Isotopic Effects of the Electronic Transitions of Cr 3+ in Ruby (Al 2 O 3 : Cr 3+ ).

1. Isotopic Effects of the Electronic Transitions of Cr3+ in Ruby (Al2O3: Cr3+). Anant K. Ramdas, Purdue University, DMR 0705793 Research goal: To delineate the isotopic dependence of the atomic like R1 and R2 electronic transitions of Cr3+ substitutional impurities replacing Al randomly in dilute concentrations in corundum (Al2O3) i.e. in ruby, measurements being made under ultrahigh resolution and low temperatures. We and Jayaprakash Bhosale, graduate student of AKR supported on the project, have investigated the isotopic signatures of Cr3+ manifested in R1 and R2 transitions of ruby measured under the ultrahigh resolution of a Fourier Transform Spectrometer (0.009cm-1) and at 5K. The absorption spectrum in Fig. 1 displays the spin-orbit splitting (ΔS.O.), of the 4A2 ground state of Cr3+ in ruby (Δ = 0.393 cm-1); based on the natural abundances of the stable isotopes of Cr (Cr50, Cr52, Cr53 and Cr54) given in the accompanying table where the spectral signatures are labeled accordingly. It is at first sight surprising that the R1 and R2 lines of the different isotopes are shifted with respect to one another; the lighter it is, the more the shift towards lower frequencies. Imbusch et al1 attribute this isotopic effect to an interaction between the impurity atom (Cr3+ in ruby) and the zero point vibrations of the host atoms and the Cr3+ impurities. The more massive the isotope, the smaller its displacement with respect to lattice; it can be shown the shifts, referred to a ‘hypothetical, infinitely massive Cr, will follow ‘a-bM-1/2’, a and b being constants and M = isotopic mass of Cr3+ ) The phenomenon is reminiscent of our work on the band gap renormalization effects in the elemental semiconductors, diamond, silicon, and germanium2 in which the lattice vibrations are governed by the isotopic composition of the semiconductor; in the spirit of ‘virtual crystal’ approximation, control the frequencies and amplitudes of lattice vibration. Electron-phonon interaction then ‘renormalizes’ the band gaps even at O°K, thanks to zero-point vibrations and a change in the lattice parameter as dictated by the anharmonicity of the potentials which the constituent atoms occupy. Figure 2 clearly shows that the frequencies of the R1 and R2 lines of Cr3+ in ruby clearly show the M-1/2 dependence. Fig 1 1. G.F. Imbusch et al, Phys. Rev. 136, A481 (1964). 2. A.K. Ramdas, S. Rodriguez, S. Tsoi and E.E. Haller, Solid State Commun. 133, 709 (2005).

2. Isotopic Effects of the Electronic Transitions of Cr3+ in Ruby (Al2O3: Cr3+). Anant K. Ramdas, Purdue University, DMR 0705793 Future Plans:The novel results highlighted in this research highlight open new opportunities for such experiments with ions like Cr3+ incorporated in different hosts e.g. MgO, and other ions like Ti2+. Such studies will illuminate the nature of the ground states of ions in laser materials like YAG (yitrium-aluminum-garnet) and LiNbO3 Education/Broader Impact: The research reported here is the outcome of a close collaboration between the two PIs [Ramdas (Experimental) and Rodriguez (Theorist)]; Jayaprakash Bhosale (Graduate Student) and Professor S. Venugopalan (SUNY, Binghamton). J. Bhosale and R. Garrelts are the current graduate research students. Collaborations with Professor Eugene Haller (UCB), Dr. Thomas Anthony (formerly of GE), Professor Manuel Cardona (Max Planck Institute, Stuttgart), and Professor Ram-Mohan (WPI) are examples of the interactive and intellectually stimulating ambience in which our graduate students and undergraduates carry out their research; this experience prepares them for an exciting future in universities as well as national and industrial laboratories. Fig 2