Low-energy electronic interactions in ferrimagnetic ${\mathrm{Sr}}_2\mathrm{CrRe}{\mathrm{O}}_6$ thin films

We reveal in this study the fundamental low-energy landscape in the ferrimagnetic ${\mathrm{Sr}}_2\mathrm{CrRe}{\mathrm{O}}_6$ double perovskite and describe the underlying mechanisms responsible for the three low-energy excitations below 1.4 eV. Based on resonant inelastic x-ray scattering and magnetic dynamics calculations, and experiments collected from both ${\mathrm{Sr}}_2\mathrm{CrRe}{\mathrm{O}}_6$ powders and epitaxially strained thin films, we reveal a strong competition between spin-orbit coupling, Hund's coupling, and the strain-induced tetragonal crystal field. We also demonstrate that a spin-flip process is at the origin of the lowest excitation at 200 meV, and we bring insights into the predicted presence of orbital ordering in this material. We study the nature of the magnons through a combination of ab initio and spin-wave theory calculations, and show that two nondegenerate magnon bands exist and are dominated either by rhenium or chromium spins. The rhenium band is found to be flat at about 200 meV (±25 meV) through X-L-W-U high-symmetry points and is dispersive toward Γ.

Figure 1

Incident photon energy versus energy loss RIXS mapping, near the $L_3$ edge of rhenium for a powder of SCRO at $T=10$ K. In addition to the elastic line at 0 eV, four zones (I–IV) are identified. (I) The lowest energy part of the spectrum (energy $\mathrm{loss}<1.4$ eV) includes d-d transitions between the $t_{2\mathrm{g}}$ orbitals of rhenium, namely intra-$t_{2\mathrm{g}}$, and potential quasiparticle excitations. (II) The broader feature between 4 and 6 eV resonates 4 eV higher than the ones in zone I. Its spectral weight is identified as d-d transitions between the $e_g$ and $t_{2\mathrm{g}}$ orbitals. The strong signal located at 8 eV results from transitions between oxygen $2p$ and rhenium $5d$ (charge transfer) and the linearly incident-energy-dependent intensity in zone IV is induced by fluorescence.

Figure 2

RIXS spectra for different momentum transfer. (a) Low-energy RIXS spectra (zone I in the map of Fig. 1) collected from the compressive SCRO thin film for different momentum transfer $q$ expressed in the double perovskite cubic system (dp), at a temperature of 17 K. The spectra are normalized by the integrated intensity between 0.05 and 1.4 eV. Three excitations are resolved at 0.2, 0.65, and 1 eV, in addition to the elastic line at 0 eV. The black curve represents the sum of four Voigt functions that are used to fit the experimental data collected at the $X$ point. (b) Schematic unit cell of the fcc SCRO in real space, and the corresponding reciprocal space and Brillouin zone. The $X$ marks represent the momenta that have been probed, with the same color code used for the spectrum.

Figure 3

RIXS spectra collected at different temperatures for (a) compressive SCRO film at $q=$ (6.4, 0.34, 6.8) and (b) tensile SCRO film at $q=$(6, 0.34, 7.2) in the 17–300-K range. The elastic line at 0 eV has been removed for a better reading of the low-energy excitations in the experimental data, and the spectra are normalized by the integrated intensity between 0.05 and 1.4 eV. (c),(d) Best-matched edrixs calculations at 17 K in presence of an exchange magnetic field. The calculated intermediate and final state allowed us to identify the peak near 0.2 eV as the result of a spin-flip process. The insets show the electronic level splitting due to the Hund's coupling and strain-induced tetragonal crystal field (${\mathrm{\Delta }}_{\mathrm{t}}$).

Figure 4

RIXS calculations and experimental data for (a) compressive and (b),(c) tensile strained SCRO at $T=17$ K. A large set of input parameters, $0.2\le \lambda \le 0.4$ eV, $-0.4\le {\mathrm{\Delta }}_{\mathrm{t}}\le 0.4$ eV, $0\le \mathrm{OO}\le 0.2$ eV, and $U=0$, 2 eV, are used to match the experimental data. The best set is found to be $U=2, \lambda ={\mathrm{\Delta }}_{\mathrm{t}}=0.3$ eV, and $J_{\mathrm{h}}=0.25$ eV, although the quality of the fit is poor, especially for the excitation at 0.2 eV for tensile SCRO. The agreement between experiment and calculation is not improved with OO as shown in (c).

Figure 5

Experimental and calculated energy scans at $q=\left(00\frac{1}{2}\right)$ for the OO-induced reflections in tensile SCRO. (a) Calculated intensity of the OO-induced reflection at $\left(00\frac{1}{2}\right)$ and an incident energy $E_{\mathrm{i}}=10.565$ keV, as a function of the azimuthal angle $\varphi$, for different incident angle ${\theta }_{\mathrm{i}}$ and for π, σ polarization. (b) Experimental (solid lines) and calculated (dashed lines) energy-dependent intensity of the OO-induced reflection for σ polarization, ${\theta }_{\mathrm{i}}=8.5^{\circ }$ and for different $\varphi$ values. The simulation is calculated from the absorption spectra resulting from the edrixs calculation with OO for the tensile SCRO. The data are corrected for self-absorption and normalized by the Bragg reflection intensity at $q=$(0 0 2).

Figure 6

Magnon band structure. Two lowest, nondegenerate magnon bands. Color scale indicates the weight of Re spin involved in the magnon mode. Exchange parameters are obtained from the DFT and spin-wave calculation. The $X$ markers represent the experimentally measured $k$ points and their energies.