Single-ion Anisotropy

Single-ion anisotropy (often referred to simply as ``magnetocrystalline anisotropy'') is determined by the interaction between the orbital state of a magnetic ion and the surrounding crystalline field which is very strong. The anisotropy is a product of the quenching of the orbital moment by the crystalline field. This field has the symmetry of the crystal lattice. Hence the orbital moments can be strongly coupled to the lattice.

This interaction is transferred to the spin moments via the spin-orbit coupling, giving a weaker $d$-electron coupling of the spins to the crystal lattice. When an external field is applied the orbital moments may remain coupled to the lattice whilst the spins are more free to turn. The magnetic energy depends upon the orientation of the magnetisation relative to the crystal axes.

In a magnetic layer, the single-ion anisotropy is present throughout the layer volume, and so contributes to $K_{V}$. Whether this is in addition to or subtraction from $K_{V}$ depends upon the crystal orientation of the layer. In transition metals this contribution is generally much smaller than the shape anisotropy but can be comparable in magnitude in rare earth metals, hence the large interest in rare earth materials in thin film systems to tailor moment orientation such as Perpendicular magnetic Anisotropy.

The single-ion anisotropy can also contribute to the surface anisotropy via Néel interface anisotropy[19], where the reduced symmetry at the interface strongly modifies the anisotropy at the interface compared to the rest of the layer. This can be in addition to or subtraction from the interface anisotropy depending upon the crystal properties of the layer and the sample construction.