Altering critical depinning current via domain wall pile-up in magnetic nanowires

Abstract

An important role of domain wall pileup in current-driven domain wall depinning in magnetic nanowires is revealed using micromagnetic simulations. It is found that the critical current for domain wall depinning can be substantially reduced and conveniently tuned by controlling domain wall number in the pileup at pinning site, in analogy to dislocation pileup responsible for Hall-Petch effect in mechanical strength. Domain wall pinning and depinning at an s-shape bend is considered, and the effects of curvature and current crowding in magnetic circuit on domain wall behaviors are discussed.

Magnetic vortex racetrack memory

“…The simulation results show that the array of vortices move in the direction of electron flow (opposite to the direction of the current flow) as expected, at speed of 40 m/s and 200 m/s, respectively. In both cases, the vortex motion velocity v is related to the electron motion velocity u by v/u=/, same as the domain walls in Permalloy nanowires [11,12,21]. Moreover, changes in the vertical position of vortices under different currents are observed.…”

“…While switching the core polarity of a vortex at the pinning site is out of the scope of this paper, it is worth noting that ultrafast switching of magnetic vortex (via pulsed magnetic field, alternating current, and circularly polarized light) has been intensively investigated [5][6][7][8][9] and can be applied to MVRM for ultrafast data writing. The pinning strength of type I notch depends on the notch depth d. The critical depinning current, however, depends not only on the pinning strength of the notch, but also strongly on the number of vortices in the nanowire since they together generate domain wall pile-up effect which drastically amplifies the driving force to vortex motion [12]. To distinguish the intrinsic pinning strength of the notch from the extrinsic effect of the vortex number on the critical depinning current, the nanowire in Fig.…”

“…Such a drastic reduction in depinning current originates from the domain wall pile-up effect in the nanowire which is studied in detail in Ref. [12]: an array of domain walls stopped by a barrier in a magnetic nanowire form a domain wall pile-up which experiences wall-wall interaction under spin-polarized current; the wall-wall interaction gives rise to a driving force to the front domain wall in addition to its own current-induced driving force; and due to the contribution from the wall-wall interaction, the critical current to depin the front wall to pass the barrier is reduced by roughly a factor of n, the number of the domain walls in the pile-up. Such pile-up effect from the nine vortices in the nanowire behind the notch accounts for the drastically reduced current u=20m/s as compared to u cr =148.5m/s for no pile-up effect.…”

“…where γ is the gyromagnetic ratio, α the damping parameter, β the nonadiabatic spin-transfer torque coefficient, H eff the effective magnetic field, and u the electron motion velocity vector which is proportional to the electrical current density. H eff is determined by the variational derivative of the free energy F, H eff =-F/m, and F is a sum of magnetic anisotropy energy, exchange energy, magnetostatic energy, and external magnetic energy [12]:…”

“…Eq. (1) is numerically solved using our own Fortran 90 code with parallel algorithm by Message Passing Interface (MPI), which has been developed in our group and used in previous works [12,14,15]. The simulations are performed on Stampede supercomputer at Texas Advanced Computing Center for cobalt nanowires with the magnetic easy direction () tr along the z-axis and the material parameters 3.109 in Ref.…”