Spin-phonon interaction

Keywords Electron-lattice coupling, phonons, spin-phonon interaction, vibronic state,... 

Schottky anomaly is determined from the difference between an RY compound and LaX or LuX compound. Then the crystal field parameters are deduced from the Schottky anomaly data. The accuracy of the method is limited by spin-phonon interactions and exchange effects in rare earth ions which affect the Schottky effect, ft is used to find crystal field parameters, W, x which fit the specific heat data as shown in Fig. 8.4. The figure refers to a plot of C/Rq vs. T for TmAF [19]. 

The spin-Peierls 2kF instability usually occurs when U is big and is originated by spin-phonon interactions. As in the CDW case, in real systems, the interchain Coulomb interactions couple the SDW and may lead to phase transitions at T > 0. 

Thus, the proton-phonon coupling being inserted into the initial Hamiltonian is able to suppress or enlarge the coherent tunnel repolarization of the chain. The realization of this or that option depends not only on the spin-phonon interaction, but also on the form of the two-well potential of the hydrogen bond. 

There are a number of areas where the electron-phonon interaction is of central importance to the phenomenon E.g. spin-phonon interactions in paramagnetic and nuclear magnetic relaxations155), nucleation of phase transitions in impure crystals78), optical activity72 84), tunelling (as e.g. between off-centre positions of impurity ions96)). 

DETECTION OF SPIN-PHONON INTERACTIONS BY HEAT CONDUCTIVITY MEASUREMENTS. 

We begin with consideration of surface influence on resonance magnetic Adds for spherical nanoparticles. This influence defines the positions of corresponding spectral lines. As it was shown in the Sect. 3.1, the surface effect can be expressed via hydrostatic pressure p = 2 [l/R, where R is a particle radius and p, is a surface tension coefficient. It is known, that the influence of mechanical stress on resonant fields (frequencies) is defined by spin-phonon interaction coefficients. Therefore, the resonance frequency of some transition for nanoparticles can be expressed in the form ... 

Fig. 8. Temperature dependence of the B,g two-magnon response in EuBa2CUj07 crystals for temperatui es higher than Tn. The solid lines are fits using a model that accounts for spin-phonon interactions (after Knoll et al. 1990).

Hamiltonian of orhit-lattice interaction, linear in lattice variables. The response of a paramagnetic crystal to different external perturbations (electric or magnetic field, hydrostatic pressure, uniaxial pressure), the dependence of spectra on temperature, and the spin-phonon interaction, are all determined by diffo-ent combinations of these parameters. 

The crystal potential os a VV ion is also changed occasionally under thermal vibrations, which, in turn, results in luidom changes of the paramagnetic shift a and the quadrupolar interaction in eq. (134). Tc first approximation in e, the electron-deformation interaction equals i i aiid therefore the effective Hamiltonian of the spin-phonon interaction... 

The method of nuclear acoustic resonance proves to be suitable for studying the nuclear spin-phonon interaction using a moderate magnetic field. Resonance absorption of tiie ultrasound can be regarded as the phenomenon inverse to magnetic relaxation through one-phonon processes (Al tshuler and Kozyrev 1972). Therefore the considerations discussed earlier are also relevant to estimates of the magnitude of sound absorption by nuclei of the VV ions. The absorption coefficient of sound due to transitions between nuclear sublevels i, f takes the form of... 

At low temperatures, when only the ground state of the lanthanide ion in the crystal field is populated, the total magnetic moment of the ion is the sum of the induced (Van Vleck) moment and the intrinsic moment (the latter differs from zero only in the degenerate state). The contributions to the magnetostriction and the elastic constants due to changes in the intrinsic magnetic moment of the lanthanide ion with lattice strain can be written explicitly when considering the effective spin Hamiltonian. The latter contains a smaller number of independent parameters (constants of spin-phonon interaction) than the Hamiltonian of the electron-deformation interaction (18) and is more suitable in the description of experimental data. 

Constants of spin-phonon interaction of Er and Dy ions in LiRp4 crystals... 

The spin Hamiltonian of the Er + and Dy ions in the LiRp4 crystals is given by formula (118) with the Zeeman term in the form of eq. (119) and with The constants of spin-phonon interaction, calculated with the parameters of electron-deformation interaction from table 10, are given in table 25 (some of these constants were measured in EPR experiments on the uniaxially stressed LiTmF4 crystals activated by the Er and Dy + ions). In this case parameters of the magnetostriction Bx T, h) in eq. (235) can be written as follows... 

RFeOj are insulators and the experimentally measured = k. As one can see in fig. 18a, at the temperatures Tjs and T2s K has minima. At T,s spins are oriented along the a-axis, at T2 along the c-axis (fig. 18b). Anomalous behaviour of k(T) of Smo.gGdo FeOj in the SOFT region is connected with unusual behaviour of the sound velocity (fig. 18c). Both anomalies are due to a strong spin phonon interaction. 

From the measured Schottky anomaly one can often deduce successfully the crystal-field parameters. The former is determined from the difference between a RX compound and LaAT or LuX . A typical example is shown in fig. 17.1. The method has been applied to concentrated systems as well as to dilute alloys (see for example Hoenig et al., 1974 Heiniger et al., 1974). The accuracy of the measurements is limited by spin-phonon interactions and exchange effects among the RE-ions which distort the Schottky contribution. Often one finds several crystal-field parameters W, x which fit equally well the specific heat. 

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