The Advantages of Using Spherical Harmonics to Analyse Data on Magnetocrystalline Anisotropy and Other Non‐Linear Anisotropic Properties

Abstract

It is important, in considering certain physical properties, to allow for the existence of non-linear anisotropy. Using magnetocrystalline anisotropy as a n example, the role of symmetry is discussed in relation t o the description of non-linear anisotropy and to the analysis of the corresponding experimental data (with particular reference to uniaxial and cubic symmetry). The advantages of using orthonormal functions, such as spherical harmonics, are demonstrated, both in general terms and also by specific application t o experimental data on magnetocrystalline anisotropy.Es ist wichtig, die Existenz der nichtlinearen Anisotropie in Betracht zu ziehen, wenn bestimmte physikalische Eigenschaften zu beschreiben sind. An Hand der magnetokristallinen Anisotropie wird die Rolle der Symmetrie im Verhaltnis zur nichtlinearen Anisotropie und den entsprechenden experimentellen Ergebnissen analysiert (besonders in Beziehung zu der einachsigen und kubischen Symmetrie). Es wird im allgemeinen und speziell in der Analyse der experimentellen Ergebnisse der magnetokristallinen Anisotropie gezeigt, daB die Verwendung orthonormierter Funktionen, wie z. B. der Kugelfunktionen, von bedeutendem Vorteil ist.

Magnetocrystalline anisotropy and first-order magnetisation processes in (Pr1-xNdx)2Fe14B compounds

“…There is a simple relationship between anisotropy constants Ki in (1) and anisotropy coefficients k r in ( 2 ) [22]:…”

Determining the preferred directions of magnetisation in cubic crystals using symmetric polynomial inequalities

“…with the constraint α 2 1 + α 2 2 + α 2 3 = 1 and some anisotropy constants K 1 , K 2 depending on the material. Alternatively, an expansion of the anisotropy functional in orthonormal spherical harmonics can be advantageous [5,15].…”

Anisotropy effects of La‐Co substitutions in M‐type Sr hexaferrites

“…In addition the study takes advantage of computer simulations based on an extended Stoner-Wohlfarth model including arbitrary angular distribution functions of the crystallites and the anisotropy constants up to sixth order. The program incorporates as well the anisotropy coefficients χ 2,0 , χ 4,0 , χ 6,0 , which appear in the expansion of the anisotropy energy in terms of zonal spherical harmonics [5].…”