Increasing the spin coherence time $T_2$ is a major area of interest for spin defect systems such as the silicon ($V_{\text{Si}}$) and carbon ($V_{\text{C}}^{\pm }$) vacancies in $4H\text{−}\mathrm{SiC}$. Usually as temperature increases, $T_2$ decreases due to the thermal bath. Observations of electron-paramagnetic resonance and direct systematic measurements of $T_2$ has seen an anomaly where $T_2$ increases with increasing temperature. In this work, we investigate the mechanisms that cause the $T_2$ temperature anomaly. We find that due to a spontaneous symmetry lowering from a motional Jahn-Teller distortion, a polaron quasiparticle is generated from the vibronic coupling. Initially, for temperatures from 8 to $20–40\mathrm{K}$, the coherence temperature dependence is dominated by phonon-assisted spin relaxation. At temperatures around $20–40\mathrm{K}$, depending on the vacancy, a thermally activated polaron hopping turns on and motional narrowing dominates and increases $T_2$ with increasing temperature. As temperatures reach $120–160\mathrm{K}$, the energy barrier gets high enough to slow the polaron hopping. At this point the Larmor precession dominates, leading to decoherence. Our calculated temperature-dependent coherence agrees with what has been seen experimentally, giving a full theoretical framework for the mechanisms that cause the $T_2$ temperature anomaly of increasing $T_2$ with increasing temperature. The theoretical framework presented here also gives insight into these mechanisms being a probable universal phenomenon that could occur in many other defect center spin systems.

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• Jahn-Teller effect
• Point defects
• Polarons
• Silicon vacancies
• Spin coherence
• Carbides