The properties of isolated chiral skyrmions in thin magnetic films

Leonov, A. O.; Monchesky, T. L.; Romming, Niklas; Kubetzka, André; Bogdanov, A. N.; Wiesendanger, R.

doi:10.1088/1367-2630/18/6/065003

Cited by 311 publications

(364 citation statements)

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“…There has been a renewed interest in chiral helimagnetism in the last few years since the discovery of twodimensional localized modulations called chiral skyrmions [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…Chiral interactions provide a unique stabilization mechanism, protecting twodimensional localized states from this instability [4,6]. That is why noncentrosymmetric magnets and other chiral condensed matter systems are of special interest in fundamental physics and mathematics as a particular class of materials where skyrmions can exist [7,8].…”

Section: Introductionmentioning

confidence: 99%

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Direct observation of attractive skyrmions and skyrmion clusters in the cubic helimagnet Cu2OSeO3

Loudon¹,

Leonov

Bogdanov

et al. 2018

Phys. Rev. B

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Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. Publisher statement: © 2018 American Physical Society A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP URL' above for details on accessing the published version and note that access may require a subscription. We report the discovery of attractive magnetic skyrmions and their clusters in noncentrosymmetric ferromagnets. These three-dimensional solitons have been predicted to exist in the cone phase of chiral ferromagnets [J. Phys: Condens. Matter 28, 35LT01 (2016)] and are fundamentally different from the more common repulsive axisymmetric skyrmions that occur in the magnetically saturated state. We present real-space images of these skyrmion clusters in thin (∼70 nm) single-crystal samples of Cu 2 OSeO 3 taken using transmission electron microscopy and develop a phenomenological theory describing this type of skyrmion.

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“…There has been a renewed interest in chiral helimagnetism in the last few years since the discovery of twodimensional localized modulations called chiral skyrmions [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Direct observation of attractive skyrmions and skyrmion clusters in the cubic helimagnet Cu2OSeO3

Loudon¹,

Leonov

Bogdanov

et al. 2018

Phys. Rev. B

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“…The field-driven cascading phase transition of skyrmion cluster states has been observed at both low and high temperatures. In addition, intermittent jumps between skyrmion cluster states, referred to as telegraph noise (16), have been noticed at elevated temperatures near the Curie temperature T c .…”

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confidence: 99%

Direct imaging of magnetic field-driven transitions of skyrmion cluster states in FeGe nanodisks

Zhao

Jin

Wang

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

136

111

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Magnetic skyrmion is a nanosized magnetic whirl with nontrivial topology, which is highly relevant for applications on future memory devices. To enable the applications, theoretical efforts have been made to understand the dynamics of individual skyrmions in magnetic nanostructures. However, directly imaging the evolution of highly geometrically confined individual skyrmions is challenging. Here, we report the magnetic field-driven dynamics of individual skyrmions in FeGe nanodisks with diameters on the order of several skyrmion sizes by using Lorentz transmission electron microscopy. In contrast to the conventional skyrmion lattice in bulk, a series of skyrmion cluster states with different geometrical configurations and the fielddriven cascading phase transitions are identified at temperatures far below the magnetic transition temperature. Furthermore, a dynamics, namely the intermittent jumps between the neighboring skyrmion cluster states, is found at elevated temperatures, at which the thermal energy competes with the energy barrier between the skyrmion cluster states.T he complex spin configurations in helimagnets have attracted considerable attention recently, with the topologically stable particle-like spin texture with a size down to the nanoscale, namely magnetic skyrmion, as the focus of interest (1). Magnetic skyrmion is characterized as a nanoscale topological particle producing unconventional spin electronic phenomena (2, 3) that holds great promise for future spintronic devices, including racetrack memory (4), magnetic random access memory, and magnetic sensors (1). Essentially, such schemes rely on the controllable formation and manipulation of individual skyrmions at nanostructured elements with various shapes such as disks, stripes, or wires (5-7). Investigation of skyrmions in confined geometries has therefore become one of the major topics in the field of skyrmion physics (5-10).Unlike ordinary magnetic vortices in microsized soft magnetic disks due to the minimization of the dipolar energy (11), the key ingredient of stabilizing skyrmions in helimagnets is the antisymmetry Dzyaloshinskii−Moriya (DM) interactions originating from the broken inversion symmetry (12). The competition of the DM coupling with ferromagnetic exchange interaction results in periodic helical ground state in helimagnets. Under the action of a magnetic field and temperature, these magnetic helices transfer into skyrmion crystal with triangular lattice configuration, and finally to the field-polarized ferromagnetic state. Notably, both ferromagnetic and DM couplings occur among the neighboring spins and belong to short-range interaction. Thus, it was demonstrated theoretically that skyrmions cluster states, characterized by certain arrangements of limited skyrmions, still persist even in submicrometer objects (8, 13). There, the longrange lattice form of skyrmions in 2D or bulk helimagnets is broken, but a short-ranged ordering with specific geometrical symmetries still remains, and the number of skyrmions in the cluster...

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“…Long-range homochiral modulations (helices) were found in the noncentrosymmetric cubic ferromagnet MnSi several decades ago and since then, other cubic ferromagnets with B20 structures have been investigated intensively [5][6][7] as have other chiral magnetic materials 8,9 . Isolated chiral skyrmions have been discovered recently in PdFe/Ir(111) nanolayers with induced DM interactions and strong easy-axis anisotropy [10][11][12] .…”

mentioning

confidence: 99%

“…In the discretized version, we consider classical spins of unit length on a threedimensional cubic lattice with the following energy functional: In what follows, the Dzyaloshinskii-Moriya constant is set to 0.7265 which corresponds to one-dimensional modulations with a period of 10 lattice spacings in zero field. The discrete model (7) is particularly useful when the continuum model becomes invalid for localized solutions with sizes of few lattice constants 12,15 . The model also allows to operate with smaller arrays of spins as compared with the continuum model.…”

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confidence: 99%

Three-dimensional chiral skyrmions with attractive interparticle interactions

Leonov

Monchesky

Loudon

et al. 2016

J. Phys.: Condens. Matter

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We introduce a new class of isolated three-dimensional skyrmion that can occur within the cone phase of chiral magnetic materials. These novel solitonic states consist of an axisymmetric core separated from the host phase by an asymmetric shell. These skyrmions attract one another. We derive regular solutions for isolated skyrmions arising in the cone phase of cubic helimagnets and investigate their bound states.PACS numbers: 75.30. Kz, 12.39.Dc, The Dzyaloshinskii-Moriya (DM) interaction in noncentrosymmetric magnets is a result of their crystallographic handedness 1 and is responsible for the formation of long-range modulations with a fixed sense of the magnetization rotation 1,2 and the stabilization of two-dimensional axisymmetric localized structures called skyrmions 3,4 . Long-range homochiral modulations (helices) were found in the noncentrosymmetric cubic ferromagnet MnSi several decades ago and since then, other cubic ferromagnets with B20 structures have been investigated intensively 5-7 as have other chiral magnetic materials 8,9 . Isolated chiral skyrmions have been discovered recently in PdFe/Ir(111) nanolayers with induced DM interactions and strong easy-axis anisotropy 10-12 .Chiral skyrmions are two-dimensional topological solitons with an axisymmetric structure localized in nanoscale cylindrical regions. They exist as ensembles of weakly repulsive particles in the saturated phase of noncentrosymmetric magnets 4,13,14 in which all the atomic spins are parallel to an applied magnetic field. In cubic helimagnets, below a certain critical field, H D , the saturated phase transforms into the chiral helical state with the propagation direction along the applied field called the cone phase 2 . Unlike the saturated phase, the boundary values imposed by the longitudinal modulations of the cone phase violate a rotational symmetry of the system, and are thus incompatible with the axisymmetric arrangement of skyrmions investigated in Refs. 4, 10, 11, and 13. Then, the question arises: "are there any localized states compatible with the encompassing cone phase?"In our report we address this compatibility problem and derive regular solutions for asymmetric skyrmions embedded into the cone phase. We demonstrate that unlike the repulsive axisymmetric skyrmions existing in the saturated states, chiral solitons in the cone phase have an attractive interskyrmion potential and form biskyrmion and multiskyrmion states.We consider the standard model for magnetic states in (color online). Magnetic structure of an isolated skyrmion in the cone phase: calculated contour plots of mz(x, y) in three layers with ∆ψc = 2π/3. Details of the magnetization distribution are given in Fig. 2. cubic non-centrosymmetric ferromagnets 1,2 ,where m = (sin θ cos ψ; sin θ sin ψ; cos θ) is the unity vector along the magnetization M, A is the exchange stiffness constant, D is the Dzyaloshinskii-Moriya (DM) coupling energy, and H is the applied magnetic field.Chiral modulations along the applied field with the period L D = 4πA/|D| correspon...

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The properties of isolated chiral skyrmions in thin magnetic films

Cited by 311 publications

References 72 publications

Direct observation of attractive skyrmions and skyrmion clusters in the cubic helimagnet Cu2OSeO3

Direct observation of attractive skyrmions and skyrmion clusters in the cubic helimagnet Cu2OSeO3

Direct imaging of magnetic field-driven transitions of skyrmion cluster states in FeGe nanodisks

Three-dimensional chiral skyrmions with attractive interparticle interactions

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