Theory of Atomic-Scale Direct Thermometry Using Electron Spin Resonance via Scanning Tunneling Microscopy.

Knowledge of the occupation ratio and energy splitting of a two-level system provides a direct method for temperature readout. This principle was demonstrated for an individual two-level magnetic atom using Electron Spin Resonance via Scanning Tunneling Microscopy (ESR-STM). The temperature determination involves two steps: measuring the energy splitting with ESR-STM and determining the equilibrium occupation of a nearby atom using the peak height ratio in the ESR spectrum. Here we present a theory addressing three aspects: the impact of shot noise and back-action on thermometry precision, the role of spin geometry in enhancing signal-to-noise ratio, and the method's capability to detect thermal gradients as small as 5 mK/nm. We predict ESR-STM thermometry achieves 10 mK resolution at around 1 K temperatures, offering new avenues for nanoscale thermal measurements.