page_title: Magnetocrystalline anisotropy
section_title: Hexagonal system
hierarchical_section_title: Magnetocrystalline anisotropy / Thermodynamic theory / Uniaxial anisotropy / Hexagonal system
caption_attribution_description: English: An illustration of a form of magnetic anisotropy in which the preferred directions form an "easy cone".
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 hexagonal system the c axis is an axis of sixfold rotation symmetry. The energy density is, to fourth 
  order,
  The uniaxial anisotropy is mainly determined by the first two terms. Depending on the values  K₁  and  K₂, there are four different kinds of anisotropy (isotropic, easy axis, easy plane and easy cone):
   K₁ = K₂ = 0: the ferromagnet is isotropic.
   K₁ > 0 and  K₂ > −K₁: the c axis is an easy axis.
   K₁ > 0 and  K₂ < −K₁: the basal plane is an easy plane.
   K₁ < 0 and  K₂ < −K₁/2: the basal plane is an easy plane.
   −2K₂ < K₁ < 0: the ferromagnet has an easy cone (see figure to right).
  The basal plane anisotropy is determined by the third term, which is sixth-order. The easy directions are projected onto three axes in the basal plane.
  Below are some room-temperature anisotropy constants for hexagonal ferromagnets. Since all the values of  K₁ and  K₂ are positive, these materials have an easy axis.
  Higher order constants, in particular conditions, may lead to first order magnetization processes FOMP.
caption: A representation of an easy cone. All the minimum-energy directions (such as the arrow shown) lie on this cone.
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