Microscopic theory of spin-orbit torques and skyrmion dynamics

We formulate a general microscopic approach to spin-orbit torques in thin ferromagnet/heavy-metal bilayers in linear response to electric current or electric field. The microscopic theory we develop avoids the notion of spin currents and spin-Hall effect. Instead, the torques are directly related to a local spin polarization of conduction electrons, which is computed from generalized Kubo-St\v{r}eda formulas. A symmetry analysis provides a one-to-one correspondence between polarization susceptibility tensor components and different torque terms in the Landau-Lifshitz-Gilbert equation for magnetization dynamics. The spin-orbit torques arising from Rashba or Dresselhaus type of spin-orbit interaction are shown to have different symmetries. We analyze these spin-orbit torques microscopically for a generic electron model in the presence of an arbitrary smooth magnetic texture. For a model with spin-independent disorder we find a major cancelation of the torques. In this case the only remaining torque corresponds to the magnetization-independent Edelstein effect. Furthermore, our results are applied to analyze the dynamics of a Skyrmion under the action of electric current.Comment: 13 pages, 4 figure

Magnetoelectric domain wall dynamics and its implications for magnetoelectric memory

Domain wall dynamics in a magnetoelectric antiferromagnet is analyzed, and its implications for magnetoelectric memory applications are discussed. Cr$_2$O$_3$ is used in the estimates of the materials parameters. It is found that the domain wall mobility has a maximum as a function of the electric field due to the gyrotropic coupling induced by it. In Cr$_2$O$_3$ the maximal mobility of 0.1 m/(s$\times$Oe) is reached at $E\approx0.06$ V/nm. Fields of this order may be too weak to overcome the intrinsic depinning field, which is estimated for B-doped Cr$_2$O$_3$. These major drawbacks for device implementation can be overcome by applying a small in-plane shear strain, which blocks the domain wall precession. Domain wall mobility of about 0.7 m/(s$\times$Oe) can then be achieved at $E=0.2$ V/nm. A split-gate scheme is proposed for the domain-wall controlled bit element; its extension to multiple-gate linear arrays can offer advantages in memory density, programmability, and logic functionality.Comment: 5 pages, 2 figures, revised and corrected version, accepted in Applied Physics Letter

Thermoelectric efficiency of topological insulators in a magnetic field

We study the thermoelectric properties of three-dimensional topological insulators in magnetic fields with many holes (or pores) in the bulk. We find that at high density of these holes in the transport direction the thermoelectric figure of merit, ZT, can be large due to the contribution of the topologically protected conducting surfaces and the suppressed phonon thermal conductivity. By applying an external magnetic field a subgap can be induced in the surface states spectrum. We show that the thermoelectric efficiency can be controlled by this tunable subgap leading to the values of ZT much greater than 1. Such high values of ZT for reasonable system parameters and its tunability by magnetic field make this system a strong candidate for applications in heat management of nanodevices, especially at low temperatures.Comment: 9 pages, 4 figures, Proceedings of MMM 201

Staggered Dynamics in Antiferromagnets by Collective Coordinates

Antiferromagnets can be used to store and manipulate spin information, but the coupled dynamics of the staggered field and the magnetization are very complex. We present a theory which is conceptually much simpler and which uses collective coordinates to describe staggered field dynamics in antiferromagnetic textures. The theory includes effects from dissipation, external magnetic fields, as well as reactive and dissipative current-induced torques. We conclude that, at low frequencies and amplitudes, currents induce collective motion by means of dissipative rather than reactive torques. The dynamics of a one-dimensional domain wall, pinned at 90$^{\circ}$ at its ends, are described as a driven harmonic oscillator with a natural frequency inversely proportional to the length of the texture.Comment: 4 pages, 2 figure

Stripes in thin ferromagnetic films with out-of-plane anisotropy

We examine the T=0 phase diagram of a thin ferromagnetic film with a strong out-of-plane anisotropy in the vicinity of the reorientation phase transition (with Co on Pt as an example). The phase diagram in the anisotropy-applied field plane is universal in the limit where the film thickness is the shortest length scale. It contains uniform fully magnetized and canted phases, as well as periodically nonuniform states: a weakly modulated spin-density wave and strongly modulated stripes. We determine the boundaries of metastability of these phases and point out the existence of a critical point at which the difference between the SDW and stripes vanishes. Out-of-plane magnetization curves exhibit a variety of hysteresis loops caused by the coexistence of one or more phases. Additionally, we study the effect of a system edge on the orientation of stripes. We compare our results with recent experiments.Comment: added references and clarified derivations in response to referee comment