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First-principles calculations of spin-orbit torques in Mn$_2$Au/heavy-metal bilayers

Using the non-equilibrium Green's function technique, we calculate spin-orbit torques in a Mn$_2$Au/heavy-metal bilayer, where the heavy metal (HM) is W or Pt. Spin-orbit coupling (SOC) in the bulk of Mn$_2$Au generates strong fieldlike torquance, which is parallel on the two sublattices and scales linearly with the conductivity, and a weaker dampinglike torquance that is antiparallel on the two sublattices. Interfaces with W or Pt generate parallel dampinglike torques of opposite signs that are similar in magnitude to those in ferromagnetic bilayers and similarly insensitive to disorder. The dampinglike torque efficiency depends strongly on the termination of the interface and on the presence of spin-orbit coupling in Mn$_2$Au, suggesting that the dampinglike torque is not due solely to the spin-Hall effect in the HM layer. Interfaces also induce antiparallel fieldlike and dampinglike torques that can penetrate deep into Mn$_2$Au.