Session R47: Spin-Orbit Torque III and Chiral Domain Walls

Highly efficient domain wall motion in ferrimagnetic trilayers

The current-induced domain wall motion arising from chiral spin torque forms the basis of a number of technologies such as the racetrack memory and 3-terminal based MRAM devices. One of the main impediments towards this implementation is the high current density usually needed to move domain walls reliably. Here, we show that in ferrimagnetic trilayers, we can reduce the critical current required to move domain walls by 2-5 times compared to a ferromagnetic trilayer while dramatically increasing the velocity for the same current densities. This in part, is effected by the use of a Pt underlayer which is grown as a mixture of (111) and (100) phase, resulting in a \textasciitilde 50{\%} greater Slonczewski-like SOT compared to (111) Pt, as measured by harmonic Hall voltage measurements of current-induced effective fields.   

Dramatic effect of curvature on DW velocity in chiral domain walls

The use of current pulses to manipulate domain walls (DWs) in nanowires is one of the most exciting developments in spintronics over the past decade, promising a range of novel devices. However, even after more than 10 years of work on current induced DW motion it has not been realized that the curvature of the nanowire can affect the speed of chiral DWs. Here we show that simply changing the sign of the curvature of a nanowire, dramatically changes the speed of N\'{e}el DWs in perpendicularly magnetized nanowires, by up to a factor of 10. We find that, DWs have an increased or decreased velocity in wires of a given curvature, independent of the DW chirality and the sign of the current induced torques. The fundamental origin of this effect is due to a current induced tilting of the DW that breaks the symmetry of the DW's motion with respect to the curvature of the wire. Whilst the strong dependence of the DW velocity on the nanowire's curvature may offer added device functionalities, we find that in synthetic antiferromagnetic nanowires, the influence of the curvature on the DW's velocity can be completely removed.   

Dispersive elastic properties of Dzyaloshinskii domain walls

Recent studies on the asymmetric field-driven growth of magnetic bubble domains in perpendicular thin films exhibiting an interfacial Dzyaloshinskii-Moriya interaction (DMI) have provided a wealth of experimental evidence to validate models of creep phenomena, as key properties of the domain wall (DW) can be altered with the application of an external in-plane magnetic field. While asymmetric growth behavior has been attributed to the highly anisotropic DW energy, $\sigma(\theta)$, which results from the combination of DMI and the in-plane field, many experimental results remain anomalous. In this work, we demonstrate that the anisotropy of DW energy alters the elastic response of the DW as characterized by the surface stiffness, $\tilde\sigma(\theta)=\sigma(\theta)+\sigma’’(\theta)$, and evaluate the impact of this stiffness on the creep law. We find that at in-plane fields larger than and antiparallel to the effective field due to DMI, the DW stiffness decreases rapidly, suggesting that higher energy walls can actually become more mobile than their low energy counterparts. This result is consistent with experiments on CoNi multilayer films where velocity curves for domain walls with DMI fields parallel and antiparallel to the applied field cross over at high in-plane fields.   

Current-induced spin torques in inversion broken materials

The spin-orbit interaction has been providing richness and greatness of magnetism and spintronics. In solid states, it couples electron's momentum and spins, which make it possible to electrically excite or detect spin accumulation/currents. Looking at localized spins, it helps magnetic anisotropies emerge (together with the magnetic-dipole interaction) where the sample's real space symmetry, such as surface-induced two-fold and crystalline-induced four-fold, is reflected on the magnetic energy landscape. Along this line, we can also think of what will happen when we lower the sample symmetry to ``inversion broken''. In this case, an electron propagating along one direction is, on the symmetry argument, no longer required to be on the same state as ones moving to the opposite direction. The spin-orbit interaction picks up this and causes a preferential spin direction for each electronic state, as a whole, forming spin textures in momentum space. These spin textures are a fascinating playground for developing spin-charge conversion effects. Although the electric excitation of spin textured materials has been known as the Edelstein effect [1] for more than two decades, its real spintronic use, e.g. magnetisation control [2], has been a much more recent interest. By employing microwave techniques to electrically exert magnetic torques through spin textures, we have successfully excite ferromagnetic resonance using this mechanism and characterise spin-orbit properties in our samples [3]. In this talk, I will summarise our recent results on spin torque effects using spin textures in inversion-broken materials. I will show microscopic origins of current-induced magnetisation control by the Edelstein effects in single ferromagnetic layers [3,4], as well as similar experiments by using non-magnetic inversion-broken layers [5] where we observed two spin torques, one arising from the spin-texture effect that co-exist with the other one from the spin-Hall effect. As the final part, I will present our latest results from our research. [1] Edelstein, Solid State. Comm. 73 233 (1990). [2] Chernyshov, et al., Nature Phys., 5 656 (2009). [3] Fang et al., Nature Nanotech. 9 211 (2011). [4] Kurebayashi, et al., Nature Nanotech, 9 211 (2014). [5] Skinner et al., Nature Comm. 6 6730 (2015).   

Current-driven domain wall ratchet in a nanomagnet with functionally graded Dzyaloshinskii-Moriya interaction

We develop a concept of functionally graded Dzyaloshinskii-Moriya interaction, which provides novel ways of efficient control of the magnetization dynamics. Using this approach we realize the ratchet motion of the domain wall in a magnetic nanowire driven by spin polarized current with potential applications in magnetic devices such as race-track memory and magnetic logical devices. By engineering the spatial profile of Dzyaloshinskii-Moriya parameters we provide a unidirectional motion of the domain wall along the wire. We base our study on phenomenological Landau-Lifshitz-Gilbert equations using a collective variable approach [1]. In effective equations of motion the functionally graded Dzyaloshinskii-Moriya interaction appears as a driving force, which can either suppress the action of the pumping by the current or can reinforce it. All analytical predictions are well confirmed by numerical simulations. \\ [1] K. V. Yershov et al., Phys. Rev. B {\bf 93}, 094418 (2016).   

Universal absence of Walker breakdown for spin--orbit and spin Hall torque driven domain walls

We consider ferromagnetic domain wall motion driven by spin--orbit and spin Hall torques, hereafter referred to as SOTs. Regardless of the relative importance of the reactive and dissipative components of the SOT, we find that for experimentally relevant spin--orbit coupling strengths it is possible to achieve universal absence of Walker breakdown. Specializing to the well-known Rashba and spin Hall SOTs we find dramatically different behavior for large current densities. The contribution from the Rashba SOT cancels exactly against the contribution from the spin-transfer torque, and the net velocity levels off to a constant as a function of current density. The different symmetry of the spin Hall SOT prevents such a cancellation, making the velocity an ever increasing linear function of the current. This effect is robust against the presence of interfacial Dzyaloshinskii--Moriya interaction, and is found both in perpendicular anisotropy ferromagnets and in shape anisotropy-dominated stripes. In the light of recent theoretical [Phys.Rev.B~\textbf{90}, 094411 (2014); arXiv:1610.00894] and experimental [Nat.Nano.~\textbf{10}, 221 (2015)] interest in antiferromagnetically coupled racetracks we consider the impact of these results in bilayer stripes coupled by interlayer exchange.   

Rashba conducting strips coupled to ferro- and antiferromagnetic layers

A system composed of a conducting planar strip with Rashba spin-orbit coupling (RSOC), magnetically coupled to a layer of localized magnetic moments, at equilibrium, is studied within a microscopic Hamiltonian with numerical techniques at zero temperature. In particular, transport properties for the cases of ferromagnetic (FM) and antiferromagnetic (AFM) coupled layers are computed in linear response on strips of varying width. In the case of an AFM localized order, results for the optical conductivity, for small strip widths, suggest the proximity to a metal-insulator transition. More interesting, in the proximity of this transition, and in general at intermediate values of the RSOC, it is observed a large spin-Hall conductivity that is two orders of magnitude larger than the one for the FM order for the same values of the RSOC and strip widhts. There are clearly two different regimes for small and for large RSOC, which is also present in the behavior of Rashba helical currents. Different contributions to the optical and the spin-Hall conductivities, of inter- or intraband origin, or coming from the hopping or spin-orbit terms of the Hamiltonian, are examined. Finally, the stability of the AFM order when magnetic moments are allowed to rotate is studied.   

Origins of open circuit voltage hysteresis driven by transverse charge current in ferromagnet/normal metal structures

We quantify the current-induced ensemble spin polarization due to non-equilibrium occupation of the `spin-momentum locked' surface states in a 3D topological insulator, using the Boltzmann transport formalism in the relaxation-time approximation. Despite these states' high in-plane spin projection, practically achievable spin density polarization is minuscule in linear response. Using an open circuit voltage scheme identical to those used by others to claim observation of unphysically large polarizations in topological insulators, we experimentally demonstrate potential switching and hysteresis on ferromagnetic contacts driven by the charge current in a topologically-trivial metal thin film beneath it. Our comprehensive study includes the effects of varying parameters (such as the current density, thin film thickness, types of metal materials, and temperature) and aims to resolve the different origins that contribute to this phenomenon.   

Spin-to-charge and spin-to-spin conversion in the presence of SOC active interfaces

The inversion symmetry breaking at the interface between different materials generates strong spin-orbit coupling (SOC). We will study various transport phenomena in metal junctions induced by this interaction. We will calulate the perpendicular electrical current generated as a response to a non-equilibrium spin density using a scattering matrix approach. We will investigate the spin loss that occurs at the interface due to the presence of this interaction. We will show how this spin loss is intrinsically related with the so-called spin swapping effect, where a secondary spin current is generated due to the interplay between the SOC and the non-equilibrium spin distribution. Then we will see how this spin-to-charge conversion occurs in an aluminium-tungsten junction through DFT-based transport calculations.   

Spin-transfer torque in Co/Graphene/Co vertical heterostructures: A route toward magnetic memories with low write energy and ultrahigh magnetoresistance.

The MgO-based magnetic tunnel junctions (MTJs) are presently the workhorse of first generation spintronics, based on magnetoresistitive phenomena, as well as for second generation spintronics largely focused on spin-transfer torque (STT) phenomena. Although MgO-based MTJs offer large tunneling magnetoresistance (TMR), required to detect current-driven magnetization switching from parallel to antiparallel state, they demand high bias voltage to initiate the switching dynamics which can lead to tunnel barrier degradation. Thus, an ideal physical system for envisioned STT-based memory devices and their integration with low-power CMOS technology would exhibit high TMR and low resistance-area (RA) product, ensuring small write voltages and write energy. Using first-principles quantum transport formalism, we predict that Co/Gr$_n$/Co vertical heterostructures, where Co(111) electrodes sandwich $n$ layers of graphene, offer such physical system. Although Co/Gr$_1$/Co junctions show similar STT magnitude as Co/Cu/Co spin valves in the linear-response regime, TMR$>$100\% requires Co/Gr$_3$/Co junctions whose RA product is still two orders of magnitude smaller than in MgO-based MTJs, while their magnetization switching can be initiated with bias voltages as small as $V_b < 0.1$ V.   

Switchable spin – orbit gaps in Fe(001)

In this contribution we will present results of a recent study of the influence of spin-orbit interaction (SOI) on the electronic properties of a prototypical ferromagnet, Fe(001). Using high resolution angle-resolved photoemission spectroscopy we demonstrated openings of the SOI - induced electronic band gaps, spin-orbit gaps (SOG), near the Fermi level. The SOG and thus the Fermi surface could be manipulated by changing the remanent magnetization direction. The experimental results were compared with the first-principles calculations and one-step photoemission calculations. Switchable SOG are the basis of many fundamental and technologically relevant phenomena, such as magnetocrystalline anisotropy, anisotropic magnetoresistance, intrinsic anomalous Hall effect or spin relaxation. We envision that a methodology similar to the one introduced here could be used to judge the potential of new materials for spintronic applications.   

Experimental Study of Magnetic Properties of Ultra-Thin Cobalt Films

The origin of spintronics can be traced back to the tunneling experiments made by M. Julliere in 1970 where normal and ferromagnetic metals are intercalated. More recently, superconducting spintronics have been subject of intensive research where the proximity of a superconductor next to the ferromagnet can lead to triplet superconductivity. This is the result of Cooper pairs inside of a magnetic inhomogeneity produced by the magnetization of the ferromagnets used. Despite several achievements such as the discovery of the Giant Magnetoresistance and the generation of exotic superconducting states found in spin valve like structures, a full control and understanding of the magnetic properties of the ferromagnetic materials used has not been easily attained. As a first step towards making novel spintronic devices, we investigate in detail the variation of remanent and saturation magnetization of Cobalt ultra-thin films of thicknesses between 1 to 10 nm. The results indicate that the remanent magnetization in Cobalt changes its direction around a thickness value of 1.8nm. Furthermore, we find that the saturation magnetization increases as the thickness decreases. This result is in contraposition to previous works.