Manipulating small spin textures that can serve as bits of information by electric and spin currents is one of the main challenges in the field of spintronics. Ferromagnetic skyrmions attracted a lot of attention because they are small in size and are better than domain walls at avoiding pinning sites while moved by electric current. Moreover, recently in ferromagnet/heavy-metal bilayers they were shown to move very efficiently by the so-called "spin-orbit" torques. We formulate the general theory of these torques including their microscopic treatment in disordered systems [1]. This allows us to calculate the skyrmion Hall angle, which was recently revealed by X-ray microscopy. We show that this angle depends on dynamical deformations of the skyrmion due to the spin-orbit torques [1, 2].

Meanwhile, the ferromagnetic skyrmions also have certain disadvantages, such as the presence of stray fields and transverse to current dynamics, making them harder to employ in spintronic devices. To avoid these unwanted effects, we propose a novel topological object: the antiferromagnetic skyrmion [3] and explore its properties using the microscopic analysis, generalized Thiele equation, and micromagnetic simulations. This topological texture has no stray fields and we show that its dynamics are faster compared to its ferromagnetic analogue. More importantly, we show that due to unusual topology the antiferromagnetic skyrmions experience no skyrmion Hall effect (zero velocity component transverse to the current), and thus are good candidates for spintronic memory and logic applications.

[1] I. Ado, O. A. Tretiakov, and M. Titov, Phys. Rev. B 95, in press (2017).
[2] K. Litzius, I. Lemesh, B. Kruger, P. Bassirian, L. Caretta, K. Richter, F. Buttner, K. Sato, O. A. Tretiakov, J. Forster, R. M. Reeve, M. Weigand, I. Bykova, H. Stoll, G. Schutz, G. S. D. Beach, and M. Klaui, Nature Phys. 13, 170 (2017).
[3] J. Barker and O. A. Tretiakov, Phys. Rev. Lett., 116, 147203 (2016).