Unidirectional tilt and enhancement of the Walker limit for domain walls in stripes with Dzyaloshinskii-Moriya interaction

Efficient manipulations of chiral textures like domain walls and skyrmions are crucial for the development of prospective spintronic devices [1-2]. Domain walls moving in stripes with perpendicular anisotropy and Dzyaloshinskii-Moriya interaction (DMI) exhibit a tilt resulting in a decrease of their maximal velocity [3]. Beside the direct current influence [3], the tilt is usually caused by in-plane fields [4] or an edge roughness [5]. In this work, we show that the domain wall tilt can appear as a result of competition of the in-plane anisotropy and DMI. We also describe the field-driven dynamics of the tilted domain wall.

We consider an infinitely long biaxial stripe with interfacing DMI (Fig. 1) and biaxial anisotropy. The first easy axis of anisotropy is perpendicular to the stripe plane and the second easy axis lies within the stripe plane and makes an angle α with the stripe axis. The shape anisotropy forces α=0, while α≠0 can appear due to other effects, e.g. exchange bias from underlying antiferromagnet. The second anisotropy rotates the in-plane magnetization inside the domain wall according to the in-plane easy axis direction. The optimum of the DMI energy is reached when the magnetization rotates perpendicularly to the domain wall plane. In stripes the energy balance between these two energy terms and the energy of the domain wall tension results in a unidirectional tilt by angle χ of the domain wall plane (χ=0 corresponds to the domain wall perpendicular to the stripe), determined by α. There is a metastable state of the wall, tilted into the opposite direction in a certain range of anisotropy and DMI values. This is related to the symmetry break between the two opposite directions of the magnetization rotation inside the domain wall due to the presence of a weak DMI. Furthermore, the dynamics of the domain wall in the presence of a biaxial anisotropy and DMI exhibits a symmetry break with respect to the magnetic field and the easy axis direction A. The domain wall reveals fast and slow motion regimes for the opposite signs of α. The slow regime is characterized by a smaller Walker field b and switch of the magnetization direction inside the domain wall in a certain field below b . The latter results in an increase of the domain wall speed. The velocity of the domain wall is inversely proportional to cos χ. The maximum of the Walker field corresponds to α≠0 (Fig. 2).

In conclusion, we describe a unidirectional tilt of a domain wall in a biaxial stripe with DMI, which appears at equilibrium without external magnetic field and demonstrate the enhancement of the Walker field and velocity [6]. The domain wall dynamics reveal fast and slow regimes depending on the orientation of the easy axis of the in-plane anisotropy and the applied magnetic field.

References: [1] K.-S. Ryu, L. Thomas, S.-H. Yang et al., Nat. Nanotech., Vol. 8, 527 (2013); [2] O. Pylypovskyi, D. Sheka, V. Kravchuk et al., Sci. Rep. Vol. 6, 23316 (2016); [3] O. Boulle, S. Rohart, L. Buda-Prejbeanu et al., Phys. Rev. Lett. Vol. 111, 217203 (2013); [4] C. Muratov, V. Slastikov, A. Kolesnikov et al., Phys. Rev. B. Vol. 96, 134417 (2017); [5] E. Martinez, S. Emori, N. Perez et al. J. Appl. Phys. Vol. 115, 213909 (2014); [6] O. Pylypovskyi, V. Kravchuk, O. Volkov et al., ArXiv, 2001.03408 (2020)