physics of magnon spin transport in a single function η representing the extent to which a given magnon mode will contribute to the inverse spin Hall voltage in the detector wire. By writing the parameters of the function η and analyzing their transformations under relevant symmetry operations, we can predict aspects of the thermally driven non-local magnon signals. By offering symmetry-enforced constraints on the inverse spin Hall voltage measurements, our results enable us to identify which symmetries are broken in the system and subsequently gain insight into the physical mechanisms of magnon spin transport. We envision that our symmetry-based phenomenological model will help us understand the spin transport in polar antiferromagnetic insulators.