Understanding the spin-selective transitions of defect spins by ab intio theory of spin-spin and spin-orbit coupling*

Color centers in semiconductors with coupled spins, such as the NV center in diamond, the silicon vacancy (V_Si), and the di-vacancy (V_CV_Si) in silicon carbide (SiC), implement quantum bits for sensing and other quantum applications. Optical manipulation of the spin includes the excitation of the fundamental high-spin transition and spin-selective non-radiative relaxation via intermediate low-spin states facilitated by spin-spin and spin-orbit coupling. This and the zero-field splittings of the ground and excited states permit a variety of spin-photon protocols. Optimal engineering of such interfaces requires a deep understand the different spin-selective couplings and the resulting spin-relaxation paths. In the case of the silicon vacancy in SiC, recent experiments obtained spin-dependent lifetimes and intercrossing rates based on an effective model with only one intermediate state instead of five theoretically predicted ones.  Here we address the open question regarding the spin-relaxation mechanism using our embedding approach (CI-cRPA) based on configuration interaction and a screened electron-electron interaction derived from hybrid density functional theory.  Our approach yields a fine structure of the quartet states of V_Si consistent with literature and enables us to draw a quantitative picture of the spin-orbit coupling in the spin-relaxation path. Besides V_Si, we also address the di-vancancy in SiC and the NV center in diamond.

[1] N. Morioka et al. Phys. Rev. Appl. 17, 054005 (2022).