Spin current compensation from competing magnon modes in ferrimagnets

Abstract We investigate thermal spin pumping in gadolinium iron garnet, focusing on the mode-resolved dynamics of antiferromagnetic magnons and their impact on spin and heat transport. Antiferromagnets support both right-handed and left-handed magnon modes, which we treat as positive and negative frequency branches, analogous to electrons and holes in semiconductors. Using a two-sublattice model with a minimal exchange interaction scheme, we derive the temperature-dependent spin-wave spectrum and evaluate the associated thermal spin pumping coefficients. Our analysis reveals that the competition between left- and right-handed modes gives rise to a compensation temperature, where the net thermally generated spin current vanishes. Importantly, we show that this compensation point does not necessarily coincide with the crossing of magnon dispersion branches. While previous research considers a detailed microscopic model including all magnetic sublattices and exchange couplings, our approach demonstrates that key features of mode-resolved spin transport can be captured by a simplified and analytically transparent model. These findings advance the understanding of spin-caloritronic phenomena in ferrimagnets and offer new perspectives for the design of chiral magnon-based spintronic devices.