Millisecond spin relaxation times of distinct electron and hole subensembles in MA$_x$FA$_{1-x}$PbI$_3$ perovskite crystals
The unique combination of outstanding optical quality and attractive spin properties opens new avenues for optical spin control in hybrid organic-inorganic perovskite semiconductors. Using the optically detected magnetic resonance technique, we study the spins of electrons and holes in mixed-cation MA$_x$FA$_{1-x}$PbI$_3$ single crystals with $x = 0.4$ and 0.8. Multiple distinct spin subensembles with $g$-factors spanning from 2.9 to 3.6 for electrons and from 0.5 to 1.2 for holes are resolved, revealing diverse localization environments. We measure the longitudinal spin relaxation times, $T_1$, reaching 2 ms and remaining in the $μ$s range even for weakly localized carriers at the cryogenic temperature of 1.6 K. The magnetic-field dependence of $T_1$ is dominated by the random nuclear (Overhauser) fields with strengths of $\sim 0.4-0.8$ mT for electrons and $\sim 4-12$ mT for holes, corresponding to $μ$s-long correlation times of the hyperfine field determined by carrier hopping between shallow localization sites. The temperature dependence of $T_1$ reveals a weak localization potential of the charge carriers and shows a correlation between $T_1$ and the inhomogeneity of the spin ensemble. These results establish mixed-A-site perovskite single crystals as a promising solid-state platform with long-lived spin states for quantum information applications.