  Terahertz (THz) field pulses can now be applied in Scanning Tunnelling
Microscopy (THz-STM) junction experiments to study time resolved dynamics. The
relatively slow pulse compared to the typical electronic time-scale calls for
approximations based on a time-scale separation. Here, we contrast three
methods based on non-equilibrium Green's functions (NEGF): (i) the
steady-state, adiabatic results, (ii) the lowest order dynamic expansion in the
time-variation (DE), and (iii) the auxiliary mode (AM) propagation method
without approximations in the time-variation. We consider a concrete THz-STM
junction setup involving a hydrogen adsorbate on graphene where the localized
spin polarization can be manipulated on/off by a local field from the tip
electrode and/or a back-gate affecting the in-plane transport. We use
steady-state NEGF combined with Density Functional Theory (DFT-NEGF) to obtain
a Hubbard model for the study of the junction dynamics. Solving the Hubbard
model in a mean-field approximation, we find that the near-adiabatic first
order dynamical expansion provides a good description for STM voltage pulses up
to the 1 V range.
