Dynamic probes of quantum spin chains with the Dzyaloshinskii-Moriya interaction

We consider the spin-1/2 anisotropic XY chain in a transverse (z) field with the Dzyaloshinskii-Moriya interaction directed along z-axis in spin space to examine the effect of the Dzyaloshinskii-Moriya interaction on the zz, xx and yy dynamic structure factors. Using the Jordan-Wigner fermionization approach we analytically calculate the dynamic transverse spin structure factor. It is governed by a two-fermion excitation continuum. We analyze the effect of the Dzyaloshinskii-Moriya interaction on the two-fermion excitation continuum. Other dynamic structure factors which are governed by many-fermion excitations are calculated numerically. We discuss how the Dzyaloshinskii-Moriya interaction manifests itself in the dynamic properties of the quantum spin chain at various fields and temperatures

Skyrmion Hall Effect Revealed by Direct Time-Resolved X-Ray Microscopy

Magnetic skyrmions are highly promising candidates for future spintronic applications such as skyrmion racetrack memories and logic devices. They exhibit exotic and complex dynamics governed by topology and are less influenced by defects, such as edge roughness, than conventionally used domain walls. In particular, their finite topological charge leads to a predicted "skyrmion Hall effect", in which current-driven skyrmions acquire a transverse velocity component analogous to charged particles in the conventional Hall effect. Here, we present nanoscale pump-probe imaging that for the first time reveals the real-time dynamics of skyrmions driven by current-induced spin orbit torque (SOT). We find that skyrmions move at a well-defined angle {\Theta}_{SH} that can exceed 30{\deg} with respect to the current flow, but in contrast to theoretical expectations, {\Theta}_{SH} increases linearly with velocity up to at least 100 m/s. We explain our observation based on internal mode excitations in combination with a field-like SOT, showing that one must go beyond the usual rigid skyrmion description to unravel the dynamics.Comment: pdf document arxiv_v1.1. 24 pages (incl. 9 figures and supplementary information

Accurate extraction of anisotropic spin–orbit torques from harmonic measurements

One of the most powerful ways to manipulate spins in nanometer scale devices is by converting a charge current to a spin current via spin orbit coupling. The resulting spin orbit torques SOTs have been investigated and utilized extensively in the past decade. Quantitatively, however, SOTs may exhibit a non trivial angular dependence which is not well explored. Here, we develop a nested iterative analysis to determine the magnitude of SOTs from harmonic Hall measurements. This updated method largely improves the fit quality in the full magnetic field range and accurately retrieves even higher order, anisotropic spin orbit torque coeficients. The numerical implementation of our algorithm is fast, robust, and designed for easy integration into existing analysis schemes. We verify our code using simulated data with and without anisotropic SOTs. Accurately quantifying higher order SOT terms can be especially useful for modeling non uniform magnetic textures such as domain walls and skyrmions and current induced magnetization switching characteristic

Fermionic SK-models with Hubbard interaction: Magnetism and electronic structure

Models with range-free frustrated Ising spin- and Hubbard interaction are treated exactly by means of the discrete time slicing method. Critical and tricritical points, correlations, and the fermion propagator, are derived as a function of temperature T, chemical potential \mu, Hubbard coupling U, and spin glass energy J. The phase diagram is obtained. Replica symmetry breaking (RSB)-effects are evaluated up to four-step order (4RSB). The use of exact relations together with the 4RSB-solutions allow to model exact solutions by interpolation. For T=0, our numerical results provide strong evidence that the exact density of states in the spin glass pseudogap regime obeys \rho(E)=const |E-E_F| for energies close to the Fermi level. Rapid convergence of \rho'(E_F) under increasing order of RSB is observed. The leading term resembles the Efros-Shklovskii Coulomb pseudogap of localized disordered fermionic systems in 2D. Beyond half filling we obtain a quadratic dependence of the fermion filling factor on the chemical potential. We find a half filling transition between a phase for U>\mu, where the Fermi level lies inside the Hubbard gap, into a phase where \mu(>U) is located at the center of the upper spin glass pseudogap (SG-gap). For \mu>U the Hubbard gap combines with the lower one of two SG-gaps (phase I), while for \mu<U it joins the sole SG-gap of the half-filling regime (phase II). We predict scaling behaviour at the continuous half filling transition. Implications of the half-filling transition between the deeper insulating phase II and phase I for delocalization due to hopping processes in itinerant model extensions are discussed and metal-insulator transition scenarios described.Comment: 29 pages, 26 Figures, 4 jpeg- and 3 gif-Fig-files include

Localization of nonlinear excitations in curved waveguides

Motivated by the example of a curved waveguide embedded in a photonic crystal, we examine the effects of geometry in a ``quantum channel'' of parabolic form. We study the linear case and derive exact as well as approximate expressions for the eigenvalues and eigenfunctions of the linear problem. We then proceed to the nonlinear setting and its stationary states in a number of limiting cases that allow for analytical treatment. The results of our analysis are used as initial conditions in direct numerical simulations of the nonlinear problem and localized excitations are found to persist, as well as to have interesting relaxational dynamics. Analogies of the present problem in contexts related to atomic physics and particularly to Bose-Einstein condensation are discussed.Comment: 14 pages, 4 figure

Dynamics and inertia of skyrmionic spin structures

Skyrmions are topologically protected winding vector fields characterized by a spherical topology. Magnetic skyrmions can arise as the result of the interplay of various interactions, including exchange, dipolar and anisotropy energy in the case of magnetic bubbles and an additional Dzyaloshinskii-Moriya interaction in the case of chiral skyrmions. Whereas the static and low-frequency dynamics of skyrmions are already well under control, their gigahertz dynamical behaviour has not been directly observed in real space. Here, we image the gigahertz gyrotropic eigenmode dynamics of a single magnetic bubble and use its trajectory to experimentally confirm its skyrmion topology. The particular trajectory points to the presence of strong inertia, with a mass much larger than predicted by existing theories. This mass is endowed by the topological confinement of the skyrmion and the energy associated with its size change. It is thereby expected to be found in all skyrmionic structures in magnetic systems and beyond. Our experiments demonstrate that the mass term plays a key role in describing skyrmion dynamics.