Low magnetic field anomalies of spin relaxation in silicon in the low temperature limit

The electron spin relaxation rate of donors in silicon is predicted to follow a magnetic field dependence of $1/T_{1}\propto B^{5}$ at low temperatures, where only spontaneous emission of phonons is relevant [1]. This behaviour has been observed in experiments on individual P donors [2,3]. However, these measurements also showed a deviation from the theoretical prediction at low fields (\textless 2 T). Here we present an extensive analysis of single donor relaxation rates at low magnetic fields, down to 0.3 T. To maintain a high spin readout contrast at low field we use steered initialisation, where a real-time feedback loop corrects for spin loading errors. Using a vector magnet, we investigate the dependence of the relaxation rate on the magnetic field direction. This allows us to disentangle valley-repopulation and single-valley contributions [1], and to study the potential impact of extrinsic relaxation mechanisms, such as evanescent-wave Johnson noise [4]. \newline [1] F.A. Zwanenburg et al., Rev. Mod. Phys. 85, 961 (2013). [2] A. Morello et al., Nature(London) 467, 687 (2010). [3] Y.-L. Hsueh et al., Phys. Rev. Lett. 113, 245406 (2014). [4] L. S. Langsjoen et al., Phys. Rev. B 89, 115401 (2014).