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

TL;DR

The study targets millisecond-scale spin coherence in semiconductor perovskites, addressing spin relaxation as a barrier to quantum functionality. Using time-resolved Faraday rotation with periodic pulsed excitation, the authors observe resonant spin amplification and spin mode locking in bulk FA0.95Cs0.05PbI3, enabling direct access to transverse ($T_2$) and longitudinal ($T_1$) spin times. They report electron spin coherence times approaching $T_2\approx$1 ms, electron $T_1\approx0.4$ ms, and hole $T_1\approx0.12$ ms at $T=1.6$ K, with electron and hole $g$-factors near $|g_e|\approx3.6$ and $|g_h|\approx1.3$, and observe SML for holes in MA-containing perovskites as well. This work positions lead halide perovskites as promising platforms for all-optical spin control and quantum technologies, with potential further gains from isotopic purification or dynamic decoupling.

Abstract

Long spin coherence times of carriers are essential for implementing quantum technologies using semiconductor devices for which, however, a possible obstacle is spin relaxation. For the spin dynamics, decisive features are the band structure, crystal symmetry, and quantum confinement. Perovskite semiconductors recently have come into focus of studies of their spin states, notivated by efficient optical access and potentially long-living coherence. Here, we report an electron spin coherence time $T_2$ of the order of 1 ms, measured for a bulk FA$_{0.95}$Cs$_{0.05}$PbI$_3$ lead halide perovskite crystal. Using periodic laser pulses, we synchronize the electron spin Larmor precession about an external magnetic field in an inhomogeneous ensemble, the effect known as spin mode locking. It appears as a decay of the optically created ensemble spin polarization within the dephasing time $T_2^*$ of up to 20 ns and its revival during the spin coherence time $T_2$ reaching the millisecond range. This exceptionally long spin coherence time in a bulk crystal is complemented by millisecond-long longitudinal spin relaxation times $T_1$ for electrons and holes, measured by optically-detected magnetic resonance. These long-lasting spin dynamics highlight perovskites as promising platform for the quantum devices with all-optical control.

Figures (11)

• Figure 1: Coherent spin dynamics of electrons in a FA$_{0.95}$Cs$_{0.05}$PbI$_3$ crystal at $T=1.6$ K. (a) Photoluminescence spectrum excited at 3.1 eV photon energy. The photon energy of 1.471 eV used in TRFR is marked by the green arrow. (b) Faraday rotation dynamics measured in a Voigt magnetic field of 50 mT. $T_\text{R}=13.2$ ns. The red arrow indicates the time delay of $\Delta t=-200$ ps between pump and probe pulses used for the RSA measurement in panel C. (c) Resonant spin amplification versus magnetic field in Voigt geometry. (d) Magnetic field dependence of the electron spin dephasing time $T_{\rm 2,e}^*$ obtained from RSA (closed symbols) and FR dynamics (open symbols). The line shows a fit with eq. \ref{['eq:InhDeph']} using the fitting parameter $\Delta g_{\rm e}=0.003$.
• Figure 2: Spin mode locking of electrons and holes in FA$_{0.95}$Cs$_{0.05}$PbI$_3$ crystals at $T=1.6$ K. (a) Faraday rotation dynamics measured in a Voigt magnetic field of 1 T. $T_\text{R}=13.2$ ns. (b) Schematic illustration of the spectrum of precession modes in a spin ensemble without (black line) and with SML effect (red line). (c) Faraday rotation dynamics measured at negative delays for sample #2 (green line), where the SML of holes is pronounced. $B_{\rm V}=0.6$ T. Also, the electron (red line) and hole (blue line) spin dynamics extracted by fitting the experimental dynamics with eq. \ref{['eq:TRFR']} are shown. (d) Magnetic field dependence of the electron (red symbols) and hole (blue symbols) Larmor precession frequencies in sample #2. The lines are linear fits with slopes corresponding to the electron and hole $g$-factors of $g_{\rm e}=3.65$ and $g_{\rm h}=-1.34$.
• Figure 3: Dependence of SML on laser repetition period and temperature in FA$_{0.95}$Cs$_{0.05}$PbI$_3$ crystal. (a) Faraday rotation dynamics measured with laser system with low repetition rate of 30 kHz ($T_\text{R}=33.3$$\mu$s). $B_{\rm V}=2$ T and $T=1.6$ K. Inset shows zoomed oscillations at negative delays. (b) SML amplitude dependence on laser repetition period measured for $T=1.6$ K at $B_{\rm V}=0.6$ T. The data are normalized on the FR amplitude at short positive delays. The dashed line is a fit with sum of two exponents, which gives $T_{2,e}=20$$\mu$s and 1 ms.
• Figure 4: ODMR in FA$_{0.95}$Cs$_{0.05}$PbI$_3$ crystal at $T=1.6$ K. (a) ODMR signal dependence on the Faraday magnetic field, measured for $f_{rf}=0.5$ GHz and $f_\text{mod}=0.1$ kHz. The insert shows a scan across the low magnetic field peak with smaller field strength steps. (b) Modulation frequency dependence of the ODMR signal at $f_{rf}=1.5$ GHz for the electrons (red, $B_\text{F}=29$ mT) and the holes (blue, $B_\text{F}=91$ mT). The dashed lines are fits using eq. \ref{['eq:RSI']}. (c) Magnetic field dependence of the electron (red) and hole (blue) longitudinal spin relaxation times $T_1$.
• Figure S1: Resonant spin amplification in FA$_{0.95}$Cs$_{0.05}$PbI$_3$ crystals for the magnetic field range from $-10$ to $100$ mT. The singal is detected at the time delay of $\Delta t=-200$ ps, $T_\text{R}=13.2$ ns, and $T=1.6$ K. The low field part of this scan is shown in Figure \ref{['fig:Intro']}c. The peak widths from this RSA scan are used to determine spin the dephasing time for $B_\text{V}<100$ mT in Figure \ref{['fig:Intro']}d.