High-resolution spectroscopy of ${\mathrm{Nd}}^{3+}$ in ${\mathrm{Nd}}_2\mathrm{Ba}\mathrm{Ni}{\mathrm{O}}_5$ and ${\mathrm{Y}}_2\mathrm{Ba}\mathrm{Ni}{\mathrm{O}}_5:\mathrm{Nd}(5\%)$ powder samples is used to study ${\mathrm{Nd}}^{3+}$ crystal-field levels and exchange splittings in these quasi-one-dimensional model compounds. We demonstrate that the ${\mathrm{Nd}}^{3+}$ ground-state splitting in the magnetically ordered state of ${\mathrm{Nd}}_2\mathrm{Ba}\mathrm{Ni}{\mathrm{O}}_5$ ($T_N=47.5\pm 1\mathrm{K}$, as found from our spectroscopic data) accounts for the low-temperature magnetic properties and for the $4\text{−}\mathrm{meV}$ mode observed earlier in inelastic neutron scattering experiments. Crystal-field analysis is performed. Its results show that the directions of ordered magnetic moments in ${\mathrm{Nd}}_2\mathrm{Ba}\mathrm{Ni}{\mathrm{O}}_5$ are determined by the single-ion anisotropy of ${\mathrm{Nd}}^{3+}$. We argue that the crystal-field parameters obtained for Nd-nickelate (in this work) and Er-nickelate (in our earlier work) can be used to predict the energy-level patterns and magnetic properties of other rare-earth linear-chain nickelates.

A family of linear chain nickelates $({\mathrm{Er}}_x{\mathrm{Y}}_{1-x}{)}_2{\mathrm{BaNiO}}_5$ $(x=1,$ 0.8, 0.6, 0.4, 0.2, and 0.1) was studied by high-resolution spectroscopy of the ${\mathrm{Er}}^{3+}$ ion. Energies of 38 crystal-field levels of ${\mathrm{Er}}^{3+}$ and exchange splittings for most of them in a magnetically ordered state were measured. Composition-dependent Néel temperatures were found. Crystal-field calculations were performed starting from the analysis in the framework of the exchange-charge model. The wave functions found were used to calculate magnetic $g$ factors for crystal-field levels of ${\mathrm{Er}}^{3+}$ and the magnetic susceptibility $\chi \mathrm{}\left(T\right)\mathrm{}$ of the concentrared $x=1\mathrm{}$ compound. The latter was compared to the detailed $\chi \mathrm{}\left(T\right)\mathrm{}$ curve $(2.0\mathrm{}\mathrm{K}<T<\mathrm{}300\mathrm{}\mathrm{K})$ measured for the ${\mathrm{Er}}_2{\mathrm{BaNiO}}_5$ powdered sample. From the experimentally measured temperature dependences for the ground-state splittings in the compounds with different composition, we derive, within the molecular-field approximation, the ordered magnetic moments of the nickel and erbium subsystems as functions of temperature and concentration of erbium ions, and plot the staggered magnetization function of nickel chains for a staggered magnetic field along the chain direction.

High-resolution polarized broadband (1800-23 000 cm(-1)) optical absorption spectra of Tb(3+) in TbFe(3)(BO(3))(4) single crystals are studied between room temperature and 4.2 K. The spectral signatures of the structural (R32-P3(1)21, T(S ) = 192 K) and magnetic (T(N ) = 41 K) phase transitions are found and analyzed. Energies and symmetries of the Tb(3+) crystal-field (CF) levels were determined for both the high-temperature R32 and the low-temperature P3(1)21 structures of TbFe(3)(BO(3))(4) and compared with the calculated ones. It follows unambiguously from the spectral data that the ground state is the Γ(1) + Γ(2) quasi-doublet of the local D(3) point symmetry group for Tb(3+) in the R32 high-temperature structure. The CF calculations revealed the CF parameters and wavefunctions for Tb(3+) in TbFe(3)(BO(3))(4). The value of the Tb-Fe exchange integral and of the effective magnetic field created by the ordered Fe subsystem were estimated as J(fd) = 0.26 K and B(eff) = 3.92 T, using the observed splitting Δ = 32 cm(-1) of the Tb(3+) ground quasi-doublet at the temperature 5 K. The reliability of the obtained parameters was proven by modeling the literature data on the magnetic susceptibility of TbFe(3)(BO(3))(4). Lattice distortions below T(S) were evidenced by the observed changes of probabilities of the forced electric dipole transitions of Tb(3+).

Resolved hyperfine structure and narrow inhomogeneously broadened lines in the optical spectra of a rare-earth-doped crystal are favorable for the implementation of various sensors. Here, a well-resolved hyperfine structure in the photoluminescence spectra of LiYF₄:Ho single crystals and the anticrossings of hyperfine levels in a magnetic field are demonstrated using a self-made setup based on a Bruker 125HR high-resolution Fourier spectrometer. This is the first observation of the resolved hyperfine structure and anticrossing hyperfine levels in the luminescence spectra of a crystal. The narrowest spectral linewidth is only 0.0022 cm⁻¹. This fact together with a large value of the magnetic g factor of several crystal-field states creates prerequisites for developing magnetic field sensors, which can be in demand in modern quantum information technology devices operating at low temperatures. Very small random lattice strains characterizing the quality of a crystal can be detected using anticrossing points.