Application of CTRW (continuous time random walks) to dipole hopping transport is reviewed. Conditions of applicability of basic kinetic equations to spin systems are indicated. Correct versions of derivation of the CTRW-equations are presented. Existence of different forms of memory kernels is demonstrated. Correction of Scher-Lax memory kernel within geometrical memory approach is fulfilled in accordance with leading terms of concentration expansion. Approximate solution for autocorrelation function is considered. Modern state of numerical simulation and experimental measurements of autocorrelation function in nuclear polarization delocalization are described. It is shown, that application of the CTRW was more successful in description of dipole transport than for hopping conductivity.

Stark structure of ³H₆, ³H₅, ³H₄, ³F₄, ³F₃, ³F₂ and ¹G₄ multiplets of impurity non-Kramers Tm³⁺ ions in the orthorhombic YF₃ crystal has been determined from luminescence studies. High frequency electron paramagnetic resonance (EPR) spectra (~ 207 GHz) of Tm³⁺ ions have been measured at temperature 4.2 K in external magnetic field applied perpendicular to the b-axis of YF₃:Tm³⁺ single crystal. The results of measurements are interpreted in the frameworks of the crystal field theory. The set of crystal field parameters related to the crystallographic system of coordinates of the YF₃ lattice has been obtained and used to reproduce satisfactory the crystal field energies and the EPR spectra.

Measurements of ⁸⁹Y nuclear spin-lattice relaxation in SrY₂O₄:Ho³⁺ crystals for the magnetic field B parallel to the crystal c axis show that ⁸⁹Y at T < 20 K relaxes due to fluctuating magnetic field created only by Ho1³⁺ transitions between the ground and the first excited Zeeman sublevels of the ⁵I₈ multiplet.

The AC/DC magnetic susceptibility and heat capacity of microsized and nanosized DyF₃ particles were measured. These measurements were used to estimate the influence of the size of DyF₃ particles on their magnetic properties. Dipolar ferromagnetic transition was observed in susceptibility measurements for DyF₃ microparticles at T_C  = 2.54 K, whereas DyF₃ nanosized particles remain paramagnetic down to the lowest achieved temperature of 1.8 K. This peculiar behaviour might indicate the change of magnetic properties due to crossover from macro to nanoscale physics.

The electron paramagnetic resonance spectra (X-band, f ~ 9.42 GHz) of Yb³⁺ ions have been measured at temperature 15 K in YF₃:Yb³⁺ single crystals. The principal values of the g-tensors, g_b = g₁ = 1.67, g₂ = 2.42, g₃ = 5.41, and directions n₁ = [0, 1, 0], n₂ = [±sin(54.8°), 0, cos(54.8°)], n₃ = [∓sin(35.2°), 0, cos(35.2°)] of the corresponding principal axes for the Yb³⁺ ions which replace Y³⁺ ions at two magnetically nonequivalent sites with the local C_s symmetry in the orthorhombic crystal lattice have been obtained from analysis of the angular dependences of the spectra taken in the static magnetic fields lying in the crystallographic (bc) and (ac) planes. Experimental data are interpreted in the frameworks of the crystal field theory. Using the obtained set of crystal field parameters for Yb³⁺ ions in the YF₃ host related to the crystallographic system of coordinates, we can reproduce satisfactorily the crystal field energies of Yb³⁺ ions determined earlier from optical measurements.

The first observation of the resolved Mims electron-nuclear double resonance (ENDOR) spectra from the nearby and remote nuclei of ¹⁹F and ⁷Li nuclei on impurity Ce³⁺ ions in LiYF₄ crystal is reported. It shows that LiYF₄:Ce³⁺ system can be exploited as a convenient matrix for performing spin manipulations and adjusting quantum computation protocols while ENDOR technique could be used for the investigation of electron-nuclear interaction with all the nuclei of the system and exploited for the electron-nuclear spin manipulations.

Calcium phosphate (CaP) based materials are widely recognized as the most suitable matrix for bone tissue engineering. The cationic and anionic substitution of CaP structure by the elements and groups of biological importance is the effective way to improve the properties of CaP based substances to achieve the material's desired parameters. Some aspects of application of the conventional electron paramagnetic resonance (EPR) approaches for characterization of CaP powders and ceramics such as hydroxyapatite (HAp) and tricalcium phosphates (TCP) containing intrinsic impurities or intentional dopants like manganese, copper, iron are demonstrated. It is shown that the radiation induced EPR spectra for the nominally pure HAp and TCP reveal the presence of stable nitrogen containing or hydrogen radicals and depend on the CaP synthesis route. It is found that the experimental values of the hyperfine splitting (A) for the nitrogen containing radicals in TCP differ from those known for HAp. The observed narrowing of the central EPR line and increase of its amplitude with the concentration of Mn²⁺ in the range from 0.05 up to 5 wt. % could be exploited for the quantitative determination of manganese in CaP. Analysis of the EPR spectra of the iron containing CaP allows to determine the presence of iron in Fe³⁺ state. The values of the components of g and A for Cu²⁺ ions in TCP are determined and it is demonstrated that they can be influenced by the presence of the codoped Mn²⁺. Therefore, conventional EPR can be used to study cation-cation codoping.

g-tensor components for a Kramers doublet of an impurity ion doped into dielectric crystal are expressed through coefficients of expansion of the doublet wavefunctions in the basis of full momentum of the impurity ion taking into account isotropic reduction of orbital momentum in Zeeman energy due to covalence. Mixing of terms and multiplets of the impurity ion is considered rigorously in the expansion of doublet wavefunctions. The obtained expressions can be useful in calculations and analysis of g-factors dependence on the impurity ion Hamiltonian parameters. The derived formulas are applied to calculation of g-factors of the ground Kramers doublet of Ce³⁺ ion doped in LiYF₄ crystal. It is shown that considering reduction of orbital momentum of the 4f electron of the Ce³⁺ ion in Zeeman energy can significantly improve agreement with experimentally measured g-factors for this compound, available in literature.

Investigation of the mechanochemical doping of PbF₂ powders with Er³⁺ ions with electron paramagnetic resonance and X-ray diffraction is presented. In the analysis of the results a possibility of the structural transformation between the cubic β-PbF₂ and orthorhombic α-PbF₂ phases in the course of synthesis was taken into account. It is shown that regardless of the initial state of PbF₂ it reveals high efficiency of the mechanochemical doping with Er³⁺ ions. Obtained particles are found in (α/β)-PbF₂ structurally inhomogeneous state with the majority of the Er³⁺ ions located in the equilibrium α-PbF₂ fraction. Preferrable location of the Er³⁺ ions in the α-PbF₂ phase is related to the fact that the formation of the cation vacancies necessary for a mechanically activated diffusion of erbium ions into the particles and nucleation of the α-PbF₂ phase proceed in parallel and is mediated by dislocations created in the course of synthesis. Annealing of the sample leads to a conversion of its entire volume into the metastable β-PbF₂ phase with all the Er³⁺ centers possessing the cubic symmetry.