Band structure engineering of two-dimensional magnonic vortex crystals

Behncke, Carolin; Hänze, Max; Adolff, Christian F.; Weigand, Markus; Meier, Guido

doi:10.1103/physrevb.91.224417

Cited by 27 publications

(26 citation statements)

References 27 publications

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“…These solitons and their dynamics have attracted much attention of physicists due to their fundamental properties [9] and technological promise [10,11]. In particular, the collective gyration modes of arrays of vortex disks have been studied theoretically [12] and experimentally [13][14][15][16] as reprogrammable metamaterials whose functionalities can be controlled by changing vortices' polarities and chiralities [17].…”

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confidence: 99%

Chiral Edge Mode in the Coupled Dynamics of Magnetic Solitons in a Honeycomb Lattice

Kim

Tserkovnyak

2017

Phys. Rev. Lett.

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Motivated by a recent experimental demonstration of a chiral edge mode in an array of spinning gyroscopes, we theoretically study the coupled gyration modes of topological magnetic solitons, vortices and magnetic bubbles, arranged as a honeycomb lattice. The soliton lattice under suitable conditions is shown to support a chiral edge mode like its mechanical analogue, the existence of which can be understood by mapping the system to the Haldane model for an electronic system. The direction of the chiral edge mode is associated with the topological charge of the constituent solitons, which can be manipulated by an external field or by an electric-current pulse. The direction can also be controlled by distorting the honeycomb lattice. Our results indicate that the lattices of magnetic solitons can serve as reprogrammable topological metamaterials.Introduction.-The term metamaterials refer to a class of man-made composite materials which can offer functionalities beyond those found in nature via collective dynamics of constituent elements [1] [7] that a honeycomb lattice of spinning gyroscopes can support a chiral edge mode that is protected from small perturbations such as lattice distortions and thus can be identified as a topological mechanical metamaterial. As discussed in Ref. [7], an open challenge for its practical applications is to find a feasible way to keep gyroscopes spinning.Quantum-mechanically, nature has already endowed us a permanent gyroscope: spin of a particle. This intrinsic angular momentum manifests itself macroscopically through the gyrotropic force in the dynamics of magnetic solitons with topologically nontrivial textures such as magnetic bubbles (also known as skyrmions) and vortices [8]. These solitons and their dynamics have attracted much attention of physicists due to their fundamental properties [9] and technological promise [10,11]. In particular, the collective gyration modes of arrays of vortex disks have been studied theoretically [12] and experimentally [13][14][15][16] as reprogrammable metamaterials whose functionalities can be controlled by changing vortices' polarities and chiralities [17].When viewing topological magnetic solitons as gyroscopes, it is natural to expect that a honeycomb lattice of the solitons can support a chiral edge mode as its mechanical analogues [6,7]. In this Letter, we verify the expectation both by numerically solving the equations of motion for the dynamics of coupled solitons and by mapping the system to the Haldane model for an electron in graphene, which is known to exhibit the quantum Hall effect [18]. We also show that the direction of the edge mode can be controlled either by changing the topological charge of the solitons or by distorting the geometry of the honeycomb lattice. We conclude the Letter with

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confidence: 99%

Chiral Edge Mode in the Coupled Dynamics of Magnetic Solitons in a Honeycomb Lattice

Kim

Tserkovnyak

2017

Phys. Rev. Lett.

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“…Although the investigated crystals have a confined size, the fundamental interactions equally apply to larger crystals. This leads to a dispersion relation of gyrational waves that has been observed experimentally in two-dimensional vortex arrangements 7 . Magnetic vortices form in thin film ferromagnetic disks.…”

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confidence: 58%

Collective modes in three-dimensional magnonic vortex crystals

Hänze

Adolff

Schulte

et al. 2016

Sci Rep

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Collective modes in three-dimensional crystals of stacked permalloy disks with magnetic vortices are investigated by ferromagnetic resonance spectroscopy and scanning transmission X-ray microscopy. The size of the arrangements is increased step by step to identify the different contributions to the interaction between the vortices. These contributions are the key requirement to understand complex dynamics of three dimensional vortex crystals. Both vertical and horizontal coupling determine the collective modes. In-plane dipoles strongly influence the interaction between the disks in the stacks and lead to polarity-dependent resonance frequencies. Weaker contributions discern arrangements with different polarities and circularities that result from the lateral coupling of the stacks and the interaction of the core regions inside a stack. All three contributions are identified in the experiments and are explained in a rigid particle model.

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“…Since neighboring vortices couple due to stray fields emerging at the surfaces of the ferromagnetic elements [10], the motions of closely packed vortices are strongly influenced by their surrounding ferromagnetic structures [11,12]. The interaction between laterally arranged elements has been studied for pairs [13,14], chains [15], and two-dimensional arrangements [16][17][18] of vortices. In laterally coupled arrangements it has been shown recently that memorylike writing processes are possible based on the excitation of the gyrotropic mode [19], where bits are stored as polarization patterns.…”

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confidence: 99%

Two-body problem of core-region coupled magnetic vortex stacks

et al. 2016

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The dynamics of all four combinations of possible polarity and circularity states in a stack of two vortices is investigated by time-resolved scanning transmission x-ray microscopy. The vortex stacks are excited by unidirectional magnetic fields leading to a collective oscillation. Four different modes are observed that depend on the relative polarizations and circularities of the stacks. They are excited to a driven oscillation. We observe a repulsive and attractive interaction of the vortex cores depending on their relative polarizations. The nonlinearity of this core interaction results in different trajectories that describe a two-body problem.

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Band structure engineering of two-dimensional magnonic vortex crystals

Cited by 27 publications

References 27 publications

Chiral Edge Mode in the Coupled Dynamics of Magnetic Solitons in a Honeycomb Lattice

Chiral Edge Mode in the Coupled Dynamics of Magnetic Solitons in a Honeycomb Lattice

Collective modes in three-dimensional magnonic vortex crystals

Two-body problem of core-region coupled magnetic vortex stacks

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