Theory of Optically Detected Magnetic Resonance of a Silicon Vacancy in SiC: a Quantum Sensor of Magnetic Fields*

We simulate optically detected magnetic resonance (ODMR) of the negatively charged silicon vacancy in 6H-SiC (V_Si^–), using Lindblad master equations, and compare with experimental data [1]. An emerging candidate for quantum magnetometry, V_Si^– can be described as a synthetic atom with S=3/2 ground and excited manifolds, separated by 1.397 eV, and a metastable state in the energy gap in between [1-3]. Fitting our calculations to experimental results, we extract the zero field splittings and g-factors of the ground and excited spin manifolds: 2D_g = 124 MHz, 2D_e = 1.22 GHz, g_g = 2.003, g_e = 2.0045; microwave magnetic and electric field strengths: B₁ = 0.25 mT, E₁ = 750 V/cm; Stark coupling coefficients [4]: d_⊥/h = 20 Hz (V/cm)^-1; hyperfine couplings: A = 1.4 MHz; intersystem crossing rates from the excited manifold to the metastable state (metastable state to the ground manifold): 31.4 MHz and 27.8 MHz (1.8 MHz and 1.6 MHz); ground and excited coherence times: T_2,g = 29 μs and T_2,e = 16 ns; and lower bounds of ground and excited manifold spin relaxation times: T_1,g > 2 ms, T_1,e > 10 μs. Finally, we simulated ODMR of V_Si^–  in an isotopically purified sample and predict, in a simple picture, an order of magnitude improvement in magnetometer sensitivity.

[1] H. Kraus, V. Soltamov, D. Riedel, et al. Nature Phys 10, 157 (2014).

[2] H. Kraus, V. Soltamov, F. Fuchs, et al. Sci Rep 4, 5303 (2014).

[3] C. Cochrane, J. Blacksberg, M. Anders, et al. Sci Rep 6, 37077 (2016).

[4] A. Falk, P. Klimov, B. Buckley, et al. Phys. Rev. Lett. 112, 187601 (2014).