Macroscopic behaviour of ferromagnets with random and statistically vanishing anisotropy

A model is defined in which the anisotropy tensor is a random function of space point characterised by its mean square value σ and a correlation lenght a_c, and the exchange density A is uniform. If the magnetic moment density is M, it is shown that two dimensionless numbers can be defined a_c/a_p, where a_p is a typical Bloch wall width$\text{(}\text{A}\text{δ}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, and 4πM²/σ they define four types of macroscopic behaviour. For 4πM²/σ<1, the pole fields are a perturbation; if a_c<a_p, as in rare earth amorphous alloys, there is some frustration in the ground state and if a_p <a_c, as in inhomogeneous weak ferromagnets the magnetization direction is mainly fixed by the local anisotropy. For 4πM²/σ#62; 1, as in iron alloys, if a_p#62;a_c one has the case of soft alloys, the shape anisotropy is the dominant effect and if a_p<a_c the usual domain theory applies.