Rare Earth Ions In Solids Research Articles

Observation of sub-kilohertz resonance in Rf-optical double resonance experiment in rare earth ions in solids

We have observed kilohertz and sub-kilohertz resonance structures in RF-optical double resonance experiments of rare-earth-doped solids, when the frequency of the RF field is scanned across the hyperfine transitions while monitoring the resonant optical absorption of a CW laser. The effect is observed only when the laser spectral width is broad compared to the hyperfine structure. The observed line widths are apparently free of the inhomogeneous widths of hyperfine levels and the line shape has peculiar double peak structure. The effect is modelled with a resonance involving three atomic levels interacting with three electromagnetic fields, two optical and one RF, in a triangular or “delta’ configuration. While the ordinary optical-RF two-field resonance is limited by spin inhomogeneous width, the simultaneous excitation of three coupled transitions leads to narrow and highly nonlinear resonance structures that are not averaged by the inhomogeneous distribution of hyperfine transition.

Branching ratios, cross sections, and radiative lifetimes of rare earth ions in solids: Application to Tm3+ and Ho3+ ions in LiYF4

The measurement of branching ratios, cross sections and radiative lifetimes for rare earth ions in solids is considered. The methods are applied to Tm and Ho in YLF as a test case. De-activation rates for electric dipole and magnetic dipole emission are calculated for many of the lower lying manifolds in Tm:YLF and Ho:YLF in the context of the Judd-Ofelt theory to determine radiative lifetimes. Measured values for the branching ratios as well as the absorption and emission cross sections are also presented for many of the excited state manifolds. From these measurements, a methodology is developed to extract measured values for the radiative lifetimes. These results are compared with the Judd-Ofelt theory as a guide for consistency and for determining the accuracy of the Judd-Ofelt theory in predicting branching ratios and radiative lifetimes. The parameters generated by the methods covered here have potential applications for more accurate modeling of Tm:Ho laser systems.

Excitation effects in non-radiative multiphonon decays of rare earth doped laser materials

The non-radiative decay process of rare earth ions in solids, which are known to constitute a whole class of laser materials, has been considered up to now to be independent of excitation intensity. We shall show here that the multiphonon non-radiative decay probabilities of rare earth ions in glasses are reduced at high excitation state densities for the larger energy gaps. The classical exponential energy gap law is shown to ‘rotate’ at higher excitation around the 3.2-phonon point. The observed effect is described in term of a spatial saturation of the accepting mode term with effective diffusion lengths ranging between 54 and 20 Å for excited state density from 10 17 to 10 19 cm −3. This effect which is predicted to be general for multiphonon processes at large gives hints for the obtention of laser effects from otherwise non-radiative transitions provided the excitation density is sufficient to allow the coupling between ions through a common phonon diffusion volume.

Bottleneck in multiphonon nonradiative transitions

The nonradiative decay process of rare-earth ions in solids has been considered up to now to be independent of excitation intensity. In this paper we show that the multiphonon nonradiative decay probabilities of rare-earth ions in a germanate glass are reduced at high excitation state densities for the larger energy gaps. The classical exponential energy gap law is shown to 'rotate' at higher excitation around the 3.2-phonon point. The observed effect is described in terms of a spatial saturation of the accepting mode term with an effective diffusion length ranging between 45 and 20 \AA{} for excited state density from 2\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 8\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ at an active ion concentration of 2.5\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.

Temperature and energy gap dependence of energy transfer between rare-earth ions in solids

In this paper we develop a model to explain the temperature dependence of energy transfer between rare-earth ions for situations in which the energy gap is small. When the gap is large, and many phonons are required the transfer rate follows the well-known exponential law. When just a few phonons are required, however, the temperature dependence may be quite different, and may even be more efficient at low temperatures; this is shown to be the case of Er to Ho transfer in YAG. We show that for small energy gaps, the redistribution of the ions with temperature may be a driving factor in the transfer. As the number of phonons increases, this redistribution becomes less important and the exponential law emerges.

On the temperature dependence of the rate of energy transfer between rare earth ions in solids

Abstract We have conducted a number of experiments in order to ascertain the temperature dependence of the rate of energy transfer between rare earth ions in solids. The mechanism of such dependence is peculiar to each donoracceptor pair. We report typical examples and point to some criteria that emerge from our studies.

Determination of oscillator strengths in Pr 3+:YAlO 3 by Raman heterodyne and hole burning spectroscopy

The energy separation of several MHz between the nuclear spin substates of rare-earth ions in solids considerably exceeds the homogeneous width of the optical resonance lines, which is typically a few kHz. High-resolution laser experiments like coherent Raman scattering or hole burning experiments, however, can easily resolve optical transitions between individual nuclear spin states. Here, we discuss the calculation and experimental verification of the relative oscillator strengths for all possible transitions between the nuclear spin substates of the 3H 4 ground state and 1D 2 excited state of Pr 3+ : YAlO 3 The oscillator strengths depend on the relative orientation of the quantization axes of the eigenstates in the ground and excited state. We determine the tensor orientation from the orientation dependence of the nuclear magnetic resonance (NMR) spectra, using Raman heterodyne detection and we use spectral hole burning to assign the orientations to the two nonequivalent lattice sites of the Pr 3+ ions in the host lattice.

Submillimetre EPR spectrometer

A wide-band submillimetre EPR spectrometer is described. A set of tunable backward wave oscillators and quasioptic lens system enables one to operate in the frequency region 79–535 GHz. The sample is placed in a magnetic field of up to 1 T at 4.2 K. The spectrometer is intended for the investigation of EPR spectra of rare-earth ions in solids with zero field splittings of the ground states near the frequency of operation and/or electron systems with ag-factor exceeding 5. The spectrometer’s capabilities are demonstrated with an investigation of the EPR spectra of Dy2+ and Dy3+ ions in CaF2. As a result the exact value of the zero field splitting between the ground Γ8 quartet and the first exited Γ7 doublet of Dy3+ in CaF2, Δ=257±0.5 GHz, has been measured directly.

RADIATIVE ENERGY TRANSFER AND "NON-NATURAL" EXCITATION IN THE QUANTUM EFFICIENCY DETERMINATION OF 1.55 µm Er3+ EMISSION IN SILICA FIBERS

One of the most usual way to determine quantum efficiency of Rare Earth ions in solids is to compute the radiative lifetime (τo) of the considered level through Judd's theory and to measure the emission decay time (τ) ; the ratio τ/τo being the desired quantum efficiency. By such way the quantum efficiency of Er3+ at 1.55 µm in silica fibers is estimated to be 100% [1]. However a number of pitfalls can be encountered [2] in such determination, namely radiative energy transfer and non-natural excitation linked with crystal field splittings. The purpose of this paper is to show that, taking such effects into account, Er3+ efficiency at 1.55 µm is found to be much less in silica fiber than usually accepted. We show that quantum efficiency of Er3+ in silica fibers should range between 30 to 45% instead of the 100% usually believed.

On the correlation between energy structure and the mechanism of recombination for rare earth ions in solids

An efficient mechanism of rare earth (RE) intra-ion excitation due to nonradiative bound exciton (BE) recombination is discussed. We first show that some RE ions, those which can change their charge state, bind excitons. RE bound excitons recombine nonradiatively due to the impurity Auger effect, i.e. energy transfer to core states, which results in core excitation, followed by an intra-ion emission. The correlation between the energy structure of an RE-BE system and the recombination mechanism is discussed from examples of Eu, Yb and Sm impurities in ZnS, and Eu in Ca xCd 1−xF 2 crystals.

Enhancement of the second-order Judd-Ofelt transition rates for high-lying (4f) states

The Judd-Ofelt approximation to the forced electric dipole transition strengths has been used with considerable success to model the sharp intra-configurational (4f)n-(4f)n spectra of rare earth ions in solids. However, discrepancies are observed when the model is applied to the highest lying (4f)n states. We describe here a modification of the standard second order Judd-Ofelt theory which allows us to calculate the enhanced transition rates in cases where one state is close to the perturbing band. When mixing with one configuration dominates, our theory requires no new adjustable parameters; both the enhanced even parameters and a new set of odd parameters can be calculated from the three even Judd-Ofelt parameters determined by fitting the transition rates between the low-lying states. Our theory is able to account for the transition rates we observe from the (4f)2 1S0 state of Pr3+ : LaF3 (just below the 4f5d band), without resort to third or fourth order configurational interaction terms.

Complete second-order calculations of intensity parameters for one-photon and two-photon transitions of rare-earth ions in solids

Biorthogonal perturbation methods originally developed for lanthanide crystal-field calculations are applied to 4f-4f electric dipole transition intensities for the system Pr3+-Cl-. The results confirm earlier suggestions that ligand polarization contributions are crucial to understanding the relative signs of the intensity parameters. They also show that ‘covalent’ or ‘charge transfer’ excitations from occupied ligand states to 4f orbitals give significant contributions. Our calculations are also applied to two-photon absorption and electronic Raman scattering amplitudes. The major second-order contribution to these processes comes from excitations from 4f to 5d orbitals.

A study of excited state dynamics of rare earth ions in solids by coherent transients and spectral holeburning

Barriers to spectral resolution imposed by instrumental limits and inhomogeneous broadening can often be removed by linear and nonlinear laser spectroscopy. This is illustrated by the case of LaF 3:Pr 3+. Six orders of magnitude increase in resolution has been demonstrated, and this uncovered new mechanisms for optical dephasing such as coupling to nuclear spin fluctuations. The importance of the time-scale of the experimental probe is stressed, and the information obtained from spectral holeburning and coherent transients can be very different. This was found in CaF 2:Pr 3+ where the fluorine nuclear spin-flips exhibit a wide range of time-scales.

Electronic matrix elements in the radiationless relaxation theory of rare-earth ions in solids

The first-order approximate expressions for the electronic matrix elements in the radiationless relaxation theory of rare-earth ions in solids are given. The non-radiative effects of ligand vibrations and the forbiddenness of non-radiative transitions in some special cases are described.

Optical Spectra of Transparent Rare Earth Compounds

S Hufner 1978 New York: Academic xi + 237 pp price £15.60 Many excellent monographs on the spectra of dilute rare earth ions in solids have been produced during the past 20 years, a point which has not escaped the author of this monograph, which treads roughly the same path, though here and there different aspects are presented. The theoretical introduction is standard in its progression from a compact package of free ion theory into that for the crystal field.

Crystal-field parameters of PrCl3using the multiple-scattering-Xαmethod

The multiple-scattering-Xalpha method is used to calculate the crystal-field parameters for Pr3+:LaCl3. The necessity of using more than one Watson sphere for highly charged clusters is discussed. The calculation shows that this multiple-scattering-Xalpha method can be applied successfully to the description of crystal-field effects in rare-earth ions in solids.

Radiationless relaxation of rare-earth ions in solids: Phenomenological effects of f→f and f→d transitions and the origin of multiphonon relaxation in first-order perturbation theory

In this paper, the phenomenological effects of d→f and f→f processes are examined. The relationship between radiationless multiphonon decay and excitation processes is obtained in terms of the first-order adiabatic relaxation theory. A detailed analysis is given of the experimentally observed temperature dependence of the lifetimes and intensities of Sm2+ 5D0 fluorescence in KCl and SrF2. From this analysis, rate constants for the nonradiative d?5D0 processes are evaluated. The observed characteristics of radiationless f→f and f→d relaxation processes are compared in terms of the theoretical dependence of the rate constant on the energy gap, on temperature, and on the frequencies of the phonon modes of the host crystals. The main features of the first-order relaxation theory are compared with those of an earlier high-order treatment in the crude Born–Oppenheimer approximation. The role of potential-surface displacements (signifying coupling strengths) in the first-order perturbation treatment of multiphonon relaxation is discussed. It is shown that in the zero-displacements limit, the first-order multiphonon rate constant is identically zero. In this limit, multiphonon processes can only arise from high-order terms in the perturbation expansion.

Theory of Zeeman effect for rare earth ions in crystal field with D2 symmetry and application to rare earth garnets

Rare earth ions in solids frequently exhibit sharp-line optical spectra. In this paper a part of the theory of the Zeeman effect for the lines is developed, first for a single rare earth ion in D2 symmetry, and secondly for rare earth ions at different inequivalent sites in garnet crystals. The results for the case in which the crystal field and Zeeman splittings are comparable have application for magnetic garnets such as the rare earth iron garnets, while the results for the case where the Zeeman splittings are treated as a perturbation on the crystal field states have application for nonmagnetic garnets such as the rare earth aluminum or gallium garnets. In both cases it is found that when the magnetic field is restricted to the xy plane of the local site coordinate, there exists an antiunitary symmetry operation which simplifies the energy level and transition probability calculations, and which leads to the assignment of a quantum number ζ = ± 1 to the states. There are shown to be two types of states: Type A, for which the assignment of ζ value is not sensitive to the choice of coordinate axes, and Type B states for which it is. It is also shown, in the case of rare earth ions with an odd number of 4f electrons, that the Types of the states are determined by the relative signs of the principal values of the g factors. Furthermore, it is found that the dependence of line intensity on magnetic field direction for A→A and B→B transitions is clearly different from that of A→B and B→A transitions. Finally, and most important, it is shown that studies of the energies and intensities of the Zeeman lines as a function of magnetic field direction in suitable crystal planes can be used to distinguish between spectra arising from different inequivalent rare earth ion sites in garnets. This result has immediate importance for experimental study of site selectivity problems in garnets, and, when combined with the other conclusions of this work, leads to definite suggestions for experimental determinations of at least some of the details of the states.

Faraday Rotation of Rare-Earth Ions. I. Theory

A general expression for the complex Faraday rotation is obtained by generalizing the Kramers-Heisenberg dispersion formula. It shows that the pure rotation is proportional to the sum of circular dichroism in in all resonance transitions weighted by the appropriate resonance-dispersion factors. The cases of free ions and rare-earth ions in solids are discussed. It is shown how ${\mathrm{Gd}}^{3+}$ and ${\mathrm{Eu}}^{2+}$, having the same electronic structure, may possess very different rotatory powers in a given frequency range through the difference in their optical spectra. The formula for the anomalous rotatory dispersion about sharp lines is also given.