Spin pumping from antiferromagnetic insulator spin-orbit-proximitized by adjacent heavy metal: A first-principles Floquet-nonequilibrium Green's function study

Motivated by recent experiments [P. Vaidya {\em et al.}, Science {\bf 368}, 160 (2020)] on spin pumping from sub-THz radiation-driven uniaxial antiferromagnetic insulator (AFI) MnF$_2$ into heavy metal (HM) Pt hosting strong spin-orbit (SO) coupling, we compute and compare pumped spin currents in Cu/MnF$_2$/Cu and Pt/MnF$_2$/Cu heterostructures. Recent theories of spin pumping by AFI have relied on simplistic Hamiltonians (such as tight-binding) and the scattering approach to quantum transport yielding the so-called interfacial spin mixing conductance (SMC), but the concept of SMC ceases to be applicable when SO coupling is present directly at the interface. In contrast, we use more general first-principles quantum transport approach which combines noncollinear density functional theory with Floquet-nonequilibrium Green's functions in order to take into account: {\em SO-proximitized AFI} as a new type of quantum material, different from isolated AFI and brought about by AFI hybridization with adjacent HM layer; SO coupling at interfaces; and evanescent wavefunctions penetrating from Pt or Cu into AFI layer to make its interfacial region {\em conducting} rather than insulating as in the original AFI. The DC component of pumped spin current $I_\mathrm{DC}^{S_z}$ vs. precession cone angle $\theta_{\vb*{l}}$ of the N\'eel vector $\vb*{l}$ of AFI {\em does not} follow putative $I^{S_z}_\mathrm{DC} \propto \sin^2 \theta_{\vb*{l}}$, except for very small angles $\theta_{\vb*{l}} \lesssim 10^\circ$ for which we can define an {\em effective} SMC from the prefactor and find that it doubles from MnF$_2$/Cu to MnF$_2$/Pt interface. In addition, the angular dependence $I^{S_z}_\mathrm{DC}(\theta_{\vb*{l}})$ differs for opposite directions of precession of the N\'{e}el vector, leading to twice as large SMC for the right-handed than for the left-handed chirality of the precession mode.