Spectrum of spin eigenmodes localized on a ferromagnetic skyrmion pinned by a geometrical defect (bump) of magnetic films is studied theoretically. By means of direct numerical solution of the corresponding eigenvalue problem and finite element micromagnetic simulations we demonstrate, that the curvature can induce localized modes with higher azimuthal and radial quantum numbers, which are absent for planar skyrmions (for the same parameters). The eigenfrequencies of all modes, except the breathing and gyromodes decreases with increasing curvature. Due to the translational symmetry break, the zero translational mode of the skyrmion gains a finite frequency and forms the gyromode, which describes the uniform rotation of skyrmions around the equilibrium position. In order to treat the gyromotion analytically we developed a Thiele-like collective variable approach. We show that Néel skyrmions in curvilinear films experience a driving force originating from the gradient of the mean curvature. The gyrofrequency of the pinned skyrmion is proportional to the second derivative of the mean curvature at the point of equilibrium.
Curvilinear nanomagnets can support magnetic skyrmions stabilized at a local curvature without any intrinsic chiral interactions. Here, we propose a new mechanism to stabilize chiral Néel skyrmion states relying on the \textit{gradient} of curvature. We illustrate our approach with an example of a magnetic thin film with perpendicular magnetic anisotropy shaped as a circular indentation. We show that in addition to the topologically trivial ground state, there are two skyrmion states with winding numbers $\pm 1$ and a skyrmionium state with a winding number $0$. These chiral states are formed …
The influence of the geometrical curvature of chiral magnetic films on the static and dynamic properties of hosted skyrmions are studied theoretically. We predict the effects of the curvature-induced drift of skyrmions under the action of the curvature gradients without any external stimuli. The strength of the curvature-induced driving force essentially depends on the skyrmion type, Neel or Bloch, while the trajectory of motion is determined by the type of magnetic ordering: ferro- or antiferromagnetic. When moving on the surface, skyrmions undergo deformations that depend on the type of skyr…
Topologically stable structures include vortices in a wide variety of matter, such as skyrmions in ferro- and antiferromagnets, and hedgehog point defects in liquid crystals and ferromagnets. These are characterized by integer-valued topological quantum numbers. In this context, closed surfaces are a prominent subject of study as they form a link between fundamental mathematical theorems and real physical systems. Here we perform an analysis on the topology and stability of equilibrium magnetization states for a thin spherical shell with easy-axis anisotropy in normal directions. Skyrmion solu…
Motivated by recent experiments in Gd$_3$Ru$_4$Al$_{12}$, we demonstrate the emergence of atomic scale Skyrmions in interacting spins on a breathing kagome lattice with competing nearest neighbor ferromagnetic and next nearest neighbor antiferromagnetic exchange interactions. In the presence of an applied longitudinal magnetic field, the ground state magnetic order evolves from a helical phase at low fields to a Skyrmion phase at intermediate fields before finally entering a polarized phase at high fields. The size of each Skyrmion spans only two unit cells of the lattice, in contrast to tens …
Magnetic skyrmions are topological spin textures that can be used as information carriers for the next-generation information storage and processing. The electric-field controlling of skyrmions in such devices is essential but remains technologically challenging. Here, using the first-principles calculation and the Ginzburg-Landau theory, we propose a reliable process for writing and deleting skyrmions by electric fields, on the platform of a multiferroic heterostructure, particularly the $\text{Cr}_{2}\text{Ge}_{2}\text{Te}_{6} $/$ \text{In}_{2}\text{Se}_{3} $ heterostructure. We show that th…
In quantum matters hosting electron-electron correlation and spin-orbit coupling, spatial inhomogeneities, arising from competing ground states, can be essential for determining and understanding topological properties. A prominent example is Hall anomalies observed in SrRuO3 films, which were interpreted in terms of either magnetic skyrmion-induced topological Hall effect (THE) or inhomogeneous anomalous Hall effect (AHE). To clarify this ambiguity, we systematically investigated the AHE of SrRuO3 ultrathin films with controllable inhomogeneities in film thickness (tSRO). By harnessing the st…
Using semiclassical method combined with stereographic projection approach, we investigate the magnetic dynamics of the skyrmion crystal (SkX), formed in planar ferromagnet with both Dzyaloshinskii-Moriya interaction and uniform magnetic field. The topologically non-trivial ground state of SkX is described in stereographic projection by the complex valued function with simple poles at skyrmions' positions. We use the earlier proposed ansatz for this ground state function in the form of the sum of individual skyrmions. The dynamics follows from the second variation of the classical action. Nume…
Beyond-adiabatic flat Chern bands from a double-helix skyrmion crystal
College of Physics Science and Technology, Yangzhou University（扬州大学物理科学与技术学院）；Lanzhou Center for Theoretical Physics, Lanzhou University（兰州大学理论物理中心）；Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University（教育部量子理论与应用重点实验室，兰州大学）；School of Mathematics and Physics, Southwest University of Science and Technology（西南科技大学数学与物理学院）；College of Physics, Nanjing University of Aeronautics and Astronautics（南京航空航天大学物理学院）；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）
The topological Hall effect (THE), given by a composite of electric and topologically non-trivial spin texture is commonly observed in magnetic skyrmion crystals. Here we present a study of the THE of electrons coupled to antiferromagnetic Skyrmion lattices (AF-SkX). We show that, in the strong Hund coupling limit, topologically non-trivial phases emerge at specific fillings. Interestingly, at low filling an external field controlling the magnetic texture, drives the system from a conventional insulator phase to a phase exhibiting THE. Such behavior suggests the occurrence of a topological tra…
In this short review a broad range of chiral phenomena observed in magnetic films (spin cycloid and skyrmion structures formation as well as chirality dependent domain wall motion) is considered under the perspective of spin flexoelectricity, i.e. the relation between bending of magnetization pattern and electric polarization. The similarity and the difference between the spin flexoelectricity and the newly emerged notion of spin flexomagnetism is discussed. The phenomenological arguments based on the geometrical idea of curvature-induced effects are supported by analysis of the microscopic me…
Non-collinear triangular antiferromagnets with a coplanar spin arrangement and vanishing net magnetic moment can exhibit a large anomalous Hall effect owing to their non-vanishing momentum space Berry curvature. Here we show the existence of a large field induced topological Hall effect in the non-coplanar triangular antiferromagnetic geometry of Mn3Sn. A detailed magnetic and Hall effect measurements demonstrate the presence of three distinct Hall contributions; a high temperature anomalous Hall effect, a low temperature topological Hall effect and an intermediate temperature region with coex…
A recent observation of thermal Hall effect of magnetic origin in underdoped cuprates calls for critical re-examination of low-energy magnetic dynamics in undoped antiferromagnetic compound on square lattice, where traditional, renormalized spin-wave theory was believed to work well. Using Holstein-Primakoff boson formalism, we find that magnon-based theories can lead to finite Berry curvature in the magnon band once the Dzyaloshinskii-Moriya spin interaction is taken into account explicitly, but fail to produce non-zero thermal Hall conductivity. Assuming accidental doping by impurities and m…
Perovskite SrRuO$_3$ is a prototypical itinerant ferromagnet which allows interface engineering of its electronic and magnetic properties. We report synthesis and investigation of atomically flat artificial multilayers of SrRuO$_3$ with the spin-orbit semimetal SrIrO$_3$ in combination with band-structure calculations with a Hubbard $U$ term and topological analysis. They reveal an electronic reconstruction and emergence of flat Ru-4d$_{xz}$ bands near the interface, ferromagnetic interlayer coupling and negative Berry-curvature contribution to the anomalous Hall effect. We analyze the Hall ef…
