Magnetoelastic strain dependence

A. B. Shick, D. L. Novikov, A. J. Freeman. Relativistic spin-polarized theory of magnetoelastic coupling and magnetic anisotropy strain dependence Application to Co/Cu(001). Phys. Rev. B, 56(22) (1997) R14259-R14262. 

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... 

The relative influence of the surface (or interface) effects, of course, must decrease with increasing thickness t of the layer(s). Since the surface effects contribute per unit surface area , one defines, for the layer, effective parameters such that Beff, or heff, equals gbuik 2bsurt/t. Here, the factor 2 is put in, because a layer has two surfaces. In practice, this simple l/t dependence works satisfactorily. For nanocrystallites, both the volume fraction and the volume to surface ratio of the crystallites (i.e. their radius) must be taken into account (see also section 8). In connection to these effects, (non-linear) contributions to the magnetoelastic coefficients due to surface strains and surface roughness are expected to be considerable. 

In this section we present experimental results on the temperature dependence of elastic constants for intermetallic rare-earth compounds in which magnetoelastic effects due to the presence of crystal fields are dominant. There are systematic studies of these effects for given structures across the rare-earth series. Examples are the rare-earth monopnictides, especially the rare-earth antimonides (RSb), the rare-earth dialuminides (RAlj) and rare-earth compounds with the CsCl structure. From such experiments one obtains the single-ion magnetoelastic coupling constants gj. across the series and in a few cases the quadrupolar coupling constant gf [eq. (38)] too. The case of a cooperative Jahn-TeUer effect will be treated separately in sect. 2.4.3. The examples presented here can be explained mostly with the single-ion strain susceptibility Xr [ <1- (35) instead of eq. 

Finally, we discuss the parastriction (or magnetostriction) effect. In an applied magnetic field the magnetoelastic coupling induces strains because of the field dependence of the quadrupolar moments of the rare-earth ions according to... 

Fig. 24. Magnetic field dependence of the three C44 modes for T= 4.3 K in CeAlj. Full lines are strain susceptibilities for ( , k ) and (Uj, k ) modes. Broken lines indicate rota-tionally invariant magnetoelastic interaction (Liithi and Lingner 1979).

Upon rotating the magnetic field in the (011) plane of a single crystal of LaS doped with 2000 ppm Er, Bloch et al. (1982) found an angular-dependent linewidth. They assumed a T7 ground state of Er followed by a Tg excited state. Internal strains of Fs type are coupled to the lanthanide ions via magnetoelastic effects. The spin Hamiltonian... 

The second effect due to the surface is related to strains. Because of magnetostriction, strains are effective in the m direction. But the corresponding energy is weak, and the d dependence will be still weaker in cubic symmetry if Aioo Aui =A. However, if exterior strains occur, the -dependent part of the magnetoelastic energy can be written ... 

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