Identifying the origin of out-of-plane spin polarization in the noncollinear antiferromagnet Mn$_3$Ge

Abstract

The noncollinear antiferromagnets Mn$_3$Sn/Ge emerge as promising spin-current sources with both in-plane and out-of-plane spin polarizations, thereby enabling field-free magnetization switching. However, the microscopic origin of the out-of-plane spin polarization remains under debate, specifically whether it arises from the magnetic spin Hall effect (MSHE) or the spin swapping (SSW). Here, we comparatively evaluate the spin torques in single-crystal Mn$_3$Ge/Py bilayers with different crystallographic orientations using the ferromagnetic resonance technique. The distinct angular dependences of the measured spin-torque signals provide clear evidence for the bulk MSHE, which depends on antiferromagnetic order. In addition, we identify the antiferromagnetic-order independent component originating from the interfacial SSW. The coexisting MSHE and SSW, with comparable magnitudes, give rise to the out-of-plane spin polarization. Our study disentangles the origins of spin-torque generation in noncollinear antiferromagnets, providing valuable insights for their spintronic applications.