This material is prefaced a publication of papers selected at XIX International Youth Scientific School "Actual problems of magnetic resonance and its application", Kazan, 24 – 28 October 2016.

Famous Anderson-Weiss-Kubo model of magnetic resonance is reconsidered in order to bridge existing gaps in its applications for solutions of fundamental problems of spin dynamics and theory of master equations. The model considers the local field fluctuations as one-dimensional normal random process. We refined the conditions of applicability of perturbation theory to calculate the spin depolarization. It is shown that for very slow fluctuations the behavior of the longitudinal magnetization is simply related to the correlation function of the local field. The effect could be checked by the experimental studies of magnetic resonance in quasi-Ising paramagnets.

Experimental and theoretical investigations of dynamics and relaxation of multiple quantum (MQ) nuclear magnetic resonance (NMR) coherences of the zeroth and second orders are performed in a quasi-one-dimensional chain of nuclear spins of ¹⁹F in calcium fluorapatite. MQ NMR dynamics are studied on the preparation period of the MQ NMR experiment in the approximation of nearest neighbor interactions. The density matrix of the system at the end of the preparation period is used as the initial condition for the study of the relaxation process on the evolution period of the MQ NMR experiment. The relaxation asymptotics of the intensity of the MQ NMR coherence of the zeroth order is obtained. Relaxation of the MQ NMR coherence of the second order is investigated with ZZ part of the dipole-dipole interactions. The experimental data qualitatively agree with the results of the developed theory.

The superconducting fluctuations above critical temperature in the Bi₂Sr₂Ca_1-xY_xCu₂O₈ single crystals are studied. The boundaries of the superconducting fluctuations area are defined by the MWA measurement. The estimation of the fluctuations lifetimes is made.

Samples LiTbF₄ and TbF₃ were synthesized by modified methods of colloidal chemistry. The magnetization of these samples was measured in the external magnetic field at 100 Oe and 1 T and in temperature range 2-300 K. Temperatures of phase transition to the magnetic ordering dipolar ferromagnet state were determined for synthesized samples.

The Hamiltonian of the magnetic subsystem containing rare-earth ions involves energies of the localized 4f-electrons in free ions, energies of interactions of the 4f-electrons with the static crystal field in the perfect crystal lattice as well as in the homogeneously deformed lattice, interactions with the external magnetic field and lattice vibrations (electron-phonon interaction), magnetic dipolar and exchange interactions between the ions. This Hamiltonian is used in calculations of different measurable physical parameters versus temperature and the magnetic field strength and direction (energy levels of rare earth ions, the magnetization, magnetic dc- and ac-susceptibilities, elastic constants, lattice deformations).

The crystal field analysis based on calculations in the framework of the semi phenomenological exchange charge model was carried out. The set of crystal field parameters for Ce³⁺ and Pr³⁺ ions in the matrix CeF₃ related to the crystallographic system of coordinates has been obtained and used to reproduce satisfactory the crystal field energies of Ce³⁺ and Pr³⁺ ions.

A rhombohedral layered α-NaFeO₂-type compound, Li_x[Ni_(1+x)/3Sb_(2-x)/3]O₂ (x=0.8) has been prepared from the sodium analogue by ion exchange at 570 K. In contrast to the stoichiometric composition Li₃Ni₂SbO₆, it shows considerable Li/Ni inversion and no long-range Ni/Sb ordering. The temperature dependence of the ⁷Li NMR spin-lattice relaxation rate and linewidth data measured at temperature range from 30-450 K show the sharp increase of lithium ions mobility comparing to the stoichiometric compound Li₃Ni₂SbO₆. From the NMR data the activation energy was estimated by different methods.

The superparamagnetic γ-Fe₂O₃ nanoparticles (average diameter of 2.5 nm) encapsulated in poly(propylene imine) dendrimer have been investigated by electron magnetic resonance (EMR). EMR measurements have been recorded in perpendicular and parallel configurations in the wide temperature range (4.2-300 K). It has been shown that the model based on the spin value S = 30, corresponding to the total magnetic moment of the nanoparticle, can be used to interpret the experimental results and the proof of the quantum behavior of γ-Fe₂O₃ nanoparticles.

This paper covers same results of the research directed at developing an absolute vector proton magnetometer POS-4 based on the switching bias magnetic fields methods. Due to the high absolute precision and stability magnetometer POS-4 found application not only for observatories and to directional drilling support of oi and gas well. Also we discuss the some basic errors of measurements and discuss the long-term experience in the testing of magnetic observatories ART and PARATUNKA.

This article provides suggestions and ideas on the use of magnetic observatories to observe the stability of the gyromagnetic ratio of the proton and the electron in order to detect the effects of new fundamental physics and cosmology. The idea consist in long continuous recording of the signals Overhauser and optical pumping K magnetometers. Such systems can be highly effective network for forecasting earthquakes due to highest long term sensitivity.