We use a recently found method to characterize all multiplicative fourth-order difference equations admitting a variational structure. We use this result to give a simplified classification algorithm ...for such equations and a characterization of the associated symplectic structures. Finally, we discuss several examples of equations of this family from the literature and propose new ones.
Spin torque oscillators with nanoscale electrical contacts are able to produce coherent spin waves in extended magnetic films, and offer an attractive combination of electrical and magnetic field ...control, broadband operation, fast spin-wave frequency modulation, and the possibility of synchronizing multiple spin-wave injection sites. However, many potential applications rely on propagating (as opposed to localized) spin waves, and direct evidence for propagation has been lacking. Here, we directly observe a propagating spin wave launched from a spin torque oscillator with a nanoscale electrical contact into an extended Permalloy (nickel iron) film through the spin transfer torque effect. The data, obtained by wave-vector-resolved micro-focused Brillouin light scattering, show that spin waves with tunable frequencies can propagate for several micrometres. Micromagnetic simulations provide the theoretical support to quantitatively reproduce the results.
Magnonic crystals, materials with periodic modulation of their magnetic properties, represent the magnetic counterpart of photonic, phononic and plasmonic crystals, and have been largely investigated ...in recent years because of the possibility of using spin waves as a new means for carrying and processing information over a very large frequency bandwidth. Here, we review recent Brillouin light scattering studies of 2D magnonic crystals consisting of single- and bi-component arrays of interacting magnetic dots or antidot lattices. In particular, we discuss the principal properties of the magnonic band diagram of such systems, with emphasis given to its dependence on both magnetic and the geometrical parameters. Thanks to the possibility of tailoring their band structure by means of several degrees of freedom, planar magnonic crystals offer a good opportunity to design an innovative class of nanoscale microwave devices.
We report the observation of a Pt layer thickness dependence on the induced interfacial Dzyaloshinskii-Moriya interaction in ultrathin Pt(d_{Pt})/CoFeB films. Taking advantage of the large spin-orbit ...coupling of the heavy metal, the interfacial Dzyaloshinskii-Moriya interaction is quantified by Brillouin light scattering measurements of the frequency nonreciprocity of spin waves in the ferromagnet. The magnitude of the induced Dzyaloshinskii-Moriya coupling is found to saturate to a value of 0.45 mJ/m^{2} for Pt thicknesses larger than ∼2 nm. The experimental results are explained by analytical calculations based on the three-site indirect exchange mechanism that predicts a Dzyaloshinskii-Moriya interaction at the interface between a ferromagnetic thin layer and a heavy metal. Our findings open up a way to control and optimize chiral effects in ferromagnetic thin films through the thickness of the heavy-metal layer.
The application of Brillouin light scattering to the study of the spin-wave spectrum of one- and two-dimensional planar magnonic crystals consisting of arrays of interacting stripes, dots and ...antidots is reviewed. It is shown that the discrete set of allowed frequencies of an isolated nanoelement becomes a finite-width frequency band for an array of identical interacting elements. It is possible to tune the permitted and forbidden frequency bands, modifying the geometrical or the material magnetic parameters, as well as the external magnetic field. From a technological point of view, the accurate fabrication of planar magnonic crystals and a proper understanding of their magnetic excitation spectrum in the gigahertz range is oriented to the design of filters and waveguides for microwave communication systems.
Coalgebra symmetry for discrete systems Gubbiotti, G; Latini, D; Tapley, B K
Journal of physics. A, Mathematical and theoretical,
05/2023, Letnik:
56, Številka:
20
Journal Article
Recenzirano
Odprti dostop
Abstract
In this paper we introduce the notion of coalgebra symmetry for discrete systems. With this concept we prove that all discrete radially symmetric systems in standard form are ...quasi-integrable and that all variational discrete quasi-radially symmetric systems in standard form are Poincaré–Lyapunov–Nekhoroshev maps of order
N
− 2, where
N
are the degrees of freedom of the system. We also discuss the integrability properties of several vector systems which are generalisations of well-known one degree of freedom discrete integrable systems, including two
N
degrees of freedom autonomous discrete Painlevé I equations and an
N
degrees of freedom McMillan map.
In this paper we present a simple, algorithmic test to establish if a Hamiltonian system is maximally superintegrable or not. This test is based on a very simple corollary of a theorem due to ...Nekhoroshev and on a perturbative technique called the multiple scales method. If the outcome is positive, this test can be used to suggest maximal superintegrability, whereas when the outcome is negative it can be used to disprove it. This method can be regarded as a finite dimensional analog of the multiple scales method as a way to produce soliton equations. We use this technique to show that the real counterpart of a mechanical system found by Jules Drach in 1935 is, in general, not maximally superintegrable. We give some hints on how this approach could be applied to classify maximally superintegrable systems by presenting a direct proof of the well-known Bertrand's theorem.
We measure and analyze the chirality of Dzyaloshinskii-Moriya-interaction (DMI) stabilized spin textures in multilayers of Ta|Co_{20}F_{60}B_{20}|MgO. The effective DMI is measured experimentally ...using domain wall motion measurements, both in the presence (using spin-orbit torques) and absence of driving currents (using magnetic fields). We observe that the current-induced domain wall motion yields a change in effective DMI magnitude and opposite domain wall chirality when compared to field-induced domain wall motion (without current). We explore this effect, which we refer to as current-induced DMI, by providing possible explanations for its emergence, and explore the possibility of its manifestation in the framework of recent theoretical predictions of DMI modifications due to spin currents.
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