Strongly Correlated States of Transition Metal Spin Defects: The Case of an Iron Impurity in Aluminum Nitride

We investigate the electronic properties of an exemplar
transition
metal impurity in an insulator, with the goal of accurately describing
strongly correlated defect states. We consider iron in aluminum nitride,
a material of interest for hybrid quantum technologies, and we carry
out calculations with quantum embedding methods, density matrix embedding
theory (DMET) and quantum defect embedding theory (QDET), and with
spin-flip time-dependent density functional theory (TDDFT). We show
that both DMET and QDET accurately describe the ground state and low-lying
excited states of the defect and that TDDFT yields photoluminescence
spectra in agreement with experiments. In addition, we provide a detailed
discussion of the convergence of our results as a function of the
active space used in the embedding methods, thus defining a protocol
to obtain converged data directly comparable with experiments.