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Journal of Physics C Solid State Physics

Diffusion of localized optical excitations and trap emission in ruby

J. Heinrichs, Anil Kumar, Neeraj Kumar

Published Feb 14, 1977• 0 citations
Publisher

Abstract

Using the critical percolation conductance method the energy-dependent diffusion coefficient associated with thermally assisted transfer of the R 1 line excitation between single Cr 3+ ions with strain-induced randomness has been calculated in the 4 A 2 to E( 2 E) transition energies. For localized states sufficiently far away from the mobility edge the energy transfer is dominated by dipolar interactions, while very close to the mobility edge it is determined by short-range exchange interactions. Using the above energy-dependent diffusion coefficient a macroscopic diffusion equation is solved for the rate of light emission by Cr 3+ ion-pair traps to which single-ion excitations are transferred. The dipolar mechanism leads to good agreement with recent measurements of the pair emission rate by Koo et al. (Phys. Rev. Lett., vol.35, p.1669 (1975)) right up to the mobility edge.

DOI
10.1088/0022-3719/10/3/009

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Physical review. B, Solid state•Feb 15, 1973•22 citations
Using the critical percolation conductance method the energy-dependent diffusion coefficient associated with thermally assisted transfer of the R 1 line excitation between single Cr 3+ ions with strain-induced randomness has been calculated in the 4 A 2 to E( 2 E) transition energies. For localized states sufficiently far away from the mobility edge the energy transfer is dominated by dipolar interactions, while very close to the mobility edge it is determined by short-range exchange interactions. Using the above energy-dependent diffusion coefficient a macroscopic diffusion equation is solved for the rate of light emission by Cr 3+ ion-pair traps to which single-ion excitations are transferred. The dipolar mechanism leads to good agreement with recent measurements of the pair emission rate by Koo et al. (Phys. Rev. Lett., vol.35, p.1669 (1975)) right up to the mobility edge.
The energy transfer between single Cr 3+ ions and N 2 pairs in ruby is interpreted by energy diffusion on single ions. It is shown that the superexchange is responsible for this diffusion. The probability of transfer between single ions and the diffusion coefficient are evaluated. Experimental results on the transfers from fourth next-neighbour pairs to single ions and to third next-neighbour pairs are given. It appears that the diffusion is weak on the fourth NN pairs. The temperature dependence of the transfer probabilities are determined and interpreted.
Fluorescence-line-narrowing and time-resolved studies have been conducted in ruby crystals and powders, in concentrations varying from 0.025 to 0.9 at.%. The resonance fluorescence component of the R1{R}_{1}R1​ line at low temperatures is observed to increase dramatically as the laser is tuned from line center toward the low-energy wing of the inhomogeneously broadened absorption. This is presumed to indicate the presence of weakly coupled pairs in the wings of the line. Intraline and interline (${R}_{1}\ensuremath{\rightarrow}{N}_{1,2}$) energy transfer have also been studied, and an elaboration of earlier work is given. Time-resolved selective-excitation scans have revealed numerous channels in the vicinity of the RRR lines by which the different pairs can be directly excited. These are assumed to be Cr ions near enough to a pair to be in a highly perturbed environment. Various experimental results are shown to be consistent with a model of rapid transfer between resonant Cr ions which feeds the pairs via a weak, nonresonant coupling to these perturbed ions. Macroscopic strain broadening is also shown to be favored over microscopic broadening, and the implications for Anderson localization in ruby are discussed.
The optical spectrum due to the exchange coupled Cr 3+ ions in ruby has been studied theoretically. The effect of the lowering of the Cr 3+ site symmetry due to the formation of a pair was taken into account. For the 2nd neighbor pair, a good fitting of the excited state energies between theory and experiment was obtained. The effect of the higher order exchange is found to be very important for this pair. It is also found that the deviation of the Cr 3+ site symmetry from C 3 is rather large for this pair. For the 4th neighbor pair, the level diagram of the excited state was obtained and the absorption intensities were calculated. Most of the observed lines in this pair are explained by this theory. The lines so called N 1 and N 2 are found to be the transitions due to the exchange induced electric dipole.
We study the time development of spectral profile of an inhomogeneously broadened system of a low concentration of optically active random two-level impurity ions excited with a narrow-band laser pulse. The spectral transport is due to phonon-assisted spatial migration of optical excitations among the impurity ions. The basic two-site transfer rate is assumed to be site symmetric and independent of the energy levels of the initial and final sites when the thermal energy is much larger than the inhomogeneous width. A "direct transfer" model relevant to some current works is solved exactly for dipolar interaction at a low-impurity concentration. In this model transitions are allowed only between the initial site of excitation and rest of the ions. The result agrees well with a previous "exact" Monte Carlo calculation for a short time. The result is improved systematically for longer times by using a pair model, a 3-site model, and a 4-site model. In the first two models, energy transfer is allowed along one and two nearest-neighbor percolation bonds, respectively, starting from the initial site of excitation. In a 4-site model additional transfer is included between the initial ion and its second neighbor. Transitions to the background ions without back transfer are allowed in all cases. Finally, the theoretical results are compared with recent experimental data.
The critical concentration for single-ion-single-ion energy transfer in ruby is calculated using Anderson's method for transport between ions which are characterized by inhomogeneously broadened energy levels. The excitation on the chromium impurity is assumed to propagate by virtue of superexchange interactions. Using a continuum approximation, we find that the single-ion excitation is localized below concentrations of \ensuremath{\sim}0.3-0.4%, a range not inconsistent with that concentration at which a sudden change in the fluorescent lifetime of ruby occurs.
A rather simple method of determining the lifetimes of the excited states of exchange-coupled ion pairs in ruby is described. The technique utilizes a chopped pump light and phasesensitive detection. It has permitted a great increase in the resolution of optical transitions, and in particular, it allows for a virtual elimination of the vibronic sidebands of the RRR lines, in order that the true pair spectrum may stand out clearly. Furthermore, transitions originating from different excited levels may be definitely distinguished, thus aiding in the identification of particular transitions with a given pair type. The chronospectroscopic method is of potential value in the studies of energy-transfer mechanisms between single ions and pairs. It has also provided evidence for a fourth-neighbor absorption band at 6050 \AA{}.