Magnetic-Shape Anisotropy in Polygonal Prisms

Abstract

It is shown that only a uniaxial magnetic shape anisotropy can be exhibited by a body of arbitrary shape if the applied magnetic field (H) is large enough to make the magnetization uniform throughout the sample. A square plate will accordingly be isotropic around an axis perpendicular to the plate but uniaxial around any other axis. The purpose of this paper is to emphasize this aspect of shape anisotropy for very high fields and to illustrate the anisotropies which are observed experimentally for several polygonal prisms using typical laboratory values of H. Two interesting examples are equilateral triangles and squares cut from thin plates, which when measured with H in the plane of the plates, yield torque curves of sin6θ and sin4θ, respectively. It is also demonstrated that the easy axes for a cube are the cube edges for fields less than about 6Bs but become face diagonals for larger fields. For thin square plates, the easy axes are diagonals for fields less than about 11Bs but are square edges for larger fields. For a square sample whose height is 0.8 of the square edge, the easy axes reorient for fields near Bs by splitting on either side of the square edges, giving sin8θ components, and then rotating to the diagonals with increasing field. Rotation of the easy axes has not been observed in any of the triangular samples. Although a large reduction in shape anisotropy occurs as large fields are applied, appreciable anisotropy remains at fields as large as 15Bs for some of the samples studied. Experimental anisotropy values are given as a function of H/Bs for several regular polygonal prisms.