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The composition-dependent behavior of the Dzyaloshinskii-Moriya interaction(DMI), the spin-orbit torque (SOT), as well as anomalous and spin Hallconductivities of Mn$_{1-x}$Fe$_x$Ge alloys have been investigated byfirst-principles calculations using the relativistic multiple scatteringKorringa-Kohn-Rostoker (KKR) formalism. The $D_{\rm xx}$ component of the DMIexhibits a strong dependence on the Fe concentration, changing sign at $x\approx 0.85$ in line with previous theoretical calculations as well as withexperimental results demonstrating the change of spin helicity at $x \approx0.8$. A corresponding behavior with a sign change at $x \approx 0.5$ ispredicted also for the Fermi sea contribution to the SOT, as this is closelyrelated to the DMI. In the case of anomalous and spin Hall effects it is shownthat the calculated Fermi sea contributions are rather small and thecomposition-dependent behavior of these effects are determined mainly by theelectronic states at the Fermi level. The spin-orbit-induced scatteringmechanisms responsible for both these effects suggest a common origin of theminimum of the AHE and the sign change of the SHE conductivities.

Composition-dependent magnetic response properties of Mn$_{1-x}$Fe$_x$Ge alloys