Transient and steady state magneto-optical studies of the $\mathrm{CsPb}{\mathrm{Br}}_3$ crystal

We have studied the magneto-optical properties of photoexcitations in $\mathrm{CsPb}{\mathrm{Br}}_3$ single crystal using the technique of picosecond time-resolved quantum beatings (QBs) in the circularly polarized photoinduced reflection as well as steady state magnetocircular dichroism (MCD) in $\mathrm{CsPb}{\mathrm{Br}}_3$ film. In the Voigt geometry at magnetic field strength $B$ > 0, we observed fast and slow QB oscillations that we attribute to the Larmor precession frequency of electrons and holes, respectively. From the linear frequency dependence on $B$, we extract the carrier anisotropic Landé $g$ factors for applied B along [010] and [001]; for electrons $|g_{\left[001\right]}^{\mathrm{e}}|=1.95\pm 0.04$ and $|g_{\left[010\right]}^{\mathrm{e}}|=1.82\pm 0.04$, whereas for holes $|g_{\left[001\right]}^{\mathrm{h}}|=0.69\pm 0.02$ and $|g_{\left[010\right]}^{\mathrm{h}}|=0.76\pm 0.02$. These values are in excellent agreement with a k·p model calculation applied to $\mathrm{CsPb}{\mathrm{Br}}_3$. Surprisingly, at $B=0$, we still observed QB oscillation of ∼500 MHz that we interpret as due to the Overhauser field that originates from the spin-aligned nuclei caused by the Knight field. From the measured MCD spectrum vs $B$, we obtained the $g$ factor of the bright excitons $g_{\mathrm{ex}}=2.18\pm 0.08$ showing that the $g$ value of holes in $\mathrm{CsPb}{\mathrm{Br}}_3$ is positive. We also measured the temperature and magnetic field dependencies of the electron and hole spin dephasing times which support the Elliot-Yafet spin-relaxation mechanism.

Figure 1

(a) The absorption spectrum of $\mathrm{CsPb}{\mathrm{Br}}_3$ thin film (black line) measured at 50 K. The red dashed line is a fit using the Elliott equation [13] with exciton energy at 2.34 eV and exciton binding energy of 20 meV. (b) The absorption (red) and photoinduced absorption (PA) (blue) spectra between 500 to $4000\mathrm{c}{\mathrm{m}}^{-1}$ using a Fourier-transform infrared spectrometer measured at 50 K. The PA spectrum shows free carrier absorption (FCA) $<2000\mathrm{c}{\mathrm{m}}^{-1}$. (c) The temperature dependent photoluminescence (PL) spectrum of $\mathrm{CsPb}{\mathrm{Br}}_3$ thin film excited at 447 nm with power of 0.5 mW. (d) The PL spectrum of $\mathrm{CsPb}{\mathrm{Br}}_3$ crystal measured at various excitation powers at $T=4\mathrm{K}$. The inset shows the PL intensity as a function of the laser fluence in logarithmic scale and a linear fit with a slope $\gamma$ of 1.4.

Figure 2

(a) A picture of the cuboid-shaped $\mathrm{CsPb}{\mathrm{Br}}_3$ single crystal with (001) top facet and (110) side facet. (b) X-ray diffraction patterns of (001) and (110) crystal facets. (c) Schematic of the experimental apparatus for degenerate pump-probe transient circularly polarized photoinduced reflection [c-PPR(t)], using two lock-in amplifiers. PEM is a photoelastic modulator for modulating the pump beam polarization between left $\left({\delta }^{+}\right)$ and right $\left({\delta }^{-}\right)$ circular polarizations; $\lambda /4$ is a quarter wavelength plate; LP is a linear polarizer; and BS is a beam-splitter. The $\mathrm{CsPb}{\mathrm{Br}}_3$ crystal was mounted in a cryostat and cooled down to 4 K. An electromagnet generates a magnetic field B up to 700 mT parallel to the crystal surface (Voigt geometry).

Figure 3

Photoinduced quantum beatings (QBs) in $\mathrm{CsPb}{\mathrm{Br}}_3$ single crystal excited at 405 nm measured at various magnetic field strengths at 4 K. Magnetic field dependence of the transient circularly polarized photoinduced reflection [c-PPR(t)] measured on (a)–(d) the (001) facet with B directed along [010] and (e)–(h) the (110) facet with B along [001], using probe at 533 nm. The insets show the corresponding fast Fourier transform (FFT) spectra with two FFT peaks for the fast and slow oscillatory frequencies. (d) and (h) Fast and slow QB frequencies vs $B$ and the obtained $g$ factors.

Figure 4

(a) and (b) Probe beam spectrum of the quantum beating (QB) fast Fourier transform (FFT) amplitude for the fast (blue, ${\mathrm{T}}^{-}$) and slow (red, ${\mathrm{T}}^{+}$) oscillations measured at $B=400\mathrm{mT}$, excited at 405 nm on (a) the (110) facet with B along [001] and (b) the (001) facet with B along [010]. Transient circularly polarized photoinduced reflection [c-PPR(t)] dynamics measured at three different fields on (c) the (110) surface with $\mathbf{B}\parallel \left[001\right]$ and (d) (001) with $\mathbf{B}\parallel \left[010\right]$, using 533 nm probe wavelength. Magnetic field response of the c-PPR (Mc-PPR) measured at fixed delay time $\mathrm{\Delta }t=1\mathrm{ns}$ on (e) the (110) surface with $\mathbf{B}\parallel \left[001\right]$ and (f) the (001) surface with $\mathbf{B}\parallel \left[010\right]$. The dashed (red) lines are fits using Eq. (3) with extracted zero-field splitting $\mathrm{\Delta }{E}_{\left(110\right)}=2\mu \mathrm{eV}$ and $\mathrm{\Delta }{E}_{\left(001\right)}=50\mathrm{neV}$, respectively.

Figure 5

Magnetic circular dichroism (MCD) of a $\mathrm{CsPb}{\mathrm{Br}}_3$ thin film measured at 4 K in the Faraday configuration. (a) MCD spectra obtained at various magnetic fields. (b) MCD peak vs the magnetic fields and the extracted exciton Landé $g$ factor of the exciton $g_{\mathrm{exc}}=2.18\pm 0.08$ using a linear fit (red line).

Figure 6

(a) Spin lifetime of photoinduced electrons (blue squares) and holes (red circles) vs the magnetic field measured at 4 K with B along [010], which is extracted from the quantum beating (QB) dynamics [Eq. (4)]. The lines through the data points are fits using Eq. (5). (b) Spin dephasing rate of electrons (blue square) and holes (red circle) as a function of temperatures for $B=100\mathrm{mT}$. The lines through the data points are fits using Eq. (6).