Multiply periodic states appear in a wide variety of physical contexts, such as the Rayleigh-Bénard convection, Faraday waves, liquid crystals and skyrmion crystals recently observed in chiral ...magnets. Here we study the phase diagram of an anisotropic frustrated magnet which contains five different multiply periodic states including the skyrmion crystal. We clarify the mechanism for stabilization of these states and discuss how they can be observed in magnetic resonance and electric polarization measurements. We also find stable isolated skyrmions with topological charge 1 and 2. Their spin structure, interactions and dynamics are more complex than those in chiral magnets. In particular, magnetic resonance in the skyrmion crystal should be accompanied by oscillations of the electric polarization with a frequency depending on the amplitude of the a.c. magnetic field. These results show that skyrmion materials with rich physical properties can be found among frustrated magnets. We formulate rules to help the search.
Magnetic skyrmions are particle-like topological excitations recently discovered in chiral magnets. Their small size, topological protection and the ease with which they can be manipulated by ...electric currents generated much interest in using skyrmions for information storage and processing. Recently, it was suggested that skyrmions with additional degrees of freedom can exist in magnetically frustrated materials. Here, we show that dynamics of skyrmions and antiskyrmions in nanostripes of frustrated magnets is strongly affected by complex spin states formed at the stripe edges. These states create multiple edge channels which guide the skyrmion motion. Non-trivial topology of edge states gives rise to complex current-induced dynamics, such as emission of skyrmion-antiskyrmion pairs. The edge-state topology can be controlled with an electric current through the exchange of skyrmions and antiskyrmions between the edges of a magnetic nanostructure.
Axisymmetric solitonic states (chiral skyrmions) were first predicted theoretically more than two decades ago. However, until recently they have been observed in a form of skyrmionic condensates ...(hexagonal lattices and other mesophases). In this paper we report experimental and theoretical investigations of isolated chiral skyrmions discovered in PdFe/Ir(111) bilayers two years ago by Romming et al (2013 Science 341 636). The results of spin-polarized scanning tunneling microscopy analyzed within the continuum and discrete models provide a consistent description of isolated skyrmions in thin layers. The existence region of chiral skyrmions is restricted by strip-out instabilities at low fields and a collapse at high fields. We demonstrate that the same equations describe axisymmetric localized states in all condensed matter systems with broken mirror symmetry, and thus our findings establish basic properties of isolated skyrmions common for chiral liquid crystals, different classes of noncentrosymmetric magnets, ferroelectrics, and multiferroics.
During recent years it has been shown that hidden oscillations, whose basin of attraction does not overlap with small neighborhoods of equilibria, may significantly complicate simulation of dynamical ...models, lead to unreliable results and wrong conclusions, and cause serious damage in drilling systems, aircrafts control systems, electromechanical systems, and other applications. This article provides a survey of various phase-locked loop based circuits (used in satellite navigation systems, optical, and digital communication), where such difficulties take place in MATLAB and SPICE. Considered examples can be used for testing other phase-locked loop based circuits and simulation tools, and motivate the development and application of rigorous analytical methods for the global analysis of phase-locked loop based circuits.
We report the most precise observations to date concerning the spin structure of magnetic skyrmions in a nanowedge specimen of cubic B20 structured FeGe. Enabled by our development of advanced ...differential phase contrast (DPC) imaging (in a scanning transmission electron microscope (STEM)) we have obtained high spatial resolution quantitative measurements of skyrmion internal spin profile. For hexagonal skyrmion lattice cells, stabilised by an out-plane applied magnetic field, mapping of the in-plane component of magnetic induction has revealed precise spin profiles and that the internal structure possesses intrinsic six-fold symmetry. With increasing field strength, the diameter of skyrmion cores was measured to decrease and accompanied by a nonlinear variation of the lattice periodicity. Variations in structure for individual skyrmions across an area of the lattice were also studied utilising a new increased sensitivity DPC detection scheme and a variety of symmetry lowering distortions were observed. To provide insight into fundamental energetics we have constructed a phenomenological model, with which our experimental observations of spin profiles and field induced core diameter variation are in good agreement with predicted structure in the middle of the nanowedge crystal. In the vicinity of the crystal surfaces, our model predicts the existence of in-plane twisting distortions which our current experimental observations were not sensitive to. As an alternative to the requirement for as yet unidentified sources of magnetic anisotropy, we demonstrate that surface states could provide the energetic stabilisation needed for predomination over the conical magnetic phase.
Metrological support of digital electronic voltage transformers and low-power voltage sensors (converters, transformers) is presented. The methods and reference measurement facilities are described ...for the State Primary Special Standard of the coefficient of the ratio error and phase displacement of the AC electric voltage of the power frequency in the range from 0.1 /√3 to 750 /√3 kV, and the units of electrical capacitance and the loss angle tangent at AC voltage of the power frequency in the range from 1 to 500 kV in GÉT 175-2023, used for metrological support of the measurement facilities mentioned above. The results of the GÉT 175-2023 studies are presented—the expanded uncertainties in GÉT 175-2023 in the reproduction of the units of ratio error and phase displacement of the AC electric voltage of power frequency for metrological support of analog low-power voltage sensors (transformers, converters) include the uncertainty budget of the uncertainties of the current comparator, the low-voltage (reference) and high-voltage measurement measures, and the high-voltage MVÉ-01 bridge (SA7400MA1 amplifier), and are 9.62 · 10
−5
and 12.2 · 10
−5
rad, respectively. The expanded uncertainties in GÉT 175-2023 when reproducing the units of the ratio error and the phase displacement of the AC electric voltage of power frequency for metrological support of electronic digital voltage transformers and digital low-power voltage sensors (transformers, converters) include the uncertainty budget of the “high voltage–current” converter, “current–low voltage” converter, “low voltage–digital copy of voltage” converter, and the digital comparator, and are equal to 10.8 · 10
−5
and 7.64 · 10
−5
rad, respectively. GÉT 175-2023 makes it possible to solve the problems of the metrological support of electronic digital voltage transformers and digital low-power voltage sensors (transformers converters).
The skyrmion lattice state (SkL), a crystal built of mesoscopic spin vortices, gains its stability via thermal fluctuations in all bulk skyrmion host materials known to date. Therefore, its existence ...is limited to a narrow temperature region below the paramagnetic state. This stability range can drastically increase in systems with restricted geometries, such as thin films, interfaces and nanowires. Thermal quenching can also promote the SkL as a metastable state over extended temperature ranges. Here, we demonstrate more generally that a proper choice of material parameters alone guarantees the thermodynamic stability of the SkL over the full temperature range below the paramagnetic state down to zero kelvin. We found that GaV
Se
, a polar magnet with easy-plane anisotropy, hosts a robust Néel-type SkL even in its ground state. Our supporting theory confirms that polar magnets with weak uniaxial anisotropy are ideal candidates to realize SkLs with wide stability ranges.
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