Domain wall propagation due to the synchronization with circularly polarized microwaves P. Yan and X. R. Wang Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China Finding a new control parameter for magnetic domain wall (DW) motion in magnetic nanostruc- tures is important in general and in particular for the spintronics applications. Here, we show that a circularly polarized magnetic field (CPMF) at GHz frequency (microwave) can efficiently drive a DW to propagate along a magnetic nanowire. Two motion modes are identified: rigid-DW propaga- tion at low frequency and oscillatory propagation at high frequency. Moreover, DW motion under a CPMF is equivalent to the DW motion under a uniform spin current in the current perpendicular to the plane magnetic configuration proposed recently by Khvalkovskiy et al. [Phys. Rev. Lett. 102 , 067206 (2009)], and the CPMF frequency plays the role of the current. Controlled manipulation of magnetic domain-wall (DW) propagation in nanowires has spurred intensive research in recent years[1–12] in nano-magnetism be- cause of its fundamental interest and the potential im- pact in spintronic device technology. Both static mag- netic fields[1–4] and electric currents[5–12] can be the control parameters. However, their control mechanisms are different, and they have different advantages and dis- advantages. Thus, finding any new control parameter for DW motion should be of great interest. Although it is known both theoretically[13] and experimentally[14] that a microwave can be used to ma- nipulate the motion of single domain magnetic particles (macrospins or Stoner particles), a microwave was hardly thought to be an effective control parameter for DW mo- tion. In this letter, we show that a circularly polarized magnetic field (CPMF) at GHz frequency (microwave) can efficiently drive a magnetic DW to propagate along a nanowire at a high speed. Similar to a spin-polarized current, a CPMF can generate both Slonczewski-like and field-like spin-transfer torques (STTs) inside a DW. Un- like the STTs generated by a spin-polarized current, the field-like STT is much bigger than the Slonczewski-like STT. Thus, a CPMF generates more useful STT[7] in comparison with that of a spin-polarized current. More- over, its driving mechanism is very different from those of a static axial magnetic field and a spin-polarized current. In order to appreciate the CPMF-driven DW motion, let us recall the driving mechanisms of a static axial mag- netic field and a spin-polarized current. A DW propa- gates along a wire under a static magnetic field because the Zeeman energy must be released to compensate the dissipated energy due to the non-existence[15] of a static DW in a static magnetic field. An electric current, on the other hand, moves DWs by the STT due to the transfer of spin angular momentum from conduction electrons to local spins[5]. A spin-polarized current can transfer two types of torques to a local magnetization ⃗ M = M$_{s}$ ⃗ m . One is the Slonczewski-like STT [5] of b ⃗ m × ( ⃗ m × ⃗ s ) (b- term), where ⃗ s is the polarization direction of the spin- polarized current. The other one is a field-like torque[6] here ⃗ h$_{eff}$ = − 1 µ 0 δU/δ ⃗ M is the effective magnetic field that is the variational derivative of the free energy density U [ ⃗ M ] with respect to magnetization ⃗ M , γ = g | e | / 2 m$_{e}$ is the gyromagnetic ratio, µ 0 is the vacuum magnetic per- meability and α is the phenomenological Gilbert damping constant[16] which measures dissipative effect. Eq. (1) is a nonlinear partial differential equation that can be solved exactly only in some special cases[1, 17]. A macrospin can synchronize its motion with a CPMF. A synchronized motion generates a damping field that forces the spin to move perpendicularly to the synchro- nized motion, leading to a dramatic effect of a CPMF on a Stoner particle[13, 14]. Thus, it is natural to study the CPMF effect on DW motion since a DW may also synchronize its motion with a CPMF due to the DW We consider a head-to-head (HH) DW in a magnetic nanowire whose easy axis is along the wire axis defined as the z-axis shown in Fig. 1. The motion of the magne- tization ⃗ M = M$_{s}$ ⃗ m , is governed by the Landau-Lifshitz- Gilbert (LLG) equation[16] of c ⃗ m × ⃗ s (c-term). b and c are parameters roughly pro- portional to current[5, 6]. The effects of b- and c-terms on DW propagation are very different. b-term is incapable of generating a sustained wall motion, except at very large current, while c-term can drive a DW to propagate along the carrier direction[7]. Unfortunately, c-term is normally much smaller than b-term[11]. A large current density is needed to achieve a technologically useful DW propagation velocity[9], but the associated Joule heating could affect device performance. Thus, it should be inter- esting if one can generate a large c-term (in comparison with b-term) either in a new architecture or by using a new control parameter. One solution along the first line of the thinking is provided by Khvalkovskiy et al. [12] who proposed a current perpendicular to the plane magnetic configuration in a sandwiched magnetic nanowire struc- ture. Here we provide a solution along the second line of the thinking. arXiv:1001.1800v1 [cond-mat.mes-hall] 12 Jan 2010 ∂ ⃗ m ∂t = − γ ⃗ m × ⃗ h$_{eff}$ + α ⃗ m × ∂ ⃗ m ∂t , (1)