page_title: Magnetocrystalline anisotropy
section_title: Cubic anisotropy
hierarchical_section_title: Magnetocrystalline anisotropy / Thermodynamic theory / Cubic anisotropy
caption_attribution_description: English: Magnetic energy vs direction of magnetization for a ferromagnet with cubic anisotropy.
context_page_description: 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. These directions are usually related to the principal axes of its crystal lattice. It is a special case of magnetic anisotropy.
context_section_description: In a cubic crystal the lowest order terms in the energy are
  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).
  If  K₂ is not assumed to be zero, the easy axes depend on both  K₁ and  K₂. These are given in the table below, along with hard axes (directions of greatest energy) and intermediate axes (saddle points) in the energy). In energy surfaces like those on the right, the easy axes are analogous to valleys, the hard axes to peaks and the intermediate axes to mountain passes.
  Below are some room-temperature anisotropy constants for cubic ferromagnets. The compounds involving Fe₂O₃ are ferrites, an important class of ferromagnets. In general the anisotropy parameters for cubic ferromagnets are higher than those for uniaxial ferromagnets. This is consistent with the fact that the lowest order term in the expression for cubic anisotropy is fourth order, while that for uniaxial anisotropy is second order.
caption: Energy surface for cubic anisotropy with  K1 < 0. Same conventions as for  K1 > 0.
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