Millisecond spin coherence of electrons in semiconducting perovskites revealed by spin mode locking

Technical Summary: Millisecond Spin Coherence in Semiconducting Perovskites

Problem and Motivation
Long spin coherence times ($T_2$) are a prerequisite for implementing quantum technologies using semiconductor devices. However, achieving millisecond-scale coherence in semiconductors has remained a significant challenge, with typical values in nanostructures limited to the microsecond range due to spin relaxation mechanisms like the Dyakonov-Perel effect. While millisecond coherence has been demonstrated in localized defect states (e.g., NV centers in diamond) or superconductors, these systems often lack efficient optical access for spin manipulation. Lead halide perovskites have emerged as promising candidates due to their simple band structure, spatial inversion symmetry (which suppresses Dyakonov-Perel relaxation), and strong optical properties. Despite evidence of nanosecond-scale coherent spin precession in perovskites, the individual spin coherence time $T_2$ in bulk crystals had not been determined, as measurements are typically hindered by ensemble dephasing ($T_2^*$) caused by $g$-factor inhomogeneity and nuclear spin fluctuations.

Methodology
The authors investigated the coherent spin dynamics of resident electrons and holes in bulk $FA_{0.95}Cs_{0.05}PbI_3$ single crystals at cryogenic temperatures (1.6 K). The study employed three primary optical techniques based on time-resolved Faraday rotation (TRFR):

1. Resonant Spin Amplification (RSA): Used in weak magnetic fields to measure the ensemble spin dephasing time $T_2^*$ by observing constructive interference of spin precession modes synchronized with the laser repetition period ($T_R$).
2. Spin Mode Locking (SML): Applied in stronger magnetic fields where $T_2^* < T_R$. This technique relies on the synchronization of spin precession modes by periodic laser pulses, allowing the observation of a "revival" of the spin polarization signal just before the arrival of the next pump pulse. This effect enables the measurement of the intrinsic spin coherence time $T_2$, distinct from the ensemble dephasing time.
3. Optically Detected Magnetic Resonance (ODMR) with Resonant Spin Inertia: Used to measure the longitudinal spin relaxation time ($T_1$) by detecting the depolarization of optically oriented spins under a radio-frequency (rf) magnetic field.

The experiments utilized tunable laser repetition periods ranging from 13.2 ns to 1 ms to probe the limits of spin coherence.

Key Results

• Ensemble Dephasing ($T_2^*$): In weak magnetic fields, the electron spin dephasing time was measured to be up to 21 ns, limited by the spread of $g$-factors ($\Delta g_e \approx 0.003$).
• Spin Coherence Time ($T_2$): By employing the SML effect, the authors measured the intrinsic electron spin coherence time. The SML signal persisted as the laser repetition period was extended, revealing two distinct coherence times for electrons: a shorter component of 20 $\mu$s and a dominant, exceptionally long component of 1 ms. This represents one of the longest $T_2$ times reported for solid-state systems without isotopic purification or dynamic decoupling.
• Hole Dynamics: Hole spin mode locking was also observed, though with a shorter coherence time ($T_2^* \approx 1-2$ ns). The hole $T_2$ was determined to be greater than the laser repetition period of 13.2 ns.
• Longitudinal Relaxation ($T_1$): Using ODMR, the authors measured longitudinal spin relaxation times of 0.4 ms for electrons and 0.15 ms for holes. The electron $T_1$ showed a strong dependence on the magnetic field, increasing from 2 $\mu$s to 0.4 ms as the field increased, consistent with localized carriers interacting with nuclear spin fluctuations.
• Material Generality: The SML effect was also observed in $MA_{0.4}FA_{0.6}PbI_3$ crystals, specifically for resident holes, indicating that the phenomenon is not limited to a single chemical composition.

Significance and Claims
The paper claims the first observation of the Spin Mode Locking effect in bulk semiconductors, specifically in lead halide perovskite crystals. The primary significance lies in the demonstration of millisecond-scale spin coherence times for both electrons and holes in a bulk crystal system at 1.6 K.

The authors highlight that these results position lead halide perovskites as a unique platform for quantum technologies. Unlike defect-based systems (e.g., NV centers) which offer long coherence but weak optical transitions, or quantum dots which offer optical access but shorter coherence, perovskites combine:

1. Long Coherence: Millisecond $T_2$ and $T_1$ times comparable to or exceeding those in superconductors and defect centers, achieved without isotopic purification.
2. Efficient Optical Control: Strong oscillator strengths for band-to-band transitions, enabling all-optical generation, detection, and manipulation of spin states.

The authors suggest that these properties could facilitate quantum operations within the millisecond window, potentially supporting the requirements for quantum communication (e.g., quantum repeaters) and computation, provided the system can be operated at cryogenic temperatures. They note that further improvements may be possible through isotopic purification or dynamic decoupling protocols.