Magnetic anisotropy

Magnetic anisotropy is a directional dependence of a material's magnetic properties. A preferred direction must be distinguished from an externally imposed magnetic field.

Dependence of a crystal's magnetic energy on magnetization direction relative to its lattice, commonly generated by spin-orbit coupling and the crystal environment. A half-filled orbital shell with $L=0$ suppresses first-order orbital anisotropy, although smaller admixture and dipolar effects can remain.

A magnetic energy preference for an axis, with the two opposite directions equivalent in a purely uniaxial model. An easy-axis energy can be written $K{\sin }^2\theta$ for $K>0$. A unidirectional term distinguishes the two directions and can instead shift a hysteresis.

A directional magnetic preference that distinguishes a Magnetization direction from its reverse, unlike a purely uniaxial easy-axis energy. A pinned interface can supply such a preference and produce exchange bias. In a simple model its interfacial energy term is proportional to $-J_{\mathrm{int}}\cos \theta$.

A displacement of a ferromagnetic hysteresis loop's field centre caused by coupling to a prepared, sufficiently pinned magnetic environment, commonly an antiferromagnet. Field cooling through the ordering/blocking range can establish a unidirectional interfacial spin preference. With switching fields $H_{-},H_{+}$, the shift is $H_E=(H_{+}+H_{-})/2$, distinct from coercive half-width $(H_{+}-H_{-})/2$. Reversing the cooling field, testing a full major loop and comparing uncoupled/zero-field-cooled controls help identify genuine bias.

The tensor connecting spin to magnetic moment in an effective spin Hamiltonian. Its principal values specify direction-dependent Zeeman coupling.