Level mixing and anisotropy effect in resonant Raman electron paramagnetic transitions in ruby for $B$ perpendicular to $c$

Doubly resonant Raman electron paramagnetic transitions in ruby (Al${}_2$O${}_3$:Cr${}^{3+}$) have been investigated using dye laser excitation tuned across the range of the Zeeman components of its well-known $R_1$ emission line. With magnetic field B normal to c, the optic axis of ruby, it is seen that the Raman electron paramagnetic resonance (EPR) lines exhibit significant intensity enhancements due to the simultaneous occurrence of “in resonance” and “out resonance,” as visualized in the Kramers-Heisenberg formalism of inelastic light scattering. The specific Raman EPR features observed in the present study, together with their resonances, however, differ markedly from those observed in our previous investigation with $\mathbf{B}\parallel \mathbf{c}$. These differences can be traced to level mixing effects within the Zeeman multiplet of the ${}^4{A}_2$ (ground) state on the one hand, and the negligible value of $g_{\perp }$ for the $\mathrm{Ē}$ (excited) state of the $R_1$ emission line on the other. Furthermore, we note that with B⊥c and under resonant conditions, the experimentally observed Δ$m$ $=$ ±1 pair of Stokes and anti-Stokes Raman lines are not connected by time-reversal symmetry.

Figure 1

Zeeman components of the $R_1$ emission line of ruby (a) B∥c, PL${}_n$ ($n$ $=$ 2–7), and (b) B⊥c, (${\mathrm{PL}}_n,{{\mathrm{PL}}^{\prime }}_n$) ($n$ $=$ 1–4).

Figure 2

(a) The photoluminescence spectrum of the (${\mathrm{PL}}_n,{{\mathrm{PL}}^{\prime }}_n$) doublets observed at 6 T. (b) The magnetic-field dependence of (${\mathrm{PL}}_n,{{\mathrm{PL}}^{\prime }}_n$) doublets. Dots denote experimental data and the solid lines are calculated using the known $g$${}_{\perp }$ values of the ground and excited states of the $R_1$ line. Note that there are two nearly overlapping lines corresponding to each (${\mathrm{PL}}_n,{{\mathrm{PL}}^{\prime }}_n$) doublet, reflecting the very small splitting between the $\mathrm{Ē}$ (±1/2) excited states of $R_1$.

Figure 3

Calculated magnetic-field dependence of the Zeeman sublevels of the ${}^4{A}_2$ ground state for B⊥c.

Figure 4

(a) Raman EPR spectrum of Cr${}^{3+}$ in ruby for B⊥c. The Stokes and the anti-Stokes Raman EPR shifts recorded with incident photon energy $\hslash {\omega }_{\mathrm{L}}=14395.0\hspace{0.5em}{\mathrm{cm}}^{-1}$, B $=$ 6 T, and $T$ $=$ 8 K. (b) The Raman EPR transition energies as a function of B. The solid lines are calculated results using the spin Hamiltonian for B⊥c.

Figure 5

Graphical illustration of the occurrence of double resonances when $\hslash {\omega }_{\mathrm{L}}$ is scanned across the spectral range of ${\mathrm{PL}}_n^{*}$ with B⊥c. Scattered photon energies $\hslash {\omega }_{\mathrm{S}}$ of Raman EPR lines are parallel to the diagonal line labeled $\hslash {\omega }_{\mathrm{L}}$. The simultaneous coincidence of $\hslash {\omega }_{\mathrm{L}}$ and $\hslash {\omega }_{\mathrm{S}}$ for different ${\mathrm{PL}}_n^{*}$ is depicted at B $=$ 6 T. The Raman transitions corresponding to each $\hslash {\omega }_{\mathrm{S}}$ line (1a–3a and 1–3) are given in the text. The photoluminescence lines ${\mathrm{PL}}_1^{*}$–${\mathrm{PL}}_4^{*}$, being independent of $\hslash {\omega }_{\mathrm{L}}$, appear in the figure as horizontal lines parallel to the abscissa.

Figure 6

Doubly resonant Raman EPR spectra of ruby for B⊥c, B $=$ 6 T, and $T$ $=$ 8 K. In the insets, scattered photon transitions causing anti-Stokes lines are shown as blue vertical lines, while those causing Stokes transitions are the dark brown vertical lines. The net Raman EPR transition in each case is indicated by the green arrows. In (a) $\hslash {\omega }_{\mathrm{L}}={\mathrm{PL}}_2^{*}$, and in (b) $\hslash {\omega }_{\mathrm{L}}={\mathrm{PL}}_3^{*}$.