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

Overview

Journal Nano Lett

Publisher American Chemical Society

Date 2025 Feb 2

PMID 39893655

Authors

Yelko Del Castillo

Joaquin Fernandez-Rossier

Affiliations

Soon will be listed here.

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.

References

Wang Y, Chen Y, Bui H, Wolf C, Haze M, Mier C . An atomic-scale multi-qubit platform. Science. 2023; 382(6666):87-92. DOI: 10.1126/science.ade5050. View

Farinacci L, Veldman L, Willke P, Otte S . Experimental Determination of a Single Atom Ground State Orbital through Hyperfine Anisotropy. Nano Lett. 2022; 22(21):8470-8474. PMC: 9650725. DOI: 10.1021/acs.nanolett.2c02783. View

Yang K, Paul W, Natterer F, Lado J, Bae Y, Willke P . Tuning the Exchange Bias on a Single Atom from 1 mT to 10 T. Phys Rev Lett. 2019; 122(22):227203. DOI: 10.1103/PhysRevLett.122.227203. View

Choi T, Paul W, Rolf-Pissarczyk S, MacDonald A, Natterer F, Yang K . Atomic-scale sensing of the magnetic dipolar field from single atoms. Nat Nanotechnol. 2017; 12(5):420-424. DOI: 10.1038/nnano.2017.18. View

Aslam N, Zhou H, Urbach E, Turner M, Walsworth R, Lukin M . Quantum sensors for biomedical applications. Nat Rev Phys. 2023; 5(3):157-169. PMC: 9896461. DOI: 10.1038/s42254-023-00558-3. View

Yang K, Bae Y, Paul W, Natterer F, Willke P, Lado J . Engineering the Eigenstates of Coupled Spin-1/2 Atoms on a Surface. Phys Rev Lett. 2017; 119(22):227206. DOI: 10.1103/PhysRevLett.119.227206. View

Willke P, Bae Y, Yang K, Lado J, Ferron A, Choi T . Hyperfine interaction of individual atoms on a surface. Science. 2018; 362(6412):336-339. DOI: 10.1126/science.aat7047. View

Willke P, Singha A, Zhang X, Esat T, Lutz C, Heinrich A . Tuning Single-Atom Electron Spin Resonance in a Vector Magnetic Field. Nano Lett. 2019; 19(11):8201-8206. DOI: 10.1021/acs.nanolett.9b03559. View

Hoffmann E, Nilsson H, Matthews J, Nakpathomkun N, Persson A, Samuelson L . Measuring temperature gradients over nanometer length scales. Nano Lett. 2009; 9(2):779-83. DOI: 10.1021/nl8034042. View

10.

Baumann S, Paul W, Choi T, Lutz C, Ardavan A, Heinrich A . Electron paramagnetic resonance of individual atoms on a surface. Science. 2015; 350(6259):417-20. DOI: 10.1126/science.aac8703. View

11.

van Weerdenburg W, Steinbrecher M, van Mullekom N, Gerritsen J, von Allworden H, Natterer F . A scanning tunneling microscope capable of electron spin resonance and pump-probe spectroscopy at mK temperature and in vector magnetic field. Rev Sci Instrum. 2021; 92(3):033906. DOI: 10.1063/5.0040011. View

12.

Natterer F, Patthey F, Bilgeri T, Forrester P, Weiss N, Brune H . Upgrade of a low-temperature scanning tunneling microscope for electron-spin resonance. Rev Sci Instrum. 2019; 90(1):013706. DOI: 10.1063/1.5065384. View

13.

Seifert T, Kovarik S, Juraschek D, Spaldin N, Gambardella P, Stepanow S . Longitudinal and transverse electron paramagnetic resonance in a scanning tunneling microscope. Sci Adv. 2020; 6(40). PMC: 7527223. DOI: 10.1126/sciadv.abc5511. View

14.

Natterer F, Yang K, Paul W, Willke P, Choi T, Greber T . Reading and writing single-atom magnets. Nature. 2017; 543(7644):226-228. DOI: 10.1038/nature21371. View

15.

Brites C, Lima P, Silva N, Millan A, Amaral V, Palacio F . Thermometry at the nanoscale. Nanoscale. 2012; 4(16):4799-829. DOI: 10.1039/c2nr30663h. View

16.

Drost R, Uhl M, Kot P, Siebrecht J, Schmid A, Merkt J . Combining electron spin resonance spectroscopy with scanning tunneling microscopy at high magnetic fields. Rev Sci Instrum. 2022; 93(4):043705. DOI: 10.1063/5.0078137. View

17.

Esat T, Borodin D, Oh J, Heinrich A, Tautz F, Bae Y . A quantum sensor for atomic-scale electric and magnetic fields. Nat Nanotechnol. 2024; 19(10):1466-1471. PMC: 11486657. DOI: 10.1038/s41565-024-01724-z. View

18.

Kovarik S, Robles R, Schlitz R, Seifert T, Lorente N, Gambardella P . Electron Paramagnetic Resonance of Alkali Metal Atoms and Dimers on Ultrathin MgO. Nano Lett. 2022; 22(10):4176-4181. DOI: 10.1021/acs.nanolett.2c00980. View

19.

Zhang X, Wolf C, Wang Y, Aubin H, Bilgeri T, Willke P . Electron spin resonance of single iron phthalocyanine molecules and role of their non-localized spins in magnetic interactions. Nat Chem. 2021; 14(1):59-65. DOI: 10.1038/s41557-021-00827-7. View

20.

Willke P, Paul W, Natterer F, Yang K, Bae Y, Choi T . Probing quantum coherence in single-atom electron spin resonance. Sci Adv. 2018; 4(2):eaaq1543. PMC: 5815865. DOI: 10.1126/sciadv.aaq1543. View