We report high-resolution optical absorption spectra for $\mathrm{Nd}{\mathrm{Fe}}_3{\left(\mathrm{B}{\mathrm{O}}_3\right)}_4$ trigonal single crystal, which is known to exhibit a giant magnetoelectric effect below the temperature of magnetic ordering $T_N=33\mathrm{K}$. The analysis of the temperature-dependent polarized spectra reveals the energies and, in some cases, symmetries and exchange splittings of ${\mathrm{Nd}}^{3+}$ 84 Kramers doublets. We perform crystal-field calculations starting from the exchange-charge model, obtain a set of six real crystal-field parameters, and calculate wave functions and magnetic $g$ factors. In particular, the values $g_{\perp }=2.385$ and $g_{\Vert }=1.376$ were found for the ${\mathrm{Nd}}^{3+}$ ground-state doublet. We obtain $B_{\mathit{loc}}=7.88\mathrm{T}$ and $\mid J_{\mathit{FN}}\mid =0.48\mathrm{K}$ for the values of the local effective magnetic field at liquid-helium temperatures at the ${\mathrm{Nd}}^{3+}$ site and the Nd-Fe exchange integral, respectively, using the experimentally measured ${\mathrm{Nd}}^{3+}$ ground-state splitting of $8.8{\mathrm{cm}}^{-1}$. To check the reliability of our set of crystal-field parameters, we model the magnetic susceptibility data from literature. A dimer containing two nearest-neighbor iron ions in the spiral chain is considered to partly account for quasi-one-dimensional properties of iron borates, and then the mean-field approximation is used. The results of calculations with the exchange parameters for ${\mathrm{Fe}}^{3+}$ ions $J_{\mathit{nn}}=-6.25\mathrm{K}$ (intrachain interactions) and $J_{\mathit{nnn}}=-1.92\mathrm{K}$ (interchain interactions) obtained from fitting agree well with the experimental data.

We report structural and magnetic properties studies of large high-quality single crystals of the frustrated magnet ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$. Powder x-ray diffraction analysis confirms that ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ adopts the pyrochlore structure. Room-temperature x-ray diffraction and time-of-flight neutron-scattering experiments show that the crystals are stoichiometric in composition with no measurable site disorder. The temperature dependence of the magnetic susceptibility shows no magnetic ordering at temperatures down to 0.5 K. Fits to the magnetic susceptibility data using a Curie-Weiss law reveal a ferromagnetic coupling between the Nd moments. Magnetization versus field measurements show a local Ising anisotropy along the $〈111〉$ axes of the ${\mathrm{Nd}}^{3+}$ ions in the ground state. Specific heat versus temperature measurements in zero applied magnetic field indicate the presence of a thermal anomaly below $T\sim 7$ K, but no evidence of magnetic ordering is observed down to 0.5 K. The experimental temperature dependence of the single-crystal bulk dc susceptibility and isothermal magnetization are analyzed using crystal field theory and the crystal field parameters and exchange coupling constants determined.

Optical absorption spectra of the ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ single crystals and luminescence spectra of the ${\mathrm{Y}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7:\mathrm{Yb}$ (1%) polycrystalline samples were registered at temperatures $4.2–300\mathrm{K}$. These spectra and earlier published data on magnetic properties of ${\mathrm{Yb}}^{3+}$ ions and on the temperature dependence of the electric field gradient at Yb nuclei in ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ were used to analyze the crystal-field parameters in rare-earth titanates with the pyrochlore structure. The self-consistent sets of crystal-field parameters for rare-earth ions in the $16d$ sites with the $D_{3d}$ symmetry that describe satisfactory all known single-ion magnetic properties and low-energy excitations in $R_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ crystals ($R=\mathrm{Tb}$, Ho, Er, Tm, Yb) are presented.

We report the observation of optically resolved isotope, hyperfine, and superhyperfine structure in the spectrum of ${\mathrm{Nd}}^{3+}$ ions in ${\mathrm{YLiF}}_4,$ isotopically pure in ${}^7\mathrm{Li}.$ This observation was made on the ${(4f}^3-{4f}^3),$ ${}^4{I}_{9/2}{\mathrm{}\left(1\right)\mathrm{}}^4{F}_{3/2}\mathrm{}\left(1\right)\mathrm{}$ transition of ${\mathrm{Nd}}^{3+}$ ions present as impurities at ppm levels. The optical linewidths of the transitions of the even mass number isotopes, ${}^{142}\mathrm{Nd},$ ${}^{144}\mathrm{Nd},$ ${}^{146}\mathrm{Nd},$ ${}^{148}\mathrm{Nd},$ and ${}^{150}\mathrm{Nd},$ are only 45 MHz which makes it very easy to resolve the isotope shift of 115 MHz/unit mass. The hyperfine structure of the two odd mass number isotopes, ${}^{143}\mathrm{Nd}$ and ${}^{145}\mathrm{Nd},$ are resolved and the hyperfine parameters are determined in both the ground and electronically excited states. Some of the transitions have linewidths as narrow as 10 MHz. These are the narrowest optical inhomogeneous linewidths observed in solids. In addition, each even isotope line is split by 30 MHz. The observed splitting is assigned to a superhyperfine coupling between ${\mathrm{Nd}}^{3+}$ and its nearest-neighbor fluorine nuclei. Here, a superhyperfine splitting has been resolved in an optical spectrum. The optical line shapes for the even isotopes are calculated as the sum of all transitions between the superhyperfine components $({\mathrm{Nd}}^{3+}$ with its eight nearest-neighbor F nuclei) of the ground and excited electronic states, considering both magnetic dipole-dipole (including spin-transfer contributions) and contact interactions. The results are in quantitative agreement with experiment.

The experimental temperature dependence (T = 2–300 K) of single crystal bulk and site susceptibilities of rare earth titanate pyrochlores R2Ti2O7 (R = Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb) is analyzed in the framework of crystal field theory and a mean field approximation. Analytical expressions for the site and bulk susceptibilities of the pyrochlore lattice are derived taking into account long range dipole–dipole interactions and anisotropic exchange interactions between the nearest neighbor rare earth ions. The sets of crystal field parameters and anisotropic exchange coupling constants have been determined and their variations along the lanthanide series are discussed.