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The electron-paramagnetic-resonance spectra of 1% ${\mathrm{Ce}}^{3+}$, 1% ${\mathrm{Yb}}^{3+}$, 0.1% ${\mathrm{Er}}^{3+}$, and 1% ${\mathrm{Nd}}^{3+}$ in Pr${\mathrm{F}}_{3}$ were observed at 4.2 \ifmmode^\circ\else\textdegree\fi{}K. The $g$ factors are found to be ${g}_{x}=0.39\ifmmode\pm\else\textpm\fi{}0.03$, ${g}_{y}=0.946\ifmmode\pm\else\textpm\fi{}0.002$, ${g}_{z}=2.69\ifmmode\pm\else\textpm\fi{}0.02$, $\ensuremath{\theta}=15.{5}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}0.{5}^{\ensuremath{\circ}}$ for ${\mathrm{Ce}}^{3+}$; ${g}_{x}=2.801\ifmmode\pm\else\textpm\fi{}0.015$, ${g}_{y}=4.48\ifmmode\pm\else\textpm\fi{}0.03$, ${g}_{z}=11.36\ifmmode\pm\else\textpm\fi{}0.20$, $\ensuremath{\theta}=41.{5}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}{1}^{\ensuremath{\circ}}$ for ${\mathrm{Er}}^{3+}$; ${g}_{x}=3.47\ifmmode\pm\else\textpm\fi{}0.03$, ${g}_{y}=5.427\ifmmode\pm\else\textpm\fi{}0.03$, ${g}_{z}=1.205\ifmmode\pm\else\textpm\fi{}0.01$, $\ensuremath{\theta}={9}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}{1}^{\ensuremath{\circ}}$ for ${\mathrm{Yb}}^{3+}$; and ${g}_{x}=1.500\ifmmode\pm\else\textpm\fi{}0.005$, ${g}_{y}=1.094\ifmmode\pm\else\textpm\fi{}0.003$, ${g}_{z}=2.937\ifmmode\pm\else\textpm\fi{}0.017$, $\ensuremath{\theta}={67}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}{2}^{\ensuremath{\circ}}$ for ${\mathrm{Nd}}^{3+}$. The $y$ axis is chosen in the plane perpendicular to the $c$ axis. The other orthogonal axes show no clear relation to the crystal faces, the $z$ axis being rotated $\ensuremath{\theta}$ degrees from the $c$ axis. The hyperfine splitting due to ${\mathrm{Er}}^{167}$ of 47\ifmmode\pm\else\textpm\fi{}3 G and due to ${\mathrm{Yb}}^{171}$ of 577\ifmmode\pm\else\textpm\fi{}10 G were observed in the $y$-axis spectra. The spin-bath relaxation rates ${T}_{b}^{\ensuremath{-}1}$ for these same trivalent rare earths PrF were observed in the temperature range $1.3lTl4.5$ \ifmmode^\circ\else\textdegree\fi{}K at frequencies \ensuremath{\sim}8.9 GHz. The ${\mathrm{Nd}}^{3+}$ data were fitted by ${T}_{b}^{\ensuremath{-}1}=2.85T+0.214\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}{T}^{9}+0.378\ifmmode\times\else\texttimes\fi{}{10}^{11}{e}^{\frac{\ensuremath{-}61.5}{T}}$ ($c$ axis); the ${\mathrm{Er}}^{3+}$ data by ${T}_{b}^{\ensuremath{-}1}=143T+0.125\ifmmode\times\else\texttimes\fi{}{10}^{10}{e}^{\frac{\ensuremath{-}56.4}{T}}$ ($x$ axis showing a strong cross-relaxation first term; the ${\mathrm{Ce}}^{3+}$ data by ${T}_{b}^{\ensuremath{-}1}=0.753T+0.276\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}{T}^{9}+0.171\ifmmode\times\else\texttimes\fi{}{10}^{11}{e}^{\frac{\ensuremath{-}78.3}{T}}$ ($c$ axis) where an Orbach term $\ensuremath{\propto}{e}^{\frac{\ensuremath{-}95}{T}}$ may also be added, possibly indicating relaxation via the first excited level of ${\mathrm{Pr}}^{3+}$; and the ${\mathrm{Yb}}^{3+}$ data by single terms proportional to ${T}^{2}$, which is probably due to cross relaxation to pairs.

The orbit-lattice interaction has been used to explain the temperature-dependent crystal-field parameter b 4 of Eu ++ in CaF 2 and SrF 2 . By admixing the excited 4 f 6 n s configuration, this theory is successful in explaining the temperature dependence of b 4 , but the theoretical estimate in the magnitude dependence is about a factor 10 3 smaller than the observed value. The covalency is believed to be the main source of this discrepancy. It is also shown that in the point-charge approximation, the effect due to thermal expansion is too small to account for the measured temperature-dependent part of b 4 .

Hyperfine structure splittings for the M = − ½ → ½ transition of trivalent gadolinium in single crystal thorium oxide have been measured from 1.25 to 350 K. The temperature dependence of these splittings is interpreted in terms of a modified Simanek-Orbach theory.

The projection operator is used to derive the collective coordinates of vibration for the molecular cluster XY3Z6 (nine nearest-neighbor oxygens surrounding a rare-earth ion) having C3h symmetry in the rare-earth ethyl sulphates. Group theory shows that the purely vibrational modes transform as 4A′ + 4A″ + 5E′ + 3E″ (in the notation of Eyring, Walter and Kimball). When the symmetry of the XY3Z6 molecular cluster belongs to the point group D3h, the appropriate collective coordinates of vibration can be easily obtained from the coordinates with C3h symmetry.

The projection operator and an alternative method are used to derive symmetrical normal coordinates of the XY8 cluster having cubic coordination. The first method uses the fact that the projection operator picks out from an arbitrary displacement the part lying in any particular subspace. The second method makes use of the orbit-lattice interaction based on the point-charge model, V 01 = ∑ t ∂Vc ∂Qt O Q t and the behavior of the spherical harmonics which are involved in Vc)o under the cubic transformation in order to pick out the symmetrical normal coordinates from the orbit-lattice interaction.

The Van Vleck orbit-lattice interaction appropriate for the trigonal X Y 3 Z 6 molecular cluster transforming as D 3 h has been computed from the collective coordinates. The comparison of this interaction with the approximations made by Orbach and the Berkeley group is also made. This interaction has been applied to estimate the spin-lattice relaxation times for Ce 3+ and Sm 3+ in lanthanum ethyl sulfate and in yttrium ethyl sulfate, and Dy 3+ in dysprosium ethyl sulfate. The agreement between the estimated relaxation rates and the data is quite acceptable. In addition, the exponential term with Δ =72 K for Sm 3+ in lanthanum ethyl sulfate has been identified as arising from the relaxation process attributed to the optical phonons at energies around 78 K which have been determined from the infrared spectra. The theoretical estimate based on this relaxation process has been made and it agrees with the experimental result within one order of magnitude.

The EPR for Mn 2+ (0.01%) in Cd 1- x Mg x Te (0≤ x ≤0.2) mixed crystals grown by the Bridgeman technique has been studied at the X -band. The hyperfine interaction constants A and g -factors have been found to be less dependent on the composition x than the crystalline field constants a . An empirical equation has been formulated in order to obtain the EPR parameters for Mn 2+ in II-VI compounds as a whole. This law shows an exponential dependence of the EPR parameters on the effective distance between the magnetic ion and the anion. This law is used to estimate unknown parameters for Mn 2+ in Cd 1- x Te as a function of x . Some lines in the EPR spectra showed a broadening with x . The temperature dependence of the constants A for these crystals has been found to be a little larger than those for ionic crystals such as MgO, CaF 2 , and NaCl. The composition dependence of the Debye temperatures has been determined from these data. Measurements were also made of the temperature dependence of the peak-to-pe...

The electron spin resonance of Eu ++ in SrF 2 have been studied from 4°K to 800°K. The experiment showed that the hyperfine coupling constant A decreased in magnitude by approximately 3.5% over that temperature range. The calculation of the temperature dependence of A is made by using the mechanism proposed by Simanek and Orbach with the introduction of the “modified Debye temperature.” The contribution due to acoustic phonons and optical phonons are calculated separately, the theoretical prediction agrees well with the experimental values. The zero-point contribution to the hyperfine coupling constant is -1.73×10 -5 cm -1 and the hyperfine coupling constant in the “rigid lattice” at T =0°K is -34.42×10 -4 cm -1 .

The Van Vleck orbit-lattice interaction appropriate for the ethyl sulfate crystal has been applied to estimate the relaxation rates of Pr 3+ in YES and LaES, Tb 3+ in YES, and Ho 3+ in YES and HoES. The estimates based on our theory along with the phonon bottleneck effect are in good agreement with the experimental data.

MARSHALL et al.1,2 have demonstrated experimentally that the isotope shift in the crystal-field splittings of the magnetic ions doped in some host lattices, δD, is proportional to the mass difference of the isotopic magnetic ions and decreases with temperature. Based on the result that the phonon-induced crystal-field splitting is approximately proportional to the mean square displacement of the atoms3, I have shown4 that the isotope shift in the crystal-field splittings of two isotopic magnetic ions is approximately proportional to the difference between the mean square displacements of these two isotopes, 〈u02〉1 and 〈u02〉2 In this communication, I shall try to use this result to explain the temperature dependence of the isotope shifts measured by Marshall et al.1.

The pulsed-saturation method at 8.9 kMc/sec was used to measure the spin-lattice relaxation rate ${{T}_{1}}^{\ensuremath{-}1}$ for ${\mathrm{Eu}}^{2+}$, ${\mathrm{Ho}}^{2+}$, and ${\mathrm{Tm}}^{2+}$ in Ca${\mathrm{F}}_{2}$, for ${\mathrm{Yb}}^{3+}$ in yttrium gallium garnet, yttrium aluminum garnet, and lutetium gallium garnet; for ${\mathrm{Nd}}^{3+}$ in yttrium gallium garnet and yttrium aluminum garnet; and for ${\mathrm{Sm}}^{3+}$ in lanthanum ethyl sulphate at low temperatures. The experimental data in most cases are in satisfactory agreement with the theoretical predictions based on the combined Van Vleck-Orbach theory. Besides the expected conventional processes, a process ${{T}_{1}}^{\ensuremath{-}1}\ensuremath{\propto}{T}^{5}$ was observed for ${\mathrm{Eu}}^{2+}$ in Ca${\mathrm{F}}_{2}$ in the temperature range 15\ifmmode^\circ\else\textdegree\fi{}K30\ifmmode^\circ\else\textdegree\fi{}K. Furthermore, a pronounced anisotropy in ${T}_{1}$ (a factor \ensuremath{\sim}6) for ${\mathrm{Sm}}^{3+}$ in lanthanum ethyl sulphate was found both experimentally and theoretically.