Pressure and temperature dependence of the zero-field splitting in the ground state of NV centers in diamond: A first-principles study

temperature dependence of the zero-field splitting in the ground state of NV centers in diamond: Nitrogen-vacancy centers in diamond (NV) attract great attention because they serve as a tool in many important applications. The NV center has a polarizable spin S = 1 ground state and its spin state can be addressed by optically detected magnetic resonance (ODMR) techniques. The m S = 0 and m S = ±1 spin levels of the ground state are separated by about 2.88 GHz in the absence of an external magnetic field or any other perturbations. This zero-field splitting (ZFS) can be probed by ODMR. As this splitting changes as a function of pressure and temperature, the NV center might be employed as a sensor operating at the nanoscale. Therefore, it is of high importance to understand the intricate details of the pressure and temperature dependence of this splitting. Here we present an ab initio theory of the ZFS of the NV center as a function of external pressure and temperature including detailed analysis on the contributions of macroscopic and microscopic effects. We found that the pressure dependence is governed by the change in the distance between spins as a consequence of the global compression and the additional local structural relaxation. The local structural relaxation contributes to the change of ZFS with the same magnitude as the global compression. In the case of temperature dependence of ZFS, we investigated the effect of macroscopic thermal expansion as well as the consequent change of the microscopic equilibrium positions. We could conclude that theses effects are responsible for about 15% of the observed decrease of ZFS.