Three-dimensional Rayleigh hysteresis of oriented core samples from the German Continental Deep Drilling Program: susceptibility tensor, Rayleigh tensor, three-dimensional Rayleigh law

Rayleigh hysteresis, as defined by the well-known Rayleigh relations, has been observed not only when magnetization of pyrrhotite-bearing KTB-samples is measured in parallel to a weak dc magnetic field, but also in experiments where field and measuring directions have been adjusted strictly perpendicularly to each other. Nine-tupels of independent Rayleigh hysteresis loops could thus be compiled. Their characteristic coefficients χijk of initial susceptibility together with the Rayleigh loss coefficients αjk have been proved to determine completely the samples’ weak-field magnetic anisotropy. Interpreting the coefficient matrices (χijk) and (αjk) as the tensor of initial susceptibility and the Rayleigh tensor, respectively, generalization of the isotropic Rayleigh relations in terms of corresponding tensor relationships has been suggested for the anisotropic case. Application to the KTB samples showed 3-D Rayleigh hysteresis measurements to be an excellent tool for rock magnetic analysis in terms of ore content and crystalline texture. In particular, a magnetocrystalline double texture of the basal planes of pyrrhotite precipitates and their [1120] directions of easy magnetization have been clearly detected. Surprisingly, the well-known theorem α=const. X2I, formulated by Néel (1942) for the isotropic case, has been found to hold true even in tensor generalization (αjk)=const (X2jk). To reach sufficient resolution for the measurements performed, a sensitive vibrating coil magnetometer (VCM) has been developed.