Second-order nonlinear optical and linear ultraviolet-visible absorption properties of the type-II multiferroic candidates $\mathrm{RbFe}{\left(A{\mathrm{O}}_4\right)}_2$ ($A=\mathrm{Mo},\mathrm{Se},\mathrm{S}$)

Motivated by the search for type-II multiferroics, we present a comprehensive optical study of a complex oxide family of type-II multiferroic candidates: $\mathrm{RbFe}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2, \mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$, and $\mathrm{RbFe}{\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$. We employ rotational-anisotropy second harmonic generation spectroscopy (RA SHG), a technique sensitive to point symmetries, to address discrepancies in literature-assigned point/space groups and to identify the correct crystal structures. At room temperature we find that our RA SHG patterns rotate away from the crystal axes in $\mathrm{RbFe}{\left(A{\mathrm{O}}_4\right)}_2$ ($A=\mathrm{Se},\mathrm{S}$), which identifies the lack of mirror symmetry and in-plane two-fold rotational symmetry. Also, the SHG efficiency of $\mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$ is two orders of magnitude stronger than $\mathrm{RbFe}{\left(A{\mathrm{O}}_4\right)}_2$ ($A=\mathrm{Mo},\mathrm{S}$), which suggests broken inversion symmetry. Additionally, we present temperature-dependent linear optical characterizations near the band edge of this family of materials using ultraviolet-visible absorption spectroscopy. Included is experimental evidence of the band gap energy and band gap transition type for this family. Subband gap absorption is also presented, which reveals prominent optical transitions, some with an unusual central energy temperature dependence. Furthermore, we find that by substituting the $A$ site in $\mathrm{RbFe}{\left(A{\mathrm{O}}_4\right)}_2$ ($A=\mathrm{Mo},\mathrm{Se},\mathrm{S}$), the aforementioned transitions are spectrally tunable. Finally, we discuss the potential origin and impact of these tunable transitions.

Figure 1

(a) Crystal structure of each compound using the literature assigned point group organized by atomic weight of the $A$ site with increasing weight towards the right. The in-page plane corresponds to the (001) plane ($ab$ plane) and the out-of-page axis corresponds to the $c$ axis of each crystal. (b) RA SHG spectroscopic results of each material. The first row displays measurements from the parallel channel detection scheme. The markers correspond to raw data points and the filled in pattern corresponds to data fitting. The a- and b-axis locations shown in the first pattern are consistent across each plot. Estimated maximum signal amplitudes are listed next to each pattern and are relative to the signal level of $\mathrm{RbFe}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2$. The second row compares fitted data with simulated results for the trigonal point groups proposed in literature. (c) Table comparing the literature assigned point group to the point group used to fit the RA SHG data of each compound.

Figure 2

Room temperature UV-VIS measurements and feature fittings for all three compounds. The color scheme is consistent across all panels where black corresponds to $\mathrm{RbFe}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2$, blue to $\mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$, and red to $\mathrm{RbFe}{\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$. (a) Absorbance measurements for all three compounds at room temperature. (b) Direct Tauc plot, ${\left(\alpha \hslash \omega \right)}^2=A\left(\hslash \omega -E_g\right)$, versus photon energy, using absorbance measurements as the absorption coefficient to estimate band gap energies for each compound. Markers correspond to absorbance data used in the Tauc equation and the solid lines correspond to the linear fitting (Appendix pp2). (c) Example of subband gap resonance anharmonic oscillator fitting to determine the central energy and FWHM of the observed features. The contribution of the Urbach tail on the high energy side of each feature is excluded in the fitting. Markers correspond to the absorbance data and the solid lines correspond to Gaussian fittings. (d) Estimated room temperature band gap and central feature energies as compared to the atomic weight of the $A$ site. Uncertainty levels for the band gap energy are estimated to be $\sim \pm 1\%$ using protocols from Ref. [33]. Peak energy error bars are determined predominantly from the spectrometer calibration uncertainties, which are correlated to the spectral resolution, as fitting errors are relatively negligible.

Figure 3

(a) Absorbance temperature dependence of the most prominent resonance below the band gap for $\mathrm{RbFe}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2, \mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$, and $\mathrm{RbFe}{\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$ respectively. Black, blue, and red correspond with compounds $\mathrm{RbFe}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2, \mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$, and $\mathrm{RbFe}{\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$ respectively in all three panels. (b) Fitted peak energy temperature dependence. The grey bar in the trendline for $\mathrm{RbFe}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2$ indicates the temperature at which the phase transition from $\overline{3}m$ to $\overline{3}$ occurs. Uncertainty levels for the peak energy are again determined from the spectrometer resolution. (c) Fitted resonance full width half maximum (FWHM) temperature dependence. Markers indicated fitted data and dashed lines are present for guidance. For the FWHM, uncertainty levels are determined by the fitting error which is captured in the marker size.

Figure 4

(a) Absorbance temperature dependence of the band gap and band gap features. Black, blue, and red correspond to compounds $\mathrm{RbFe}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2, \mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$, and $\mathrm{RbFe}{\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$ respectively in all three panels. (b) Markers correspond to the band gap temperature dependence from 0 to 295 K determined using the direct Tauc model fitting on the linear regime of the band edge (above any band edge resonances). A correction for the Urbach tail is also employed (Appendix pp2). The solid line represents a fitting of the data using the thermodynamic model from Eq. (8). Again, uncertainty levels for the band gap energy are estimated to be $\sim \pm 1\%$ [33]. (c) Fitted peak energy temperature dependence and FWHM from 0 to 80 K for the peaks indicated by the arrows in panel (a). Only values of resonances present in $\mathrm{RbFe}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2$ and $\mathrm{RbFe}{\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$ are listed as the resonance at 3.18 eV for $\mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$ is only distinguishable from the band edge at 5 K. Markers indicate fitted data and dashed lines are present for guidance. Uncertainty levels are determined from the spectrometer resolution and fitting errors for the peak energy and FWHM, respectively.

Figure 5

Normalized RA SHG response of $\mathrm{RbFe}{\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$ at oblique incidence ($\theta \approx {15}^{\circ }$) in the $S_{\mathrm{in}}-P_{\mathrm{out}}$ channel at room temperature. Red markers indicate measured SHG response values. The red filled-in pattern is the fitting for the modeled RA-SHG response under $\overline{3}$. The black filled-in pattern is the fitting for the modeled RA SHG response under 3. The angle shown is the offset angle using the $\overline{3}$ model.

Figure 6

(a) Direct transition Tauc plot for $\mathrm{RbFe}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2, \mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$, and $\mathrm{RbFe}{\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$ at 5 K. (b) Comparison between an indirect and direct Tauc plot for $\mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$ given by the relation ${\left(\alpha \hslash \omega \right)}^{1/n}=A\left(\hslash \omega -E_g\right)$, where $\hslash \omega$ is the photon energy.

Figure 7

(a) SHG scanning image of $\mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$ single crystal. The relative position of the $a$ and $b$ crystal axes are shown in the bottom left corner (b) Polar RA SHG plots at various sites on the crystal. The site locations are given by the corresponding numbers in (a) and (b).

Figure 8

Modeled refractive index ($n$) and extinction coefficient ($k$) as a function of energy for $\mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$.

Figure 9

Comparison of RA SHG pattern using two different optical band-pass filters (BPFs) with the following center wavelength and bandwidth: 400 ± 20 nm (3.1 ± 0.15 eV) and 400 ± 5 nm (3.1 ± 0.04 eV). The transmission spectrum of each BPF is overlaid with the absorbance spectrum of $\mathrm{RbFe}{\left(A{\mathrm{O}}_4\right)}_2$ ($A=\mathrm{Se},\mathrm{S}$) at room temperature. (a),(b) RA SHG response of $\mathrm{RbFe}{\left(\mathrm{Se}{\mathrm{O}}_4\right)}_2$ is shown in the top left corner for the two BPFs. (c),(d) RA SHG response of $\mathrm{RbFe}{\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$ is shown in the top left corner for the two BPFs. The green Gaussian profile represents the estimated spectral range of the SHG response and has a FWHM of 13.90 nm (0.11 eV) and central wavelength of 400 nm (3.1 eV).