Temperature Sensitivity of ${}^{14}\mathrm{N}\mathrm{V}$ and ${}^{15}\mathrm{N}\mathrm{V}$ Ground State Manifolds

We measure electron and nuclear spin transition frequencies in the ground state of nitrogen-vacancy (NV) centers in diamond for two nitrogen isotopes (${}^{14}\mathrm{N}\mathrm{V}$ and ${}^{15}\mathrm{N}\mathrm{V}$) over temperatures ranging from 77 K to 400 K. Measurements are performed using Ramsey interferometry and direct optical readout of the nuclear and electron spins. We extract coupling parameters $Q$ (for ${}^{14}\mathrm{N}\mathrm{V}$), $D$, $A_{\mathrm{\mid }\mathrm{\mid }}$, $A_{\perp }$, ${\gamma }_e\mathrm{/}{\gamma }_n$, and their temperature dependences for both isotopes. The temperature dependences of the nuclear-spin transitions within the $m_s=0$ spin manifold near room temperature are found to be +0.52(1) ppm/K for ${}^{14}\mathrm{N}\mathrm{V}$ ($\mathrm{\mid }{m}_I=-1>\leftrightarrow \mathrm{\mid }{m}_I=+1>$) and -1.1(1) ppm/K for ${}^{15}\mathrm{N}\mathrm{V}$ ($\mathrm{\mid }{m}_I=-1\mathrm{/}2>\leftrightarrow \mathrm{\mid }{m}_I=+1\mathrm{/}2>$). An isotopic shift in the zero-field splitting parameter $D$ between ${}^{14}\mathrm{N}\mathrm{V}$ and ${}^{15}\mathrm{N}\mathrm{V}$ is measured to be $\sim$ 120 kHz. Residual transverse magnetic fields are observed to shift the nuclear spin transition frequencies, especially for ${}^{15}\mathrm{N}\mathrm{V}$. We have precisely determined the set of parameters relevant for the development of nuclear-spin-based diamond quantum sensors with greatly reduced sensitivity to environmental factors.