  Electron spin resonance (ESR) spectroscopy in scanning tunneling microscopy
(STM) has enabled probing the electronic structure of single magnetic atoms and
molecules on surfaces with unprecedented energy resolution, as well as
demonstrating coherent manipulation of single spins. Despite this remarkable
success, the field could still be greatly advanced by a more quantitative
understanding of the ESR-STM physical mechanisms. Here, we present a theory of
ESR-STM which quantitatively models not only the ESR signal itself, but also
the full background tunneling current, from which the ESR signal is derived.
Our theory is based on a combination of Green's function techniques to describe
the electron tunneling and a quantum master equation for the dynamics of the
spin system along with microwave radiation interacting with both the tunneling
current and the spin system. We show that this theory is able to quantitatively
reproduce the experimental results for a spin-1/2 system (TiH molecules on MgO)
across many orders of magnitude in tunneling current, providing access to the
relaxation and decoherence rates that govern the spin dynamics due to intrinsic
mechanisms and to the applied bias voltage. More importantly, our work
establishes that: (i) sizable ESR signals, which are a measure of
microwave-induced changes in the junction magnetoresistance, require
surprisingly high tip spin polarizations, (ii) the coupling of the
magnetization dynamics to the microwave field gives rise to the asymmetric ESR
spectra often observed in this spectroscopy. Additionally, our theory provides
very specific predictions for the dependence of the relaxation and decoherence
times on the bias voltage and the tip-sample distance. Finally, with the help
of electromagnetic simulations, we find that the transitions in our ESR-STM
experiments can be driven by the ac magnetic field at the junction.
