Geometric origin of the intrinsic transverse spin transport in a canted-antiferromagnet/heavy-metal heterostructure

We theoretically study the conditions under which an intrinsic spin Nernst effect–a transverse spin current induced by an applied temperature gradient–can occur in a canted-antiferromagnet insulator, such as ${\mathrm{LaFeO}}_3$ and other materials of the same family. The spin Nernst effect may provide a microscopic mechanism for an experimentally observed anomalous thermovoltage in ${\mathrm{LaFeO}}_3/\mathrm{Pt}$ heterostructures, where spin is transferred across the insulator/metal interface when a temperature gradient is applied to ${\mathrm{LaFeO}}_3$ parallel to the interface [W. Lin et al., Nat. Phys. 18, 800 (2022)]. We find that ${\mathrm{LaFeO}}_3$ exhibits an intrinsic spin Nernst effect when inversion symmetry is broken on the axes parallel to both the applied temperature gradient and the direction of spin transport, which can result in a spin injection across the insulator/metal interface. Our paper provides a general derivation of a symmetry-breaking-induced spin Nernst effect, which may open a path to engineering a finite spin Nernst effect in systems where it would otherwise not arise.