Various methods for analyzing data on anisotropic scalar properties in cubic symmetry: Application to magnetic anisotropy energy of nickel

In cubic symmetry, the description of a scalar anisotropic physical quantity $E$ relative to a static property of a given material can be made with the help of various expansions in terms of symmetrical polynomials or cubic harmonics. A general method for generating the relevant symmetrical polynomials up to an arbitrary order is presented and a new set of cubic harmonics particularly suitable to this problem is tabulated up to order $l=36\mathrm{}$. The relations of the latter with the symmetrical polynomials are set up. A careful study of the very important case where $E$ can be accurately measured only in the planes {100} and {110} is made. From the knowledge of the Fourier expansions of $E$ in these planes the conditions for deriving $E$ in a unique way for arbitrary directions are given. It is also shown that some of the coefficients appearing in the former expansions of $E$ may always be determined unambiguously whatever the order up to which these expansions have to be performed. Practical applications of these results are developed with specific reference to the magnetic anisotropy energy of nickel at low temperatures. This study demonstrates the advantages of this method of analysis over the usual procedures.