Proposal for a standard problem for micromagnetic simulations including spin-transfer torque

Najafi, Massoud; Krüger, Benjamin; Bohlens, Stellan; Franchin, Matteo; Fangohr, Hans; Vanhaverbeke, A.; Allenspach, R.; Bolte, Markus; Merkt, U.; Pfannkuche, Daniela; Möller, Dietmar P. F.; Meier, Guido

doi:10.1063/1.3126702

Cited by 43 publications

(32 citation statements)

References 33 publications

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“…Micromagnetic simulations were performed using MuMax3 [22], [23]. The material parameters used in the simulations corresponds to that of Co/Pt multilayers as shown in Table 1 [24], [25].…”

Section: Methodsmentioning

confidence: 99%

Mitigation of Magnus Force in Current-Induced Skyrmion Dynamics

et al. 2015

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Current-driven skyrmions drift from the intended direction of motion in a thin magnetic film due to the presence of the Magnus force and are annihilated upon reaching the film edge. This paper proposes two methods to engineer a 1D potential well to confine the skyrmion motion in the center region of nanowires and thus preventing annihilation. By patterning the magnetic anisotropy of the film or by adding a layer of magnetic material at the edges, the barrier height and width of the potential well can be controlled. Magnetic skyrmions in such nanowires can then be guided to traverse only along the axis of the nanowire, even in nanowires with steep bends. In addition, we also report a compression mechanism where the skyrmion size and separation distance can be reduced by modifying the potential well, thus increasing the skyrmion packing density in a nanowire. The guided motion and high skyrmion density made possible by our proposed methods will allow for the realization of high density skyrmion based memory.Index Terms-Magnetic skyrmions, micromagnetic simulations, perpendicular magnetic anisotropy, spin structures.

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“…Micromagnetic simulations were performed using MuMax3 [22], [23]. The material parameters used in the simulations corresponds to that of Co/Pt multilayers as shown in Table 1 [24], [25].…”

Section: Methodsmentioning

confidence: 99%

Mitigation of Magnus Force in Current-Induced Skyrmion Dynamics

et al. 2015

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“…[11,12,13] Vortices are formed when the in-plane magnetization curls around a center region. In this few-nanometerlarge center region, called the vortex core, the magnetization turns out of plane to minimize the exchange energy.…”

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confidence: 99%

Proposal of a Robust Measurement Scheme for the Nonadiabatic Spin Torque Using the Displacement of Magnetic Vortices

et al. 2010

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The strength of the non-adiabatic spin torque is currently under strong debate, as its value differs by orders of magnitude as well in theoretical predictions as in measurements. Here, a measurement scheme is presented that allows to determine the strength of the non-adiabatic spin torque accurately and directly. Analytical and numerical calculations show that the scheme allows to separate the displacement due to the Oersted field and is robust against uncertainties of the exact current direction. PACS numbers: 75.60.Ch, 72.25.Ba A spin-polarized current flowing through a ferromagnetic sample interacts with the magnetization and exerts a torque on the local magnetic moments. For conduction electron spins that follow the local magnetization adiabatically it has been shown that the interaction via spin transfer can be described by adding a current-dependent term to the Landau-LifshitzGilbert equation.[1] This equation has been extended by an additional term that takes the non-adiabatic influence of the itinerant spins into account.[2] Theoretically, several mechanisms have been proposed as the origin of the non-adiabatic spin torque, leading to different orders of magnitude for its strength. [2,3,4,5,6] Thus a precise measurement of the non-adiabatic spin torque is necessary to give insight into its microscopic origin. A determination of its strength is further important for a reliable prediction of the current-driven domain-wall velocity. [2] Currently measured values of the non-adiabatic spin torque for permalloy differ by one order of magnitude, [7,8,9,10] thus the strength of the non-adiabatic spin torque is under strong debate. In these experiments the observed motion of a domain wall was compared with micromagnetic simulations to determine the non-adiabatic spin torque. This analysis is highly susceptible to surface roughness and Oersted fields.Due to its high symmetry and spacial confinement a vortex in a micro-or nanostructured magnetic thin-film element is a promising system for the investigation of the spin-torque effect. [11,12,13] Vortices are formed when the in-plane magnetization curls around a center region. In this few-nanometerlarge center region, called the vortex core, the magnetization turns out of plane to minimize the exchange energy. There are four different ground states of a vortex. These states are labeled by the direction of the out-of-plane magnetization, called polarization p, and the sense of rotation of the in-plane magnetization, called chirality c. Polarizations of p = 1 and p = −1 denote a core that points parallel or antiparallel to the z axis, respectively. A chirality of c = 1 denotes a counterclockwise curling of the in-plane magnetization while c = −1 denotes a clockwise curling.It is known that vortices are displaced from their equilibrium position when excited by spin-polarized electric current pulses. [12,13,14,15,16,17,18,19,20] The spatial confinement of the vortex core within the film element yields an especially accessible system for measurements with scanning probe...

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“…This quantity is correlated with the displacement of the vortex core from the structure center and thus serves as a measure for the response of the system to an excitation [19]. Figure 3 shows the simulated response as a function of excitation frequency at a fixed low field amplitude of 1 mT, which is insufficient to cause switching.…”

Section: Simulations Resultsmentioning

confidence: 99%

Micromagnetic Simulations on GPU, A Case Study: Vortex Core Switching by High-Frequency Magnetic Fields

et al. 2012

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Abstract-Since magnetic vortex cores have two ground states, they are candidates for digital memory bits in future MRAM devices. Vortex core switching can be induced by exciting the gyrotropic eigenmode e.g. by applying cyclic magnetic fields with typically a sub-GHz 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' 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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Proposal for a standard problem for micromagnetic simulations including spin-transfer torque

Cited by 43 publications

References 33 publications

Mitigation of Magnus Force in Current-Induced Skyrmion Dynamics

Mitigation of Magnus Force in Current-Induced Skyrmion Dynamics

Proposal of a Robust Measurement Scheme for the Nonadiabatic Spin Torque Using the Displacement of Magnetic Vortices

Micromagnetic Simulations on GPU, A Case Study: Vortex Core Switching by High-Frequency Magnetic Fields

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