Spin-dependent Raman and Brillouin light scattering on excitons in CsPbBr$_3$ perovskite crystals

TL;DR

The paper addresses the spin properties of excitons and charge carriers in CsPbBr$_3$ by employing spin-dependent Raman and Brillouin light scattering in magnetic fields up to 10 T. The authors resonantly probe exciton-polaritons to extract electron, hole, and exciton $g$-factors and their anisotropies, and they develop and test mechanisms for spin-flip processes, including carrier–resident carrier exchange, exciton–phonon coupling, and trion-mediated pathways, with a notable observation of a double electron spin-flip. They identify X$_2$ and X$_1$ exciton spin-flip lines, showing that $g_{X2ot}=2.72$ matches $g_e+g_h$ and that strain can lift degeneracies into X$_1^*$ and X$_1^{**}$, illustrating the role of local strain. Brillouin scattering on exciton-polaritons reveals two resonant lines whose field-induced splitting reflects the modified exciton–polaritons dispersions under a magnetic field, enabling mapping of polariton dispersions. Overall, the study provides detailed spin–related parameters for CsPbBr$_3$, clarifies the mechanisms of spin-flip scattering in lead halide perovskites, and demonstrates the usefulness of resonant Raman and Brillouin scattering for investigating exciton physics and spin dynamics in these materials.

Abstract

The spin properties of excitons and charge carriers in CsPbBr$_3$ lead halide perovskite crystals are investigated by spin-dependent light scattering in magnetic fields up to 10 T. Spin-flip Raman scattering spectra measured under resonant excitation of exciton-polaritons show a rich variety of features provided by the Zeeman splittings of excitons and of electrons and holes interacting with the excitons. The magnitudes and anisotropies of their Landé $g$-factors are measured. A detailed consideration of the responsible mechanisms is presented and discussed in relation to the experimental data, in particular on the polarization properties of the Raman spectra. We consider several mechanisms for the combined spin-flip Raman scattering processes involving resident carriers and photoexcited excitons and suggest new ones, involving trions in the intermediate scattering state. A double electron spin-flip caused by the exciton interaction with two localized or donor-bound electrons is revealed. The spectral lines of Brillouin light scattering on exciton-polaritons shift in energy and become polarization-sensitive in magnetic field, evidencing the splitting of the exciton-polariton dispersion.

Figures (9)

• Figure 1: Raman spectra of the CsPbBr$_3$ crystal in magnetic field. (a) Reflectivity (red line) and photoluminescence (blue line) spectra measured at $T=1.6$ K. The PL is excited at 2.540 eV. The rrow at 2.3305 eV indicates the laser energy used for SFRS measurements. (b) Light scattering in cross circular polarization configuration $\sigma^+ \sigma^-$: Brillouin scattering spectrum on exciton-polaritons at zero magnetic field (blue line). SFRS spectra at $B_{\rm F}=6$ T and 9 T in Faraday geometry ($\mathbf{B}_{\rm F} \parallel \mathbf{k}$ and $\mathbf{B} \perp \mathbf{c}$, as shown in inset). The Stokes shifted signals correspond to positive Raman shifts. The hole (h), electron (e), and exciton (X$_1$, X$_2$) spin-flip lines are clearly seen. Also, a double electron (2e) spin-flip line can be resolved. (c) Faraday magnetic field dependences of the Raman shifts of the electron, hole, exciton and double electron SFRS lines. The experimental data are shown by the symbols. The lines are linear fits using Eq. \ref{['eq:Zeeman']} to evaluate the $g$-factors. The solid lines for the charge carriers give $g_{e\perp}=2.06$ and $g_{h\perp}=0.65$. The dashed line for the X$_2$ exciton gives a fit with $g_{X2\perp}=2.72$, which exactly matches the relation $g_X=g_e+g_h$. (d) Angular dependence of the electron, hole, and exciton $g$-factors. Here the $g_X$ corresponds to the $g_{X2}$ from panel (c). The solid lines are fits with Eq. \ref{['eq:anisotropy']}. (e, f) Scheme of the experimental geometry for the sample tilted in the Voigt (e) and the Faraday (f) geometries.
• Figure 2: SFRS spectra in Voigt geometry. (a) Spin-flip Raman scattering spectra measured at $B_{\rm V}=5$ T using co- (HH, blue line) and cross- (HV, red line) linear polarizations. Laser photon energy is 2.3305 eV, $T=1.6$ K, and $\mathbf{B}_{\rm V} \perp \mathbf{c}$. (b, c, d) Mechanisms of carrier spin flips for electron (b), hole (c), and double electron (d). The different colors of excitation (blue) and detection (green) arrows in panels (b,c) show that the signal is obtained in cross-linear polarized configuration (HV or VH), while using the same colors in panel (d) indicates processes active in co-linear polarized configurations (HH or VV).
• Figure 3: (a), (b) Raman spectra in the Faraday geometry for all 4 configurations of excitation-detection circular polarization. The experimental geometry is shown in the inset of (a): the magnetic field is parallel to the sample c-axis, $\theta_B = 0^\circ$. The polarization properties almost coincide with the case of a Faraday magnetic field oriented perpendicular to the crystal c-axis (see Fig. \ref{['fig:SI4']}). The Brillouin light scattering lines are relatively strong for the shown configuration. (c-f) Schemes of mechanisms of electron spin-flip. Note, that the mechanisms for hole spin-flip work analogously, and therefore are not shown. The colors of the excitation and detection arrows stand for their polarizations: blue for $\sigma^+$ and green for $\sigma^-$.
• Figure 4: Strain effect on exciton spin-flip. (a) SFRS spectra of a CsPbBr$_3$ crystal measured in cross-circular polarizations at $B_{\rm F}=8$ T applied in the Faraday geometry ($\mathbf{B}_{\rm F} \parallel \mathbf{k}$, $\mathbf{B}_{\rm F} \perp \mathbf{c}$). The blue spectrum is recorded for strain-free sample mounting, and the red one is for the sample glued on a copper sample holder. $T=1.6$ K. (b) Scheme of the exciton spin-flip process with changing the spin by $\pm 1$ via the emission of an acoustic phonon. The blue arrow indicates $\sigma^{+}$ excitation and the green arrow $\sigma^{-}$ scattering. (c, d) Schematic illustration of the spin-flip transitions on the exciton without and with removing the degeneracy of the $\pm 1$ and $0$ states by strain.
• Figure 5: Alternative mechanisms of SFRS involving an exciton Raman shift (Stokes process). (a, b) Scheme of the combined electron and hole spin flips: e+h SF (a) and e-h SF (b). (c, d) Alternative schemes for the $\Delta E_e+\Delta E_h$ Raman shift via a positive (c) and anegative (d) trion intermediate state. The spin-flip of the electron (c) or hole (d) in the intermediate state is assisted by the emission of a resonant acoustic phonon. In the schemes, the blue arrows stand for $\sigma^{+}$ excitation, while the green arrows indicate $\sigma^{-}$ scattering. Note that for the e-h SF (b), both $\sigma^{+}\sigma^{-}$ and $\sigma^{-}\sigma^{+}$ scattering are possible in the Stokes range.