Quantum classical approach to spin and charge pumping and the ensuing radiation in terahertz spintronics: Example of the ultrafast light-driven Weyl antiferromagnet Mn3Sn

The interaction of a femtosecond laser pulse with magnetic materials has been intensely studied for more than two decades in order to understand ultrafast demagnetization in single magnetic layers or terahertz emission from their bilayers with nonmagnetic spin-orbit (SO) materials. However, in contrast to well-understood spin and charge pumping by dynamical magnetization in spintronic systems driven by microwaves or current injection, analogous processes in light-driven magnets and radiation emitted by them remain largely unexplained due to the multiscale nature of the problem. Here we develop a multiscale quantum-classical formalism---where conduction electrons are described by quantum master equation (QME) of the Lindblad type, classical dynamics of local magnetization is described by the Landau-Lifshitz-Gilbert (LLG) equation, and incoming light is described by classical vector potential, while outgoing electromagnetic radiation is computed using the Jefimenko equations for retarded electric and magnetic fields---and apply it to a bilayer of antiferromagnetic Weyl semimetal ${\mathrm{Mn}}₃\mathrm{Sn}$, hosting noncollinear local magnetization, and SO-coupled nonmagnetic material. Our $\mathrm{QME}+\mathrm{LLG}+$Jefimenko scheme makes it possible to understand how a femtosecond laser pulse directly generates spin and charge pumping and electromagnetic radiation by the ${\mathrm{Mn}}₃\mathrm{Sn}$ layer, including both odd and even high harmonics (of the pulse center frequency) up to order $n\ensuremath{\le}7$. The directly pumped spin current then exerts spin torque on local magnetization whose dynamics, in turn, pumps additional spin and charge currents radiating in the terahertz range. By switching on and off LLG dynamics and SO couplings, we unravel which microscopic mechanism contributes the most to emitted terahertz radiation---charge pumping by local magnetization of ${\mathrm{Mn}}₃\mathrm{Sn}$ in the presence of its own SO coupling is far more important than standardly assumed (for other types of magnetic layers) spin pumping and subsequent spin-to-charge conversion within the adjacent nonmagnetic SO-coupled material.