Continuous-wave and pulsed EPR study of the negatively charged silicon vacancy with $S=\frac{3}{2}$ and $C_{3v}$ symmetry in $n$-type $4H-\mathrm{SiC}$

The $T_{V2a}$ center, which was suggested to be the excited triplet state $\mathrm{}(S=1\mathrm{})\mathrm{}$ of the neutral silicon vacancy related defect [Sörman et al., Phys. Rev. B $61,$ 2613 (2000)] in the electron-irradiated n-type $4H-\mathrm{SiC}$ has been studied by continuous wave and pulsed electron paramagnetic resonance (EPR). The spin multiplicity of $T_{V2a}$ has been determined to be quartet $\mathrm{}(S=3/2\mathrm{})\mathrm{}$ by the nutation method of pulsed EPR technique. From the temperature dependence of the signal intensity, it has been revealed that the $T_{V2a}$ spectrum is arising from an electronic ground state. From the measurement of the ${}^{13}\mathrm{C}$ hyperfine interactions of the nearest neighbors which has been enabled by the selective enhancement of the $T_{V2a}$ signals through the spin polarization by a laser light (808 nm) illumination, the center is unambiguously identified to be a single silicon vacancy. It is proposed that the center is a negatively charged silicon vacancy of $C_{3v}$ symmetry with the crystal field distorted slightly from regular tetrahedron. The triply degenerate $t_2$ state of an electronic configuration $a_1^2{t}_2^3$ under $T_d$ symmetry splits into $a_1$ and e by the distortion to $C_{3v}.$ The high spin configuration $[a_1{e}^2$ or $e^2{a}_1]$ which reduces the electron repulsion energy is preferred rather than the low spin configuration expected from the symmetry-lowering crystal field alone. The important role of the many-electron effect in determining the ground-state configuration is demonstrated clearly by $T_{V2a}$ in which the electron-electron interactions (the electronic repulsion and the electron exchange) compete against the crystal-field splitting.