Gigantic Kerr rotation induced by a $d\text{−}d$ transition resonance in $M{\mathrm{Cr}}_2{\mathrm{S}}_4$ $(M=\mathrm{Mn},\mathrm{Fe})$

The magneto-optical Kerr effect (MOKE) has been investigated for ferrimagnetic spinel compounds $M{\mathrm{Cr}}_2{\mathrm{S}}_4$ ($M=\mathrm{Mn}$ and Fe). In $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{S}}_4$, the gigantic magneto-optical response, reaching up to 4.3° in Kerr rotation, is observed at the energy of the intra-atomic $d\text{−}d$ transition of ${\mathrm{Fe}}^{2+}$, ${}^{5}E\to {}^{5}T_2$. By analyzing the resonance feature in the framework of the ligand field theory, we have clarified that the large oscillator strength enhanced by the strong covalency of the ligand sulfur as well as the local breakdown of inversion symmetry at the ${\mathrm{Fe}}^{2+}$ site is responsible for the gigantic signal. In $\mathrm{Mn}{\mathrm{Cr}}_2{\mathrm{S}}_4$, the spin-forbidden $d\text{−}d$ transition $({}^{6}A_1\to {}^{4}T_1)$ of ${\mathrm{Mn}}^{2+}$ is revealed in the MOKE spectra, which is not discernible in the optical reflectivity spectra.

Figure 1

(a) Optical conductivity spectra in the energy region of $0.1–0.5\mathrm{eV}$ for $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{S}}_4$. The broken lines represent the results of fitting with the three-component Lorentz oscillator model. (b) Temperature dependence of the crystal field splitting $\Delta E$, the sum of oscillator strengths $S_{\text{total}}$, the average damping constant ${\gamma }_{\mathrm{av}}$, the spin-orbit coupling constant $\zeta$, and magnetization $M$.

Figure 2

The $d\text{−}d$ transition of ${\mathrm{Fe}}^{2+}$ in the tetrahedral-coordination environment, ${}^{5}E\to {}^{5}T_2$, analyzed by the ligand field theory. The light $\mathbf{k}$ vector is set to [001] direction. In the “single domain” panel, all the spins are assumed to be aligned to the [001] direction, whereas in the “multidomain” panel, there are an equal number of [100], [010], and [001] magnetic domains. The ratios of the oscillator strength are shown for the $\Delta M_z=+1,0,-1$ transition, which are represented by the filled, hatched, and open arrows, respectively.

Figure 3

Temperature dependence of the magneto-optical Kerr rotation $\left(\theta \right)$ and ellipticity $\left(\eta \right)$ spectra of $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{S}}_4$ in the energy region of $0.2–4.5\mathrm{eV}$. The abscissa scale is magnified for the $d\text{−}d$ transition of ${\mathrm{Fe}}^{2+}$, ${}^{5}E\to {}^{5}T_2$. Note that the ordinate scale is also different between $0.2–0.5\mathrm{eV}$ and $0.5–4.5\mathrm{eV}$.

Figure 4

Temperature dependence of the real and imaginary part of ${\epsilon }_{xy}$ for the $d\text{−}d$ transition of ${\mathrm{Fe}}^{2+}$, ${}^{5}E\to {}^{5}T_2$ in $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{S}}_4$. The results of fitting for the spectra at $10\mathrm{K}$ in the framework of the ligand field theory are shown in the insets.

Figure 5

Temperature dependence of the magneto-optical Kerr rotation $\left(\theta \right)$ and ellipticity $\left(\eta \right)$ spectra for $\mathrm{Mn}{\mathrm{Cr}}_2{\mathrm{S}}_4$. The main panel is that of the energy region of the $d\text{−}d$ transition of ${\mathrm{Mn}}^{2+}$, ${}^{6}A_1\to {}^{4}T_1$. Insets show the spectra at $T=10\mathrm{K}$ in an extended photon energy region of $0.7–4.5\mathrm{eV}$.