Distinct Magneto-Optical Response of Frenkel and Wannier Excitons in CrSBr

TL;DR

The paper addresses how excitons in a 2D magnetic semiconductor respond to magnetic order and lattice vibrations. It combines high-field magneto-optical spectroscopy (up to 85 T) with first-principles QS-GW calculations including ladder diagrams to resolve two exciton species in CrSBr: XA (Frenkel-like, localized) and XB (Wannier-Mott-like, delocalized). The key findings show that XB redshifts by ~95 meV through the AFM→FM transition while XA shifts by ~7–10 meV, with XB exhibiting a larger spatial extent and strong coupling to out-of-plane lattice modes; XA remains relatively inert to phonons. The results reveal a mixed exciton regime that challenges traditional ligand-field and Rydberg pictures, highlighting the necessity of ab initio approaches for predicting magnetic excitons in 2D correlated materials and informing magneto-optical device design.

Abstract

This study shows that CrSBr hosts Frenkel-like and Wannier-Mott-like excitons whose distinct spatial character explains their contrasting sensitivity to magnetic order and lattice vibrations, challenging the standard dichotomy in describing excitons.

Figures (3)

• Figure 1: Optical response and band structure of CrSBr (a) Low-temperature ($\sim$5 K) derivative of reflectivity spectra of bulk CrSBr in AFM phase (blue) and FM phase (red) induced by the magnetic field (2.5 T) applied along $c$-axis of the crystal (hard magnetisation axis)telford2020layered. Arrows indicate the positions of two prominent excitonic features labeled XA and XB. (b) Evolution of the reflectivity spectra derivative as a function of the magnetic field presented in false-colour maps. (c) and (d). Calculated CrSBr band structures in AFM phase with the decomposition of the XA and XB exciton wavefunctions in the band basis, highlighted by orange shading. The pie chart insets illustrate contributions of atomic orbitals to the exciton wavefunctions, showing a strong onsite Cr component for XA. (e) Calculated oscillator strength of excitonic transitions in 1.3-1.9 eV energy range.
• Figure 2: High magnetic field studies of excitons wave function extensions (a) and (b): Evolution of the reflectance spectrum as a function of magnetic field between 0 and 85 T. (c): shifts in $X_A$ and $X_B$ transition energies measured at 2 K, as a function of the magnetic field in the FM phase, along with a parabolic fit, Eq. \ref{['eq:diamagnetic']} with diamagnetic coefficients $\sigma_A=0.05$ meV/T$^2$ and $\sigma_B=0.22$ meV/T$^2$. The ratio of $\sigma_B/\sigma_A > 4$ confirms that $X_B$ is spatially more delocalised. The inset shows a schematic of the experimental setup where the CrSBr sample is placed in a coil of a pulse magnet. The optical fibre directs the broadband white light to the surface of the sample, and the reflected signal is collected by the surrounding bundle of fibre. (d) and (e): isosurfaces for the XA and XB exciton wavefunctions overlaid on the crystal structure in the AFM phase, showing exciton confinement within a single layer. (f) and (g): same as (d) and (e), but for the FM phase, revealing much stronger interlayer hybridisation for the $X_B$ exciton.
• Figure 3: Temperature dependence of magneto-optical response of CrSBr (a) and (b) Shifts of the excitonic transition as a function of the magnetic field, measured at different temperatures for XA and XB (for linear scale see SI Fig. S8). Arrows indicate the inflexion (kink) points in the optical response related AFM-to-FM phase transition. (c) normalised magnetisation curve measured at 2 K, taken from Ref. telford2022coupling. (d) Dependence of the saturation field on temperature, extracted from optical spectra, with the dashed line serving as a guide to the eye. (e) Red and blue points represent absolute values of the energy shift between 0 T and $\sim$85 T of XA and XB transitions as a function of temperature. Triangles are the results of the XA and XB energy shifts predicted by our $\mathrm{QS}G\hat{W}$ calculations within the frozen-phonon approximation. The short and long-dash lines are guides to the eye (for theory and experiment, respectively). (f) The out-of-plane distortion of the lattice mediated by the A$_{g}$ phonon mode.