Symmetry breaking in the formation of magnetic vortex states in a permalloy nanodisk

Im, Mi‐Young; Fischer, Peter; Yamada, K.; Sato, Tomonori; Kasai, S.; Nakatani, Yoshinobu; Ono, Teruo

doi:10.1038/ncomms1978

Cited by 118 publications

(103 citation statements)

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“…Here, we use the term circular vortex to identify a vortex with CW or CCW chirality. For a fixed polarity, in a circular vortex, both CCW and CW configurations are energetically equivalent (degeneracy in the energy landscape) [9]. On the other hand, for a radial vortex, the core polarity fixes the chirality (radial and antiradial for positive or negative vortex core polarity, respectively), because of the nonsymmetric i-DMI field.…”

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confidence: 99%

“…Magnetic 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].…”

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confidence: 99%

“…Magnetic 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], are attracting a growing interest for their potential technological applications in ultralow power devices beyond CMOS, thanks to their fundamental properties and the possible use of spin-transfer [18] and spin-orbit [2,3,4] torques for their nucleation and manipulation. For example, DWs and skyrmions are at the basis of racetrack memories [3,4,12,19], while vortices can be used as an alternative to the uniform state to store information in magnetoresistive devices [5,11], such as magnetic tunnel junctions (MTJs).…”

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confidence: 99%

“…(1.1) has been extended to include Oersted field [1], as an additional contribution to the effective field, and the Slonczewski spin-transfer-torque term for the MTJs [8,9,10]:…”

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confidence: 99%

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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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confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

“…(1.1) has been extended to include Oersted field [1], as an additional contribution to the effective field, and the Slonczewski spin-transfer-torque term for the MTJs [8,9,10]:…”

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confidence: 99%

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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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“…The magnetic vortex is characterized by an in-plane circulating domain structure, the circularity c, which rotates either clockwise (CW, c ¼ þ 1) or counter-clockwise (CCW, c ¼ À 1) and an out-of-plane magnetization, the polarity p pointing either up (p ¼ þ 1) or down (p ¼ À 1) [12][13][14][15][16][17][18] . In the context of skyrmions, the magnetic vortex structure (VS) can be described by a topological charge, the skyrmion number of np/2 ¼ ±1/2 with the winding number of n ¼ H [a (f)/2p]dS ¼ þ 1 (refs 19-21).…”

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Stochastic formation of magnetic vortex structures in asymmetric disks triggered by chaotic dynamics

Lee

Vogel

et al. 2014

Nat Commun

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The non-trivial spin configuration in a magnetic vortex is a prototype for fundamental studies of nanoscale spin behaviour with potential applications in magnetic information technologies. Arrays of magnetic vortices interfacing with perpendicular thin films have recently been proposed as enabler for skyrmionic structures at room temperature, which has opened exciting perspectives on practical applications of skyrmions. An important milestone for achieving not only such skyrmion materials but also general applications of magnetic vortices is a reliable control of vortex structures. However, controlling magnetic processes is hampered by stochastic behaviour, which is associated with thermal fluctuations in general. Here we show that the dynamics in the initial stages of vortex formation on an ultrafast timescale plays a dominating role for the stochastic behaviour observed at steady state. Our results show that the intrinsic stochastic nature of vortex creation can be controlled by adjusting the interdisk distance in asymmetric disk arrays.

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Magnetization Configurations and Reversal in Small Magnetic Elements

Reeve

Vafaee

Kläui

2019

Materials Science and Technology

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In this article, we present an overview of various static magnetization configurations and their dynamic reversal modes for elements of typical sizes from a few nanometers to a few micrometers. Initially, commonly employed techniques for the magnetic imaging and characterization of such systems are briefly reviewed. We then concisely outline the basic theoretical details of micromagnetism and in particular the main energy terms that determine the formation and dynamics of different states. To describe the simplest case of a single‐domain system, we present Stoner–Wohlfarth theory and compare its predictions to experimental studies. For larger elements, we discuss the formation of nonuniform and multidomain states, based on a fine balance of the aforementioned energy terms. In particular, for the most widely studied high‐symmetry geometries, the interplay between these energy terms and the element shape for the formation of the prevalent states is discussed. Next, the dynamic reversal of the elements is presented, beginning with the Landau–Lifshitz–Gilbert equation that governs uniform dynamics of single‐domain systems. Further reversal modes including curling, buckling, and domain wall motion are presented for nonuniform states, by a number of case studies. The work is primarily motivated from a fundamental standpoint, but links to potential device applications are highlighted throughout.

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Symmetry breaking in the formation of magnetic vortex states in a permalloy nanodisk

Cited by 118 publications

References 24 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

Stochastic formation of magnetic vortex structures in asymmetric disks triggered by chaotic dynamics

Magnetization Configurations and Reversal in Small Magnetic Elements

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