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Correlation between spin structure oscillations and domain wall velocities
Bisig, Andre   Staerk, Martin   Mawass, Mohamad-Assaad   Moutafis, Christoforos   Rhensius, Jan   Heidler, Jakoba   Buettner, Felix   Noske, Matthias   Weigand, Markus   Eisebitt, Stefan   Tyliszczak, Tolek   Van Waeyenberge, Bartel   Stoll, Hermann   Schuetz, Gisela   Klaeul, Mathias  
NATURE COMMUNICATIONS, AUG 2013

Magnetic sensing and logic devices based on the motion of magnetic domain walls rely on the precise and deterministic control of the position and the velocity of individual magnetic domain walls in curved nanowires. Varying domain wall velocities have been predicted to result from intrinsic effects such as oscillating domain wall spin structure transformations and extrinsic pinning due to imperfections. Here we use direct dynamic imaging of the nanoscale spin structure that allows us for the first time to directly check these predictions. We find a new regime of oscillating domain wall motion even below the Walker breakdown correlated with periodic spin structure changes. We show that the extrinsic pinning from imperfections in the nanowire only affects slow domain walls and we identify the magneto-static energy, which scales with the domain wall velocity, as the energy reservoir for the domain wall to overcome the local pinning potential landscape.

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Micromagnetic modeling of anisotropic damping in magnetic nanoelements
Dvornik, Mykola   Vansteenkiste, Arne   Van Waeyenberge, Bartel  
PHYSICAL REVIEW B, AUG 29 2013

We report a numerical implementation of the Landau-Lifshitz-Baryakhtar theory that dictates that the micromagnetic relaxation term obeys the symmetry of the magnetic crystal, i.e., replacing the single intrinsic damping constant with a tensor of corresponding symmetry. The effect of anisotropic relaxation is studied in a thin saturated ferromagnetic disk and an ellipse with and without uniaxial magnetocrystalline anisotropy. We investigate the angular dependence of the linewidth of magnonic resonances with respect to the given structure of the relaxation tensor. The simulations suggest that the anisotropy of the magnonic linewidth is determined by two factors: the projection of the relaxation tensor onto the plane of precession and the ellipticity of the latter.

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Implementation of a finite-difference micromagnetic model on GPU hardware
Vansteenkiste, Arne   Van de Wiele, Ben   Dupre, Luc   Van Waeyenberge, Bartel   De Zutter, Daniel  
INTERNATIONAL JOURNAL OF NUMERICAL MODELLING-ELECTRONIC NETWORKS DEVICES AND FIELDS, JUL-AUG 2013

We have developed a micromagnetic simulator for graphical processing units (GPU), using the CUDA framework. In this paper, we discuss the optimization of the effective field calculation, both from a mathematical and from a hardware-specific point of view. By using a finite-difference discretization scheme, the long-range magnetostatic field can be calculated using fast Fourier transforms, an approach well suited for the GPU. We show how the implementation can be tuned to the GPU hardware and how the performance can be further increased by dealing with the large number of zeros that typically occurs in the micromagnetic field computation. Additionally, we show how the ferromagnetic exchange interaction can be readily included in the magnetostatic field calculation without any additional computational cost. The resulting high-performance software can be used to run large-scale simulations that would have been very time-consuming on regular CPU hardware. As an example, we present a case study on the de-pinning of domain walls in racetrack memory devices. Copyright (c) 2012 John Wiley & Sons, Ltd.

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Generation of propagating backward volume spin waves by phase-sensitive mode conversion in two-dimensional microstructures
Braecher, T.   Pirro, P.   Westermann, J.   Sebastian, T.   Laegel, B.   Van de Wiele, B.   Vansteenkiste, A.   Hillebrands, B.  
APPLIED PHYSICS LETTERS, APR 1 2013

We present the generation of propagating backward volume (BV) spin waves in a T shaped Ni81Fe19 microstructure. These waves are created from counterpropagating Damon Eshbach spin waves, which are excited using microstrip antennas. By employing Brillouin light scattering microscopy, we show how the phase relation between the counterpropagating waves determines the mode generated in the center of the structure, and prove its propagation inside the longitudinally magnetized part of the T shaped microstructure. This gives access to the effective generation of backward volume spin waves with full control over the generated transverse mode. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4800005]

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Direct Excitation of Propagating Spin Waves by Focused Ultrashort Optical Pulses
Au, Y.   Dvornik, M.   Davison, T.   Ahmad, E.   Keatley, P. S.   Vansteenkiste, A.   Van Waeyenberge, B.   Kruglyak, V. V.  
PHYSICAL REVIEW LETTERS, FEB 25 2013

An all-optical experiment long utilized to image phonons excited by ultrashort optical pulses has been applied to a magnetic sample. In addition to circular ripples due to surface acoustic waves, we observe an X-shaped pattern formed by propagating spin waves. The emission of spin waves from the optical pulse epicenter in the form of collimated beams is qualitatively reproduced by micromagnetic simulations. We explain the observed pattern in terms of the group velocity distribution of Damon-Eshbach magnetostatic spin waves in the reciprocal space and the wave vector spectrum of the focused ultrafast laser pulse. DOI: 10.1103/PhysRevLett.110.097201

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A micromagnetic study of the reversal mechanism in permalloy antidot arrays
Van de Wiele, B.   Manzin, A.   Vansteenkiste, A.   Bottauscio, O.   Dupre, L.   De Zutter, D.  
JOURNAL OF APPLIED PHYSICS, MAR 1 2012

A numerical analysis is focused on the influence of patterning and finite-size effects on the hysteresis properties and magnetization reversal of permalloy antidot films with square lattice and square holes. Simulations are performed by solving the Landau-Lifshitz equation. The aim is to explain the relationships between the shape of the hysteresis loop and the different stages of the reversal process. In particular, the switching mechanism is characterized by the nucleation of domain chains that destroy the periodic symmetry in the magnetization present when infinite periodicity is considered. This behavior is strongly influenced by the demagnetizing effects arising both at the film boundaries and at the hole edges. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3689846]

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Micromagnetic Simulations on GPU, A Case Study: Vortex Core Switching by High-Frequency Magnetic Fields
Van de Wiele, Ben   Vansteenkiste, Arne   Kammerer, Matthias   Van Waeyenberge, Bartel   Dupre, Luc   De Zutter, Daniel  
IEEE TRANSACTIONS ON MAGNETICS, JUN 2012

Since magnetic vortex cores have two ground states, they are candidates for digital memory bits in future magnetic random access memory (MRAM) devices. Vortex core switching can be induced by exciting the gyrotropic eigenmode, e.g., by applying cyclic magnetic fields with typically a sub-gigahertz frequency. However, recent studies reveal that other modes exist that can be excited at higher frequencies, but still lead to switching with relatively small field amplitudes. Here, we perform a full scan of the frequency/amplitude parameter space to explore such excitation modes. The enormous amount of simulations can only be performed in an acceptable time span when the micromagnetic (CPU) simulations are drastically accelerated. To this aim, we developed MUMAX, a GPU-based software tool that speeds up micromagnetic simulations with about two orders of magnitude compared to standard CPU micromagnetic tools. By exploiting MUMAX's numerical power we were able to explore new switching opportunities at moderate field amplitudes in the frequency range between 5 and 12 GHz.

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Commensurability and chaos in magnetic vortex oscillations
Petit-Watelot, Sebastien   Kim, Joo-Von   Ruotolo, Antonio   Otxoa, Ruben M.   Bouzehouane, Karim   Grollier, Julie   Vansteenkiste, Arne   Van de Wiele, Ben   Cros, Vincent   Devolder, Thibaut  
NATURE PHYSICS, SEP 2012

Magnetic vortex dynamics in thin films is characterized by gyrotropic motion, the sense of gyration depending on the vortex core polarity, which reverses when a critical velocity is reached. Although self-sustained vortex oscillations in nanoscale systems are known to be possible, the precise role of core reversal in such dynamics remains unknown. Here we report on an experimental observation of periodic core reversal during self-sustained vortex gyration in a magnetic nanocontact system. By tuning the ratio between the gyration frequency and the rate of core reversal, we show that commensurate phase-locked and incommensurate chaotic states are possible, resulting in Devil's staircases with driving currents. These systems could have the potential to serve as tunable nanoscale radiofrequency electrical oscillators for secure communications, allowing schemes such as encryption by chaos on demand.

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Magnetic vortex core reversal by rotating magnetic fields generated on micrometer length scales
Curcic, Michael   Stoll, Hermann   Weigand, Markus   Sackmann, Vitalij   Juellig, Patrick   Kammerer, Matthias   Noske, Matthias   Sproll, Markus   Van Waeyenberge, Bartel   Vansteenkiste, Arne   Woltersdorf, Georg   Tyliszczak, Tolek   Schuetz, Gisela  
PHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS, OCT 2011

Unidirectional switching of the magnetic vortex core can be achieved in micron-sized ferromagnetic platelets by excitation of the gyrotropic mode of the vortex structure with in-plane rotating magnetic fields. Circulating fields with a switchable sense of rotation (clockwise, CW or counter clockwise, CCW) have been generated on a micrometer length scale at frequencies up to 1 GHz by two orthogonal electric RF currents with 908 phase shift flowing through crossed but not isolated striplines. Decoupling of these currents is realized by balanced symmetric RF sources. The amplitudes of the rotating magnetic fields and their spatial distributions are calculated and the stripline geometry is discussed. By taking advantage of this technique, unidirectional vortex core reversal by excitation with CW or CCW rotating magnetic fields has been observed by time resolved scanning transmission X-ray microscopy. An area with reversed magnetization, the "dip," was observed near the vortex core before vortex core reversal. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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MUMAX: A new high-performance micromagnetic simulation tool
Vansteenkiste, A.   Van de Wiele, B.  
JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS, NOV 2011

We present MUMAX, a general-purpose micromagnetic simulation tool running on graphical processing units (GPUs). MUMAX is designed for high-performance computations and specifically targets large simulations. In that case speedups of over a factor 100 x can be obtained compared to the CPU-based OOMMF program developed at NIST. MUMAX aims to be general and broadly applicable. It solves the classical Landau-Lifshitz equation taking into account the magnetostatic, exchange and anisotropy interactions, thermal effects and spin-transfer torque. Periodic boundary conditions can optionally be imposed. A spatial discretization using finite differences in two or three dimensions can be employed. MUMAX is publicly available as open-source software. It can thus be freely used and extended by community. Due to its high computational performance, MUMAX should open up the possibility of running extensive simulations that would be nearly inaccessible with typical CPU-based simulators. (C) 2011 Elsevier B.V. All rights reserved.

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Magnetic vortex core reversal by excitation of spin waves
Kammerer, Matthias   Weigand, Markus   Curcic, Michael   Noske, Matthias   Sproll, Markus   Vansteenkiste, Arne   Van Waeyenberge, Bartel   Stoll, Hermann   Woltersdorf, Georg   Back, Christian H.   Schuetz, Gisela  
NATURE COMMUNICATIONS, APR 2011

Micron-sized magnetic platelets in the flux-closed vortex state are characterized by an in-plane curling magnetization and a nanometer-sized perpendicularly magnetized vortex core. Having the simplest non-trivial configuration, these objects are of general interest to micromagnetics and may offer new routes for spintronics applications. Essential progress in the understanding of nonlinear vortex dynamics was achieved when low-field core toggling by excitation of the gyrotropic eigenmode at sub-GHz frequencies was established. At frequencies more than an order of magnitude higher vortex state structures possess spin wave eigenmodes arising from the magneto-static interaction. Here we demonstrate experimentally that the unidirectional vortex core reversal process also occurs when such azimuthal modes are excited. These results are confirmed by micromagnetic simulations, which clearly show the selection rules for this novel reversal mechanism. Our analysis reveals that for spin-wave excitation the concept of a critical velocity as the switching condition has to be modified.

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Magnetic antivortex-core reversal by rotating magnetic fields
Kamionka, Thomas   Martens, Michael   Chou, Kang Wei   Drews, Andre   Tyliszczak, Tolek   Stoll, Hermann   Van Waeyenberge, Bartel   Meier, Guido  
PHYSICAL REVIEW B, JUN 27 2011

Magnetic vortices and antivortices are usually observed coexisting in cross-tie walls within ferromagnetic thin films. An antivortex can be isolated by utilizing the shape anisotropy. The isolation offers the possibility to investigate its fundamental dynamics as a two-dimensional oscillator in a confining potential. Hitherto, the gyration mode of vortices and its excitation has been studied intensely. Here, a detailed investigation of the coupling of an antivortex to in-plane rotating magnetic fields is presented. The resonant response is imaged by time-resolved scanning transmission x-ray microscopy to determine the amplitude as well as the phase of the gyration. The experimental results are compared with the analytical model of a two-dimensional harmonic oscillator derived from the Thiele equation. As a cause for deviations from the model, a buckled energy landscape due to local defects is discussed.

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Coupled Vortex Oscillations in Spatially Separated Permalloy Squares
Vogel, Andreas   Kamionka, Thomas   Martens, Michael   Drews, Andre   Chou, Kang Wei   Tyliszczak, Tolek   Stoll, Hermann   Van Waeyenberge, Bartel   Meier, Guido  
PHYSICAL REVIEW LETTERS, MAR 29 2011

We experimentally study the magnetization dynamics of pairs of micron-sized permalloy squares coupled via their stray fields. The trajectories of the vortex cores in the Landau-domain patterns of the squares are mapped in real space using time-resolved scanning transmission x-ray microscopy. After excitation of one of the vortex cores with a short magnetic-field pulse, the system behaves like coupled harmonic oscillators. The coupling strength depends on the separation between the squares and the configuration of the vortex-core polarizations. Considering the excitation via a rotating in-plane magnetic field, it can be understood that only a weak response of the second vortex core is observed for equal core polarizations.

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Vortex Core Switching by Coherent Excitation with Single In-Plane Magnetic Field Pulses
Weigand, Markus   Van Waeyenberge, Bartel   Vansteenkiste, Arne   Curcic, Michael   Sackmann, Vitalij   Stoll, Hermann   Tyliszczak, Tolek   Kaznatcheev, Konstantine   Bertwistle, Drew   Woltersdorf, Georg   Back, Christian H.   Schuetz, Gisela  
PHYSICAL REVIEW LETTERS, FEB 20 2009

The response of magnetic vortex cores to subnanosecond in-plane magnetic field pulses was studied by time-resolved x-ray microscopy. Vortex core reversal was observed and the switching events were located in space and time. This revealed a mechanism of coherent excitation by the leading and trailing edges of the pulse, lowering the field amplitude required for switching. The mechanism was confirmed by micromagnetic simulations and can be understood in terms of gyration around the vortex equilibrium positions, displaced by the applied field.

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X-ray imaging of the dynamic magnetic vortex core deformation
Vansteenkiste, A.   Chou, K. W.   Weigand, M.   Curcic, M.   Sackmann, V.   Stoll, H.   Tyliszczak, T.   Woltersdorf, G.   Back, C. H.   Schuetz, G.   Van Waeyenberge, B.  
NATURE PHYSICS, MAY 2009

Magnetic thin-film square-or disc-shaped nanostructures with adequate dimensions exhibit a magnetic vortex state: the magnetization vectors lie in the film plane and curl around the structure centre. At the very centre of the vortex, a small, stable core exists where the magnetization points either up or down(1,2). The discovery of an easy core reversal mechanism(3) did not only open the possibility of using such systems as magnetic memories, but also initiated the fundamental investigation of the core switching mechanism itself(4-15). Theoretical modelling predicted that the reversal is mediated by the creation and annihilation of a vortex-antivortex pair(3,4,16), but experimental support has been lacking until now. We used high-resolution time-resolved magnetic X-ray microscopy to experimentally reveal the first step of the reversal process: the dynamic deformation of the vortex core. In addition, we have measured a critical vortex velocity above which reversal must occur(5,17). Both observations support the previously proposed reversal mechanism.

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Chiral symmetry breaking of magnetic vortices by sample roughness
Vansteenkiste, A.   Weigand, M.   Curcic, M.   Stoll, H.   Schuetz, G.   Van Waeyenberge, B.  
NEW JOURNAL OF PHYSICS, JUN 3 2009

Finite-element micromagnetic simulations are employed to study the chiral symmetry breaking of magnetic vortices, caused by the surface roughness of thin-film magnetic structures. An asymmetry between vortices with different core polarizations has been experimentally observed for square-shaped platelets. For example, the threshold fields for vortex core switching were found to differ for core up and down. This asymmetry was, however, not expected for these symmetrically shaped structures, where both core polarizations should behave symmetrically. Three-dimensional finite element simulations are employed to show that a small surface roughness can break the symmetry between vortex cores pointing up and down. A relatively small sample roughness is found to be sufficient to reproduce the experimentally observed asymmetries. It arises from the lack of mirror-symmetry of the rough thin-film structures, which causes vortices with different handedness to exhibit asymmetric dynamics.

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Time-resolved X-ray microscopy of spin-torque-induced magnetic vortex gyration
Bolte, M.   Meier, G.   Kruger, B.   Drews, A.   Eiselt, R.   Bocklage, L.   Bohlens, S.   Tyliszczak, T.   Vansteenkiste, A.   Van Waeyenberge, B.   Kang Wei Chou   Puzic, A.   Stoll, H.  
Physical Review Letters, 2 May 2008

Time-resolved x-ray microscopy is used to image the influence of alternating high-density currents on the magnetization dynamics of ferromagnetic vortices. Spin-torque-induced vortex gyration is observed in micrometer-sized permalloy squares. The phases of the gyration in structures with different chirality are compared to an analytical model and micromagnetic simulations, considering both alternating spin-polarized currents and the currentpsilas Oersted field. In our case the driving force due to spin-transfer torque is about 70% of the total excitation while the remainder originates from the currentpsilas Oersted field. This finding has implications to magnetic storage devices using spin-torque driven magnetization switching and domain-wall motion.

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Influence of domain wall pinning on the dynamic behavior of magnetic vortex structures: Time-resolved scanning x-ray transmission microscopy in NiFe thin film structures
Vansteenkiste, A.   De Baerdemaeker, J.   Chou, K. W.   Stoll, H.   Curcic, M.   Tyliszczak, T.   Woltersdorf, G.   Back, C. H.   Schuetz, G.   Van Waeyenberge, B.  
PHYSICAL REVIEW B, APR 2008

Artificial domain wall pinning sites were created in micron-sized thin-film Ni(80)Fe(20) structures, and their influence on the vortex dynamics was investigated by using time-resolved scanning transmission x-ray microscopy. The domain wall pinning sites were introduced by means of focused ion beam etching in the form of antidots. The vortex gyration frequency increased in square-shaped structures but not in similarly modified disk-shaped structures, where no domain walls are present. This demonstrates that the domain wall pinning is causing the increased frequency. The effect is explained by the confinement of the domain wall motion to the portion of the structure that is circumscribed by the antidots and is in agreement with micromagnetic simulations.

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Polarization Selective Magnetic Vortex Dynamics and Core Reversal in Rotating Magnetic Fields
Curcic, Michael   Van Waeyenberge, Bartel   Vansteenkiste, Arne   Weigand, Markus   Sackmann, Vitalij   Stoll, Hermann   Faehnle, Manfred   Tyliszczak, Tolek   Woltersdorf, Georg   Back, Christian H.   Schuetz, Gisela  
PHYSICAL REVIEW LETTERS, NOV 7 2008

We report on the observation of magnetic vortex dynamics in response to rotating magnetic fields in submicron platelets. Unlike linear fields or spin polarized currents, which excite both vortex core polarization states, an in-plane rotating field can selectively excite one of the polarization states. We demonstrate by direct imaging with time-resolved scanning x-ray microscopy that the rotating field only excites the gyrotropic mode if the rotation sense of the field coincides with the vortex gyration sense and that such a field can selectively reverse the vortex polarization.

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Direct observation of the vortex core magnetization and its dynamics
Chou, K. W.   Puzic, A.   Stoll, H.   Dolgos, D.   Schuetz, G.   Van Waeyenberge, B.   Vansteenkiste, A.   Tyliszczak, T.   Woltersdorf, G.   Back, C. H.  
APPLIED PHYSICS LETTERS, MAY 14 2007

Square-shaped thin film structures with a single magnetic vortex were investigated using a scanning transmission x-ray microscope. The authors report on the direct observation of the vortex core in 500x500 nm(2), 40 nm thick soft magnetic Ni-Fe samples. The static configuration of the vortex core was imaged as well as the gyrotropic motion of the core under excitation with an in-plane alternating magnetic field. This enabled them to directly visualize the direction of the out-of-plane magnetization in the vortex core (up or down). The reversal of the core was effected by short bursts of an alternating magnetic field. An asymmetry appears in the core's trajectory for its orientation pointing up and down, respectively. (C) 2007 American Institute of Physics.

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