Temperature-dependent behaviors of single spin defects in solids determined with Hz-level precision

TL;DR

This study achieves Hz-level precision in measuring how the properties of single nitrogen-vacancy centers in diamond vary with temperature, revealing detailed interactions and enabling nanoscale thermometry.

Contribution

It introduces a high-precision measurement method for temperature-dependent properties of single solid-state spin defects, validated with first-principles calculations.

Findings

Hyperfine interactions vary with temperature.

Measured coefficients with Hz-level precision.

Temperature effects linked to thermal expansion and vibrations.

Abstract

Revealing the properties of single spin defects in solids is essential for quantum applications based on solid-state systems. However, it is intractable to investigate the temperature-dependent properties of single defects, due to the low precision for single-defect measurements in contrast to defect ensembles. Here we report that the temperature dependence of the Hamiltonian parameters for single negatively charged nitrogen-vacancy (NV$^{-}$) centers in diamond is precisely measured, and the results find a reasonable agreement with first-principles calculations. Particularly, the hyperfine interactions with randomly distributed $^{13}$C nuclear spins are clearly observed to vary with temperature, and the relevant coefficients are measured with Hz-level precision. The temperature-dependent behaviors are attributed to both thermal expansion and lattice vibrations by first-principles calculations. Our results pave the way for taking nuclear spins as more stable thermometers at nanoscale. The methods developed here for high-precision measurements and first-principles calculations can be further extended to other solid-state spin defects.