Theory of Optically Detected Magnetic Resonance of a Silicon Vacancy in Silicon Carbide

Optically detected magnetic resonance (ODMR) is one tool that can be used to probe the spin character of optically-active color centers in a nondestructive manner, with applications including the identification of radiation-induced defects in semiconductors and quantum magnetometry [1,2]. In ODMR, a color center is optically pumped while a Zeeman magnetic field is swept and the resulting photoluminescence (PL) is measured on a detector. A microwave field is also applied to induce resonant Rabi oscillations, seen as extrema in the PL contrast, and creates a characteristic and reproducible curve. A detailed and fully quantitative simulation of the ODMR of a color center would provide confidence that the foundations of nonequilibrium optical and spin dynamics relevant for ODMR are sufficiently understood, while allowing for the extraction of reliable parameters for spin coherence times, optical transition rates, and microwave coupling strengths.<br/><br/>In this work we simulate room-temperature ODMR of the negatively charged silicon vacancy V_Si^– V(2) site in 6H-SiC, an emerging candidate for quantum magnetometry, using Lindblad master equations and density matrix populations and compare with experimental results [2]. V_Si^– in 6H-SiC ODMR can be described as a synthetic atom with S=3/2 ground and excited spin manifolds, separated by 1.397 eV, and a metastable state in the energy gap between these manifolds [2,3]. The Hamiltonian of each spin manifold can be divided into terms which cause coherent transitions between states and subsequent resonances, the magnetic and electric components of the microwave field, and terms that dictate the positions of the resonances, the Zeeman field and zero field splitting. In ODMR the ground and excited spin manifolds are coupled via absorption, spontaneous emission, and nonradiative pathways through the metastable state and we simulate these processes, as well as pure dephasing, with a Lindblad master equation [4]. Using the steady-state solution of the master equation and excited manifold density matrix populations, we calculate ODMR curves to compare with experimental results [2].<br/><br/>Through comparison of our calculations with experimental results [2], we show that a vast amount of information is contained in a single ODMR curve. By fitting our model to experimental results [2] we are able to extract spin Hamiltonian parameters such as zero field splitting, g-factors, microwave electric and magnetic field strengths, Stark coupling coefficients [5], and hyperfine couplings. We are also able to extract absorption, spontaneous emission, and intersystem crossing rates as well as coherence times T₂*. Finally, we stress the flexibility of these calculations and their natural extension to ODMR theories of other color centers and polytypes of SiC, and their natural extension to color centers in other wide or ultra-wide bandgap materials, which would be desirable for quantum sensing applications or radiation-induced defect identification.<br/><br/>We acknowledge support from NSF DMR-1921877 and AFOSR MURI "REDESIGN".<br/><br/>[1] Kraus, H., Soltamov, V., Fuchs, F. et al. Magnetic field and temperature sensing with atomic-scale spin defects in silicon carbide. <i>Sci Rep</i> 4, 5303 (2014).<br/>[2] Kraus, H., Soltamov, V., Riedel, D. et al. Room-temperature quantum microwave emitters based on spin defects in silicon carbide. <i>Nature Phys</i> <b>10</b>, 157–162 (2014).<br/>[3] Biktagirov, T., Schmidt, W., Gerstmann, U. et al. Polytypism driven zero-field splitting of silicon vacancies in 6H-SiC. <i>Physical Review B</i> <b>98</b>, 195204 (2018).<br/>[4] Breuer, H. and Petruccione, F. The Theory of Open Quantum Systems. Vol. 9780199213900. Oxford: Oxford University Press, (2007).<br/>[5] Falk, A., Klimov, P., Buckley, B. et al. Electrically and Mechanically Tunable Electron Spins in Silicon Carbide Color Centers. <i>Physical Review Letters</i> <b>112</b>, 187601, (2014).