Domain Wall Tilt and Enhancement of the Walker Limit in Stripes with Dzyaloshinskii-Moriya Interaction and Perpendicular Anisotropy

The efficiency of manipulation of domain walls and skyrmions in ferromagnetic racetracks with perpendicular anisotropy determines perspectives of development of data storage and logic devices relying on spintronic and spin-orbitronic concepts [1, 2]. The domain wall dynamics is dependent on its orientation with respect to the racetrack axis. In-plane fields [3], edge roughness [4] and current [5] result in the domain wall tilt in samples, possessing Dzyaloshinskii-Moriya interaction (DMI). Here, we show theoretically, that the tilt can appear in equilibrium and describe the domain wall dynamics under the action of external field. We consider a thin biaxial stripe with DMI of interfacial type [6]. The main easy axis of anisotropy is perpendicular to the plane, and the direction of the second easy axis lies in the stripe plane under the angle α to the stripe axis. While the shape anisotropy results in α = 0, a general case α ≠ 0 can appear under the influence of other effects, e.g crystalline structure [7]. While the second easy axis defines the preferable in-plane magnetization within the domain wall, the DMI forces the domain wall being perpendicular to the magnetization gradient. The competition between these two energy contributions and the domain wall tension results in the unidirectional tilt of the whole domain wall. If the DMI is weak enough, there is an additional metastable domain wall state, tilted into the opposite direction. The symmetry break is observed not only for static magnetization texture, but also in the domain wall dynamics under the action of external magnetic field. The domain wall reveals fast and slow motion regimes for the opposite signs of A. The maximum of the Walker field and Walker velicities is determined by the angle A of the second easy axis anisotropy and does not coincide with a shape-induced anisotropy direction A=0. The domain wall possesses the switch of the magnetization direction inside the domain wall in the slow motion regime, which results in the faster motion.

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