Micromagnetic Study of Domain Wall-Pinning Characteristics With Step-Like Thickness Change in Thin Film

Abstract

The pinning characteristics of a domain wall with a step-like thickness change along the wall is investigated in 0.15-to 0.5-m-thick films with an in-plane anisotropy using micromagnetic simulation based on the Landau-Lifshitz-Gilbert equation. The asymmetric Bloch wall having the structure in which the magnetostatic coupling develops between spins near the step when the wall is pinned shows the bi-directional pinning effect for magnetic fields applied along the magnetic domain. The wall energy of the pinned wall decreases with increasing step depth due to the largely decrease of the exchange energy component. The depinning field for the negative applied fields which drive the wall in the direction of the nongrooved region (thick film region) is considerably larger than that for the positive ones which drive the wall in the direction of the grooved region (thin film region). The depinning fields for both the positive and negative applied fields increase with decreasing film thickness.

Domain-wall pinning by steplike thickness change in magnetic thin film

“…The simulation results performed by varying the shape of thickness change have suggested that the depinning field decreased as a slope becomes gentler. 6 Although observation of a negative wall depinning from …”

“…5 In the previous work, micromagnetic simulation has reported that steplike thickness change along a domain wall can produce wall pinning in an in-plane magnetization thin film. 6,7 The simulation results have indicated that a bidirectional pinning effect for magnetic fields applied along the magnetic domain was obtained at the step.…”

“…[6][7][8][9] As illustrated in Fig. 1, a steplike thickness change ͑⌬h͒ along the domain wall ͑x direction͒ is assumed to clarify the wall-pinning characteristics with thickness change.…”

“…Material parameters used in the simulation are as follows: saturation induction 4M s = 8000 G, uniaxial anisotropy constant K u = 3200 ergs/ cm 3 , exchange constant A =10 −6 erg/ cm, gyromagnetic ratio ␥ = 1.76ϫ 10 7 ͑s Oe͒ −1 , and damping constant ␣ = 0.5. 6,7 The grid element spacing is 5 nm for the film thickness h ഛ 300 nm and 10 nm for h Ͼ 300 nm, respectively. The easy axis is along the x direction and magnetic fields ͑H p ͒ are applied along the magnetic domain.…”