Phenomenological theory of magnetic anisotropy in thin films and multilayers

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Within a phenomenological approach the density of induced uniaxial anisotropy in nanostructures K(r) is treated as a physical field additional to the magnetization M(r). The equilibrium distributions of K(r) are formed under the influence of the surfaces and internal interactions. The functions K(r) and M(r) are calculated for a magnetic layer between two nonmagnetic spacers. It is shown that the transition from the phase with magnetization in plane to the perpendicular phase occurs continuously via an intermediate phase which is inhomogeneous across the layer-thickness. The theory explains experimentally observed thickness dependences of the effective anisotropy and gives a method to obtain values of the characteristic parameters for the theory from experimental data. It is shown that the separation of the induced anisotropy into volume and surface contribution is valid only for thick films.