Title: Temperature dependent spin-phonon coupling of boron-vacancy centers in hexagonal boron nitride

Abstract: The negatively charged boron-vacancy center ($\mathrm{V}_{\mathrm{B}}^-$) in hexagonal boron nitride (hBN) has recently emerged as a highly promising quantum sensor. Compared to the nitrogen-vacancy (NV) center in diamond, the change with temperature of the spin transition energy of $\mathrm{V}_{\mathrm{B}}^-$ is more than an order of magnitude larger, making it a potential nanoscale thermometer with superior sensitivity. However, the underlying mechanism of the observed large temperature dependence remains an open question. In this work, using isotopically purified $\mathrm{h}{}^{10}\mathrm{B}{}^{15}\mathrm{N}$, we systematically characterize the zero-field splitting, hyperfine interaction, and spin relaxation time of $\mathrm{V}_{\mathrm{B}}^-$ from 10 to 350$~$K. We carry out first-principle calculations of the $\mathrm{V}_{\mathrm{B}}^-$ spin-phonon interaction and show that a second-order effect from finite-temperature phonon excitations is responsible for the observed changes in experiments. By fitting our experimental results to a physically motivated model, we extract the dominant phonon mode which agrees well with our simulations. Finally, we investigate the dynamic nuclear spin polarization process at cryogenic temperatures. Our results provide key insights in $\mathrm{V}_{\mathrm{B}}^-$ centers and their utilization as nanoscale thermometers and phonon sensors.