Optimal spin current pattern for fast domain wall propagation in nanowires

One of the important issues in nanomagnetism is to lower the current needed for a technologically useful domain wall (DW) propagation speed. Based on the modified LandauLifshitz-Gilbert (LLG) equation with both Slonczewski spin-transfer torque and the field-like torque, we derive an optimal temporally and spatially varying spin current pattern for fast DW propagation along nanowires. Under such conditions, the DW velocity in biaxial wires can be enhanced as much as tens of times higher than that achieved in experiments so far. Moreover, the fast variation of spin polarization can efficiently help DW depinning. Possible experimental realizations are discussed. Copyright c © EPLA, 2010 Fast magnetic domain wall (DW) propagation along nanowires by means of electrical currents is presently under intensive study in nanomagnetism experimentally [1–5] and theoretically [6–8]. In addition to the technological interest such as race track memory [1], DW dynamics is also an interesting fundamental problem. The dynamics of a single DW can be qualitatively understood from one-dimensional (1D) analytical models [9] that predict a rigid-body propagation below the Walker breakdown and an oscillatory motion above it [9,10]. The latter process is connected with a series of complicated cyclic transformations of the DW structure and a drastic reduction of the average DW velocity. The Walker limit is thus the maximum velocity at which DW can propagate in magnetic nanowires without changing its inner structure. From a technological point of view, such a limit seems to represent a major obstacle since the fidelity of data transmission may depend on preserving the DW structure while the utility requires speeding up the DW velocity adequately. Various efforts have been made to overcome this limit through the geometry design. For instance, Lewis et al. [11] proposed a chirality filter consisting of (a)E-mail: [email protected] a cross-shaped trap to preserve the DW structure. Yan et al. [12] demonstrated the removal of Walker limit via a micromagnetic study on the current-driven DW motion in cylindrical Permalloy nanowires. Our focus is to find a way to increase the velocity-current slope below the Walker breakdown. A DW propagates under a spin-polarized current through angular-momentum transfer from conduction electrons to the local magnetization, known as the spintransfer torque (STT) [13], which is different from the magnetic-field–driven DW propagation originated from the energy dissipation [10,14,15]. Two configurations have been studied so far. One is the mostly studied case in which current is along the wire axis [1–5]. The STT exerted in this configuration is very small because the angle between the current spin polarization direction and local magnetization is very small everywhere. Very recently, an alternative setup where the spin current is injected perpendicular to the wire is proposed [16] and experimentally realized [17]. The STT is much larger in this perpendicular configuration. Generally speaking, two types of spin torques exist: the Slonczewski torque [13] (a-term) Ta =−γ aJ MsM× (M× s) and the field-like torque [18,19] (b-term) Tb =−γbJM× s, where γ = |e|/me, M, Ms = |M|, and s are the gyromagnetic