Floquet spin states in graphene under ac driven spin-orbit interaction

We study the role of periodically driven time-dependent Rashba spin-orbit coupling (RSOC) on a monolayer graphene sample. After recasting the originally $4\times 4$ system of dynamical equations as two time-reversal related two-level problems, the quasi-energy spectrum and the related dynamics are investigated via various techniques and approximations. In the static case the system is a gapped at the Dirac point. The rotating wave approximation (RWA) applied to the driven system unphysically preserves this feature, while the Magnus-Floquet approach as well as a numerically exact evaluation of the Floquet equation show that this gap is dynamically closed. In addition, a sizable oscillating pattern of the out-of-plane spin polarization is found in the driven case for states which completely unpolarized in the static limit. Evaluation of the autocorrelation function shows that the original uniform interference pattern corresponding to time-independent RSOC gets distorted. The resulting structure can be qualitatively explained as a consequence of the transitions induced by the ac driving among the static eigenstates, i.e., these transitions modulate the relative phases that add up to give the quantum revivals of the autocorrelation function. Contrary to the static case, in the driven scenario, quantum revivals (suppresions) are correlated to spin up (down) phases.Comment: 10 pages, 8 figures. Typos corrected. Accepted for publication in PR

Fast domain wall propagation under an optimal field pulse in magnetic nanowires

We investigate field-driven domain wall (DW) propagation in magnetic nanowires in the framework of the Landau-Lifshitz-Gilbert equation. We propose a new strategy to speed up the DW motion in a uniaxial magnetic nanowire by using an optimal space-dependent field pulse synchronized with the DW propagation. Depending on the damping parameter, the DW velocity can be increased by about two orders of magnitude compared the standard case of a static uniform field. Moreover, under the optimal field pulse, the change in total magnetic energy in the nanowire is proportional to the DW velocity, implying that rapid energy release is essential for fast DW propagation.Comment: 4 pages, 3 figures; updated version replace

Switching speed distribution of spin-torque-induced magnetic reversal

The switching probability of a single-domain ferromagnet under spin-current excitation is evaluated using the Fokker-Planck equation(FPE). In the case of uniaxial anisotropy, the FPE reduces to an ordinary differential equation in which the lowest eigenvalue $\lambda_1$ determines the slowest switching events. We have calculated $\lambda_1$ by using both analytical and numerical methods. It is found that the previous model based on thermally distributed initial magnetization states \cite{Sun1} can be accurately justified in some useful limiting conditions.Comment: The 10th Joint MMM/Intermag, HA-0

Synchronization in an array of linearly stochastically coupled networks with time delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2007 Elsevier LtdIn this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays. Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.This work was jointly supported by the National Natural Science Foundation of China under Grant 60574043, the Royal Society of the United Kingdom, the Natural Science Foundation of Jiangsu Province of China under Grant BK2006093, and International Joint Project funded by NSFC and the Royal Society of the United Kingdom

Graphene with time-dependent spin-orbit coupling: Truncated Magnus expansion approach

We analyze the role of ac-driven Rashba spin-orbit coupling in monolayer graphene including a spin-dependent mass term. Using the Magnus expansion as a semi-analytical approximation scheme a full account of the quasienergie spectrum of spin states is given. We discuss the subtleties arising in correctly applying the Magnus expansion technique in order to determine the quasienergy spectrum. Comparison to the exact numerical solution gives appropriate boundaries to the validity of the Magnus expansion solution.Comment: 8 pages, 4 figure

Binomial coefficients, Catalan numbers and Lucas quotients

Let $p$ be an odd prime and let $a,m$ be integers with $a>0$ and $m \not\equiv0\pmod p$. In this paper we determine $\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k$ mod $p^2$ for $d=0,1$; for example, $$\sum_{k=0}^{p^a-1}\frac{\binom{2k}k}{m^k}\equiv\left(\frac{m^2-4m}{p^a}\right)+\left(\frac{m^2-4m}{p^{a-1}}\right)u_{p-(\frac{m^2-4m}{p})}\pmod{p^2},$$ where $(-)$ is the Jacobi symbol, and $\{u_n\}_{n\geqslant0}$ is the Lucas sequence given by $u_0=0$, $u_1=1$ and $u_{n+1}=(m-2)u_n-u_{n-1}$ for $n=1,2,3,\ldots$. As an application, we determine $\sum_{0<k<p^a,\, k\equiv r\pmod{p-1}}C_k$ modulo $p^2$ for any integer $r$, where $C_k$ denotes the Catalan number $\binom{2k}k/(k+1)$. We also pose some related conjectures.Comment: 24 pages. Correct few typo

Zero-field magnetization reversal of two-body Stoner particles with dipolar interaction

Nanomagnetism has recently attracted explosive attention, in particular, because of the enormous potential applications in information industry, e.g. new harddisk technology, race-track memory[1], and logic devices[2]. Recent technological advances[3] allow for the fabrication of single-domain magnetic nanoparticles (Stoner particles), whose magnetization dynamics have been extensively studied, both experimentally and theoretically, involving magnetic fields[4-9] and/or by spin-polarized currents[10-20]. From an industrial point of view, important issues include lowering the critical switching field $H_c$, and achieving short reversal times. Here we predict a new technological perspective: $H_c$ can be dramatically lowered (including $H_c=0$) by appropriately engineering the dipole-dipole interaction (DDI) in a system of two synchronized Stoner particles. Here, in a modified Stoner-Wohlfarth (SW) limit, both of the above goals can be achieved. The experimental feasibility of realizing our proposal is illustrated on the example of cobalt nanoparticles.Comment: 5 pages, 4 figure