Interactions magneto-elastic

The volume anomaly AVq is the difference between the true volume and the volume which would exist in the absence of magneto-elastic interactions and can be obtained by extrapolation of the empirical volume temperature relation, from the high temperature phase. 

The integrated absorbed intensity from the data of fig. 16.20 shows an anomalous reduction of about 40% as the temperature is lowered below the Curie temperature. This phenomena is believed associated with a softening of the phonons via the large magneto-elastic interaction. As a result the acoustic impedance should be strongly temperature dependent. 

Vf, V = first and second order contributions in the phonon operators of the magneto-elastic interactions = electrostatic potential = components of the deformation tensor... 

In the following we outline the derivation of the magneto-elastic interactions. Further details can be found in Dohm and Fulde (1975). The starting hamiltonian is of the form (for simplicity we restrict ourselves to Bravais lattices) ... 

HStrain and Hroi represent the strain and rotational magneto-elastic interactions. Up to second order in v p the pure-strain interaction can be written as... 

A weak, field dependent coupling of modes of different polarization fi, ft has been neglected at this stage. It is apparent that the linear magneto-elastic interaction Vi enters through the single-ion (quadrupolar) susceptibility... 

From the diagrams shown in fig. 17.37 and from eq. (17.108) it is very transparent why the effect of the second order magneto-elastic interaction is not small as compared with the first order interaction. Namely the second-order interaction enters linearly into the phonon propagator while the first-order interaction enters quadratically. 

The ordered phase of systems undergoing a structural phase transition (cooperative Jahn-Teller effect) can be treated in complete analogy to the magnetically ordered phase. In order to demonstrate this we start out from the magneto-elastic interactions as given by eq. (17.32) and add to it an interaction which is described by the hamiltonian... 

Here VT, V2 describe the magneto-elastic interaction and contain terms of even power in J . The last term describes the magnetic interaction between different RE-ions. The coupling of the magneto-elastic interaction and the magnetic interactions can be discussed in terms of the mixed susceptibility... 

Fig. 17.50. Magneto-elastic coupling by invoking an interaction of the type (A, I) = (1,1).

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