3D quasi-skyrmions in thick cylindrical and dome-shape soft nanodots

Dominant higher-order vortex gyromodes in circular magnetic nanodots

The transition to the third dimension enables the creation of spintronic nanodevices with significantly enhanced functionality compared to traditional 2D magnetic applications. In this study, we extend common two-dimensional magnetic vortex configurations, which are known for their efficient dynamical response to external stimuli without a bias magnetic field, into the third dimension. This extension results in a substantial increase in vortex frequency, reaching up to 5 GHz, compared to the typical sub-GHz range observed in planar vortex oscillators. A systematic study reveals a complex pattern of vortex excitation modes, explaining the decrease in the lowest gyrotropic mode frequency, the inversion of vortex mode intensities, and the nontrivial spatial distribution of vortex dynamical magnetization noted in previous research. These phenomena enable the optimization of both oscillation frequency and frequency reproducibility, minimizing the impact of uncontrolled size variations in those magnetic nanodevices.

Symmetry Breaking-Induced Resonance Dynamics in Bloch Point Nanospheres: Unveiling Magnetic Volume Effects and Geometric Parameters for Advanced Applications in Magnetic Sensing and Spintronics

This study explores the impact of symmetry breaking on the ferromagnetic resonance of Bloch point (BP) nanospheres. Through standard Fourier analysis, we unveil two distinct oscillation mode groups characterized by low and high frequencies, respectively. Our findings emphasize the pivotal role of magnetic volume in shaping resonance amplitudes, providing new insights into the intricate dynamics of BP states. The investigation of geometric parameters reveals a quasi-monotonic decrease in resonance frequencies as a function of the asymmetry degree attributed to symmetry-breaking induced by geometric modifications. Spatial distribution analysis showcases unique resonance frequencies for the upper and lower BP hemispheres, highlighting the nuanced impact of the geometry on mode excitation. As the radius increases, additional modes emerge, demonstrating a compelling relationship between the magnetic volume and frequency. Phase analysis unveils coherent oscillations within each BP hemisphere, offering valuable insights into the rotational directions of the excitation poles. Beyond fundamental understanding, our study opens avenues for innovative applications, suggesting the potential use of nanospheres in advanced magnetic sensing, data storage, and nanoscale spintronic devices.

3D Magnetization Textures: Toroidal Magnetic Hopfion Stability in Cylindrical Samples

Topologically non-trivial magnetization configurations in ferromagnetic materials on the nanoscale, such as hopfions, skyrmions, and vortices, have attracted considerable attention of researchers during the last few years. In this article, by applying the theory of micromagnetism, I demonstrate that the toroidal hopfion magnetization configuration is a metastable state of a thick cylindrical ferromagnetic nanodot or a nanowire of a finite radius. The existence of this state is a result of the competition among exchange, magnetostatic, and magnetic anisotropy energies. The Dzyaloshinskii-Moriya exchange interaction and surface magnetic anisotropy are of second importance for the hopfion stabilization. The toroidal hopfion metastable magnetization configuration may be reached in the process of remagnetizing the sample by applying an external magnetic field along the cylindrical axis.

Magnetostatic interaction between Bloch point nanospheres

Three-dimensional topological textures have become a topic of intense interest in recent years. This work uses analytical and numerical calculations to determine the magnetostatic field produced by a Bloch point (BP) singularity confined in a magnetic nanosphere. It is observed that BPs hosted in a nanosphere generate magnetic fields with quadrupolar nature. This finding is interesting because it shows the possibility of obtaining quadrupole magnetic fields with just one magnetic particle, unlike other propositions considering arrays of magnetic elements to generate this kind of field. The obtained magnetostatic field allows us to determine the interaction between two BPs as a function of the relative orientation of their polarities and the distance between them. It is shown that depending on the rotation of one BP related to the other, the magnetostatic interaction varies in strength and character, being attractive or repulsive. The obtained results reveal that the BP interaction has a complex behavior beyond topological charge-mediated interaction.

Curvature-induced stabilization and field-driven dynamics of magnetic hopfions in toroidal nanorings

Three dimensional magnetic textures are a cornerstone in magnetism research. In this work, we analyze the stabilization and dynamic response of a magnetic hopfion hosted in a toroidal nanoring with intrinsic Dzyaloshinskii-Moriya interaction simulating FeGe. Our results evidence that unlike their planar counterparts, where perpendicular magnetic anisotropies are necessary to stabilize hopfions, the shape anisotropy originated on the torus symmetry naturally yields the nucleation of these topological textures. We also analyze the magnetization dynamical response by applying a magnetic field pulse to differentiate among several magnetic patterns. Finally, to understand the nature of spin wave modes, we analyze the spatial distributions of the resonant mode amplitudes and phases and describe the differences among bulk and surface modes. Importantly, hopfions lying in toroidal nanorings present a non-circularly symmetric poloidal resonant mode, which is not observed in other systems hosting hopfions.