Trigonal field acting at the ${\text{Cr}}^{3+}$ ${}^{2}E$ states in ruby from magneto-optical measurements under high pressure

Magneto-optical measurements on ruby under high-pressure conditions provided direct determination of the trigonal crystal field acting at the $t_{2g}$ orbitals of ${\text{Cr}}^{3+}$ in ${\text{Al}}_2{\text{O}}_3$ $\left({\text{CrO}}_6\right)$ and its dependence with pressure. The correlation study between the measured trigonal splitting and the trigonal distortion at the ${\text{Al}}^{3+}$-substituted site indicates that the trigonal splitting increases with pressure whereas the trigonal distortion slightly reduces. The result is interpreted in terms of an enhancement of the electron-lattice coupling due to trigonal distortion upon reduction in the Al-O bond distance, i.e., the Cr-O bond distance $R$. The observed variations can be explained on the basis of empirical $R$ dependence of the trigonal crystal field as $\delta V_{\text{tr}}\propto R^{-n}$ with $n=6$. It is shown that this exponent does not change when we consider the pressure variation of the local structure around ${\text{Cr}}^{3+}$ obtained from ab initio calculations. By the way, we also demonstrate that a methanol-ethanol mixture is a good pressure transmitting medium at cryogenic temperatures.

Figure 1

(Color online) (a) Typical magneto photoluminescence spectrum of ruby at high pressure. Eight major peaks (A–H) are recorded. Logarithmic intensity scale enhances the visibility of four weaker peaks (a–h). (b) Energy Zeeman splitting fan chart enlightening the two pairs of peaks (BC) and (FG) giving direct access to ${\Delta }_1$ and ${\Delta }_2$. (c) Schematic view of the Zeeman splitting of ground state $\left({{}^{4}A}_2\right)$ and first excited states $\left({}^{2}E\right)$ of ruby. Observed emission lines are described by allowed (solid arrows) and forbidden (dashed arrows) electric-dipole transitions.

Figure 2

(Color online) Pressure dependence of the FWHM of the $R_1$ line at cryogenic temperature for our single crystals (filled squares) and ruby chips dispersed in the whole pressure chamber from Ref. 22 (open circles). The right ordinate axis indicates the pressure dispersion values as calculated with equation $\Delta p=0.5\left[\text{FWHM}\left(p\right)-\text{FWHM}\left(p_0\right)\right]/0.365$. The inset shows the pressure evolution of the $R$-doublet splitting at cryogenic temperature (squares). Note the slight decrease unveiled by the linear fit (solid line).

Figure 3

(Color online) Pressure dependence of ${\left(R/R_0\right)}^3$ for both Al-O and Cr-O distances in ${\text{Al}}_2{\text{O}}_3$: ${\text{Cr}}^{3+}$ in the 0–300 GPa range obtained from ab initio calculations in Ref. 10. The parameters correspond to the local bulk modulus and its derivative $B^{\prime }$ derived by fitting the average ${\left(R/R_0\right)}^3$ values which have been calculated for Al-O and Cr-O (Ref. 10) to a Murnaghan’s equation of state (MEOS). Although MEOS is crude to derive actual values of the bulk modulus and its pressure derivative, the fit parameters reflect a bigger compressibility of the ${\text{AlO}}_6$ octahedron with respect to ${\text{CrO}}_6$ at high pressure. However, their relative variation is similar for Al-O and Cr-O within 10% of accuracy in the 0–20 GPa range. Inset: magnification of the low pressure region showing a linear dependence with slopes of $3.0\times {10}^{-3}$ and $2.8\times {10}^{-3}{\text{GPa}}^{-1}$ for Al-O and Cr-O, respectively.

Figure 4

(Color online) Variation in the hexagonal lattice parameter $a$ with pressure obtained from x-ray diffraction (Ref. 39). The inset shows the corresponding variation in the trigonal strain parameters ${\epsilon }_{11}$ and ${\epsilon }_{33}$ derived from structural data from Refs. 39, 40, 41, 42.