Anomalous B-field Dependence of Spin-flip Time in High Purity InP

We observe an anomalous B-field dependence of the spin-flip time ($T_1$) of electrons bound to shallow donors which cannot be explained by current spin-relaxation theories. We conduct resonant pump-probe measurements in high-purity InP from the low to high magnetic field regimes, with a maximum $T_1$ (400 $\mu$s) observed near the turning point $g \mu_B B \simeq k_B T$. At low $B$, the $T_1$ dependence on $B$ is consistent with an electron correlation time ($\tau_c$) in the tens of nanoseconds. The physical mechanism for the short $\tau_c$ in this high-purity sample ($n\simeq2\times 10^{14}$ cm$^{-3}$) is unclear, but a strong temperature ($T$) dependence indicates $T_1$ can be further increased by lowering $T$ below the 1.5 K experimental temperature. At high $B$, a $B^{-3}$ dependence is observed, in contrast to the expected $B^{-5}$ predicted by single-phonon spin-orbit mediated interactions. An understanding of the anomalous $B$-field dependence is expected to elucidate the effect of electron transport (low-field) and phonons (high-field) on $T_1$ for shallow donors, which is of interest for both ensemble and single-spin quantum information applications.