  The interaction of fs light pulses with magnetic materials has been intensely
studied for more than two decades in order to understand ultrafast
demagnetization in single magnetic layers or THz emission from their bilayers
with nonmagnetic spin-orbit (SO) materials. Here we develop a multiscale
quantum-classical formalism -- where conduction electrons are described by
quantum master equation 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 Jefimenko equations for retarded
electric and magnetic fields -- and apply it a bilayer of antiferromagnetic
Weyl semimetal Mn$_3$Sn with noncollinear local magnetization in contact with
SO-coupled nonmagnetic material. Our QME+LLG+Jefimenko scheme makes it possible
to understand how fs light pulse generates directly spin and charge pumping and
electromagnetic radiation by the latter, including both odd and even high
harmonics (of the pulse center frequency) up to order $n \le 7$. The directly
pumped spin current then exert spin torque on local magnetization whose
dynamics, in turn, pumps additional spin and charge currents radiating in the
THz range. By switching on and off LLG dynamics and SO couplings, we unravel
which microscopic mechanism contribute the most to emitted THz radiation --
charge pumping by local magnetization of Mn$_3$Sn in the presence of its
intrinsic 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 neighboring nonmagnetic SO-coupled material.
