Bloch-line dynamics within moving domain walls in 3D ferromagnets

Abstract

We study field-driven magnetic domain wall dynamics in garnet strips by large-scale threedimensional micromagnetic simulations. The domain wall propagation velocity as a function of the applied field exhibits a low-field linear part terminated by a sudden velocity drop at a threshold field magnitude, related to the onset of excitations of internal degrees of freedom of the domain wall magnetization. By considering a wide range of strip thicknesses from 30 nm to 1.89 µm, we find a non-monotonic thickness dependence of the threshold field for the onset of this instability, proceeding via nucleation and propagation of Bloch lines within the domain wall. We identify a critical strip thickness above which the velocity drop is due to nucleation of horizontal Bloch lines, while for thinner strips and depending on the boundary conditions employed, either generation of vertical Bloch lines, or close-to-uniform precession of the domain wall internal magnetization takes place. For strips of intermediate thicknesses, the vertical Bloch lines assume a deformed structure due to demagnetizing fields at the strip surfaces, breaking the symmetry between the top and bottom faces of the strip, and resulting in circulating Bloch line dynamics along the perimeter of the domain wall.

Multistep Bloch-line-mediated Walker breakdown in ferromagnetic strips

“…B W first increases rapidly with L y , reaches a maximum for L y ≈ 350 nm, after which B W slowly decreases, possibly reaching a plateau for the largest L y -values considered. This non-monotonic L y -dependence is reminiscent of our recent results on thickness-dependent Walker breakdown in garnet strips [10], and will be analyzed further below.…”

Depinning exponents of thin film domain walls depend on disorder strength

“…Experimental studies verifying these results are needed, and are likely to be challenging due to the need to reach very low temperatures [33,34] (to minimize thermal rounding [2]), and to control the disorder. It would be interesting to extend our study to 3D systems with 2D DWs with internal degrees of freedom [35], to consider effects due to a finite T [36], as well as the interplay of ξ with the DW and BL widths. Our model should find applications in modelling DW dynamics in a wide range of contexts where DW velocities are not so high that spin wave emission from the moving DW [37][38][39] (not captured by our line model) becomes important, including creep motion of DWs [5] and Barkhausen noise [6].…”

Barkhausen Noise from Precessional Domain Wall Motion

“…This effect is well-known especially in the nanowire geometry -important for the proposed spintronics devices such as the racetrack memory [7] -where the onset of precession of the DW magnetization above a threshold field leads to an abrupt drop in the DW propagation velocity (the Walker breakdown [8]), and hence to a non-monotonic driving field vs DW velocity relation [9]; these features are well-captured by the so-called 1d models [10].In wider strips or thin films, the excitations of the DW internal magnetization accompanying the velocity drop cannot be described by precession of an individual magnetic moment. Instead, one needs to consider the nucleation, propagation and annihilation of topological defects known as Bloch lines (BLs) within the DW [11][12][13]. BLs, i.e., transition regions separating different chiralities of the DW, have been studied in the context of bubble materials already in the 1970's [13].…”

“…In wider strips or thin films, the excitations of the DW internal magnetization accompanying the velocity drop cannot be described by precession of an individual magnetic moment. Instead, one needs to consider the nucleation, propagation and annihilation of topological defects known as Bloch lines (BLs) within the DW [11][12][13]. BLs, i.e., transition regions separating different chiralities of the DW, have been studied in the context of bubble materials already in the 1970's [13].…”