The magnon thermal Hall and spin Hall effects (SHE) driven by surface acoustic wave (SAW)-induced pseudogauge fields have been investigated in two-dimensional honeycomb compensated ferrimagnets (CFMs). Unlike antiferromagnets, where the magnon thermal Hall effect is prohibited by the degeneracy of the two magnon branches, CFMs exhibit a finite thermal Hall response because unequal easy-axis anisotropies on the two magnetic sublattices lift this degeneracy. The resulting energy splitting between the magnon branches creates a population imbalance, leading to a thermal Hall conductivity that is readily tuned by the anisotropy difference. In contrast, the SHE remains finite even in the absence of magnon-band splitting and shows only a weak dependence on the anisotropy difference. The role of four-magnon interactions is then examined within the Hartree-Fock approximation. It is found that magnon-magnon interactions suppress both the thermal Hall and spin Hall responses compared with the predictions of noninteracting linear spin-wave theory. These findings identify CFMs as a promising platform for strain-controlled magnon-mediated thermal and spin transport.

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• Magnons
• Piezoelectricity
• Spintronics
• 2-dimensional systems
• Linear spin wave theory
• Mean field theory