Magnetocrystalline anisotropy

In physics, a ferromagnetic material is said to have magnetocrystalline anisotropy if it takes more energy to magnetize it in certain directions than in others.

It is basically the orbital motion of the electrons which couples with crystal electric field giving rise to the first order contribution to magnetocrystalline anisotropy.

The magnetocrystalline anisotropy energy is generally represented as an expansion in powers of the direction cosines of the magnetization.

More than one kind of crystal system has a single axis of high symmetry (threefold, fourfold or sixfold).

Many models of magnetization represent the anisotropy as uniaxial and ignore higher order terms.

However, if K1 < 0, the lowest energy term does not determine the direction of the easy axes within the basal plane.

For this, higher-order terms are needed, and these depend on the crystal system (hexagonal, tetragonal or rhombohedral).

The energy density is, to fourth order,[7] The uniaxial anisotropy is mainly determined by these first two terms.

The energy density for a rhombohedral crystal is[2] In a cubic crystal the lowest order terms in the energy are[10][2] If the second term can be neglected, the easy axes are the ⟨100⟩ axes (i.e., the ± x, ± y, and ± z, directions) for K1 > 0 and the ⟨111⟩ directions for K1 < 0 (see images on right).

Magnetite (Fe3O4), a mineral of great importance to rock magnetism and paleomagnetism, has an isotropic point at 130 kelvin.

[9] Magnetite also has a phase transition at which the crystal symmetry changes from cubic (above) to monoclinic or possibly triclinic below.

[9] The magnetocrystalline anisotropy parameters are generally defined for ferromagnets that are constrained to remain undeformed as the direction of magnetization changes.

If a ferromagnet is single domain (uniformly magnetized), the effect is to change the magnetocrystalline anisotropy parameters.

Examples of easy and hard directions: Although easy directions often (not always [ 3 ] ) coincide with crystallographic axes of symmetry, it is important to note that there is no way of predicting easy directions from crystal structure alone. [ 4 ]
Uniaxial anisotropy energy plotted for 2D case. The magnetization direction is constrained to vary on a circle and the energy takes different values with the minima indicated by the vectors in red.
A representation of an easy cone. All the minimum-energy directions (such as the arrow shown) lie on this cone.
Energy surface for cubic anisotropy with K 1 > 0 . Both color saturation and distance from the origin increase with energy. The lowest energy (lightest blue) is arbitrarily set to zero.
Energy surface for cubic anisotropy with K 1 < 0 . Same conventions as for K 1 > 0 .