Anisotropic magnon transport in an antiferromagnetic trilayer heterostructure: is BiFeO$_3$ an altermagnet?

Magnons provide a route to ultra-fast transport and non-destructive readout of spin-based information transfer. Here, we report magnon transport and its emergent anisotropic nature in BiFeO$_3$ layers confined between ultrathin layers of the antiferromagnet LaFeO$_3$. Due to the confined state, BiFeO$_3$ serves as an efficient magnon transmission channel as well as a magnetoelectric knob by which to control the stack by means of an electric field. We discuss the mechanism of the anisotropic spin transport based on the interaction between the antiferromagnetic order and the electric field. This allows us to manipulate and amplify the spin transport in such a confined geometry. Furthermore, lower crystal symmetric and suppression of the spin cycloid in ultrathin BiFeO$_3$ stabilizes a non-trivial antiferromagnetic state exhibiting symmetry-protected spin-split bands that provide the non-trivial sign inversion of the spin current, which is a characteristic of an altermagnet. This work provides an understanding of the anisotropic spin transport in complex antiferromagnetic heterostructures where ferroelectricity and altermagnetism coexist, paving the way for a new route to realize electric-field control of a novel state of magnetism.