Functionalization of $g$-wave altermagnets: spin-splitter effect enabled by surfaces

Abstract

We investigate surfaces of a $g$-wave altermagnet(AM) and show that they provide a platform for realizing $d$-wave altermagnetism and the associated spin-splitter functionality. Using the Kubo formalism applied to a minimal slab model, we evaluate the spin-splitter effect(SSE) by computing the spin conductivity corresponding to a transverse spin current induced by a longitudinal electric field. We find a finite SSE, absent in the bulk, that emerges from surface-induced $d$-wave altermagnetism. Strikingly, the sign pattern of the $d$-wave altermagnetism on both surfaces of the slab geometry is identical to each other, leading to additive contributions to SSE from the two surfaces, with a spin-splitter angle reaching up to 15 degrees. In addition, this response is intrinsically linked to an accompanying surface-induced weak ferromagnetism, which potentially enables control of altermagnetic domains via an external magnetic field and provides a route to optimize the SSE functionality. These results can be understood in terms of a bulk-boundary correspondence between surface states and bulk altermagnetic order parameters, where the magnetic multipolar character of the latter plays a central role. Our findings strongly suggest thin-film engineering as a viable strategy to functionalize non-$d$-wave AMs.