Tensor magnetic hysteresis loop measurements of a steel cube

The change in magnetic moment of a 25.4 mm steel cube sample was measured in three orthogonal directions with fields up to magnetic saturation applied in each of the three cube directions. An analysis of the diagonal components of the resulting 3 × 3 tensor indicated the relative magnetic easy axis amongst three three directions measured. Additional information on the magnetization processes was obtained from an analysis of the off-diagonal changes in the magnetic moment tensor. Hysteresis was also observed in these off-diagonal loops. A net magnetization vector of magnitude M was considered. Deviations of magnetization components from linearity along the diagonal directions, ΔMil were related to the off-diagonal components, MiJ and MiK, by the simple relation ΔMiI ≈ ± (MiJ2 + MiK2)/2M, where i is the field direction x, y, or z and I, J, and K cyclic coordinates X, Y, and Z indicating the magnetization components measured by coils X, Y, and Z, respectively. Changes in the off-diagonal components were associated with various field dependent magnetization processes such as domain wall motion and domain vector rotation. The asymmetry of the magnetic hysteresis loop tensor is associated with either a texture of the material or the existence of internal stresses.