Anisotropy magnetoelastic

The free-energy contribution can be written as —lA(By2/Cv)EjhY2, showing explicitly the well-known magnetoelastic contribution to the magnetic anisotropy. 

Since thin magnetic films are deposited on a non-magnetic substrate, the actual strains, and thus the induced anisotropy, depend on the magnetoelastic coupling coefficients of... 

Various experimental methods have been developed for investigating the magnetoelastic properties of thin films and nanoscale magnetic systems. In the following subsections, we discuss the most important ones (i) the magnetoelastic cantilever, (ii) strain induced anisotropy, (iii) magnetostriction in spin valves, (iv) strain modulated ferromagnetic resonance, (v) secondary-electron spin-polarisation, and (vi) strain-induced anisotropy due to the spontaneous strains. 

This method is based on the Villari effect applying a uniaxial stress to a ferromagnetic substance induces a magnetoelastic anisotropy which may modify all the parameters of its magnetisation curve, e.g. magnetic susceptibility, coercive force, and so on. Some experimental techniques to measure the strain-induced anisotropy are discussed shortly below. 

The magnetoelastic energy, simply related to the magnetostriction constants, can be written in the following form in the coordinate axes connected to the local anisotropy ... 

A contribution caused by spin-orbit coupling and closely related to magnetocrystalline anisotropy is magnetoelastic anisotropy. Mechanical stress creates a strain which amounts to a lattice distortion and yields a correction to the magnetocrystalline anisotropy. Surface anisotropy is a manifestation of magnetocrystalline anisotropy, too (sections below and Ch. 3). 

In 3d atoms, the spin-orbit coupling is much smaller than the crystal-field energy, and the magnetic anisotropy is a perturbative effect [7, 8, 16]. Typical second- and fourth-order transition-metal anisotropies are of the orders of 1 MJ/m3 and 0.01 MJ/m3, respectively. A manifestation of magnetocrystalline anisotropy is magnetoelastic anisotropy, where the crystal field is changed by mechanical strain [5, 16]. 

Fig. 20. Calculated stress a as a function of film thickness for Tb-Co films. The variations of perpendicular anisotropy and magnetoelastic coefficient as functions of composition are shown in the inset. After Betz et al.

In another series of experiments, Argyle et al. (1967) have compared the magnetoelastic component of the expansitivity, measured on a single crystal of EuO from 25 to 250 K, with the magnetic heat capacity above and below the Curie temperature, and find them accurately proportional to each other. They point out that this result is compatible with models proposed by Mattis and Schultz (1963), Pytte (1965), and Callen and Callen (1965). The temperature variation of the anisotropy constant Xi, determined by a static torque method by Miyata and Argyle (1967), is found to be in... 

---