High-field domain wall propagation velocity in magnetic nanowires

Abstract

A thory of field-induced domain wall (DW) propagation is developed. The theory not only explains why a DW in a defect-free nanowire must propagate at a finite velocity, but also provides a proper definition of DW propagation velocity. This definition, valid for an arbitrary DW structure, allows one to compute the instantaneous DW velocity in a meaningful way even when the DW is not moving as a rigid body. A new velocity-field formula beyond the Walker breakdown field, which is in excellent agreement with both experiments and numerical simulations, is derived.It is a textbook knowledge[1] that a magnetic field can drive a magnetic domain wall (DW) to move. However, our understanding of the field-induced DW motion is far from complete although it has been intensively studied for more than fifty years and many interesting phenomena of magnetization dynamics have been found. Recent development in nanomagnetism[2] demands a deep understanding of DW motion in nanowires, especially how a field affects DW propagation velocity. DW dynamics is governed by the Landau-Lifshtiz-Gilbert (LLG) equation that can only be solved analytically for some special problems [3,4]. A number of theories have been widely accepted and written in books[1], such as kinetic potential approach that assumes zero-damping, Thiele dynamic force equilibrium formulation that is correct for rigid DW propagation, Schryer and Walker analytical solution that is valid only for 1D and exact only for field smaller than a so-called Walker breakdown field H W [3], Slonczewski formulation that simplifies a DW by its center and the cant angle of DW plane. None of these orthodox theories works beyond H W although they have greatly enriched our current understanding of DW dynamics. For example, kinetic potential approach cannot be a correct description of DW propagation because it violates the principle of "no damping, no propagation" that will be explained in this paper. Thiele approach is a good way to describe a rigid DW propagation for small field H < H W , but its assumptions are not valid for H > H W . Schryer and Walker's approach is for 1D and H < H W , and its predictions for H > H W are incorrect. For instance, its prediction that the v − H line for H >> H W passing through the origin differs from both experiments and micromagnetic simulations [6,7,8,9]. Its generalization predicts a saturated velocity[5] (bounded by the velocity at H W ) that does not agree either with experiments or with simulations [6,7,8,9]. Slonczewski formulation is a great simplification of LLG equation that not only replaces partial differential equations by ordinary differential ones, but also is based on Thiele rigid DW approximation although the Slonczewski equations have also been applied to the case of H > H W where it is known that DW deformation cannot be neglected. The problems with both Thiele and Slonczewski formulations can also be seen from their v − H formula[9, 10] that do not capture the trend for H > H W . Even more surprising, none of the existing theories provi...

Electric field control of multiferroic domain wall motion

“…(12) are reduced to those of a DW purely driven by a magnetic field, whose behaviours are well known. 3,4,40 In that case, the DW motion is characterized by the existence of two dynamic regimes, separated by a threshold field called Walker field.…”

“…1,2 Usually, the motion of DW in magnetic materials are driven by a magnetic field [3][4][5] or spin-polarized current. 6,7 A key concept in the context of DW motion is the so-called Walker breakdown, 3 which distinguishes the two regimes with high-and low-mobility and sets a limit to the DW velocity.…”

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“…The roadmap of DW propagation is obtained recently. 14,15 A static DW cannot exist in a static field, thus it must move with time. A moving DW must dissipate energy due to the Gilbert damping.…”

Domain-Wall Motion in Ferromagnetic Nanowires Driven by Arbitrary Time-Dependent Fields: An Exact Result

“…75.78.Fg Introduction.-The motion of magnetic domain walls (DWs) in ferromagnetic nanowires has recently become a subject of intensive research in the condensed matter physics community [1]. Manipulation of DWs by external magnetic fields, and in particular, the question of how the DW propagation velocity depends on the applied field have drawn considerable attention [2][3][4].In ferromagnetic nanowires, the dynamics of the orientation of the magnetization distribution, m(x, t) (normalized so that |m| = 1), is described by the LandauLifshitz-Gilbert (LLG) equation [5] …”

“…Manipulation of DWs by external magnetic fields, and in particular, the question of how the DW propagation velocity depends on the applied field have drawn considerable attention [2][3][4].…”