# Magnetic Anisotropy

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## magnetic anisotropy

[mag′ned·ik ‚an·ə′sä·trə·pē]## Magnetic Anisotropy

the nonidentical nature of the magnetic properties of bodies in different directions. It is caused by the anisotropic character of the magnetic interaction between atomic carriers of magnetic moment in substances.

Magnetic anisotropy is not manifested on a macroscopic scale in isotropic gases and liquids or in polycrystalline solids. On the other hand, in single crystals it leads to major observable effects, such as the difference in the value of magnetic susceptibility of paramagnetic crystals along different directions. Magnetic anisotropy is particularly great in ferromagnetic single crystals, where it is manifested in the presence of directions of easy magnetization, along which the vectors of spontaneous magnetization Jj of ferromagnetic domains are directed. The energy of magnetization of an external magnetic field that is necessary to rotate the vector J_{s} from its position along the direction of easiest magnetization to a new position along the external field is a measure of magnetic anisotropy for a given direction in a crystal. At constant temperature the energy determines the free energy of magnetic anisotropy F_{an} for a given direction. The dependence of F_{an} on the orientation of *J _{s}* in a crystal is determined on the basis of symmetry considerations. For example, for cubic crystals

*F _{an, cubc} = K_{1}(α_{1}^{2}α_{2}^{2} + α_{2}^{2}α_{2}^{3} + α_{3}^{2}α_{1}^{2}*)

where a_{1}, a_{2}, and *a _{3}* are the direction cosines of J

_{s}with respect to the axes of the crystal [100], and

*K*is the first constant of natural crystallographic magnetic anisotropy (see Figure 1). Its value and sign are determined by the atomic structure of the substance and also depend on the temperature and pressure. For example, at room temperature

_{1}*K*is of the order of 10

_{1}^{5}ergs/ cm

^{3}, or 10

^{4}joules per cu m (J/m

^{3}), in iron and of the order of —10

^{4}ergs/cm

^{3}(—10

^{3}J/m

^{3}) in nickel. As the temperature in-creases these quantities decrease, tending toward zero at the Curie point. In antiferromagnets, which contain at least two magnetic sublattices (J

_{1}and J

_{2}, there are at least two constants of magnetic anisotropy. For a uniaxial antiferromagnetic crystal, F

_{an}may be written in the form (

*a/2) (J*+

_{1z}^{2}*J*) +

_{2z}*bJ*(where z is the direction of the axis of magnetic anisotropy). The values of the constants

_{1z}J_{2Z}*a*and

*b*are of the same order as in ferromagnets. Considerable anisotropy of the magnetic susceptibility

*K*is observed in antiferromagnets; along the direction of easy magnetization

*K*tends toward zero with a drop in temperature, but in the direction perpendicular to the axis (below the Neel temperature)

*K*is independent of temperature.

The constants of magnetic anisotropy may be determined experimentally by comparing the values of the energy of magnetic anisotropy for different crystallographic directions. Another method of determining the constants of magnetic anisotropy consists in the measurement of the torque moments acting on disks of ferromagnetic single crystals in an external field, since they are proportional to the constants of magnetic anisotropy. Finally, the constants may be determined graphically from the area bounded by the magnetization curves of ferromagnetic crystals and the axis along which the magnetization is plotted, for this area is also proportional to the constants of magnetic anisotropy. The values of the constants of magnetic anisotropy also can be determined from data on electron paramagnetic resonance (for paramagnets), ferromagnetic resonance (for ferromagnets), and antiferromagnetic resonance (for antiferromagnets). In addition to natural crystallographic magnetic anisotropy, magnetoelastic anisotropy, which occurs when external unilateral stresses are applied to a specimen, is also observed in magnets as a result of magnetostriction. Magnetic anisotropy is also manifested in polycrystals when a magnetic or crystallographic structure is present.

### REFERENCES

Akulov, N. S.*Ferromagnetizm*. Moscow-Leningrad, 1939.

Bozorth, R.

*Ferromagnetizm*. Moscow, 1956. (Translated from English.)

Vonsovskii, S. V., and Ia. S. Shur.

*Ferromagnetizm*. Moscow-Leningrad, 1948.

Vonsovskii, S. V.

*Magnetizm*. Moscow, 1971.

S. V. VONSOVSKII