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Physical review. B, Condensed matter

Optical detection and phonon bottleneck of the direct decay within the E¯(E2) state of ruby

J. I. Dijkhuis, K. Huibregtse, H. W. de Wijn

Published Sep 1, 1979• 19 citations
Publisher

Abstract

Direct relaxation within the optically excited $\overline{E}(^{2}E)$ level of 700-ppm ruby is investigated in magnetic fields up to 65 kG making an angle to the $c$ axis. At low pump intensities, the experimental relaxation rates are found to be in excellent agreement with the theory by Blume et al., predicting a fifth-power dependence on field and a ${cos}^{3}\ensuremath{\theta}{sin}^{2}\ensuremath{\theta}$ dependence on orientation. The observed proportionality constant of 4.7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}19}$ ${\mathrm{G}}^{\ensuremath{-}5}$${\mathrm{s}}^{\ensuremath{-}1}$ is close to the theoretical estimate based on static experiments in ruby. When increasing optical pumping, the phonon-bath conduction is demonstrated to become the limiting process due to resonant trapping of the phonons. Following pulsed excitation, a prolonging of the decay time by a factor up to 13 is attained at excited-state concentrations ${N}^{*}\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. In stationary experiments, a nonlinear increase with ${N}^{*}$ is observed of the equilibrium population of the upper Zeeman level of $\overline{E}$ to over a decade above the nonbottlenecked value, corresponding to bottlenecking factors of over \ensuremath{\sim}200. Under the assumption of a constant phonon lifetime of the order of the flight time through the illuminated region, rate equations appear to consistently account for the experiments. A Gaussian-type resonance line, fully homogenized supposedly by magnetic interactions with the surrounding Al nuclei and ${\mathrm{Cr}}^{3+}$ ions, explains the lattice-bath equilibration. Finally, the prospect is discussed of using the $\overline{E}$ direct transition in ruby as a tunable phonon generator and detector with bandwidth 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$ in the practical frequency range of 2-15 ${\mathrm{cm}}^{\ensuremath{-}1}$.

DOI
10.1103/physrevb.20.1835

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Diffusion of bottlenecked 29- cm−1 phonons in optically excited ruby

J. I. Dijkhuis, H. W. de Wijn

Spatial and, additionally, spectral diffusion of 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonons trapped in an excited cylindrical region with diameter \ensuremath{\sim}0.1 mm has been investigated under continuous optical pumping of ruby. For 130- and 700-ppm ruby, phonon decay strictly limited by spatial diffusion is reflected in a quadratic dependence of the bottlenecking factor $\ensuremath{\sigma}$ on the excited-state concentration ${N}^{*}$ up to ${N}^{*}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. At higher ${N}^{*}$, attainable in 700- and 2500-ppm ruby, the observed reduction of $\ensuremath{\sigma}$ relative to the second-power dependence, as well as the increased width of the dependence of $\ensuremath{\sigma}$ on magnetic field, reveal that spectral diffusion from inhomogeneous packet to packet is operative. In the spatially diffusive regime, evidence for Zeeman-induced spectral diffusion is found in a characteristic narrowing of the magnetic-field dependence of the ${R}_{2}$ fluorescence upon raising $\ensuremath{\sigma}$. At full separation of the Zeeman transitions $2\overline{A}(^{2}E)\ensuremath{\leftrightarrow}\overline{E}(^{2}E)$, $\ensuremath{\sigma}$ is reduced to 15-40% relative to zero field, depending on ${N}^{*}$ and ground-state concentration. Rate equations governing the ${\mathrm{Cr}}^{3+}$ populations in the two-level scheme ($2\overline{A}$,$\overline{E}$) with inclusion of spatial diffusion and anharmonic decay of the phonons account for the second-power dependence. Diffusive phonon decay turns out to dominate from ${N}^{*}R\ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}{10}^{13}/{\mathrm{cm}}^{2}$ up to at least ${N}^{*}{R}^{2}\ensuremath{\sim}{10}^{14}/\mathrm{cm}$, with $R$ the characteristic dimension of the excited region. Spectral diffusion, treated as a perturbation, satisfactorily fits the data at higher $\ensuremath{\sigma}$, yielding a diffusive step of \ensuremath{\sim}2% of the linewidth. At low bottlenecking, the functional form of the magnetic field dependence of $\ensuremath{\sigma}$, including its width and level at full separation, is closely described by use of rate equations, taking the line shape to be Gaussian-type, and assuming the phonons associated with spin flip and those with non spin flip to belong to distinct classes.

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The population ratio $\frac{{N}_{\ensuremath{-}}}{{N}_{+}}$ of the Zeeman states of $\overline{E}(^{2}E)$ has been measured over five decades of metastable-state concentrations ${N}_{\ensuremath{-}}$ in 2500-ppm ruby at 28 kG and 1.5 K, i.e., in the absence of thermalization between ${\overline{E}}_{\ifmmode\pm\else\textpm\fi{}}$. Upon raising the pumping, $\frac{{N}_{\ensuremath{-}}}{{N}_{+}}$ falls below the value corresponding to optical feeding only due to optically induced two-phonon processes via $2\overline{A}(^{2}E)$. Rate equations account for the findings under the assumption of marginal (ballistic regime) or moderate (spatially diffusive regime) trapping of these 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonons. At high pumping, $\frac{{N}_{\ensuremath{-}}}{{N}_{+}}$ further drops to unity, reflecting disturbance of the Boltzmann equilibrium within the $^{4}A_{2}$ ground state.

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Relaxation of 29- cm−1 phonons in ruby

Ronald Goossens, J. I. Dijkhuis, H. W. de Wijn

The relaxation of resonant 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons trapped in a laser-excited cylinder of submillimeter diameter is investigated under the conditions of modulated pumping in ruby of 130, 700, and 2500 at. ppm ${\mathrm{Cr}}^{3+}$ at 1.5 K. The decay time ${T}_{\mathrm{eff}}$ of the 2\ifmmode \bar{A}\else \={A}\fi{}${(\mathrm{}}^{2}$E) population, which is a measure of the phonon relaxation time, appears to depend on the metastable population ${N}^{\mathrm{*}}$ and the cylinder diameter L as the product ${N}^{\mathrm{*}}$L only, establishing boundary-limited phonon decay. At ${N}^{\mathrm{*}}$L below 5\ifmmode\times\else\texttimes\fi{}${10}^{15}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, pure spatial diffusion prevails.At higher ${N}^{\mathrm{*}}$L, where the measured ${T}_{\mathrm{eff}}$ levels off at about 1 \ensuremath{\mu}s, dependent on the ground-state concentration, the phonon relaxation is adequately accounted for by the assumption of enhancement by mediation of frequency-shifting Orbach processes at metastable ${\mathrm{Cr}}^{3+}$ subject to diagonal exchange with ground-state ${\mathrm{Cr}}^{3+}$. Shifts away from resonance to the extent that the phonons escape the zone by ballistic flight are considered active, which predominantly involve distant ${\mathrm{Cr}}^{3+}$ neighbors.Furthermore, a random distribution of ${\mathrm{Cr}}^{3+}$ is assumed, while the exchange is calibrated with reference to pair spectra. The spin-nonflip transitions of metastable ${\mathrm{Cr}}^{3+}$ that are part of the pairs remain at resonance with the phonons because the exchange splittings of \ifmmode \bar{E}\else \={E}\fi{}${(\mathrm{}}^{2}$E) and 2\ifmmode \bar{A}\else \={A}\fi{}${(\mathrm{}}^{2}$E) are comparable. This is borne out by a separate calculation based on a perturbative molecular field. In addition, experiments have been performed as a function of an external magnetic field up to 4 T parallel to the c axis to disclose the effects of successive separation of the spin-flip and spin-nonflip transitions. The resultant complex development of ${T}_{\mathrm{eff}}$ with field as well as similar data on the ${R}_{2}$ luminescent intensity taken with continuous optical pumping are consistent with exchange-invoked relaxation and, further, yield effective spectral widths of the 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ transitions of the weakly coupled metastable ${\mathrm{Cr}}^{3+}$ of order 1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.

Physical review. B, Condensed matter•Dec 1, 1985•22 citations

Optically Induced Magnetization in Ruby

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The magnetization of ruby in a magnetic field at 300\ifmmode^\circ\else\textdegree\fi{}K is changed when the ruby is optically pumped with linearly polarized radiation from a $Q$-switched ruby laser. With a magnetic field parallel to the trigonal axis, laser light polarized parallel to this axis induces transitions from the spin \ifmmode\pm\else\textpm\fi{}\textonehalf{} levels of the $^{4}A_{2}$ ground state to the levels of the $\overline{E}(^{2}E)$ excited state. The change in ${M}_{z}$ is linearly proportional to $H$ except near the anticrossing points of the $^{4}A_{2}$ spin levels at 2.07 and 4.14 kG. At these field strengths, there is an enhancement of the magnetization caused by state mixing of the $^{4}A_{2}$ wave functions. When $H$ has a small component perpendicular to the $z$ axis, a magnetization is detected parallel to this component in the vicinity of 4.14 kG. The effect requires a long ground-state relaxation time. In a separate experiment, the relaxation of ${M}_{z}$ was found to vary from 0.13 \ensuremath{\mu}sec in zero magnetic field to a constant value of 0.57 \ensuremath{\mu}sec for fields above 60 G.

Physical Review•May 17, 1965•57 citations

Optically Induced Magnetization in Ruby

Takahiko Tamaki, 国郎 対馬

A time varying macroscopic magnetization of ruby is observed at room temperature by selectively exciting the Cr 3+ ions with a right- and a left circularly polarized light of a Q -switched ruby laser from one of the ground 4 A 2 multiplets to a proper component of the upper \bar E ( 2 E ) multiplets. Dependence of such a magnetization in the Z -direction on the irradiation power, the ellipticity and the magnetic field was measured with a pick-up coil. The signal had a value of 1.7×10 -4 emu/g at the irradiation of 67 mJ. The relaxation time of the ground state was estimated from the decay to be about 180 ns in zero magnetic field. The signal changed with the ellipticity of the exciting light, and the amplitude of the signal was always proportional to the intensity of the excitation. These experimental results were quantitatively explained by a theoretical analysis for the time varying optically induced magnetization.

Journal of the Physical Society of Japan•Jul 1, 1978•5 citations

Spectral Width of Optically Generated Bottlenecked 29- cm−1 Phonons in Ruby

J. I. Dijkhuis, A. van der Pol, H. W. de Wijn

The ruby ${R}_{2}$-line intensity at 2.1 K is observed to be nearly quadratically depedent on the ${R}_{1}$ intensity, indicative of strongly bottlenecked 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonons generated by the $2\overline{A}(^{2}E)\ensuremath{\rightarrow}\overline{E}(^{2}E)$ decay in the optical pumping cycle. The spectral width of the phonon excitation is probed by separating the degenerate phonon packets in a magnetic field and monitoring the decrease of the bottlenecking.

Physical Review Letters•Dec 6, 1976•53 citations
Direct relaxation within the optically excited E‾(2E)\overline{E}(^{2}E)E(2E) level of 700-ppm ruby is investigated in magnetic fields up to 65 kG making an angle to the ccc axis. At low pump intensities, the experimental relaxation rates are found to be in excellent agreement with the theory by Blume et al., predicting a fifth-power dependence on field and a cos3\ensuremathθsin2\ensuremathθ{cos}^{3}\ensuremath{\theta}{sin}^{2}\ensuremath{\theta}cos3\ensuremathθsin2\ensuremathθ dependence on orientation. The observed proportionality constant of 4.7 \ifmmode\times\else\texttimes\fi{} 10\ensuremath−19{10}^{\ensuremath{-}19}10\ensuremath−19 {\mathrm{G}}^{\ensuremath{-}5}$${\mathrm{s}}^{\ensuremath{-}1} is close to the theoretical estimate based on static experiments in ruby. When increasing optical pumping, the phonon-bath conduction is demonstrated to become the limiting process due to resonant trapping of the phonons. Following pulsed excitation, a prolonging of the decay time by a factor up to 13 is attained at excited-state concentrations N∗\ensuremath∼2\ifmmode×\else\texttimes\fi1017/cm3{N}^{*}\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}N∗\ensuremath∼2\ifmmode×\else\texttimes\fi1017/cm3. In stationary experiments, a nonlinear increase with N∗{N}^{*}N∗ is observed of the equilibrium population of the upper Zeeman level of E‾\overline{E}E to over a decade above the nonbottlenecked value, corresponding to bottlenecking factors of over \ensuremath{\sim}200. Under the assumption of a constant phonon lifetime of the order of the flight time through the illuminated region, rate equations appear to consistently account for the experiments. A Gaussian-type resonance line, fully homogenized supposedly by magnetic interactions with the surrounding Al nuclei and Cr3+{\mathrm{Cr}}^{3+}Cr3+ ions, explains the lattice-bath equilibration. Finally, the prospect is discussed of using the E‾\overline{E}E direct transition in ruby as a tunable phonon generator and detector with bandwidth 0.002 cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1 in the practical frequency range of 2-15 cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1.
Spatial and, additionally, spectral diffusion of 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonons trapped in an excited cylindrical region with diameter \ensuremath{\sim}0.1 mm has been investigated under continuous optical pumping of ruby. For 130- and 700-ppm ruby, phonon decay strictly limited by spatial diffusion is reflected in a quadratic dependence of the bottlenecking factor $\ensuremath{\sigma}$ on the excited-state concentration N∗{N}^{*}N∗ up to ${N}^{*}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. At higher N∗{N}^{*}N∗, attainable in 700- and 2500-ppm ruby, the observed reduction of $\ensuremath{\sigma}$ relative to the second-power dependence, as well as the increased width of the dependence of $\ensuremath{\sigma}$ on magnetic field, reveal that spectral diffusion from inhomogeneous packet to packet is operative. In the spatially diffusive regime, evidence for Zeeman-induced spectral diffusion is found in a characteristic narrowing of the magnetic-field dependence of the R2{R}_{2}R2​ fluorescence upon raising $\ensuremath{\sigma}$. At full separation of the Zeeman transitions $2\overline{A}(^{2}E)\ensuremath{\leftrightarrow}\overline{E}(^{2}E)$, $\ensuremath{\sigma}$ is reduced to 15-40% relative to zero field, depending on N∗{N}^{*}N∗ and ground-state concentration. Rate equations governing the Cr3+{\mathrm{Cr}}^{3+}Cr3+ populations in the two-level scheme (2A‾2\overline{A}2A,E‾\overline{E}E) with inclusion of spatial diffusion and anharmonic decay of the phonons account for the second-power dependence. Diffusive phonon decay turns out to dominate from ${N}^{*}R\ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}{10}^{13}/{\mathrm{cm}}^{2}$ up to at least ${N}^{*}{R}^{2}\ensuremath{\sim}{10}^{14}/\mathrm{cm}$, with RRR the characteristic dimension of the excited region. Spectral diffusion, treated as a perturbation, satisfactorily fits the data at higher $\ensuremath{\sigma}$, yielding a diffusive step of \ensuremath{\sim}2% of the linewidth. At low bottlenecking, the functional form of the magnetic field dependence of $\ensuremath{\sigma}$, including its width and level at full separation, is closely described by use of rate equations, taking the line shape to be Gaussian-type, and assuming the phonons associated with spin flip and those with non spin flip to belong to distinct classes.
The population ratio $\frac{{N}_{\ensuremath{-}}}{{N}_{+}}$ of the Zeeman states of E‾(2E)\overline{E}(^{2}E)E(2E) has been measured over five decades of metastable-state concentrations ${N}_{\ensuremath{-}}$ in 2500-ppm ruby at 28 kG and 1.5 K, i.e., in the absence of thermalization between ${\overline{E}}_{\ifmmode\pm\else\textpm\fi{}}$. Upon raising the pumping, $\frac{{N}_{\ensuremath{-}}}{{N}_{+}}$ falls below the value corresponding to optical feeding only due to optically induced two-phonon processes via 2A‾(2E)2\overline{A}(^{2}E)2A(2E). Rate equations account for the findings under the assumption of marginal (ballistic regime) or moderate (spatially diffusive regime) trapping of these 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonons. At high pumping, $\frac{{N}_{\ensuremath{-}}}{{N}_{+}}$ further drops to unity, reflecting disturbance of the Boltzmann equilibrium within the 4A2^{4}A_{2}4A2​ ground state.
The relaxation of resonant 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons trapped in a laser-excited cylinder of submillimeter diameter is investigated under the conditions of modulated pumping in ruby of 130, 700, and 2500 at. ppm Cr3+{\mathrm{Cr}}^{3+}Cr3+ at 1.5 K. The decay time Teff{T}_{\mathrm{eff}}Teff​ of the 2\ifmmode \bar{A}\else \={A}\fi{}(2{(\mathrm{}}^{2}(2E) population, which is a measure of the phonon relaxation time, appears to depend on the metastable population N∗{N}^{\mathrm{*}}N∗ and the cylinder diameter L as the product N∗{N}^{\mathrm{*}}N∗L only, establishing boundary-limited phonon decay. At N∗{N}^{\mathrm{*}}N∗L below 5\ifmmode\times\else\texttimes\fi{}1015{10}^{15}1015 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, pure spatial diffusion prevails.At higher N∗{N}^{\mathrm{*}}N∗L, where the measured Teff{T}_{\mathrm{eff}}Teff​ levels off at about 1 \ensuremath{\mu}s, dependent on the ground-state concentration, the phonon relaxation is adequately accounted for by the assumption of enhancement by mediation of frequency-shifting Orbach processes at metastable Cr3+{\mathrm{Cr}}^{3+}Cr3+ subject to diagonal exchange with ground-state Cr3+{\mathrm{Cr}}^{3+}Cr3+. Shifts away from resonance to the extent that the phonons escape the zone by ballistic flight are considered active, which predominantly involve distant Cr3+{\mathrm{Cr}}^{3+}Cr3+ neighbors.Furthermore, a random distribution of Cr3+{\mathrm{Cr}}^{3+}Cr3+ is assumed, while the exchange is calibrated with reference to pair spectra. The spin-nonflip transitions of metastable Cr3+{\mathrm{Cr}}^{3+}Cr3+ that are part of the pairs remain at resonance with the phonons because the exchange splittings of \ifmmode \bar{E}\else \={E}\fi{}(2{(\mathrm{}}^{2}(2E) and 2\ifmmode \bar{A}\else \={A}\fi{}(2{(\mathrm{}}^{2}(2E) are comparable. This is borne out by a separate calculation based on a perturbative molecular field. In addition, experiments have been performed as a function of an external magnetic field up to 4 T parallel to the c axis to disclose the effects of successive separation of the spin-flip and spin-nonflip transitions. The resultant complex development of Teff{T}_{\mathrm{eff}}Teff​ with field as well as similar data on the R2{R}_{2}R2​ luminescent intensity taken with continuous optical pumping are consistent with exchange-invoked relaxation and, further, yield effective spectral widths of the 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ transitions of the weakly coupled metastable Cr3+{\mathrm{Cr}}^{3+}Cr3+ of order 1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.
The magnetization of ruby in a magnetic field at 300\ifmmode^\circ\else\textdegree\fi{}K is changed when the ruby is optically pumped with linearly polarized radiation from a QQQ-switched ruby laser. With a magnetic field parallel to the trigonal axis, laser light polarized parallel to this axis induces transitions from the spin \ifmmode\pm\else\textpm\fi{}\textonehalf{} levels of the 4A2^{4}A_{2}4A2​ ground state to the levels of the E‾(2E)\overline{E}(^{2}E)E(2E) excited state. The change in Mz{M}_{z}Mz​ is linearly proportional to HHH except near the anticrossing points of the 4A2^{4}A_{2}4A2​ spin levels at 2.07 and 4.14 kG. At these field strengths, there is an enhancement of the magnetization caused by state mixing of the 4A2^{4}A_{2}4A2​ wave functions. When HHH has a small component perpendicular to the zzz axis, a magnetization is detected parallel to this component in the vicinity of 4.14 kG. The effect requires a long ground-state relaxation time. In a separate experiment, the relaxation of Mz{M}_{z}Mz​ was found to vary from 0.13 \ensuremath{\mu}sec in zero magnetic field to a constant value of 0.57 \ensuremath{\mu}sec for fields above 60 G.
A time varying macroscopic magnetization of ruby is observed at room temperature by selectively exciting the Cr 3+ ions with a right- and a left circularly polarized light of a Q -switched ruby laser from one of the ground 4 A 2 multiplets to a proper component of the upper \bar E ( 2 E ) multiplets. Dependence of such a magnetization in the Z -direction on the irradiation power, the ellipticity and the magnetic field was measured with a pick-up coil. The signal had a value of 1.7×10 -4 emu/g at the irradiation of 67 mJ. The relaxation time of the ground state was estimated from the decay to be about 180 ns in zero magnetic field. The signal changed with the ellipticity of the exciting light, and the amplitude of the signal was always proportional to the intensity of the excitation. These experimental results were quantitatively explained by a theoretical analysis for the time varying optically induced magnetization.
The ruby R2{R}_{2}R2​-line intensity at 2.1 K is observed to be nearly quadratically depedent on the R1{R}_{1}R1​ intensity, indicative of strongly bottlenecked 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonons generated by the $2\overline{A}(^{2}E)\ensuremath{\rightarrow}\overline{E}(^{2}E)$ decay in the optical pumping cycle. The spectral width of the phonon excitation is probed by separating the degenerate phonon packets in a magnetic field and monitoring the decrease of the bottlenecking.