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

## TL;DR

This paper introduces a new theory for measuring temperature at the atomic scale using electron spin resonance with scanning tunneling microscopy.

## Contribution

The paper presents a theoretical framework for ESR-STM thermometry, including precision limits and thermal gradient detection capabilities.

## Key findings

- ESR-STM thermometry can achieve 10 mK resolution at around 1 K temperatures.
- The method can detect thermal gradients as small as 5 mK per nanometer.
- Spin geometry significantly impacts signal-to-noise ratio in measurements.

## Abstract

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.