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

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 H_T 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 $${\mu }^{\text{−1}}{\mathrm{=H}}_T{\mathrm{-H̄}}_K{\mathrm{+Md\pi }}^{\text{−1}}{\text{[2A/(H}}_T{\mathrm{-H̄}}_K{\mathrm{)M]}}^{-\frac{1}{2}}{\mathrm{[\delta H}}_b{\text{/(1.64)8(H}}_T{\mathrm{-H̄}}_K{\mathrm{)]}}^2,$$ where H_T is the transverse bias field, H̄_T is the average anisotropy field, M is the saturation magnetization, d is the film thickness, A is the exchange constant, and δH_b is the inhomogeneity in the magnitude of the anisotropy, defined as Δ₉₀ H̄_K. This expression gives a very good fit to the data.