Diffusive spin dynamics in ferromagnetic thin films with a Rashba interaction

In a ferromagnetic metal layer, the coupled charge and spin diffusion equations are obtained in the presence of both Rashba spin-orbit interaction and magnetism. The mis-alignment between the magnetization and the non-equilibrium spin density induced by the Rashba field gives rise to Rashba spin torque acting on the ferromagnetic order parameter. In a general form, we find that the Rashba torque consists of both in-plane and out-of-plane components, ie $\bm{T}=T_{\bot}\hat{\bm{y}}\times{\hat{\bm m}}+T_{\parallel}{\hat{\bm m}}\times({\hat{\bm y}}\times{\hat{\bm m}})$. Numerical simulations on a two dimensional nano-wire discuss the impact of diffusion on the Rashba torque, which reveals a large enhancement to the ratio $T_{\parallel}/T_{\bot}$ for thin wires. Our theory provides an explanation to the mechanism that drives the magnetization switching in a single ferromagnet as observed in the recent experiments.Comment: 5 pages and 3 figure

Phenomenology of chiral damping in noncentrosymmetric magnets

A phenomenology of magnetic chiral damping is proposed in the context of magnetic materials lacking inversion symmetry breaking. We show that the magnetic damping tensor adopts a general form that accounts for a component linear in magnetization gradient in the form of Lifshitz invariants. We propose different microscopic mechanisms that can produce such a damping in ferromagnetic metals, among which spin pumping in the presence of anomalous Hall effect and an effective "$s$-$d$" Dzyaloshinskii-Moriya antisymmetric exchange. The implication of this chiral damping in terms of domain wall motion is investigated in the flow and creep regimes. These predictions have major importance in the context of field- and current-driven texture motion in noncentrosymmetric (ferro-, ferri-, antiferro-)magnets, not limited to metals.Comment: 5 pages, 2 figure

Spin-torque efficiency enhanced by Rashba spin splitting in three dimensions

We examine a spin torque induced by the Rashba spin-orbit coupling in three dimensions within the Boltzmann transport theory. We analytically calculate the spin torque and show how its behavior is related with the spin topology in the Fermi surfaces by studying the Fermi-energy dependence of the spin torque. Moreover we discuss the spin-torque efficiency which is the spin torque divided by the applied electric current in association with the current-induced magnetization reversal. It is found that high spin-torque efficiency is achieved when the Fermi energy lies on only the lower band and there exists an optimal value for the Rashba parameter, where the spin-torque efficiency becomes maximum.Comment: 7 pages, 5 figure

Diffusive versus local spin currents in dynamic spin pumping systems

Using microscopic theory, we investigate the properties of a spin current driven by magnetization dynamics. In the limit of smooth magnetization texture, the dominant spin current induced by the spin pumping effect is shown to be the diffusive spin current, i.e., the one arising from only a diffusion associated with spin accumulation. That is to say, there is no effective field that locally drives the spin current. We also investigate the conversion mechanism of the pumped spin current into a charge current by spin-orbit interactions, specifically the inverse spin Hall effect. We show that the spin-charge conversion does not always occur and that it depends strongly on the type of spin-orbit interaction. In a Rashba spin-orbit system, the local part of the charge current is proportional to the spin relaxation torque, and the local spin current, which does not arise from the spin accumulation, does not play any role in the conversion. In contrast, the diffusive spin current contributes to the diffusive charge current. Alternatively, for spin-orbit interactions arising from random impurities, the local charge current is proportional to the local spin current that constitutes only a small fraction of the total spin current. Clearly, the dominant spin current (diffusive spin current) is not converted into a charge current. Therefore, the nature of the spin current is fundamentally different depending on its origin and thus the spin transport and the spin-charge conversion behavior need to be discussed together along with spin current generation

Reversal and Termination of Current-Induced Domain Wall Motion via Magnonic Spin-Transfer Torque

We investigate the domain wall dynamics of a ferromagnetic wire under the combined influence of a spin-polarized current and magnonic spin-transfer torque generated by an external field, taking also into account Rashba spin-orbit coupling interactions. It is demonstrated that current-induced motion of the domain wall may be completely reversed in an oscillatory fashion by applying a magnonic spin-transfer torque as long as the spin-wave velocity is sufficiently high. Moreover, we show that the motion of the domain wall may be fully terminated by means of the generation of spin-waves, suggesting the possibility to pin the domain-walls to predetermined locations. We also discuss how strong spin-orbit interactions modify these results.Comment: Accepted for publication in Phys. Rev.

Current induced magnetization reversal on the surface of a topological insulator

We study dynamics of the magnetization coupled to the surface Dirac fermions of a three di- mensional topological insulator. By solving the Landau-Lifshitz-Gilbert equation in the presence of charge current, we find current induced magnetization dynamics and discuss the possibility of mag- netization reversal. The torque from the current injection depends on the transmission probability through the ferromagnet and shows nontrivial dependence on the exchange coupling. The mag- netization dynamics is a direct manifestation of the inverse spin-galvanic effect and hence another ferromagnet is unnecessary to induce spin transfer torque in contrast to the conventional setup.Comment: 4 pages, 4 figure

Dynamics of magnetization on the topological surface

We investigate theoretically the dynamics of magnetization coupled to the surface Dirac fermions of a three dimensional topological insulator, by deriving the Landau-Lifshitz-Gilbert (LLG) equation in the presence of charge current. Both the inverse spin-Galvanic effect and the Gilbert damping coefficient $\alpha$ are related to the two-dimensional diagonal conductivity $\sigma_{xx}$ of the Dirac fermion, while the Berry phase of the ferromagnetic moment to the Hall conductivity $\sigma_{xy}$. The spin transfer torque and the so-called $\beta$-terms are shown to be negligibly small. Anomalous behaviors in various phenomena including the ferromagnetic resonance are predicted in terms of this LLG equation.Comment: 4+ pages, 1 figur

Current induced domain wall dynamics in the presence of spin orbit torques

Current induced domain wall (DW) motion in perpendicularly magnetized nanostripes in the presence of spin orbit torques is studied. We show using micromagnetic simulations that the direction of the current induced DW motion and the associated DW velocity depend on the relative values of the field like torque (FLT) and the Slonczewski like torques (SLT). The results are well explained by a collective coordinate model which is used to draw a phase diagram of the DW dynamics as a function of the FLT and the SLT. We show that a large increase in the DW velocity can be reached by a proper tuning of both torques.Comment: 9 pages, 3 figure

Urban growth, regeneration and social inclusion in Porto Alegre: the City Entrance Integrated Programme case study

Since 1989 Porto Alegre has become an international reference for planning (UN Habitat, 1996) and regeneration practices associated also with the Participatory Budget process (Pacheco, 2001; Fedozzi, 1998), aiming at poverty reduction and social inclusiveness (Getúlio Vargas Foundation, 2004; UNDP, 2003; UN/UMP, 2003). Within the new city masterplan approved in 1999 the City Entrance Integrated Programme (henceforth PIEC) has been delivered since 2002 (Vargas, 2003; PMPA, 2014). The paper critically analyses the outcomes of the 4th District’s regeneration process and relate them to recent trends in terms of informal rapid urbanisation, social and ecological indicators. The findings highlight how, even though enjoying economic development and positive macro-economic trends, Porto Alegre is facing new or increasing challenges in terms of housing needs, informal urbanisation, social and environmental resilience. Unexpected internal people displacement, together with real estate speculation and the rise of new informal urbanization, provide a worrying picture of increasing inequalities across the city. The paper provides a reflection on the shortcomings and the fragility of the planning process, especially in terms of social and environmental impact, to draw some provisional conclusions and directions for further research activities