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Physical review. B, Solid state

Critical Concentration for Single-Ion-Single-Ion Energy Transfer in Ruby

S. K. Lyo

Published May 15, 1971• 71 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.3.3331

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Journal of Physics C Solid State Physics•Feb 14, 1977•0 citations
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.
The transfer of energy from single chromium ions to closely coupled pairs of chromium ions in ruby has been investigated. Ruby samples whose concentrations ranged from 0.003 to 1.0% Cr2{\mathrm{Cr}}_{2}Cr2​O3{\mathrm{O}}_{3}O3​ were prepared and in each crystal the intensity of single-ion fluorescence and of pair fluorescence was accurately measured. Radiative-decay measurements were also made in an attempt to unravel the dynamics of the transfer process. The transfer from single ions to pairs is shown to occur nonradiatively, and its efficiency is enhanced by a fast energy transfer between individual single ions. The possibility is explored that an electric quadrupole-quadrupole interaction is responsible for this transfer process.
The transfer of energy from single chromium ions to closely coupled pairs of chromium ions in ruby has been investigated. Ruby samples whose concentrations ranged from 0.003 to 1.0% Cr2{\mathrm{Cr}}_{2}Cr2​O3{\mathrm{O}}_{3}O3​ were prepared and in each crystal the intensity of single-ion fluorescence and of pair fluorescence was accurately measured. Radiative-decay measurements were also made in an attempt to unravel the dynamics of the transfer process. The transfer from single ions to pairs is shown to occur nonradiatively, and its efficiency is enhanced by a fast energy transfer between individual single ions. The possibility is explored that an electric quadrupole-quadrupole interaction is responsible for this transfer process.
The transfer of energy from single chromium ions to closely coupled pairs of chromium ions in ruby has been investigated. Ruby samples whose concentrations ranged from 0.003 to 1.0 percent Cr2O3were prepared and in each crystal the intensity of single-ion fluorescence and of pair fluorescence was accurately measured. Radiative decay measurements were also made in an attempt to unravel the dynamics of the transfer process. The transfer from single ions to pairs is shown to occur nonradiatively, and its efficiency is enhanced by a fast energy transfer between individual single ions. The possibility is explored that an electric quadrupole-quadrupole interaction is responsible for this transfer process.
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 process which results in enhanced pair fluorescence relative to single-ion fluorescence for ruby samples containing more than 0.2-wt% Cr3+{\mathrm{Cr}}^{3+}Cr3+ has been studied using microwave-optical double resonance. These experiments confirm that the enhancement is associated with energy transport among excited states of the system. However, the primary donor-level complex is not the normal ion excited state as postulated previously. Microwave-optical experiments indicate the existence of an additional excited level which is postulated to be the actual donor level. Evidence is presented which suggests that this additional level may be connected with exciton formation above a critical Cr3+{\mathrm{Cr}}^{3+}Cr3+ concentration.
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.