School of Engineering Sciences, University of Southampton, Southampton, UK.
J Phys Condens Matter. 2012 Jan 18;24(2):024219. doi: 10.1088/0953-8984/24/2/024219. Epub 2011 Dec 15.
We study field-driven domain wall (DW) motion in nanowires with perpendicular magnetic anisotropy using finite element micromagnetic simulations. Edge roughness is introduced by deforming the finite element mesh, and we vary the correlation length and magnitude of the roughness deformation separately. We observe the Walker breakdown both with and without roughness, with steady DW motion for applied fields below the critical Walker field H(c), and oscillatory motion for larger fields. The value of H(c) is not altered in the presence of roughness. The edge roughness introduces a depinning field. During the transient process of depinning, from the initial configuration to steady DW motion, the DW velocity is significantly reduced in comparison to that for a wire without roughness. The asymptotic DW velocity, on the other hand, is virtually unaffected by the roughness, even though the magnetization reacts to the edge distortions during the entire course of motion, both above and below the Walker breakdown. A moving DW can become pinned again at some later point ('dynamic pinning'). Dynamic pinning is a stochastic process and is observed both for small fields below H(c) and for fields of any strength above H(c). In the latter case, where the DW shows oscillatory motion and the magnetization in the DW rotates in the film plane, pinning can only occur at positions where the DW reverses direction and the instantaneous velocity is zero, i.e., at the beginning or in the middle of a positional oscillation cycle. In our simulations pinning was only observed at the beginnings of cycles, where the magnetization is pointing along the wire. The depinning field depends linearly on the magnitude of the edge roughness. The strongest pinning fields are observed for roughness correlation lengths that match the domain wall width.
我们使用有限元微磁模拟研究了具有垂直各向异性磁的纳米线中的场驱动畴壁(DW)运动。通过变形有限元网格来引入边缘粗糙度,并且我们分别改变粗糙度变形的相关长度和幅度。我们观察到了存在和不存在粗糙度的 Walker 击穿,在低于临界 Walker 场 H(c)的外加场下,DW 运动稳定,而在较大的场下,DW 运动呈振荡。在存在粗糙度的情况下,H(c)的值不会改变。边缘粗糙度引入了去钉扎场。在去钉扎的瞬态过程中,从初始配置到稳定的 DW 运动,DW 的速度与没有粗糙度的情况下相比显著降低。另一方面,DW 速度的渐近值几乎不受粗糙度的影响,即使在 Walker 击穿以上和以下的整个运动过程中,磁化都对边缘变形做出反应。在稍后的某个时刻,移动的 DW 可能会再次被钉扎(“动态钉扎”)。动态钉扎是一个随机过程,在低于 H(c)的小场和高于 H(c)的任何强度的场中都可以观察到。在后一种情况下,DW 表现出振荡运动,DW 中的磁化在薄膜平面内旋转,只有在 DW 反转方向并且瞬时速度为零的位置才会发生钉扎,即在位置振荡周期的开始或中间。在我们的模拟中,只有在周期的开始处观察到了钉扎,此时磁化方向沿着线。去钉扎场与边缘粗糙度的幅度呈线性关系。对于与畴壁宽度匹配的粗糙度相关长度,观察到了最强的钉扎场。