Real-space imaging of confined magnetic skyrmion tubes.

Magnetic skyrmions are topologically nontrivial particles with a potential application as information elements in future spintronic device architectures. While they are commonly portrayed as two dimensional objects, in reality magnetic skyrmions are thought to exist as elongated, tube-like objects extending through the thickness of the host material. The study of this skyrmion tube state (SkT) is vital for furthering the understanding of skyrmion formation and dynamics for future applications. However, direct experimental imaging of skyrmion tubes has yet to be reported. Here, we demonstrate the real-space observation of skyrmion tubes in a lamella of FeGe using resonant magnetic x-ray imaging and comparative micromagnetic simulations, confirming their extended structure. The formation of these structures at the edge of the sample highlights the importance of confinement and edge effects in the stabilisation of the SkT state, opening the door to further investigation into this unexplored dimension of the skyrmion spin texture.

Flat Bands, Indirect Gaps, and Unconventional Spin-Wave Behavior Induced by a Periodic Dzyaloshinskii-Moriya Interaction.

Periodically patterned metamaterials are known for exhibiting wave properties similar to the ones observed in electronic band structures in crystal lattices. In particular, periodic ferromagnetic materials are characterized by the presence of bands and band gaps in their spin-wave spectrum at tunable GHz frequencies. Recently, the fabrication of magnets hosting Dzyaloshinskii-Moriya interactions has been pursued with high interest since properties, such as the stabilization of chiral spin textures and nonreciprocal spin-wave propagation, emerge from this antisymmetric exchange coupling. In this context, to further engineer the magnon band structure, we propose the implementation of magnonic crystals with periodic Dzyaloshinskii-Moriya interactions, which can be obtained, for instance, via patterning of periodic arrays of heavy metal wires on top of an ultrathin magnetic film. We demonstrate through theoretical calculations and micromagnetic simulations that such systems show an unusual evolution of the standing spin waves around the gaps. We also predict the emergence of indirect gaps and flat bands, effects that depend on the strength of the Dzyaloshinskii-Moriya interaction. Such phenomena, which have been previously observed in different systems, are observed here simultaneously, opening new routes towards engineered metamaterials for spin-wave-based devices.

Simulation of the phase diagram of magnetic vortices in two-dimensional superconductors: evidence for vortex chain formation.

We study the superconducting vortex states induced by the interplay of long-range Pearl repulsion and short-range intervortex attraction using Langevin dynamics simulations. We show that at low temperatures the vortices form an ordered Abrikosov lattice both in low and high fields. The vortices show distinctive modulated structures at intermediate fields depending on the effective intervortex attraction: ordered vortex chain and kagome-like vortex structures for weak attraction; bubble, stripe and antibubble lattices for strong attraction. Moreover, in the regime of the chain state, the vortices display structural transitions from chain to labyrinthine (or disordered chain) and/or to disordered states depending on the strength of the disorder.

Peak effect in the critical current of type II superconductors with strong magnetic vortex pinning.

We perform 2D Langevin simulations studying the peak effect (PE) of the critical current taking into account the temperature dependence of the competing forces. We observe and report that the PE results from the competition of vortex-vortex interactions and vortex-pin interactions which have different temperature dependencies. The simulations reveal that the PE can take place only for certain pinning strengths, densities of pinning centers, and driving forces, which is in good agreement with experiments. No apparent vortex order-disorder transition is observed across the PE regime. In addition, the PE is a dynamical phenomenon, and thermal fluctuations can speed up the process for the formation of the PE.

Magnetic anisotropy terms in [110] MBE-grown REFe(2) films involving the strain term ε(xy).

The magnetic anisotropy parameters in [110] MBE-grown films of REFe(2) (RE, rare earth) compounds are not the same as those in the bulk. This is due to the presence of a shear strain ε(xy), frozen-in during crystal growth. In this paper, magnetic anisotropy parameters for [110] MBE-grown REFe(2) films, that directly involve the shear strain ε(xy), are presented and discussed. In addition to the usual first-order Callen and Callen term [Formula: see text], there are nine second-order terms, six of which involve cross-terms between ε(xy) and the cubic crystal field terms B(4) and B(6). Two of the second-order cross-terms are identified as being important: [Formula: see text] and [Formula: see text]. Of these, the rank-two term [Formula: see text] dominates over a large temperature range. It has the same angular dependence as the first-order term [Formula: see text], but with a more rapid temperature dependence. The correction at T = 0 K for TbFe(2), DyFe(2), HoFe(2), ErFe(2) and TmFe(2), amounts to ∼+9.2%, -13.9%, -11.6%, +14.3%, and 27.1%, respectively. Similar comments are made concerning the rank-four [Formula: see text] term.

Symmetry locking and commensurate vortex domain formation in periodic pinning arrays.

The spontaneous formation of domains of commensurate vortex patterns near rational fractional matching fields of a periodic pinning array has been investigated with high resolution scanning Hall probe microscopy. We show that domain formation is promoted due to the efficient incorporation of mismatched excess vortices and vacancies at the corners of domain walls, which outweighs the energetic cost of creating them. Molecular dynamics simulations with a generic pinning potential reveal that domains are formed only when vortex-vortex interactions are long range.