Multiscale model approach for magnetization dynamics simulations

Lucia, Andrea De; Krüger, Benjamin; Tretiakov, Oleg A.; Kläui, Mathias

doi:10.1103/physrevb.94.184415

Cited by 16 publications

(10 citation statements)

References 31 publications

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“…Due to the almost constant M z component of the skyrmion within the center, the created object will be named skyrmion bubble. It should be noted that the accurate calculation of critical currents to create skyrmions within the wire will require atomistic discretization due to Bloch points 27 that are formed during creation 28 . In contrast to the creation process of the skyrmion within the wire, the pinning currents and thermal stability over energy barriers at pinning sites or boundaries of the magnet can be well described in a continuous approach, as will be discussed later in detail.…”

Section: Critical Current Densitiesmentioning

confidence: 99%

Spin Torque Efficiency and Analytic Error Rate Estimates of Skyrmion Racetrack Memory

Suess

Vogler

Bruckner

et al. 2019

Sci Rep

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In this paper, the thermal stability of skyrmion bubbles and the critical currents to move them over pinning sites were investigated. For the used pinning geometries and the used parameters, the unexpected behavior is reported that the energy barrier to overcome the pinning site is larger than the energy barrier of the annihilation of a skyrmion. The annihilation takes place at boundaries by current driven motion, as well as due to the excitation over energy barriers, in the absence of currents, without forming Bloch points. It is reported that the pinning sites, which are required to allow thermally stable bits, significantly increase the critical current densities to move the bits in skyrmion-like structures to about jcrit = 0.62 TA/m². The simulation shows that the applied spin transfer model predicts experimentally obtained critical currents to move stable skyrmions at room temperature well, which is in contrast to simulations based on spin orbit torque that predict significantly too low critical currents. By calculating the thermal stability, as well as the critical current, we can derive the spin torque efficiency η = ΔE/Ic = 0.19 kBT300/μA, which is in a similar range to the simulated spin torque efficiency of MRAM structures. Finally, it is shown that the stochastic depinning process of any racetrack-like device requires an extremely narrow depinning time distribution smaller than ~6% of the current pulse length to reach bit error rates smaller than 10−9.

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Section: Critical Current Densitiesmentioning

confidence: 99%

Spin Torque Efficiency and Analytic Error Rate Estimates of Skyrmion Racetrack Memory

Suess

Vogler

Bruckner

et al. 2019

Sci Rep

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“…The necessity for a computational model, capable of performing quantitatively accurate simulations is therefore obvious and a key step. While more accurate atomistic simulations would overcome this problem, the computational power required to run such simulations for a sample of realistic experimental size makes this possibility infeasible.In this work, the annihilation of isolated Skyrmions is studied by simulating the Landau-Lifshitz-Gilbert (LLG) equation with a multiscale approach [29]. Within this approach the core of the Skyrmion is simulated atomistically, while the remaining part of a nanodisk hosting the Skyrmion is simulated using micromagnetics.…”

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confidence: 99%

“…The central part of the system was simulated atomistically (fine scale region), while the remaining part was simulated using the micromagnetic model (coarse scale region), following the approach described in Ref. [29]. The size of the fine scale region was chosen to fit the entire Skyrmion at rest, but without sacrificing too much computational time.…”

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confidence: 99%

Multiscale simulations of topological transformations in magnetic-skyrmion spin structures

Lucia¹,

Litzius²,

Krüger³

et al. 2017

Phys. Rev. B

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Magnetic Skyrmions belong to the most interesting spin structures for the development of future information technology as they have been predicted to be topologically protected. To quantify their stability, we use an innovative multiscale approach to simulating spin dynamics based on the Landau-Lifshitz-Gilbert equation. The multiscale approach overcomes the micromagnetic limitations that have hindered realistic studies using conventional techniques. We first demonstrate how the stability of a Skyrmion is influenced by the refinement of the computational mesh and reveal that conventionally employed traditional micromagnetic simulations are inadequate for this task. Furthermore, we determine the stability quantitatively using our multiscale approach. As a key operation for devices, the process of annihilating a Skyrmion by exciting it with a spin polarized current pulse is analyzed, showing that Skyrmions can be reliably deleted by designing the pulse shape.Magnetic Skyrmions [1] are topological spin structures that arise in the spin pattern of ferromagnetic systems with broken inversion symmetry, such as chiral crystals [2,3] or thin magnetic films with different top and bottom interfaces [4,5]. Skyrmion lattices [6][7][8][9] constitute the ground state for some systems, while isolated Skyrmions can appear as metastable states of some magnetic nanostructures [10]. Isolated Skyrmions have been recently considered [11][12][13][14] as the building blocks for ultradense magnetic storage devices [15].Skyrmions carry a topological charge Q = ±1 defined as [16]:where A is the area of the system and m the unit magnetization vector. Since transitions that change Q are forbidden [16] in a continuum description of m, such structures are topologically protected. Nevertheless, in a real system composed of discrete magnetic moments localized on the atomic lattice sites, no strict topological protection exists [17]. Thus it is necessary to overcome a finite energy barrier to induce transformations that change Q, such as the annihilation of a Bloch line (BL) [16,[18][19][20][21][22][23][24]. The stability against external fields is indeed a key feature of Skyrmions, making them a good candidate as information carriers in next generation storage devices [25][26][27]. The fundamental prerequisites for applications are ascertaining the stability of Skyrmions, as well as reliably annihilating them. However, the computational treatment of processes involving annihilating Skyrmions is very delicate. In analytical micromagnetic theory, singularities in the exchange field tend to arise during topological transformations, making numerical simulations very susceptible to the mesh being used [28] and therefore often inaccurate. The necessity for a computational model, capable of performing quantitatively accurate simulations is therefore obvious and a key step. While more accurate atomistic simulations would overcome this problem, the computational power required to run such simulations for a sample of realistic experimental size makes th...

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“…Micromagnetic simulations of the domain wall spin structure were performed using the multi-scale modified MicroMagnum code [75] as described in Ref. [76]. Multiscale modelling is necessary to realistically model the spin structures even for very narrow domain walls.…”

Section: Micromagnetic Simulationsmentioning

confidence: 99%

Scaling of intrinsic domain wall magnetoresistance with confinement in electromigrated nanocontacts

et al. 2019

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In this work we study the evolution of intrinsic domain wall magnetoresistance (DWMR) with domain wall confinement. Clean permalloy notched half-ring nanocontacts are fabricated using a special ultra-high vacuum electromigration procedure to tailor the size of the wire in-situ and through the resulting domain wall confinement we tailor the domain wall width from a few tens of nm down to a few nm. Through measurements of the dependence of the resistance with respect to the applied field direction we extract the contribution of a single domain wall to the MR of the device, as a function of the domain wall width in the confining potential at the notch. In this size range, an intrinsic positive MR is found, which dominates over anisotropic MR, as confirmed by comparison to micromagnetic simulations. Moreover, the MR is found to scale monotonically with the size of the domain wall, δ DW , as 1/δ b DW , with b = 2.31 ± 0.39. The experimental result is supported by quantum-mechanical transport simulations based on ab-initio density functional theory calculations.arXiv:1812.05689v1 [cond-mat.mes-hall]

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Multiscale model approach for magnetization dynamics simulations

Cited by 16 publications

References 31 publications

Spin Torque Efficiency and Analytic Error Rate Estimates of Skyrmion Racetrack Memory

Spin Torque Efficiency and Analytic Error Rate Estimates of Skyrmion Racetrack Memory

Multiscale simulations of topological transformations in magnetic-skyrmion spin structures

Scaling of intrinsic domain wall magnetoresistance with confinement in electromigrated nanocontacts

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