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

For a magnetic material, the easy and hard magnetic axes describe the directions of favourable respectively unfavourable alignment of the magnetisation. In this article, we describe how to determine these axes for cubic magnetic crystals. Usually it is assumed without further reasoning that they coincide with some principal symmetry directions of the crystal [Bozorth, Phys. Rev. 50, 1076–1081 (1936)], which is however invalid in general. In contrast, we present a full and elementary analysis using symmetric polynomial inequalities, which are well suited to the symmetry of the problem.