Micromagnetic simulations using Graphics Processing Units

López-Dı́az, L.; Aurélio, David; Torres, L.; Martínez, Eduardo; Hernández-López, M. A.; Gómez, Julian E.; Alejos, Ó.; Carpentieri, Mario; Finocchio, G.; Consolo, G.

doi:10.1088/0022-3727/45/32/323001

Cited by 130 publications

(103 citation statements)

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confidence: 99%

“…To add the i-DMI, we consider the CoFeB coupled with a Pt (heavy metal) layer as already experimentally observed [24]. The study is carried out by means of a state-of-the-art micromagnetic solver which numerically integrates the Landau-Lifshitz-Gilbert (LLG) equation [25,26,27], that includes the i-DMI contribution can be seen as an additional shape anisotropy contribution [24], thus the different magnetic states ( Fig.2(a)) can be linked to a trade-off among magnetostatic, exchange, and i-DMI energies. In particular, at low |D|, the magnetostatic energy is predominant, stabilizing a vortex with a circular chirality.…”

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Magnetic Radial Vortex Stabilization and Efficient Manipulation Driven by the Dzyaloshinskii-Moriya Interaction and Spin-Transfer Torque

et al. 2016

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Solitons are very promising for the design of the next generation of ultralow power devices for storage and computation. The key ingredient to achieve this goal is the fundamental understanding of their stabilization and manipulation. Here, we show how the interfacial Dzyaloshinskii-Moriya Interaction (i-DMI) is able to lift the energy degeneracy of a magnetic vortex state by stabilizing a topological soliton with radial chirality, hereafter called radial vortex. It has a non-integer skyrmion number S (0.5<|S|<1) due to both the vortex core polarity and the magnetization tilting induced by the i-DMI boundary conditions. Micromagnetic simulations predict that a magnetoresistive memory based on the radial vortex state in both free and polarizer layers can be efficiently switched by a threshold current density smaller than 10 6 A/cm 2 . The switching processes occur via the nucleation of topologically connected vortices and vortexantivortex pairs, followed by spin-wave emissions due to vortex-antivortex annihilations. 2Magnetic solitons, such as domain walls (DWs) [1,2,3,4], vortices [5,6,7,8,9,10,11] and skyrmions [12,13,14,15,16,17] From a fundamental point of view, the stabilization of a radial vortex gives rise to the possibility to create current densities with radial polarization for particle-trapping applications, such as skyrmion [22], analogously to what radially polarized beams can do in many optical systems [23].In order to show the main features and the possible applications of the radial vortex, extensive micromagnetic simulations have been performed. The first part of this letter focuses on the fundamental properties of the radial vortex, in terms of stability as a function of the i-DMI, 3 topology, nucleation as well as response to an in-plane field. The second part is dedicated to the analysis of the switching process of the radial vortex, underlining the differences with the circular vortex.We consider a CoFeB disk having a diameter d=250nm and a thickness t=1.0nm to have an in-plane easy axis at zero external field. To add the i-DMI, we consider the CoFeB coupled with a Pt (heavy metal) layer as already experimentally observed [24]. The study is carried out by means of a state-of-the-art micromagnetic solver which numerically integrates the Landau-Lifshitz-Gilbert (LLG) equation [25,26,27], that includes the i-DMI contribution Fig.4(a)). An H ext =5.0mT yields a uniform magnetic state. Fig.4(b) shows the results for the circular vortex (|D|=0.0mJ/m 2 ). The displacement occurs along the direction perpendicular to the external field (insets Fig.4(b)) [7,32,33,34,35]. Together with the qualitatively different vortex core shift, the field value that leads to the radial vortex core expulsion is twice the one of the circular vortex. This is ascribed to the i-DMI and, in particular, to its boundary conditions, in fact, the expulsion field increases as a function of |D|. The key reason for that is the need of a larger field to align the out-of-plane tilted spins at the sample edges 5 perpendicu...

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Magnetic Radial Vortex Stabilization and Efficient Manipulation Driven by the Dzyaloshinskii-Moriya Interaction and Spin-Transfer Torque

et al. 2016

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“…TIE analysis have been performed to retrieve the phase shift of the electron wave at the exit of the sample, 29 and then to reconstruct the in-plane magnetic induction. 31 Micromagnetic simulations have been performed using the GPMagnet software package 32 to compare with the experimental data. Real physical dimensions have been used in the models.…”

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Optimized cobalt nanowires for domain wall manipulation imaged by in situ Lorentz microscopy

Rodríguez

Magén

Snoeck

et al. 2013

Applied Physics Letters

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Direct observation of domain wall (DW) nucleation and propagation in focused electron beam induced deposited Co nanowires as a function of their dimensions was carried out by Lorentz microscopy (LTEM) upon in situ application of magnetic field. Optimal dimensions favoring the unambiguous DW nucleation/propagation required for applications were found in 500-nm-wide and 13-nm-thick Co nanowires, with a maximum nucleation field and the largest gap between nucleation and propagation fields. The internal DW structures were resolved using the transport-ofintensity equation formalism in LTEM images and showed that the optimal nanowire dimensions correspond to the crossover between the nucleation of transverse and vortex walls. In the last decade, several pioneering works envisaged different strategies to design magnetic information storage, logic devices or sensors based on magnetic domain walls (DW) as functional entities to store, transfer, and process information in ferromagnetic media. [1][2][3][4][5] These innovative ideas and promising applications have motivated extensive developments of ferromagnetic nanostructures in which DW can be "easily" created and driven either by external magnetic fields and/or spin-polarized currents. 6-12 DW in magnetic nanostructures have therefore become a major topic for the research community in the field of Nanomagnetism. The specific DW configuration is the result of the balance between the magnetostatic energy, the magnetocrystalline anisotropy, and the exchange coupling. Therefore, along with the intrinsic properties of the magnetic material, it also depends on the geometry and the dimensions of the nanostructures. 13 In magnetic nanowires (NWs), the possible DW configurations are either symmetric or asymmetric transverse walls (TWs) or vortex walls (VWs) and they move differently under the application of an external magnetic field or current. 14 Therefore, a careful analysis of the DW structure of devices as a function of dimensions, geometries, shape of constrictions, etc. is requested to determine the type of magnetic configurations appearing in a given nanostructure and the possibility of tuning and manipulating them upon the application of external magnetic fields or electric currents. 6,8,[10][11][12] Permalloy (Py) nanostructures have been extensively studied because of their low magnetocrystalline anisotropy, thus allowing the control of its magnetic properties simply adjusting its shape anisotropy. Therefore, many Py nanostructures of various shapes and sizes have been synthetized using electron beam or UV lithography processes. [1][2][3][4][5][6][7][8][9][10][11][12]15,16 The use of ferromagnetic materials alternative to Py and the development of advanced nanofabrication methods allowing creating magnetic nanostructures of dimensions less than 100 nm are however needed to explore their functionalities and possible applications. In the last years, focused electron beam induced deposition (FEBID) technique has demonstrated a capacity to produce high quality nanostructu...

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“…We have taken the approach of that of Lopez-Diaz et al used in the GPMAGNET software [36]. In this approach, we write the magnetostatic field in a (cubic) cell i (H d,i )as where N is the 3 × 3 symmetric demagnetizing tensor.…”

Section: Multimacrospin Numerical Resultsmentioning

confidence: 99%

Temperature-dependent ferromagnetic resonance via the Landau-Lifshitz-Bloch equation: Application to FePt

et al. 2014

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Using the Landau-Lifshitz-Bloch (LLB) equation for ferromagnetic materials, we derive analytic expressions for temperature-dependent absorption spectra as probed by ferromagnetic resonance. By analyzing the resulting expressions, we can predict the variation of the resonance frequency and damping with temperature and coupling to the thermal bath. We base our calculations on the technologically relevant L1 0 FePt, parametrized from atomistic spin dynamics simulations, with the Hamiltonian mapped from ab initio parameters. By constructing a multimacrospin model based on the LLB equation and exploiting GPU acceleration, we extend the study to investigate the effects on the damping and resonance frequency in μm-sized structures.

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Micromagnetic simulations using Graphics Processing Units

Cited by 130 publications

References 91 publications

Magnetic Radial Vortex Stabilization and Efficient Manipulation Driven by the Dzyaloshinskii-Moriya Interaction and Spin-Transfer Torque

Magnetic Radial Vortex Stabilization and Efficient Manipulation Driven by the Dzyaloshinskii-Moriya Interaction and Spin-Transfer Torque

Optimized cobalt nanowires for domain wall manipulation imaged by in situ Lorentz microscopy

Temperature-dependent ferromagnetic resonance via the Landau-Lifshitz-Bloch equation: Application to FePt

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