Ion-phonon Interaction Research Articles

Judd-Ofelt analysis and temperature dependent upconversion luminescence of Er3+/Yb3+ codoped Gd2(MoO4)3 phosphor

Although lanthanide doped luminescent materials have been extensively investigated, a quantitative analysis of how temperature affects upconversion luminescence is still incomplete. The Gd2(MoO4)3:Er3+/Yb3+ phosphor is synthetized by sol-gel method. Based on the absorption spectra of Er3+ ions, J-O intensity parameters and radiative transition probabilities are computed to estimate the optical properties. In view of ion-phonon interaction, the phonon-assisted energy transfer and multiphonon relaxation are responsible for the temperature dependent luminescence. Additionally, cross relaxation probability for 4I11/2+4I11/2→4I15/2+4F7/2 is determined to be 240s−1 through quantitative simulation of ion-ion interaction. These meaningful results are of vital values for the field of laser crystal and optical temperature sensing.

Effects of 946-nm thermal shift and broadening on Nd3+:YAG laser performance**Project supported by Estahban Branch, Islamic Azad University.

Spectroscopic properties of flashlamp pumped Nd3+:YAG laser are studied as a function of temperature in a range from −30 °C to 60 °C. The spectral width and shift of quasi three-level 946.0-nm inter-Stark emission within the respective intermanifold transitions of 4F3/2 → 4I9/2 are investigated. The 946.0-nm line shifts toward the shorter wavelength and broadens. In addition, the threshold power and slope efficiency of the 946.0-nm laser line are quantified with temperature. The lower the temperature, the lower the threshold power is and the higher the slope efficiency of the 946.0-nm laser line is, thus the higher the laser output is. This phenomenon is attributed to the ion-phonon interaction and the thermal population in the ground state.

导带弯曲对有限深GaN/Ga1-xAlxN球形量子点中束缚极化子的影响及其压力效应

采用三角势近似界面导带弯曲,研究了有限高势垒GaN/Ga1-x Al x N球形量子点中束缚极化子的结合能及其压力效应。数值计算了杂质态与声子之间相互作用对结合能的影响,同时与方形势垒进行了比较。结果表明,随着电子面密度的增加,导带弯曲效应增强,束缚极化子结合能逐渐下降。当电子面密度n s=(6.0,8.0)×1011/cm2且量子点半径R>10 nm时,束缚极化子的结合能趋近于一个相同且较小的值。结合能的极化效应主要来自杂质与光学声子相互作用的贡献。

The phonon effects on the impurity states in cylindrical quantum wire with a finite confining potential

Abstract The variational method and the effective mass approximation are applied to calculate the binding energies of the hydrogenic impurity states in a cylindrical quantum wire with finite deep potential well. The phonon effects on the impurity states are considered by taking both the couplings of the electron–phonon and the impurity ion–phonon into account. The numerical results for the GaAs cylindrical quantum wire are given and discussed. It is found that the ion–phonon interaction reduces the impurity binding energy and supplies key contribution to the energy shift, but the electron–phonon coupling enhances the binding energy less. Longitudinal optical (LO) phonons play more important role than interface optical (IO) phonons in the impurity potential screening. The polaron effect caused by LO phonons is more important when the wire is thinner, otherwise the LO phonons are dominant for the thicker wires.

Analysis of f-element multiphonon vibronic spectra

Theoretical modeling of multi-phonon vibronic spectra is presented based on the Huang–Rhys theory of ion–phonon interaction in a single-mode lattice. The single-mode spectral function is modified for applications to vibronic spectra involving multiple vibrational modes. It is shown that, for lanthanide and actinide ions in crystals, f–d electronic transitions exhibit two types of vibronic couplings. One type of vibronic coupling to local and pseudo-local modes obeys Frank–Condon selection rules and has a sharp line width, whereas in the second type of vibronic coupling electronic transitions couple to lattice modes in which selectivity is absent, thus forming a broad vibronic band. The model calculation reproduces very well the experimental spectra of 5f–6d transitions of Pa 4+ in Cs 2ZrCl 6 and 4f–5d transitions of Ce 3+ in Cs 2NaYCl 6.

On the Physical Nature of Uranyl Charge Transfer Vibronic Interactions

ABSTRACTWe address the electronic properties of uranyl ions in solids and solutions with an emphasis in theoretical understanding of charge transfer vibronic transitions and luminescence dynamics the O-U-O species. A general theory of ion-phonon interaction has been modified for modeling and simulating multi-phonon vibronic spectra. Spectroscopic data for uranyl ions in crystals and solutions have been analyzed to achieve a predictive understanding of the uranyl-ligand vibronic interactions. By adjusting the Huang-Rhys ion-phonon interaction parameters, an excellent agreement between theory and experiment has been accomplished for uranyl ions in the ligand environments we studied. Our modeling and simulation provide insights into the physical nature of uranyl vibronic interaction and its influence on spectroscopic properties, which are commonly utilized in characterizing photochemical properties of uranyl in complexes.

On the origin of anti-Stokes laser-induced cooling of Yb3+-doped glass

Abstract Anti-Stokes cooling between room temperature and 77 K in a new fluorochloride glass (CNBZn) doped with 1 mol% of YbF 3 has been demonstrated by using collinear photothermal deflection and conventional laser excitation spectroscopies under high photon irradiances. The cooling efficiency of CNBZn glass which is ∼2.0% relative to the absorbed laser power at 1010 nm and 300 K falls by about 20% at 77 K. A model accounting for the photon–ion–phonon interaction is in good agreement with the observed temperature dependence of the cooling process and shows its relation with the vibrational properties of the material.

Frequency Dependent Ion Hopping Based on Lattice Gas Model

The coupled phonon-lattice gas model is used to calculate the frequency dependent hopping rate of mobile ions in superionic conductors. It is found that the hopping rate is composed of several Gaussians including both contributions of the ion-phonon and ion-ion interactions. The calculated hopping rate is compared with the far infra-red conductivity for silver halides, AgI, AgCl and AgBr.

Phonon effects on sharp luminescence lines of Nd 3+ in Gd 3Sc 2Ga 3O 12 garnet (GSGG)

The widths, positions and shapes of sharp luminescence lines of the Nd 3+ ion in GSGG:Cr 3+, Nd 3+ were measured carefully from 78 to 600 K. The sharp lines studied correspond to the R 2 → Y 1, R 2 → Y 1, R 2 → Y 3, R 1 → Y 2, R 2 → Y 6, R 1 → Y 6 and R 1 → Z 5 transitions. All the lines shift to the red with increasing temperature except for the R 1 → Z 5 line which shifts to the blue. The temperature dependence of line widths and line shifts is explained in terms of an ion-phonon interaction as a perturbation and of a Debye phonon distribution. The Debye temperature is treated as an adjustable parameter to get the best fit to the experiment data. The line widths are related to Raman scattering of phonons, direct phonon processes and statistical local strain of the crystal. The line shifts are due to the stationary effect of the ion-phonon interaction. The Debye temperature of GSGG is estimated to be 500 K through the fittings of the theoretical formulas to the experimental data.

Angular momentum states for phonons and a rotationally invariant development of lattice dynamics

It is shown that the rotationally invariant harmonic model provides a realistic zero-order phonon bases for crystals and that it can also be used for molecules of three or more atoms (the triatomic molecule must be linear). A simple way to introduce the harmonic and anharmonic lattice potential coefficients if given for a rotationally invariant force system. It is then shown that all the phonons of this model may be organised exactly into sharp angular momentum states. The phonon angular momentum operator is given. Then the harmonic model is used to show how, in perturbation treatments of internal and external interactions, the correct tensorial transformation and symmetry properties are always obtained, whereas in the standard treatment they are usually hidden (lost?) and arbitrarily (and not necessarily correctly) imposed on the final result. It is also shown how the basis can provide a direct approach to the crystal symmetry conditions in the treatment of ion-phonon interactions and it is shown how to obtain a new simple selection rule for the direct process of ion-phonon transitions for the special values of the wavevector in the Brillouin zone. The application of this method can be expected to lead to more new results in such processes.

Investigation of four-wave mixing inNdxLa1−xP5O14

Four-wave mixing has been investigated in ${\mathrm{Nd}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{P}}_{5}{\mathrm{O}}_{14}$ crystals as a function of temperature, laser excitation wavelength, and power. The results are interpreted in terms of scattering from a population grating, and the relative intensity of the scattered signal is investigated as well as the grating decay time. The power dependence of the scattered intensity is explained by a model involving interaction with a three-level system, and the properties of the grating decay are associated with the exciton dynamics of the ions in the excited state. Decay patterns characteristic of both incoherent and partially coherent exciton migration can be observed under different experimental conditions. Enhanced migration due to vibronic generation of phonons resonant with the metastable state splitting is also observed. The temperature dependence of the results shows a weak coupling between the excitions and the acoustic phonons of the host. Local heating effects are found to affect the ion-ion and ion-phonon interaction parameters and produce a thermal grating under certain experimental conditions.

Mössbauer spectra in the presence of spin-phonon relaxation effects: Symmetry restrictions

The problem of evaluating the M\"ossbauer line shape in the presence of ion-phonon interactions has been considered. By means of a perturbation procedure it is shown how a limited number of matrix elements of the relaxation operator are relevant. Moreover, the restrictions imposed by the symmetry are also taken into account. In the case of ${\mathrm{Fe}}^{3+}$ in ${C}_{3}$ symmetry one has to diagonalize a 288\ifmmode\times\else\texttimes\fi{}288 matrix. By taking into account the results obtained in this paper we have reduced the problem of deriving the line shape of the M\"ossbauer spectrum to that of diagonalizing three matrices of dimensions 16, 16, and 15.

Experimental study of the optical analogue of the Mossbauer effect: Effect of the temperature on the no-phonon line of cobalt impurity luminescence in II-VI compounds

Luminescence spectra due to the 4T2 ( Gamma 8phi ) to 4A2 ( Gamma 8) no-phonon crystal-field transition are analysed in ZnS, ZnSe, ZnTe, CdTe and CdS doped with cobalt. The no-phonon line intensity, extrapolated to 0K, ranges from 0.020 (for CdTe:Co) to 0.24 (for ZnS:Co) of the total luminescence intensity. The effect of temperature on the intensity f and position Omega of the no-phonon line is interpreted according to McCumber's model of the ion-phonon interaction. The numerical value of the quadratic coupling constant alpha h(cross) ranges from 4.5*10-2 cm-1 (for ZnS:Co) to 4.4*10-1 cm-1 (for ZnTe:Co), being greater for systems with smaller f values. However, the effect of temperature on the luminescence line halfwidth 2 Gamma could not be explained within the framework of the McCumber model. Numerical analysis of the experimental data was also made in the Debye approximation. In this model the thermal dependence of f and Omega was reproduced with values of the Debye temperature by some 20-30% lower than those characteristic of pure crystals.

Microwave phonon attenuation in rare-earth garnets: Ion-phonon interactions

Significant deviations from the behavior usual for dielectrics are observed in the ultrasonic attenuation at gigahertz frequencies in Nd, Gd, and Tb garnets and are attributed to the rare-earth ions. Relaxation of low-lying electron states by Orbach processes satisfactorily explains attenuation peaks in neodymium gallium garnet and terbium scandium aluminum garnet near 60 K. Below 20 K the attenuation in all these garnets, irrespective of electronic structure, increases as the inverse of temperature and the square of frequency. Mechanisms that could explain these results based on the relaxation of low-lying states are proposed. The lack of knowledge about the parameters entering the theoretical models prevents a detailed comparison with experiment at this time.

Virtual-phonon exchange (VPE) in rare-earth ethyl sulfates

In recent years it has been shown that two paramagnetic ions could be coupled together by the virtual emission of a phonon at one site and its subsequent re-absorption at another site (1-4). This (~virtual-phonon exchange ~ (VPE) is analogous to photon exchange, which leads to the Coulomb interaction between charged particles (5). Recently the origin of nondipolar interactions between rare-earth ions in ethyl sulfates has been at tr ibuted to this mechanism (r However, numerical estimates based on Orbach's procedure (7) for estimating the ion-phonon interaction parameters lead to results which are three order of magnitude smaller than the experimental data (s,~). A more thorough and detailed calculation of the individual contributions to VPE in terms of the normal co-ordinates of the complex surrounding the paramagnetie ion has been presented (~o). Preliminary results seem to indicate that, at least in the case of Tb 3+, Ce 3+ in the ethyl sulfates, the observed departures from dipolar interactions arc due to VPE. In order to check the general validity of this result a systematic investigation was undertaken for all rare-earth ions for which experimental data were available. We start from a system composed of two ions in a crystal lattice each having a doubly-degenerate ground state. The zeroth-order states of the two-ion system have the form IA> ~ la(ll, a(2)> = la(1)> | la(2)>, where ]a(~> denotes one of the two wave functions [• of the ground doublet of the paramagnetic ion number s. The eigenstates of the whole system, ions plus phonon field, have the form

Ion-phonon interactions in paramagnetic crystals

Ion-phonon interactions in paramagnetic crystals

Validity of the Weisskopf-Wigner linewidth-lifetime relation for spectral lines broadened by phonon interaction

Abrikosov's form of a Wick theorem for spin operators is used to construct a diagrammatic expansion of the line shape in terms of the ion-phonon interaction. The Weisskopf-Wigner relation (the width of a spectral line is related to the sum of the inverse lifetimes of the states before and after the photon interaction) is valid provided all terms apart from the first in the Bethe- Saltpetre equation for the relevant two particle Green function are neglected. The neglected terms, which violate the relation, correspond to linewidth contributions from ion-phonon interaction such that there is no net transfer on energy between the ion and the lattice. This is proved for all orders of perturbation theory and for anharmonic as well as harmonic ion-phonon coupling.

Isotope Shift in theRLines of Chromium in Ruby and MgO

At 4.2\ifmmode^\circ\else\textdegree\fi{}K the $R$ lines of chromium in ruby and in MgO exhibit an isotope shift of 0.13 and 0.17 ${\mathrm{cm}}^{\ensuremath{-}1}$ per unit mass, respectively. This is a much larger value than is found for free atoms of intermediate mass. We consider the possibility that this isotope shift is caused by the interaction of the ion with the vibrating lattice. The ion-phonon interaction causes a frequency shift in these $R$ lines, and this shift depends on the amplitude of vibration of the chromium ion. The lighter chromium isotopes, however, have a larger amplitude of vibration than the heavier isotopes, and consequently the frequency shift varies from isotope to isotope. This leads to an isotope shift. For the $R$ lines of ruby and MgO: ${\mathrm{Cr}}^{3+}$ the isotope shift due to the interaction with the zero-point vibrations is calculated, and is in very good agreement with the experimental values, both in magnitude and direction.