Anisotropic Adaptation on Unstructured Grids

The efficient representation of the highly directional features in a flow field with adapted anisotropic grids forms the focus of the analysis. Anisotropic adaptation is more effective than isotropic adaptation and requires more degrees of freedom from the mesh, which also demands the use of unstructured grids in the adaptation. The size and orientation of an anisotropic element require a matrix-like local feature indicator. The Hessian, a matrix composed of the second derivatives of an appropriate flow variable, is defined and used as a feature indicator in the adaptation. The Hessian provides a metric that defines the length of an edge and the lengths of all edges are equal in the optimized mesh. The techniques to minimize the differences among edge lengths are discussed and those chosen include node enrichment, node removal, edge swapping and point smoothing. The results indicate that the mesh in which the edge lengths are equalized is not correct for three major flow features one frequently encounters. The inflections existing near the wall in a boundary layer result in coarse grids there. A “wall” Hessian is defined to replace the second derivatives and give a more appropriate spacing for high Reynolds number flow modeling. Difficulties in the adaptation of discontinuities are addressed. Remedies proposed are to limit the minimum physical edge length and smooth the Hessian such that the discontinuity refinement encompasses more layers of elements. The methodology to refine the discontinuity equally is also proposed. The invalidity of the Hessian in a free stream is corrected to give a reasonable grid size in that region. The concepts involved in the extension of the length-based approach to three dimensions are addressed. The difference and difficulties in three-dimensional adaptation are discussed

Current-Induced Dynamics and Chaos of Antiferromagnetic Bimerons

A magnetic bimeron is a topologically non-trivial spin texture carrying an integer topological charge, which can be regarded as the counterpart of skyrmion in easy-plane magnets. The controllable creation and manipulation of bimerons are crucial for practical applications based on topological spin textures. Here, we analytically and numerically study the dynamics of an antiferromagnetic bimeron driven by a spin current. Numerical simulations demonstrate that the spin current can create an isolated bimeron in the antiferromagnetic thin film via the damping-like spin torque. The spin current can also effectively drive the antiferromagnetic bimeron without a transverse drift. The steady motion of an antiferromagnetic bimeron is analytically derived and is in good agreement with the simulation results. Also, we find that the alternating-current-induced motion of the antiferromagnetic bimeron can be described by the Duffing equation due to the presence of the nonlinear boundary-induced force. The associated chaotic behavior of the bimeron is analyzed in terms of the Lyapunov exponents. Our results demonstrate the inertial dynamics of an antiferromagnetic bimeron, and may provide useful guidelines for building future bimeron-based spintronic devices.Comment: 6 pages, 4 figure

Current-driven skyrmionium in a frustrated magnetic system

Magnetic skyrmionium can be used as a nanometer-scale non-volatile information carrier, which shows no skyrmion Hall effect due to its special structure carrying zero topological charge. Here, we report the static and dynamic properties of an isolated nanoscale skyrmionium in a frustrated magnetic monolayer, where the skyrmionium is stabilized by competing interactions. The frustrated skyrmionium has a size of about $10$ nm, which can be further reduced by tuning perpendicular magnetic anisotropy or magnetic field. It is found that the nanoscale skyrmionium driven by the damping-like spin-orbit torque shows directional motion with a favored Bloch-type helicity. A small driving current or magnetic field can lead to the transformation of an unstable N\'eel-type skyrmionium to a metastable Bloch-type skyrmionium. A large driving current may result in the distortion and collapse of the Bloch-type skyrmionium. Our results are useful for the understanding of frustrated skyrmionium physics, which also provide guidelines for the design of spintronic devices based on topological spin textures.Comment: 5 pages, 5 figure

Laminar and Quasi-Turbulent Dynamics of a Magnetic Skyrmion Pipe Flow

We report the laminar and quasi-turbulent dynamic behaviors of magnetic skyrmions flowing in a pipe channel. The skyrmion flow driven by a uniform current may show a lattice structural transition. The skyrmion flow driven by a non-uniform current shows a dynamically varying lattice structure. A large uniform current could result in the compression of skyrmions toward the channel edge, leading to the transition of the skyrmion pipe flow into an open-channel flow with a free surface. Skyrmions on the free surface may form a single shear layer adjacent to the main skyrmion flow. Our results reveal the fluid nature of skyrmionic quasiparticles that may play an essential role in applications.Comment: 7 pages, 3 figure

Reversible magnetic domain reorientation induced by magnetic field pulses with fixed direction

Nanoscale magnetic domains with controllable configurations could be used for classical and quantum applications, where the switching of magnetization configurations is an essential operation for information processing. Here, we report that the magnetic domain reorientation in a notched ferromagnetic nanotrack can be realized and effectively controlled by applying uniform magnetic field pulses in a fixed in-plane direction perpendicular to the nanotrack. Our micromagnetic simulation results show that the configurations of magnetic domains in the notched nanotrack can be switched between a head-to-head state and a tail-to-tail state in a reversible manner driven by magnetic field pulses, while it is unnecessary to reverse the direction of the magnetic field. Such a unique magnetic domain reorientation dynamics is found to depend on magnetic parameters and nanotrack geometries. The reorientation dynamics of magnetic domains also depends on the strength and length of the applied magnetic field pulse. In addition, we point out that the notches at the center of the nanotrack play an important role for the stabilization of the head-to-head and tail-to-tail states during the magnetic domain reorientation. We also qualitatively explain the field-induced reorientation phenomenon with a simplified two-dimensional macrospin model. Our results may make it possible to build spintronic devices driven by a fixed magnetic field. Our findings may also motivate future studies to investigate the classical and quantum applications based on nanoscale magnetic domains.Comment: 12 pages, 14 figure

Static and dynamic properties of bimerons in a frustrated ferromagnetic monolayer

Magnetic bimeron is a topological counterpart of skyrmions in in-plane magnets, which can be used as a spintronic information carrier. We report the static properties of bimerons with different topological structures in a frustrated ferromagnetic monolayer, where the bimeron structure is characterized by the vorticity $Q_{\text{v}}$ and helicity $\eta$. It is found that the bimeron energy increases with $Q_{\text{v}}$, and the energy of an isolated bimeron with $Q_{\text{v}}=\pm 1$ depends on $\eta$. We also report the dynamics of frustrated bimerons driven by the spin-orbit torques, which depend on the strength of the dampinglike and fieldlike torques. We find that the isolated bimeron with $Q_{\text{v}}=\pm 1$ can be driven into linear or elliptical motion when the spin polarization is perpendicular to the easy axis. We numerically reveal the damping dependence of the bimeron Hall angle driven by the dampinglike torque. Besides, the isolated bimeron with $Q_{\text{v}}=\pm 1$ can be driven into rotation by the dampinglike torque when the spin polarization is parallel to the easy axis. The rotation frequency is proportional to the driving current density. In addition, we numerically demonstrate the possibility of creating a bimeron state with a higher or lower topological charge by the current-driven collision and merging of bimeron states with different $Q_{\text{v}}$. Our results could be useful for understanding the bimeron physics in frustrated magnets.Comment: 13 pages, 12 figure