Brillouin light scattering by spin waves in magnetic metamaterials based on Co nanorods

We report on the investigations of spin wave modes in arrays of densely packed Co nanorods using Brillouin light scattering. We have observed a significant role of spin wave modes along the nanorod axis in contrast to infinite magnetic nanowires. Unusual optical properties featuring an inverted Stokes/anti-Stokes asymmetry of the Brillouin scattering spectra have been observed. The spectrum of spin wave modes in the nanorod array has been calculated and compared with the experiment. Experimental observations are explained in terms of a combined numerical-analytical approach taking into account both the low aspect ratio of individual magnetic nanorods and dipolar magnetic coupling between the nanorods in the array. The optical studies of spin-wave modes in the metamaterials with low aspect ratio nanorods have revealed new magnetic and magneto-optical properties compared to continuous magnetic films or infinite magnetic nanowires. Such magnetic metamaterials are important class of active metamaterials needed for prospective data storage and signal processing applications. (c) 2012 Optical Society of America

Brillouin scattering of light by spin waves in ferromagnetic nanorods

We report the investigations of spin wave modes of arrays of Ni and Co nanorods using Brillouin light scattering. We have revealed the significant influence of spin wave modes along the nanorod axis in contrast to infinite magnetic nanowires. Unusual optical properties featuring an inverted Stokes/anti-Stokes asymmetry of the Brillouin scattering spectra have been observed. The spectrum of spin wave modes in the nanorod array has been calculated and compared with the experiment. Experimental observations are explained in terms of a combined numerical-analytical approach taking into account both the low aspect ratio of individual magnetic nanorods and dipolar magnetic coupling between the nanorods in the array. The optical studies of spin-wave modes in nanorod metamaterials with low aspect ratio nanorods have revealed new magnetic and magneto-optical properties compared to continuous magnetic films or infinite magnetic nanowires. Such magnetic artificial materials are important class of active metamaterials needed for prospective data storage and signal processing applications. © 2012 Elsevier B.V.

Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite-size spin chains with a chiral spin ground state observed on biatomic Fe chains deposited on iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the noncollinear nature of the classical ground state, there is a significant zero-point reduction of the ground-state magnetization of the spin spiral. Second, there is a critical external field from which the ground state changes from chiral spin ground state to collinear ferromagnetic order. The character of the two lowest-energy spin waves changes from edge modes to confined bulk modes over this critical field. Third, in the spin-spiral state, the spin-wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

Imaging of spin waves in atomically designed nanomagnets

The spin dynamics of all ferromagnetic materials are governed by two types of collective phenomenon: spin waves and domain walls. The fundamental processes underlying these collective modes, such as exchange interactions and magnetic anisotropy, all originate at the atomic scale. However, conventional probing techniques based on neutron1 and photon scattering2 provide high resolution in reciprocal space, and thereby poor spatial resolution. Here we present direct imaging of standing spin waves in individual chains of ferromagnetically coupled S = 2 Fe atoms, assembled one by one on a Cu2N surface using a scanning tunnelling microscope. We are able to map the spin dynamics of these designer nanomagnets with atomic resolution in two complementary ways. First, atom-to-atom variations of the amplitude of the quantized spin-wave excitations are probed using inelastic electron tunnelling spectroscopy. Second, we observe slow stochastic switching between two opposite magnetization states3, 4, whose rate varies strongly depending on the location of the tip along the chain. Our observations, combined with model calculations, reveal that switches of the chain are initiated by a spin-wave excited state that has its antinodes at the edges of the chain, followed by a domain wall shifting through the chain from one end to the other. This approach opens the way towards atomic-scale imaging of other types of spin excitation, such as spinon pairs and fractional end-states5, 6, in engineered spin chains.

Topological spin waves in the atomic-scale magnetic skyrmion crystal

We study the spin waves of the triangular skyrmion crystal that emerges in a two-dimensional spin lattice model as a result of the competition between Heisenberg exchange, Dzyalonshinkii–Moriya interactions, Zeeman coupling and uniaxial anisotropy. The calculated spin wave bands have a finite Berry curvature that, in some cases, leads to non-zero Chern numbers, making this system topologically distinct from conventional magnonic systems. We compute the edge spin-waves, expected from the bulk-boundary correspondence principle, and show that they are chiral, which makes them immune to elastic backscattering. Our results illustrate how topological phases can occur in self-generated emergent superlattices at the mesoscale.

Ondas de spin em super-redes ferromagnéticas com campo de anisotropia

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Ondas de spin em nanofilmes nagnéticos acoplados quasiperiodicamente

We studied the spin waves modes that can propagate in magnetic multilayers composed of ferromagnetic metallic films in the nanometer scale. The ferromagnetic films (iron) are separated and coupled through the nonmagnetic spacer films (chromium). The films that make up the multilayer are stacked in a quasiperiodic pattern, following the Fibonacci and double period sequences. We used a phenomenological theory taking into account: the Zeeman energy (between the ferromagnetic films and the external magnetic field), the energy of the magneto-crystalline anisotropy (present in the ferromagnetic films), the energy of the bilinear and biquadratic couplings (between the ferromagnetic films) and the energy of the dipole-dipole interaction (between the ferromagnetic films), to describe the system. The total magnetic energy of the system is numerically minimized and the equilibrium angles of the magnetization of each ferromagnetic film are determined. We solved the equation of motion of the multilayer to find the dispersion relation for the system and, as a consequence, the spin waves modes frequencies. Our theoretical results show that, in the case of trilayers (Fe/Cr/Fe), our model reproduces with excellent agreement experimental results of Brillouin light scattering, known from the literature, by adjusting the physical parameters of the nanofilms. Furthermore, we generalize the model to N ferromagnetic layers which allowed us to determine how complex these systems become when we increase the number of components. It is worth noting that our theoretical calculations generalize all the results known from the literature

Ondas de spin em quasi-cristais magnônicos

In this paper we investigate the spectra of band structures and transmittance in magnonic quasicrystals that exhibit the so-called deterministic disorders, specifically, magnetic multilayer systems, which are built obeying to the generalized Fibonacci (only golden mean (GM), silver mean (SM), bronze mean (BM), copper mean (CM) and nickel mean (NM) cases) and k-component Fibonacci substitutional sequences. The theoretical model is based on the Heisenberg Hamiltonian in the exchange regime, together with the powerful transfer matrix method, and taking into account the RPA approximation. The magnetic materials considered are simple cubic ferromagnets. Our main interest in this study is to investigate the effects of quasiperiodicity on the physical properties of the systems mentioned by analyzing the behavior of spin wave propagation through the dispersion and transmission spectra of these structures. Among of these results we detach: (i) the fragmentation of the bulk bands, which in the limit of high generations, become a Cantor set, and the presence of the mig-gap frequency in the spin waves transmission, for generalized Fibonacci sequence, and (ii) the strong dependence of the magnonic band gap with respect to the parameters k, which determines the amount of different magnetic materials are present in quasicrystal, and n, which is the generation number of the sequence k-component Fibonacci. In this last case, we have verified that the system presents a magnonic band gap, whose width and frequency region can be controlled by varying k and n. In the exchange regime, the spin waves propagate with frequency of the order of a few tens of terahertz (THz). Therefore, from a experimental and technological point of view, the magnonic quasicrystals can be used as carriers or processors of informations, and the magnon (the quantum spin wave) is responsible for this transport and processing

Magnetization dynamics in spin valves

Key technology applications like magnetoresistive sensors or the Magnetic Random Access Memory (MRAM) require reproducible magnetic switching mechanisms. i.e. predefined remanent states. At the same time advanced magnetic recording schemes push the magnetic switching time into the gyromagnetic regime. According to the Landau-Lifschitz-Gilbert formalism, relevant questions herein are associated with magnetic excitations (eigenmodes) and damping processes in confined magnetic thin film structures.rnObjects of study in this thesis are antiparallel pinned synthetic spin valves as they are extensively used as read heads in today’s magnetic storage devices. In such devices a ferromagnetic layer of high coercivity is stabilized via an exchange bias field by an antiferromagnet. A second hard magnetic layer, separated by a non-magnetic spacer of defined thickness, aligns antiparallel to the first. The orientation of the magnetization vector in the third ferromagnetic NiFe layer of low coercivity - the freelayer - is then sensed by the Giant MagnetoResistance (GMR) effect. This thesis reports results of element specific Time Resolved Photo-Emission Electron Microscopy (TR-PEEM) to image the magnetization dynamics of the free layer alone via X-ray Circular Dichroism (XMCD) at the Ni-L3 X-ray absorption edge.rnThe ferromagnetic systems, i.e. micron-sized spin valve stacks of typically deltaR/R = 15% and Permalloy single layers, were deposited onto the pulse leading centre stripe of coplanar wave guides, built in thin film wafer technology. The ferromagnetic platelets have been applied with varying geometry (rectangles, ellipses and squares), lateral dimension (in the range of several micrometers) and orientation to the magnetic field pulse to study the magnetization behaviour in dependence of these magnitudes. The observation of magnetic switching processes in the gigahertz range became only possible due to the joined effort of producing ultra-short X-ray pulses at the synchrotron source BESSY II (operated in the so-called low-alpha mode) and optimizing the wave guide design of the samples for high frequency electromagnetic excitation (FWHM typically several 100 ps). Space and time resolution of the experiment could be reduced to d = 100 nm and deltat = 15 ps, respectively.rnIn conclusion, it could be shown that the magnetization dynamics of the free layer of a synthetic GMR spin valve stack deviates significantly from a simple phase coherent rotation. In fact, the dynamic response of the free layer is a superposition of an averaged critically damped precessional motion and localized higher order spin wave modes. In a square platelet a standing spin wave with a period of 600 ps (1.7 GHz) was observed. At a first glance, the damping coefficient was found to be independent of the shape of the spin-valve element, thus favouring the model of homogeneous rotation and damping. Only by building the difference in the magnetic rotation between the central region and the outer rim of the platelet, the spin wave becomes visible. As they provide an additional efficient channel for energy dissipation, spin waves contribute to a higher effective damping coefficient (alpha = 0.01). Damping and magnetic switching behaviour in spin valves thus depend on the geometry of the element. Micromagnetic simulations reproduce the observed higher-order spin wave mode.rnBesides the short-run behaviour of the magnetization of spin valves Permalloy single layers with thicknesses ranging from 3 to 40 nm have been studied. The phase velocity of a spin wave in a 3 nm thick ellipse could be determined to 8.100 m/s. In a rectangular structure exhibiting a Landau-Lifschitz like domain pattern, the speed of the field pulse induced displacement of a 90°-Néel wall has been determined to 15.000 m/s.rn

A phenomenological model for the structure-composition relationship of the high Tc cuprates based on simple chemical principles

A simple phenomenological model for the relationship between structure and composition of the high Tc cuprates is presented. The model is based on two simple crystal chemistry principles: unit cell doping and charge balance within unit cells. These principles are inspired by key experimental observations of how the materials accommodate large deviations from stoichiometry. Consistent explanations for significant HTSC properties can be explained without any additional assumptions while retaining valuable insight for geometric interpretation. Combining these two chemical principles with a review of Crystal Field Theory (CFT) or Ligand Field Theory (LFT), it becomes clear that the two oxidation states in the conduction planes (typically d8 and d9) belong to the most strongly divergent d-levels as a function of deformation from regular octahedral coordination. This observation offers a link to a range of coupling effects relating vibrations and spin waves through application of Hund’s rules. An indication of this model’s capacity to predict physical properties for HTSC is provided and will be elaborated in subsequent publications. Simple criteria for the relationship between structure and composition in HTSC systems may guide chemical syntheses within new material systems.

Phonon-mediated two-magnon light scattering from ferromagnetic insulators

An indirect mechanism of light scattering from spin-waves in ferromagnetic insulators via two-magnon one-phonon process is proposed. Following linear response theory, an expression has been derived for the differential scattering cross-section in the mean-field-approximation.

Ferromagnetic Resonance Study on a Grid of Permalloy Nanowires

We report ferromagnetic resonance (FMR) study on a grid formed with permalloy nanowires to understand the spin wave dynamics. The presence of two sets of magnetic nanowires perpendicular to each other in the same device enables better control over spin waves. The grid was fabricated using e-beam lithography followed by DC-Magnetron sputtering and liftoff technique. It has dimensions of 800 +/- 10 and 400 +/- 10 nm as periods along X and Y directions with permalloy wires of width 145 +/- 10 nm. FMR studies were done at X-band (9.4 GHz) with the field sweep up to 1 Tesla. The in-plane angular variation of resonant fields shows that there are two well separated modes present, indicating two uniaxial anisotropy axes which are perpendicular to each other. The variation in the intensities in the FMR signal w.r.t. the grid angle is used to describe the spin wave confinement in different regions of the grid. We also explained the asymmetry in the magnetic properties caused by the geometrical property of the rectangular grid and the origin for the peak splitting for the modes occurring at higher resonant fields. Micromagnetic simulations based on OOMMF with two dimensional periodic boundary conditions (2D-PBC) are used to support our experimental findings.