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Some questions of the dynamics of the spin-triplet states (STS) are investigated. The equations of motion of the magnetization components related to the separate transitions of the EPR fine structure (FS) under the action of the constant and varying field are derived in the common case. Further consideration of the magnetization motion effects, including EPR, is restricted to the case of a non-zero constant field. It is demonstrated that at the definite condition fulfillment, the free motion of the sample magnetization after the excitation of one of the FS transitions is the precession at the frequency of the excited transition with an ellipse in the plane transverse to the constant field. At that, the square module of the magnetization vector contains as the constant part, so the part, oscillating at the double frequency of the excited transition. The tensor of the dynamic susceptibility of the spin-system (SS) to the microwave field is written at the creation of the resonance conditions for each transition of the well resolved FS. At the same condition, as above, the matrix elements of this tensor reflect the elliptical character of the magnetization precession at the stationary excitation by the transverse microwave field. Some aspects of the spin-lattice relaxation (SLR) of STS are analytically studied in the common case. The rate of the one-phonon SLR is obtained under conditions when SS is described by a single spin temperature. The SLR rates of the separate transitions of the FS are calculated at the same one-phonon mechanism. The low-frequency method of their finding is proposed with the help of the Gorter type experiment in the constant field, transforming the three-level SS into the two-level one. Three non-zero diagonal elements of the corresponding low-frequency susceptibility tensor are analytically obtained.

Some questions of the dynamics of the electron spins S=1 possessing the zero-field splitting are investigated in a strong constant magnetic field. The equations of motion of the magnetization components related to the separate transitions of the EPR fine structure (FS) are derived. It is demonstrated that the free motion of the sample magnetization is the precession at the frequency of the excited “allowed” transition with an ellipse in the plane transverse to the constant field, which is accompanied by the longitudinal magnetization component oscillation at the frequency of the “forbidden” transition. The tensor of the dynamic susceptibility of the spin-system (SS) to the microwave field is written at the creation of the resonance conditions for each transition of the well resolved FS. The matrix elements of this tensor reflect the elliptical character of the magnetization precession at the frequency of the very same transition, for which the resonance conditions are created. The SLR rates of the separate transitions of the FS are calculated at the same mechanism. The low-frequency method of their measurement is suggested with the help of the Gorter type experiment in a strong constant field transforming the three-level SS into the two-level one with the analytically derived expressions for the three non-zero diagonal elements of the low-frequency susceptibility tensor at the three directions of the constant field.

The EPR broadening model conditioned by the one-phonon mechanism of the anisotropic spin-spin reservoir spin-lattice relaxation in the weak constant field is suggested by us for the concentrated paramagnets with the dominating exchange interaction. It is shown in the given presentation that under the definite conditions the EPR linewidth by this model can be presented as the EPR linewidth by the Kubo-Tomita (KT) exchange narrowing theory, multiplied by the spin-phonon factor, proportional to the lattice temperature. The analytical results are reduced to the form suitable for the application to the obtaining of the anisotropic Dzyaloshinski-Moriya (DM) and crystal field (CF) interaction constants in materials with such interactions. The plots of the temperature and angular dependencies are built for the weak field EPR in the lightly doped lanthanum manganite (LM) single crystals agreeing with the experimental ones. The corresponding angular dependencies of the zero-field relaxation rates measurable in the Gorter type experiments are also plotted allowing at the availability of such experiments duplicating the EPR results. Тhe temperature and angular dependencies plotted according to the KT exchange narrowing theory with the subsequent account for the short range spin correlations in the case when the nature of the EPR broadening is of the pure spin-spin type (DM interaction) well agree with the experiment in KCuF3.

The expression for the double exchange Hamiltonian means that the energy density of the Hamiltonian longitudinal part includes the energy of the mobile electrons with the regard for the possibility of their being in one of the two states. That is to say, if the hopping of the mobile electrons takes place, the given magnetic system at the absence of the polarizing external field can never be the completely saturated ferromagnet, what is unambiguously confirmed by the experimental data. It is demonstrated by us that in the doped manganites the antiferromagnetic phase transforms into the ferromagnetic canted phase under the action of the mobile electron hopping. It is shown that the colossal magnetoresistance effect can be conditioned by the change of the magnetization canting angle at the application of a constant magnetic field. The evaluation of the magnetoresistance value in the ferromagnetic canted phase model is carried out and it is shown that it qualitatively and quantitatively agrees with the experiment.

As is well known, the hole-doping of lanthanum manganites leads to the appearance of the nonzero spontaneous magnetization. Ferromagnetic coupling in these compounds is found to arise from a double exchange (DE) process due to -electron hopping from Mn3+ ion via O2- ion to Mn4+ ion. Basing on this fact, the possibility of the FM canted phase stimulated by DE was stated by other authors. Recently, it was also shown that in doped manganites the transition from the antiferromagnetic (AFM) state stipulated by the    interaction to the ferromagnetic (FM) state can occur by the conversion of magnetic sublattice magnetizations into the FM canted state. It is demonstrated by us that in the doped manganites the antiferromagnetic phase transforms into the ferromagnetic canted phase under the action of the mobile electron hopping. It is shown that the colossal magnetoresistance effect can be conditioned by the change of the magnetization canting angle at the application of a constant magnetic field. The evaluation of the magnetoresistance value in the ferromagnetic canted phase model is carried out and it is shown that it qualitatively and quantitatively agrees with the experiment.

The mechanism of FMR broadening and resonance frequency shift in a ferromagnetic conducting sample (hopping conductivity) of a doped lanthanum manganite, caused by the double exchange (DE) under FMR conditions (by the dynamic double exchange, or DDE) is presented. It is shown, that the given mechanism causes the resonance frequency shift and the FMR decay  (linewidth). This shift and broadening mechanism is effective, when the variable field frequency  is of the order of the mobile electron relaxation rate . For the validity of the offered mechanism the fulfillment of the inequality  is necessary. The obtained expressions at  are in the qualitative agreement with the observed dependence of FMR linewidth on the variable field frequency, and also at the definite suppositions with the experimental data on temperature dependence of FMR spectrum. We believe, that the given research can promote the obtaining of the quantitative information on DE constants. 

Expressions are derived for the relaxation rates of both the transverse nuclear magnetization components when individual transitions are excited in the quadrupole structure and the total longitudinal nuclear magnetization component. These expressions are reduced to a form that contains the Fourier transforms of the time correlation functions only for the electron spins. Given the specific form of these correlation functions corresponding to different phase states of the electron spins and different origins of their fluctuations, the temperature dependences of the nuclear relaxation rates are ascertained in various cases, including those for dipole and isotropic hyperfine interactions. Calculations are performed for arbitrary electron and half-integer nuclear spins by taking into account the possible quadrupole splitting of the NMR spectrum without any restriction on the smallness of the ratio ћωs/kBT (ωs is the resonance frequency of the electron spins). The derived expressions are compared with available experimental data on the longitudinal and transverse nuclear relaxation in colossal-magnetoresistance lanthanum manganites in the part of their phase diagram where the corresponding samples are either paramagnetic or magnetically ordered insulators and near the points of transition to an ordered state. Interpretations alternative to the existing ones are offered.

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