Spin-orbital entanglement in Cr$^{3+}$-doped glasses

Abstract

A framework for reconstructing the one-electron spinors $Γ_7$ and $Γ_8$ of Cr$^{3+}$ embedded in glasses from optical measurements has been developed. From the spinors, the spin-orbital von Neumann entropy can be calculated. An aluminum phosphate glass doped with 1 mol % chromium is prepared, and its optical absorption spectrum is recorded to validate the method. The spin-orbit coupling constant, crystal field strength, and Racah parameters are obtained from the absorption spectrum. Subsequently, the spin-orbital entanglement entropy is calculated and analyzed for a family of chromium-doped glasses. It is found that individually, neither the spin-orbit coupling constant, nor the crystal field strength, nor the Racah parameters correlate with the entanglement entropy. In contrast, the ratio between the spin-orbit coupling constant and the crystal field strength correlates linearly with the entanglement entropy.

Figures (4)

• Figure 1: Idealized octahedral structure of CrO$_6$ in phosphate glasses.
• Figure 2: Energy splitting of d orbitals due to octahedral crystal field CF($O_h$) and to the spin-orbit coupling SOC.
• Figure 3: Left: absorption spectrum of $\rm 1~mol~\%$$\rm Cr^{3+}$ doped phosphate glass. The fitted spectrum correspond to the parameters $\Gamma_0=1850~{\rm cm^{-1}}$, $\Gamma_1=240~{\rm cm^{-1}}$, $\Gamma_2=180~{\rm cm^{-1}}$, $\gamma_1=250~{\rm cm^{-1}}$, and $\gamma_2=190~{\rm cm^{-1}}$. Right: Correlation diagram of energy levels of d$^3$ ions as a function of $Dq/(Dq+B)$. The rectangle indicates the Cr$^{3+}$-doped phosphate glass absorption bands.
• Figure 4: Spin-orbital entanglement entropy of $\Gamma_8$ espinors of Cr$^{3+}$-doped glasses versus $\xi_{3d}/Dq$ ratio. ZLAG, ZBLA and PZG stand for fluoride glasses; PT, CT, and ZT stand for tellurite glasses; AlPO stands for aluminum-phosphate glass.