Observation of anisotropic dispersive dark exciton dynamics in CrSBr

Abstract

Many-body excitons in CrSBr are attracting intense interest in view of their highly anisotropic magneto-optical coupling and their potential for novel optical interfaces within spintronic and magnonic devices. Characterizing the orbital character and propagation of these electronic excitations is crucial for understanding and controlling their behavior; however, this information is challenging to access. Ultra-high resolution resonant inelastic x-ray scattering is a momentum-resolved technique that can address these crucial questions. We present measurements collected at the Cr $L_3$-edge which show a rich spectrum of excitations with a variety of spin-orbital characters. While most of these excitations appear to be localized, the dispersion of the lowest energy dark exciton indicates that it is able to propagate along both the $a$ and $b$ directions within the planes of the crystal. This two-dimensional character is surprising as it contrasts with electrical conductivity and the behavior of the bright exciton, both of which are strongly one-dimensional. The discovery of this propagating dark exciton highlights an unusual coexistence of one- and two-dimensional electronic behaviors in CrSBr.

Figures (4)

• Figure 1: Anisotropic dispersive exciton behavior in CrSBr (a) Crystal structure. The gray cuboid shows the unit cell and the translucent blue octahedron shows the Cr coordination. (b) X-ray absorption measured in TFY mode as a function of incident photon energy, showing peaks at the Cr $L_3$ and $L_2$ edges. The data was collected in the $H0L$ plane, with an incident angle of $\theta_i = 45^{\circ}$ and a scattering angle of $2\Theta = 90^{\circ}$. The dashed vertical line indicates the energy at which the RIXS spectra in (c) were collected. $\sigma$ polarization indicates vertical linear polarization of the incoming beam along the sample $b$-axis, and $\pi$ horizontal linear polarization in the sample $a-c$ plane. (c) Exciton propagation along the $H$ and $K$ directions of the Brillouin zone. The peak positions extracted from the fit are plotted on one half of the data in each plane, showing non-dispersive behavior in most of the excitons (white), as well as dispersive propagating behavior in one of the low-energy excitons (red). A non-dispersive low energy feature, which we identify as the previously reported optically active exciton, is visible at low momentum transfers in the $H0L$ plane (blue). The $H$ dependent measurements were collected at $K=0$, with the beam polarization in the $H0L$ scattering plane. The $K$ dependent measurements were collected at $H=0$, with the photon polarization along the $H$ axis perpendicular to the $0KL$ scattering plane. (d) Line cuts showing raw spectra and Gaussian fits to the low energy excitations in the $H0L$ plane, demonstrating that two peaks can be resolved in the 1.3 to 1.5 eV energy range. The vertical dashed line marks the position of the 1.38(1) eV feature. (e) Additional data measured with the sample in the $0KL$ plane at $K=0$, demonstrating that the weak feature can also be resolved at sufficiently low momentum transfers.
• Figure 2: Low-temperature emergence of excitons in CrSBr (a) RIXS spectra with varying temperature, collected at 577.2 eV ($L_3$ edge) at $\theta_i=9.4^{\circ}$ and $2\Theta=149^{\circ}$. The prominent excitation is visible at $\sim$1.4 eV is the dark dispersive exciton and is highlighted by the pink shading at low temperature. This feature becomes weaker and broader with increasing temperature. The spectra were fit with five Gaussian functions with temperature-dependent widths and intensity, and constant energies. (b) Temperature dependence measured at lower momentum transfer to resolve the two low energy peaks. The optically active and the dark dispersive excitons both show a similar decrease in intensity at higher temperatures above $T_N$. This data was collected at $\theta_i=68.5^{\circ}$ and $2\Theta=150^{\circ}$. Data in both panels was collected in the $H0L$ plane with a $\pi$-polarized beam.
• Figure 3: Electronic character of the CrSBr excitons. (a) Low-temperature (30 K) RIXS spectra collected in the $H0L$ plane at $\theta_i=15^{\circ}$, $2\Theta=90^{\circ}$ and 577.4 eV. (b) AIM simulations that capture the main structures and polarization dependence observed in RIXS. (c),(d) Plot the orbital occupancies and spin and orbital angular momentum expectation values squared, denoted $\langle S^2\rangle$ and $\langle L^2\rangle$, respectively. We identify three manifolds of excitations: $t_{2g}\rightarrow e_g$ excitations below 1.75 eV, high spin-to-low-spin excitations from 1.75-2 eV, and a second manifold of $t_{2g}\rightarrow e_g$ excitations with reduced orbital angular momentum $L$ above 2 eV.
• Figure 4: Band structure of CrSBr without spin-orbit coupling. DFT calculated bands are in black, overlain on the Wannier projected bands in red, showing their total agreement. The symmetry labels follow the conventional labeling methodology described in Ref. Setyawan2010high based on the Bravais lattice of the unit cell.