All-electron calculation of spin-spin interactions

The decoherence time of defect-spin qubits is controlled by the interaction of nuclear and electronic spins and by that between electronic spins. A key quantity determining these interactions is the value of the electronic spin density at the nucleus, which in turn is a crucial ingredient to evaluate the hyperfine interaction (HF) and zero-field splitting (ZFS) tensors of a defect-spin qubit. Here we report all-electron calculations of the HF and ZFS tensors using real space density functional theory (DFT) calculations based on finite elements. While all-electron DFT calculations using localized basis sets (e.g. Gaussians) can be conveniently performed to determine HF and ZFS tensors of molecules and clusters, they become much more demanding for periodic solids, and plane-wave based calculations are prohibitively difficult to converge. We show that real-space, finite element DFT calculations provide robust estimates of ZFS and HF for both molecules and solids and we present results for molecules and the nitrogen-vacancy center in diamond. We also show that coarse-graining capabilities of the real space mesh included in our formulation enable efficient computations, by avoiding redundant mesh refinements far from the nuclei.