In altermagnets and fully compensated ferrimagnets, not only the electron band but also the magnon band exhibits spin splitting without net magnetization, which enables thermal activation of the magnon spin current. Here, we theoretically investigate magnetic field effects on the magnon properties of these antiferromagnets in the presence of weak easy-axis anisotropy which makes the collinear states robust against the magnetic field. For the altermagnet and compensated ferrimagnet, we analyze a two-sublattice order in the $J_1\text{−}{J}_2\text{−}{J}_2^{\prime }$ model on the square lattice and a triple-$\mathbf{Q}$ 12-sublattice order in the $J_1\text{−}{J}_3$ model on the kagome lattice, respectively, each accompanied by $d$- and $s$-wave spin splitting at zero field. It is shown that, for positive (negative) magnetic field $H$ whose energy scale is smaller than the anisotropy gap, the up- and down-spin magnon bands are shifted to lower (higher) and higher (lower) energies, respectively, like the Zeeman coupling in electron systems. In the altermagnet, with increasing field, $d$-wave splitting tends to be deformed into $s$-wave splitting, which is reflected as the change in the direction of the spin current generated by thermal gradient. In the compensated ferrimagnet, the $s$-wave nature, i.e., the population imbalance between the up- and down-spin magnons at $H=0$, can induce asymmetric field dependence of the longitudinal spin and thermal conductivities in a field-sweep process.

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• Altermagnetism
• Frustrated magnetism
• Spintronics