Magnetic surface anisotropy

To realize second-order anisotropy, the atomic environment of the transition-metal atoms must have a sufficiently low symmetry [49, 62-65]. Figure 6 illustrates that this is often, but not always, the case for surface atoms. Magnetic surface anisotropy, first analyzed by Neel [62], is important in complicated structures and morphologies such as ultrathin transition-metal films [66], multilayers [67], rough surfaces [65], small... 

With decreasing particle size, the magnetic contributions from the surface will eventually become more important than those from the bulk of the particle, and hence surface anisotropy energy will dominate over the magnetocrystalline anisotropy and magnetostatic energies. A uniaxial anisotropy energy proportional to the particle surface S... 

The description of nanomagnets requires new approaches. First, nanostructures are not periodic and tend to have large surface-to-volume ratios. Because of this the magnetization is not uniform across the nanostructure, local magnetic moments differ from site to site, exchange coupling varies throughout the nanostructure, and the anisotropy can be quite different from bulk or surface anisotropies. Second, it is hard to define properties in the similar fashion as in the bulk or as in case of molecules. 

Evidence for a surface transition (to a ferromagnetic state of the surface) has been found for ferromagnetic Gd (Weller and Alvarado, 1988 Rau and Robert, 1987). The interpretation of such experiments, however, is complicated by the fact that surface anisotropies may be much stronger than the magnetic anisotropy in the bulk, and hence complicated crossover phenomena may occur,... 

Due to the in-plane surface anisotropy [23] the easy magnetization axis in thin iron films is the in-plane [110] direction being the hard magnetization axis of bulk Fe, switching at a critical thickness to the one of bulk crystals, i.e. the [001] direction. For cobalt films the anisotropy causes the easy magnetization axis to lie in-plane in contrast to bulk-hcp Co with its easy axis perpendicular to the basal plane. Thick rare earth metal films exhibit an easy axis within the surface plane. The shape anisotropy may also change the easy magnetization axis. 

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