Magnetization Ripple and Arctic Foxes

Abstract

A model of a polycrystalline magnetic film is considered in which the film is made up of transverse strips of (N) grains, with the magnetization M everywhere parallel within a strip but varying in direction from strip to strip. It is shown that the effective crystalline anisotropy in each strip can be represented by a transverse field H_t which varies randomly from strip to strip, where H_t (rms) = K/[2M(2N)^½] (K is the crystalline anisotropy constant). It is recalled that random number sequences appear to have a periodicity of about 3.5 units, a phenomenon now recognized as having led to the assignment of a periodicity in the population of arctic foxes. A similar apparent periodicity of the transverse anisotropy field leads to an apparent periodicity of the magnetization ripple. Exchange forces, however, modify the amplitude and wavelength λ of the magnetization ripple when λ<λ₀, where λ₀=2π (A/K_u)^½ is the ``relaxation length'' (A is the exchange constant, K_u is the induced anisotropy constant). When ripple is observed in the electron microscope, an additional instrumental factor must be taken into account. A simple treatment is presented which shows that for grain sizes a<λ₀, the angular amplitude of the magnetization ripple θ(rms)≃(πa/λ₀)^½× {K/[K_u(2N)^½]}∼1° and the apparent wavelength λ≃4.6a. Both of these values are in agreement with experiment. When a∼λ₀/2π the approximation fails and the linearity between λ and a is destroyed, as observed.