Spin-split magnon bands induce pure spin current in insulating altermagnets

Altermagnets offer a promising platform for dissipationless spin transport by combining zero net magnetization with spontaneous nonrelativistic spin-split bands. Transport of angular momentum by magnons modes is another interesting aspect in altermagnets. Here, we develop a quantum-kinetic theory for thermally driven magnon currents that cleanly separates Berry-curvature-driven intrinsic contributions from Drude-like scattering-dependent terms. Applying this framework to a collinear honeycomb antiferromagnet with anisotropic altermagnetic exchange interaction and Dzyaloshinskii-Moriya interaction between next-nearest neighbor, we reveal spin-split magnon bands that support both intrinsic and extrinsic magnonic spin Nernst and Seebeck currents. For realistic parameters, we predict a sizable magnon spin-splitting angle (about 3.3 degrees) and a pure transverse spin current capable of exerting a strong spin-splitter torque suitable for magnetization switching.