Simulation of transverse and longitudinal magnetic ripple structures induced by surface anisotropy

Micromagnetic ripple structures on the surfaces of thick specimens of ultra-soft magnetic material having strong surface anisotropy Ks favouring out-of-surface magnetization have been calculated. These ripples have wavelengths of the order of 0.1 μm and extend to a depth ∼ √A/Ms, where A is the exchange constant and Ms is the saturation magnetization. The wave-vectors of the ripple structures are either transverse or parallel to the bulk magnetization. Both structures have lower energy than the one-dimensional structure discussed by O'Handley and Woods, and they exhibit stronger normal magnetization. The transverse structure requires a surface anisotropy Ks ≥ 0.80K0, where is that required for the one-dimensional structure. The threshold for longitudinal ripples is 0.84K0. It is suggested that the transverse structure probably constitutes the ground state. The magnitudes of Ks and A should be obtainable from measurements of the ripple wavelength and amplitude, and Ms.