Crystalline Field Splitting Research Articles

Isotopic Shift in the Electron-Spin-Resonance Absorption Spectrum ofCr3+in Magnesium Oxide

The fine and hyperfine structure spectra of trivalent ${\mathrm{Cr}}^{52}$ (I=0) and ${\mathrm{Cr}}^{53}(\mathrm{I}=\frac{3}{2})$ located substitutionally for magnesium in magnesium oxide at sites of axial symmetry, where the axial distortion is along a crystal [100] direction, have been re-examined at 3-cm wavelength. Spectral constants for both isotopes have been measured with a precision equivalent to determining absorption-line field positions to within \ifmmode\pm\else\textpm\fi{}10 mOe. From measurements taken at 77\ifmmode^\circ\else\textdegree\fi{}K, it is concluded that the crystalline-field splitting energy for ${\mathrm{Cr}}^{52}$ is (0.10\ifmmode\pm\else\textpm\fi{}0.01) Oe greater in magnitude than that for ${\mathrm{Cr}}^{53}$, which corresponds to a relative shift in this parameter of 1.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$. In addition, the components of the spectroscopic splitting tensor for the two isotopes are found to be the same to within the limits of experimental error. From data taken over the range 4.2 through 350\ifmmode^\circ\else\textdegree\fi{}K, it is found that the isotopic shift decreases with temperature while the crystalline-field splitting energy increases with temperature. The origin of the isotopic shift and its temperature dependence are discussed in terms of a dynamical crystal structure.

Spectrum of Trivalent Erbium Ion in the Matrix of Calcium Fluoride

In the following article the absorption and emission spectra of CaF2:Er3+ are presented, discussed, and analyzed phenomenologically. The crystalline states are listed and identified with the free ion quantum numbers by comparison with the states of erbium chloride. The oscillator strengths are determined from the absorbance spectrum and compared with the oscillator strengths reported in the literature. The study of the emission properties of the erbium ion in CaF2 includes identification of transition schemes for the major emission groups from their excitation spectra, measurements of relative intensities, decay times of fluorescence, and quantum efficiencies. The natural lifetimes and fluorescence yields were calculated using data obtained from the absorbance spectrum. By combining data obtained from the absorption and emission spectra at 77° and 4°K, the crystalline field splitting of the ground 4I15/2 multiplet was determined. The wavelengths of all emission lines at 77°K are presented, including those whose origin could not be identified. The effects of temperature and ion concentration are discussed. All pertinent data are given in a table form. The important features of the absorption and emission spectra are amply illustrated by figures, graphs, and tables. In addition to the purely spectroscopic properties of CaF2:Er3+, its properties as a potential laser material are considered and discussed. The discussion is complemented by calculation of the threshold power requirements.

Analysis of the Electronic Spectra of Neodymium Ethylsulfate

The polarized absorption spectra of single crystals of neodymium ethylsulfate [Nd(C2H5SO4)3·9H2O] have been studied between 11 000 cm—1 and 28 500 cm—1 at 77° and at 4.2°K. From the 77°K polarized absorption spectrum of crystals of different thicknesses, it is possible to identify transitions from all the Stark components of the ground level 4I9/2 to many of the Stark components of excited SLJ levels of the 4f3 configuration. The electronic transitions particularly of the 4I9/2 ground level are reliably singled out from among vibronic transitions. The experimental assignment based on selection rules and the number of transitions observed is further verified by a comparison of the experimental levels with the ``free-ion'' spectrum predicted on the basis of the parameters F2=331.33 cm—1, F4=47.956 cm—1, F6=5.313 cm—1, and ζ=880.11 cm—1. A first-order crystalline-field splitting calculation based on the parameters B20=58.4 cm—1, B40=—68.2 cm—1, B60=—42.7 cm—1, and B66=595 cm—1 gives a predicted splitting to within a mean deviation of 4 cm—1.

Spin-lattice relaxation in rare-earth salts

A general approach to spin-lattice relaxation is given for salts to which a crystalline field theory is appropriate. In particular, the theory of Elliott & Stevens for the interaction of a rare-earth ion with static ionic surroundings is generalized phenomenologically to represent the interaction of the rare-earth ion with the lattice vibrational modes. Evaluation of the spin-lattice interaction in terms of a few constants is possible. One- and two-phonon processes are investigated and the relaxation times for non-Kramers and Kramers salts computed. For the one-phonon (or direct) process the non-Kramers salts exhibit the typical behaviourT1∝H-2T-1, and the Kramers saltsT1∝H-4T-1. It is shown that, for a given Zeeman splitting of the ground doublet, the latter may exhibit an enormous anisotropy with respect to the direction of the external field, approximately proportional to the anisotropy of the temperature-independent part of the susceptibility. Application of the general theory is made to two salts, holmium and dysprosium ethyl sulphate; the former a non-Kramers, the latter a Kramers salt. It is shown that the dysprosium salt would be expected to show a relaxation time in the direct process region which will vary as sin-2θcos-2θH-4T-1, whereθis the angle the external magnetic field makes with the crystallographic symmetry axis. For two-phonon processes, the additional distinction of whether the Debye energy (KθD) is less than or greater than the crystalline field splitting Δ between the ground state and the first excited state must be made. Non-Kramers salts to which the former condition apply (KθD< Δ) are shown to possess two-phonon relaxation processes of the usual Raman type. The relaxation time is proportional toT-7and is independent of magnetic field. WhenKθD> Δ, there is present in addition a term arising from a resonance process, analogous to the resonance radiation effect in gases. Phonons of energy ~ Δ are absorbed and emitted by the spin system preferentially because of a phonon resonance with the crystalline field splitting of the spin states. As normallyKTis much less than Δ, this leads to a relaxation time proportional to exp (Δ/KT). This process will dominate the Raman process except at very high and low temperatures. It is shown to be significant right down to the liquid-helium range by comparison with the relaxation rate due to direct processes. Kramers salts, whenKθD< Δ, owing to a cancellation in the rate equation, exhibit a Raman relaxation time proportional toT-9and independent of field. This 'Van Vleck cancellation’ is shown to be a consequence of time reversal symmetry. WhenKθD> Δ, the resonance process is also present, the relaxation time again being proportional to exp (Δ/KT). The resonance process is now shown to be dominant down to 1 or 2 °K for many rare-earth salts. Experimental verification is found for the resonance relaxation process in the rare-earth ethyl sulphates. In general, it is expected that this mechanism will be significant for any magnetic salt in whichKθD> Δ.

Energy Levels of PrCl3

A review of the spectra of the Pr3+ ion in PrCl3 is presented and the spectra are reanalyzed by means of a more complete Hamiltonian than has been previously used. This new Hamiltonian includes a complete calculation of the crystalline field interaction for a field of D3h symmetry, and the first-order calculation of the orbit-orbit, mutual spin-orbit, and spin-spin interactions, as well as the usual spin-orbit and mutual electrostatic interactions. The multiplet splitting and crystalline field splitting are treated separately according to a least-squares procedure; the standard deviation of the center of gravity of the multiplets is 200 cm—1 without the orbit-orbit interaction and 105 cm—1 with the orbit-orbit interaction. The values of F2, F4, F6, ζ, and α are 305.4, 51.88, 5.321, 729.5, —, cm—1, respectively, in the first case, and 307.9, 50.23, 5.033, 755.1, —0.6542, cm—1, respectively, in the second case. The standard deviation of the calculation for 40 of the crystalline field levels is 7 cm—1. If the deviation of the 1D2 levels, which fit the calculation particularly badly, are not included, the standard deviation is then only 4 cm—1. The values of the crystalline field parameters are: A20 〈r2〉=47.26,A40 〈r4〉=−40.58,A60 〈r6〉=39.62,A66 〈r6〉=26.67 cm−1.

On the Theory of Spin-Lattice Relaxation in Paramagnetic Salts

A spin-Hamiltonian approach to the theory of spin-lattice relaxation in paramagnetic salts is developed in which the orbit-lattice interaction is treated as a perturbation connecting states of the overall spin-Hamiltonian. The approach is much simpler than previous treatments where the spin-orbit and Zeeman effects were treated as perturbations, and is applicable to a wide range of salts including both the iron group and the rare earth group. It is found that, for Kramers salts (ions with an odd number of electrons), many previous results apply quite generally, regardless of the relative size of the spin-orbit and crystalline field terms, but there are important exceptions. For the case of large crystalline field splittings, the relaxation rate (inverse of the relaxation time T1) varies as H4T and T9 for direct and Raman processes respectively, as Van Vleck has previously shown. The so-called Van Vleck cancellation leading to these dependences is derived in a very simple and quite general manner. For small crystal field splittings δ, less than, or of the order of, the lattice Debye temperature, the relaxation rate varies as H4T and a exp (-δ/kT)+bT9 for direct and Raman processes respectively. The two coefficients a and b are such that the T9 term is important only at low temperatures where the exponential term is quite small. These results are in marked contrast with earlier theories.

Preliminary Analysis of U4+ Ion Spectra in Crystals

An analysis of a number of features of the absorption spectra of U4+ ions in crystals is given. Absorption spectra of crystals of the compounds Cs2UCl6, and [N(CH3)4]2 UCl6, and to a lesser extent [N(C2H5)4]2 UCl6 have been studied at room temperature, liquid N2 and liquid He temperatures. The visible spectrum is essentially entirely vibronic. Pure electronic transitions are absent or very weak in thick crystals in agreement with a model of electric dipole transitions within the 5 f2 shell at an equilibrium site of inversion symmetry. We believe this to be the first demonstrated case of an essentially purely vibronic spectrum reported for rare earth or actinide salts. The three ``ungerade'' frequencies of the UCl6= complex are coupled to the electronic frequencies and are determined by their appearance with the same frequency of superposition in all three salts as well as by being the most intense of the vibronic lines in every group in which they appear. Other lattice modes and internal frequencies of the tetramethylammonium ion are also found to be superimposed. The weak pure electronic transitions are fairly sharp, an indication that there is still considerable shielding in the 5 fn electronic states even though this shielding is less than in 4 fn states. The independence of superimposed vibration frequencies on 5 f2 electronic states indicates the fact that the 5 f states do not contribute much to the binding. The similarity in the spectra of the three salts studied is due to the fact that the nearest-neighbor Cl— ions are the principal origin of the crystalline field in contrast to the rare earths, wherein this type of similarity is due to the fact that the crystalline field is small and each group of lines represents a multiplet level of the free ion. Evidence is presented that the crystalline field splitting is larger than hitherto believed and is the same order of magnitude as the spin-orbit interaction. Methods of attacking the problem of the experimental classification and calculation of energy levels in the situation in which three major interaction are of comparable size are discussed.

Pressure Dependence of the Paramagnetic Resonance Spectra of Two Dilute Chromium Salts

The pressure dependences of the spin-Hamiltonian parameters of trivalent chromium in ammonium aluminum alum and potassium cobalticyanide have been measured up to 10 000 kg/${\mathrm{cm}}^{2}$ near room temperature. In the case of the alum, runs have been made at 0, 24 and 50\ifmmode^\circ\else\textdegree\fi{}C. The $g$-value remains unchanged while the crystalline field splitting, $\ensuremath{\delta}$, increases by \ensuremath{\sim}30%, ${(\frac{\ensuremath{\partial}\ensuremath{\delta}}{\ensuremath{\partial}P})}_{T}$ decreasing with rising temperature and pressure.

Stress and Temperature Dependence of the Paramagnetic Resonance Spectrum of Nickel Fluosilicate

The crystalline field splitting of the ground state spin triplet of divalent nickel in the fluosilicate, NiSi${\mathrm{F}}_{6}$\ifmmode\cdot\else\textperiodcentered\fi{}6 ${\mathrm{H}}_{2}$O, has been measured at room temperature as a function of hydrostatic pressure to 10 000 kg/${\mathrm{cm}}^{2}$ and uniaxial stress to 150 kg/${\mathrm{cm}}^{2}$. The anisotropic compressibility and thermal expansion of this trigonal crystal have also been determined. Combining these data with the known variation of the splitting with temperature, its dependence on isothermal unit cell geometry and on temperature at constant unit cell dimensions is calculated. The splitting is found to be independent of volume within experimental error but proves to be quite sensitive to unit cell shape. The deduced explicit temperature dependence is three times larger than that measured at atmospheric pressure. The magnitude and geometrical variation of the crystalline field splitting may be qualitatively understood using a static, ionic model of the ${(\mathrm{N}\mathrm{i}\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}}6{\mathrm{H}}_{2}\mathrm{O})}^{2+}$ octahedral complex. A rather general analysis of the explicit temperature dependence indicates, however, that low-frequency lattice vibrations play a dominant role in determining the observed value of the splitting.The resonance line widths are observed to increase monotonically and quite nonlinearly with increasing pressure. This broadening is discussed in terms of isotropic and anisotropic exchange interactions. In agreement with earlier conclusions of Ollom and Van Vleck it is inferred that the two mechanisms are of comparable importance in this paramagnetic salt.

On the Magnetic Anisotropy in Manganese-Iron Spinels

The magnetic anisotropy energy is measured as a function of temperature in eleven single crystal compositions corresponding to MnxFe3−xO4, where x is varied from 0.00 to 1.90. The interesting features observed are as follows. (1) Small manganese concentrations in magnetite (x=0) are shown to decrease the temperature of the “isotropy point” known to exist in magnetite at low temperatures. (2) An unexpected variation in the temperature dependence and magnitude of the anisotropy energy in the x=0.4 to 1.0 composition region is shown. (3) The anisotropy energy in the composition region between x=1.0 and 1.8 is semiquantitatively shown to be related to cubic crystalline field splitting of the energy levels of ferric ions. (4) A large planar anisotropy is measured in a crystal composition given by x = 1.90 and is discussed in terms of the expected tetragonal nature of trivalent manganese. (5) Finally, a minute magnetic annealing effect at a temperature of 370°K has been shown to exist in a crystal composition corresponding to x=0.40 and the magnitude of this effect is shown to be dependent on the direction relative to the crystal axes of the applied magnetic field during the annealing process.

Magnetocrystalline Anisotropy of Mg–Fe Ferrites: Temperature Dependence, Ionic Distribution Effects, and the Crystalline Field Model

The magnetocrystalline anisotropy constant (K1) and saturation magnetization (Ms) of magnesium-iron ferrite monocrystals containing 6 to 50 mole percent magnetite were measured as a function of temperature (T) and ionic distribution. For crystals containing 6 to 25 mole percent magnetite, K1 was found to vary more rapidly with temperature when the ionic distribution in a crystal corresponds to a relatively high Ms than when it corresponds to a relatively low Ms in the same crystal. The observed changes in K1 resulting from alterations of the ionic distribution are shown to be consistent with a phenomenological one-ion anisotropy model. On this basis, the measurements yield a positive anisotropy for a ferric ion in a tetrahedral site (A) and a negative anisotropy for this ion in an octahedral site (B). Finally, the data obtained on one Mg-Fe ferrite crystal (containing 6 mole percent magnetite) were used in the Yosida-Tachiki anisotropy theory. The ferric ion cubic crystalline field splitting parameters aA and aB occurring in this theory were determined for two different states of ionic distribution in the crystal. It was found that aA = −0.0092 cm−1 and aB = +0.0232 cm−1 for the state corresponding to a relatively high Ms, and aA = −0.0135 cm−1 and aB = +0.0250 cm−1 for the state corresponding to a relatively low Ms. The theoretical anisotropy curves obtained by using these a values are in very good agreement with experiment. Furthermore, the aB values agree with aB = +0.0205 cm−1 determined by Low from paramagnetic resonance measurements on ferric ions in MgO.

Spin Relaxation Processes in a Two-Proton System

The general theory of nuclear spin relaxation, based on the Boltzmann transport equation for the density matrix, is applied to the very simple, nontrivial system of two identical spins $I=\frac{1}{2}$. A proton pair undergoing hindered rotation around one axis shows a resolvable doublet. The relaxation processes in this doublet are investigated. Explicit formulas for the longitudinal and transverse relaxation times are derived, which display a dependence on the angles of the axis of rotation with the external magnetic field and the radius vector. Experimental evidence for this dependence is discussed. General expressions for the Overhauser and saturation effects with two applied radio-frequency fields are given, which may also be applied to a magnetic ion or nucleus with $I=1$ and crystalline field splitting.

Adiabatic Demagnetization of Chromium Methylamine Alum

Adiabatic demagnetization experiments have been performed on a specimen of methylamine chromic alum, C${\mathrm{H}}_{3}$N${\mathrm{H}}_{3}$\ifmmode\cdot\else\textperiodcentered\fi{}Cr${(\mathrm{S}{\mathrm{O}}_{4}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}12${\mathrm{H}}_{2}$O, comprising a spherical mass of small crystals. Using fields up to 23 000 oersteds and starting temperatures of the order of 1.15\ifmmode^\circ\else\textdegree\fi{}K, the "free-spin" entropy of $R{log}_{e}4$ could be reduced to $0.26R$, and the magnetic susceptibility versus entropy relation has been obtained over this range of entropy. The susceptibility was measured at 210 cps with an ac mutual inductance bridge. For temperatures above 0.1\ifmmode^\circ\else\textdegree\fi{}K very good agreement is obtained between these results and the Hebb-Purcell theoretical curve with a value of 0.275\ifmmode^\circ\else\textdegree\fi{} (0.19 ${\mathrm{cm}}^{\ensuremath{-}1}$) for the crystalline field splitting of the ground level of the ${\mathrm{Cr}}^{+++}$ ion. In the neighborhood of entropy $R{log}_{e}2$ the susceptibility begins to increase rapidly and goes through a maximum at $S=0.53R$. As in the case of other paramagnetic alums previously investigated, ac losses occur in the region of maximum susceptibility (the loss component also showing a maximum), and ballistic measurements show hysteresis effects occurring on the low entropy side of the susceptibility maximum.

Paramagnetic Dispersion Measurements at 77.3°K

The dispersion of the magnetic susceptibility of some paramagnetic compounds of Fe, Mn, and Cr, was studied at 77.3\ifmmode^\circ\else\textdegree\fi{}K over a frequency range of 2 to 10 megacycles/sec. with magnetic fields up to 60,000 gauss. The results substantiate the theory of Casimir and du Pre, which is based upon the thermal coupling between the magnetic spin system and the lattice vibrations. The magnitude of the crystalline field splitting of the energy levels of the ground state was determined from the experimental results, for an assumed type of crystalline field and ionic arrangement. The splitting of chromic ammonium alum was found to differ from that of chromic potassium alum. The relaxation time for ferric ammonium alum was studied as a function of the magnetic field, and was found to fit an empirical formula which is based upon the theoretical conclusions of Van Vleck.