Magnetoelastic Losses in the Linear Response Region for Three- and Four-Axis Idealized Magnets

Abstract

In the presented studies, a description of the losses related to relaxation processes in idealized three- and four-axis ferromagnets, as well as ferrites, is considered for the case of a linear response (small perturbations) on the basis of a macroscopic approach. The description takes into account reversible 90° displacements of domain walls (DW) of concentrations (с), ways of DW pinning by linear defects, and processes of DW displacements and rotations of the spontaneous magnetization vector I⃗s, caused by a longitudinal elastic stress wave σ. As a result, the anisotropy of amplitude-independent losses emerges due to displacement processes. Frequency dependence of losses is obtained with consideration of the magnetic symmetry of the crystal, its magnetostructural parameters, and the concentration of magnetic phases ci. The paper also describes the internal frictionn Q-1, the absorption coefficient a, the velocity of propagation of elastic vibrations v and the Δ (1/E)-effect, thus allowing to reveal the texture in the distribution of DWs by their types.
 It is shown that if the relaxation times of rotation processes τ = β / 2K1 and displacement processes τc = βс / mω20 are the same, then the maxima of the dependence of internal friction on frequency Qc-1(ω) and QB-1(ω) superimpose on each other.
 The revealed features of magneto-elastic energy dissipation are of interest for laboratory studies and have promising applications in practice for determining the orientation of crystals, describing the texture, and calculating the differential ΔЕ-effect in magnets. The features of the ΔЕ-effect for the considered cases are also revealed.