Effect of Magnetostatic Interactions on the Real and Imaginary Parts of the Transverse Biased Permeability in Thin Ni-Fe Films

Abstract

It has been found that the rapid fall off of μ′ (the imaginary part of the permeability) on the low-field side of μ′ vs HT is due to the formation of locking domains, and that in this region the probability density function is not proportional to μ′. This fall off can be predicted from μ (the real part of the permeability) by assuming that the fall off in μ is due entirely to the effects of locking domains. When this is done, and Δ90, the inhomogeneity in anisotropy magnitude, is determined from the corrected probability density curves the relationship arc sin Δ90=4α90 is found nearly to hold, but a coefficient of 5 gives a better fit to the data. It is suggested that the 5 comes from anisotropies of order higher than 2 due to higher-order interactions. These interactions are responsible for triaxial anisotropy introduced by etching a polycrystalline film into small triangles, and for higher-order anisotropies found by etching small rectangles. A theoretical expression for the permeability has been found as μ−1=HT−H̄K+Mdπ−1[2A/(HT−H̄K)M]−12[δHb/(1.64)8(HT−H̄K)]2,where HT is the transverse bias field, H̄T is the average anisotropy field, M is the saturation magnetization, d is the film thickness, A is the exchange constant, and δHb is the inhomogeneity in the magnitude of the anisotropy, defined as Δ90 H̄K. This expression gives a very good fit to the data.