Not yet reviewed by Pith; the record is open.

The integration of scanning tunneling microscopy (STM) and electron spin resonance (ESR) spectroscopy has emerged as a powerful and innovative tool for discerning spin excitations and spin-spin interactions within atoms and molecules adsorbed on surfaces. However, the origin of the STM-ESR signal and the underlying mechanisms that govern the essential features of the measured spectra have remained elusive, thereby significantly impeding the future development of the STM-ESR approach. Here, we construct a model to carry out precise numerical simulations of STM-ESR spectra for a single hydrogenated Ti adatom and a hydrogenated Ti dimer, achieving excellent agreement with experimental observations. We further develop an analytic theory that elucidates the fundamental origin of the signal as well as the essential features in the measured spectra. These new theoretical developments establish a solid foundation for the on-demand detection and manipulation of atomic-scale spin states, with promising implications for cutting-edge applications in spin sensing, quantum information, and quantum computing.