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The Journal of Chemical Physics

One-dimensional energy transfer in GdCl3

Rachid Mahiou, B. Jacquier, Christine Madej

Published Nov 1, 1988• 19 citations
Publisher

Abstract

We report the observation of the intrinsic fluorescence of anydrous gadolinium trichloride GdCl3 when laser light is absorbed into the first excited state 6P7/2. With the aid of a frequency doubled pulsed dye laser, we are able to analyze carefully the excitation and emission spectra as well as the decay times over a range of temperatures including that at which the material undergoes a ferromagnetic transition at 2.2 K. At 4.4 K and above, experiments at low excitation density (N0<1014 excited ions/cm3) show that the intrinsic and the impurity induced trap fluorescence dynamics are well described in terms of a fast diffusion and trapping model. When the excitation density is increased anti-Stokes fluorescences appear efficiently; they are assigned to the 6D9/2, 6I7/2→8S7/2 transitions. High excitation density effect on the intrinsic decay as well as the decay of the anti-Stokes fluorescence are nicely reproduced by a theoretical model involving mainly an exciton–exciton annihilation process. Moreover, an excited state absorption mechanism contributes notably to the anti-Stokes fluorescence intensity at t=0 with increasing the excitation density. In the ferromagnetic phase of GdCl3, at 1.5 K, the one-dimensional nature of the exciton diffusion (8S7/2↔6P7/2) is confirmed by the ‘‘incoherent’’ exciton decay analysis using an appropriate model recently developed by Cibert et al. Finally a diffusion length spreading over 2500 visited Gd3+ normal sites is evaluated, knowing the hopping time as a function of the nearest neighbor interactions (nn) in the crude approximation of an ideal two level system in a linear chain of atoms.

DOI
10.1063/1.455544

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Figure 6.1 Anti-Stokes fluorescence emission in a two-level system. Additionally, only a fraction of the absorbed photons result in excitation of coolant atoms. The rest are absorbed by background impurities. With the absorption coefficient of the coolant atoms designated by αc and that of the background by αb, the proportion of absorbed photons that contribute to cooling is h a c b( ) = + (6.3) If the assumption is made that phonon-mediated absorp-tion is proportional to the occupation probability of the phonon mode, namely n k T= (exp[ / ]-1)B -1W , the efficiency becomes h a a aabs c c b/( )= +n n . Then at high temperatures (kBT >> ħΩ)), ηabs varies little with temperature when the background absorp-tion is low (αb/αc << 1). On the other hand at low temperatures, as n Æ 0, ηabs decreases in proportion to n . Hence the absorption efficiency drops dramatically through the important cryogenic re-gime. The overall cooling is determined by the product of the various efficiency factors. h h h n n ËÁ ˆ ¯˜ (6.4) From Eqs. 6.1 and 6.4 it is easy to show that the cooling power density per unit frequency is Pc/V = ηabsηextαtotIv(vfi – v)/v. Here Iv= I0g(v) is the intensity per unit frequency and g(v) is a normalized spectral line shape function. V is the interaction volume. If the bandwidth of the light source equals the full linewidth 2Γ of the optical transition, and the density of atoms in the interaction volume is N/V, the energy loss rate per atom is R = 2ΓηcαtotIv(V/N) = ηcαtotI0(V/N) (6.5) The condition for net cooling can be expressed in a simple way based on Eq. 6.4, since ηc must exceed zero. By assuming that the laser detuning is optimized at the phonon frequency Ω, we can rewrite the numerator using hvft – hv = ħΩ. Furthermore the average phonon energy is ħΩ ≈ kBT near the boundary of the classical regime [15]. Then the condition for laser cooling (ηc > 0) becomes h h next abs B> -1 k T h (6.6) An important limitation of refrigeration based on anti-Stokes fluorescence emerges from this condition by determining the temperature at which the cooling efficiency drops to zero (ηc = 0). By solving Eq. 6.6 as an equality, it is found that a lower bound exists for the attainable temperature. The minimum temperature Tmin that can be reached with anti-Stokes cooling found from Eq. 6.6 is T h ( / ) ( ) ( / ) = + - + Ê ËÁ ˆ ¯˜ n a a h a a 1 (6.7) According to Eq. 6.7, if the quantum efficiency is high (next ≈ 1), the temperature limit for laser cooling by anti-Stokes emission is primarily determined by the frequency of light and the background-to-resonant-absorption ratio. The dependence on these two factors arises because heat input to the system is proportional to incident photon energy and absorptive heating efficiency. Only when the background absorption coefficient vanishes could arbitrarily low temperatures be reached. For the moderate levels of background absorption encountered in practice in solids, this places a severe constraint on temperatures that can be reached by laser cooling. As a simple example of this, the anti-Stokes cooling limit predicted by Eq. 6.7 at a wavelength of 1 micron is Tmin = 145.3 K when the external quantum efficiency is ηext = 0.90 and background absorption coefficient is αb = αc/1000. The lower bound on attainable temperatures can be interpreted in another way. It arises because the cooling rate depends on phonon occupation, a factor that diminishes as temperature decreases. Eventually the rate of anti-Stokes cooling drops below the rate of heating from background impurity absorption and cooling is no longer possible [16]. For 3D refrigeration of solids to be as effective as laser cooling of gases, techniques capable of maintaining high rates of cooling through the cryogenic temperature range are needed. This is discussed further in what follows. In the remainder of this chapter momentum is incorporated into the discussion to investigate whether the fundamental temperature limitation of anti-Stokes fluorescence cooling can be evaded when the dynamics are viewed comprehensively. Judging from the successes of laser cooling of gases, cooling schemes that conserve momentum and energy simultaneously during optical interactions are the most efficient. Yet momentum is disregarded in the anti-Stokes fluorescence method. Other techniques may offer the capability of balancing the momentum and energy requirements more consistently to accommodate phonon dispersion (Fig. 6.2).

Pan Stanford Publishing eBooks•Aug 31, 2016•0 citations
We report the observation of the intrinsic fluorescence of anydrous gadolinium trichloride GdCl3 when laser light is absorbed into the first excited state 6P7/2. With the aid of a frequency doubled pulsed dye laser, we are able to analyze carefully the excitation and emission spectra as well as the decay times over a range of temperatures including that at which the material undergoes a ferromagnetic transition at 2.2 K. At 4.4 K and above, experiments at low excitation density (N0<1014 excited ions/cm3) show that the intrinsic and the impurity induced trap fluorescence dynamics are well described in terms of a fast diffusion and trapping model. When the excitation density is increased anti-Stokes fluorescences appear efficiently; they are assigned to the 6D9/2, 6I7/2→8S7/2 transitions. High excitation density effect on the intrinsic decay as well as the decay of the anti-Stokes fluorescence are nicely reproduced by a theoretical model involving mainly an exciton–exciton annihilation process. Moreover, an excited state absorption mechanism contributes notably to the anti-Stokes fluorescence intensity at t=0 with increasing the excitation density. In the ferromagnetic phase of GdCl3, at 1.5 K, the one-dimensional nature of the exciton diffusion (8S7/2↔6P7/2) is confirmed by the ‘‘incoherent’’ exciton decay analysis using an appropriate model recently developed by Cibert et al. Finally a diffusion length spreading over 2500 visited Gd3+ normal sites is evaluated, knowing the hopping time as a function of the nearest neighbor interactions (nn) in the crude approximation of an ideal two level system in a linear chain of atoms.
Observation by fluorescence of direct two photon absorption within the 8S7/2→6P7/2 transition of the Gd3+ ion following excitation with a pulse dye laser is reported. The whole fluorescence spectra correlate well with the ones obtained from the one UV photon absorption. However excitation spectra exhibits a linenarrowing compare to the OPA and an observable shift when decreasing the temperature from 4.4 K down to the ferromagnetic order below Tc = 2.2 K. At these temperatures, exciton decay exhibits a non exponential behaviour which can be only treated as a sum of two expoentials in disagreament with the OPA measurements.
Fluorescence de nagdf::(4), k::(2)gdf::(5), gdcl::(3). Excitation selective dans l'ultraviolet (excitation a 1 photon) ou dans le rouge (excitation a 2 photons) d'une des composantes stark du multiplet **(6)p::(7/2) de gd**(3+). Le declin de la fluorescence entre 4,4k et la temperature ambiante permet de determiner le mode de diffusion de l'energie d'excitation. Effet de la densite d'excitation. Mise en evidence d'une fluorescence anti-stokes issue des niveaux **(6)g::(7/2), **(6)d::(3/2) et **(6)i::(7/2). Effet d'un champ magnetique
Blue ($^{5}D_{4}\ensuremath{\rightarrow}^{7}F_{6}$) as well as uv anti-Stokes ($^{5}D_{3}\ensuremath{\rightarrow}^{7}F_{6}$) fluorescences are observed in TbF3{\mathrm{F}}_{3}F3​ at low temperature when the 5D4^{5}D_{4}5D4​ Stark components of the Tb3+{\mathrm{Tb}}^{3+}Tb3+ active ions are excited. In addition, when the 5D4^{5}D_{4}5D4​ exciton density is high enough, holes appear in the center of each excitation line of the visible emission, and in the corresponding absorption spectrum as well. Fluorescence dynamics and intensities are then studied for increasing pump powers. These properties are expressed as combinations of exciton-exciton annihilation and cross-relaxation processes. Saturation effects on both intrinsic and perturbed Tb3+{\mathrm{Tb}}^{3+}Tb3+ ions are discussed.
We report the observation of a magnon sideband in the 6P7/2 ⇐ 8S7/2 optical absorption spectrum of Gd+3 in the ferromagnetic insulator GdCl3. The transition energy and its dependence on magnetic field demonstrate this to arise from the simultaneous excitation of a magnon and optical exciton. The decrease in its intensity with increasing magnetic field suggest the source of its intensity is directly connected with the zero‐point spin deviations which occur in a ferromagnet possessing significant magnetic dipolar interactions. The magnitude of the intensity is shown to be consistent with a single‐ion transition mechanism which because of the zero‐point spin deviations allows a small probability for a double‐excitation process. This transition mechanism is distinct from that responsible for the previously observed magnon sidebands in the transition‐metal magnetic insulators.
Figure 6.1 Anti-Stokes fluorescence emission in a two-level system. Additionally, only a fraction of the absorbed photons result in excitation of coolant atoms. The rest are absorbed by background impurities. With the absorption coefficient of the coolant atoms designated by αc and that of the background by αb, the proportion of absorbed photons that contribute to cooling is h a c b( ) = + (6.3) If the assumption is made that phonon-mediated absorp-tion is proportional to the occupation probability of the phonon mode, namely n k T= (exp[ / ]-1)B -1W , the efficiency becomes h a a aabs c c b/( )= +n n . Then at high temperatures (kBT >> ħΩ)), ηabs varies little with temperature when the background absorp-tion is low (αb/αc << 1). On the other hand at low temperatures, as n Æ 0, ηabs decreases in proportion to n . Hence the absorption efficiency drops dramatically through the important cryogenic re-gime. The overall cooling is determined by the product of the various efficiency factors. h h h n n ËÁ ˆ ¯˜ (6.4) From Eqs. 6.1 and 6.4 it is easy to show that the cooling power density per unit frequency is Pc/V = ηabsηextαtotIv(vfi – v)/v. Here Iv= I0g(v) is the intensity per unit frequency and g(v) is a normalized spectral line shape function. V is the interaction volume. If the bandwidth of the light source equals the full linewidth 2Γ of the optical transition, and the density of atoms in the interaction volume is N/V, the energy loss rate per atom is R = 2ΓηcαtotIv(V/N) = ηcαtotI0(V/N) (6.5) The condition for net cooling can be expressed in a simple way based on Eq. 6.4, since ηc must exceed zero. By assuming that the laser detuning is optimized at the phonon frequency Ω, we can rewrite the numerator using hvft – hv = ħΩ. Furthermore the average phonon energy is ħΩ ≈ kBT near the boundary of the classical regime [15]. Then the condition for laser cooling (ηc > 0) becomes h h next abs B> -1 k T h (6.6) An important limitation of refrigeration based on anti-Stokes fluorescence emerges from this condition by determining the temperature at which the cooling efficiency drops to zero (ηc = 0). By solving Eq. 6.6 as an equality, it is found that a lower bound exists for the attainable temperature. The minimum temperature Tmin that can be reached with anti-Stokes cooling found from Eq. 6.6 is T h ( / ) ( ) ( / ) = + - + Ê ËÁ ˆ ¯˜ n a a h a a 1 (6.7) According to Eq. 6.7, if the quantum efficiency is high (next ≈ 1), the temperature limit for laser cooling by anti-Stokes emission is primarily determined by the frequency of light and the background-to-resonant-absorption ratio. The dependence on these two factors arises because heat input to the system is proportional to incident photon energy and absorptive heating efficiency. Only when the background absorption coefficient vanishes could arbitrarily low temperatures be reached. For the moderate levels of background absorption encountered in practice in solids, this places a severe constraint on temperatures that can be reached by laser cooling. As a simple example of this, the anti-Stokes cooling limit predicted by Eq. 6.7 at a wavelength of 1 micron is Tmin = 145.3 K when the external quantum efficiency is ηext = 0.90 and background absorption coefficient is αb = αc/1000. The lower bound on attainable temperatures can be interpreted in another way. It arises because the cooling rate depends on phonon occupation, a factor that diminishes as temperature decreases. Eventually the rate of anti-Stokes cooling drops below the rate of heating from background impurity absorption and cooling is no longer possible [16]. For 3D refrigeration of solids to be as effective as laser cooling of gases, techniques capable of maintaining high rates of cooling through the cryogenic temperature range are needed. This is discussed further in what follows. In the remainder of this chapter momentum is incorporated into the discussion to investigate whether the fundamental temperature limitation of anti-Stokes fluorescence cooling can be evaded when the dynamics are viewed comprehensively. Judging from the successes of laser cooling of gases, cooling schemes that conserve momentum and energy simultaneously during optical interactions are the most efficient. Yet momentum is disregarded in the anti-Stokes fluorescence method. Other techniques may offer the capability of balancing the momentum and energy requirements more consistently to accommodate phonon dispersion (Fig. 6.2).