Spin-modulated torque waves in ferrimagnetic tunnel junctions

Spin-transfer torque (STT) in tunnel junctions with ferromagnetic leads is one of the essential underlying phenomena of modern spintronics. Here, we present a theoretical study of STT in ferrimagnet- (FI-) based tunnel junctions where two FI metal electrodes are separated by a thin nonmagnetic insulating barrier. We show that electronic structure parameters, such as bandwidths and exchange splittings of the FI leads strongly influence STT. In particular, the STT spatial distribution within the leads shows a striking spin-modulated wavelike behavior resulting from the interplay between the exchange splittings of the two FI sublattices. Additionally, we identify the fundamental parameter for quantifying STT characteristic lengths in FI metals, which will also be accessible to experiments, for instance, by ferromagnetic resonance and spin pumping measurements.