Bloch Point Research Articles

Magnetoelectric effects in magnetic films with alternating magnetic anisotropy: the emergence and stability of Bloch points.

Magnetic topological states are a subject of intense investigation due to their potential for advancing scalable logic and information storage technologies. In this article, we investigate topological defects in magnetic films, focusing on Bloch point-like singularities in magnetization distribution with significant implications for magnetoelectric and ferroelectric properties. We explore exchange-coupled ferromagnetic films composed of alternating magnetic layers with distinct in-plane and out-of-plane magnetic anisotropy. Through micromagnetic simulations, we analyze the magnetization reversal processes and the emergence of Bloch point-like configurations induced by external magnetic fields. We identify the conditions necessary for stabilizing these states and elucidate their ferroelectric properties. Our study reveals that Bloch points act as sources of electrical charge due to the inhomogeneous distribution of magnetization, offering opportunities for implementing their electric properties in future devices.

Hyperbolic Bloch points in ferrimagnetic exchange spring

Bloch points in magnetic materials are attractive entities in view of magnetic information transport. Here, Bloch point configuration has been investigated and experimentally determined in a magnetic trilayer (Gd12Co88/Nd17Co83/Gd24Co76) with carefully adjusted composition within the ferrimagnetic GdxCo1-x alloys in order to engineer saturation magnetization, exchange length, and interlayer couplings (ferromagnetic vs antiferromagnetic). X-ray vector magnetic tomography has allowed us to determine experimentally Bloch point polarity (related to topological charge) and Bloch point helicity γ (determined by magnetostatic energy). At the bottom layer (close to the ferromagnetic interface), Bloch points adopt a standard circulating configuration with helicity γ close to π/2. Within the top layer (with much lower saturation magnetization), Bloch points nucleate within a Neel-like exchange spring domain wall created by the antiferromagnetic coupling and adopt an uncommon hyperbolic configuration, characterized by much larger helicity angles. Our results indicate a path for Bloch point engineering in future applications adjusting material parameters and domain wall characteristics.

Topological polarons in halide perovskites.

Halide perovskites emerged as a revolutionary family of high-quality semiconductors for solar energy harvesting and energy-efficient lighting. There is mounting evidence that the exceptional optoelectronic properties of these materials could stem from unconventional electron-phonon couplings, and it has been suggested that the formation of polarons and self-trapped excitons could be key to understanding such properties. By performing first-principles simulations across the length scales, here we show that halide perovskites harbor a uniquely rich variety of polaronic species, including small polarons, large polarons, and charge density waves, and we explain a variety of experimental observations. We find that these emergent quasiparticles support topologically nontrivial phonon fields with quantized topological charge, making them nonmagnetic analog of the helical Bloch points found in magnetic skyrmion lattices.

Artificial Neuron Based on the Bloch-Point Domain Wall in Ferromagnetic Nanowires.

Nanomagnetism and spintronics are currently active areas of research, with one of the main goals being the creation of low-energy-consuming magnetic memories based on nanomagnet switching. These types of devices could also be implemented in neuromorphic computing by crafting artificial neurons (ANs) that emulate the characteristics of biological neurons through the implementation of neuron models such as the widely used leaky integrate-and-fire (LIF) with a refractory period. In this study, we have carried out numerical simulations of a 120 nm diameter, 250 nm length ferromagnetic nanowire (NW) with the aim of exploring the design of an artificial neuron based on the creation and destruction of a Bloch-point domain wall. To replicate signal integration, we applied pulsed trains of spin currents to the opposite faces of the ferromagnetic NW. These pulsed currents (previously studied only in the continuous form) are responsible for inducing transitions between the stable single vortex (SV) state and the metastable Bloch point domain wall (BP-DW) state. To ensure the system exhibits leak and refractory properties, the NW was placed in a homogeneous magnetic field of the order of mT in the axial direction. The suggested configuration fulfills the requirements and characteristics of a biological neuron, potentially leading to the future creation of artificial neural networks (ANNs) based on reversible changes in the topology of magnetic NWs.

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.

Polar Bloch points in strained ferroelectric films

Topological domain structures have drawn great attention as they have potential applications in future electronic devices. As an important concept linking the quantum and classical magnetism, a magnetic Bloch point, predicted in 1960s but not observed directly so far, is a singular point around which magnetization vectors orient to nearly all directions. Here we show polar Bloch points in tensile-strained ultrathin ferroelectric PbTiO3 films, which are alternatively visualized by phase-field simulations and aberration-corrected scanning transmission electron microscopic imaging. The phase-field simulations indicate local steady-state negative capacitance around the Bloch points. The observation of polar Bloch points and their emergent properties consequently implies novel applications in future integrated circuits and low power electronic devices.

Geometry-induced Bloch point domain wall in Permalloy conical frustum nanowires for advanced spintronics applications

In this study, we investigate the pseudo-static magnetic properties of Permalloy conical frustum nanowires using micromagnetic simulations. We thoroughly examine how both the major and minor radii influence the magnetic reversal mechanism when an external magnetic field is applied parallel to the nanowire axis. The obtained results show that under specific geometrical conditions, magnetization reverts though a Bloch point-type domain wall. In these cases, hysteresis curves exhibit two Barkhausen jumps during magnetization reversal, forming a plateau field range in which a Bloch point domain wall nucleates and propagates until its annihilation after the second Barkhausen jump. The nucleation of a Bloch point domain wall in a frustum conical nanowire geometry is reported. These findings highlight the significance of this geometry in nucleating these attractive topological defects for promising applications.

Stability Enhancement by Zero‐Point Spin Fluctuations: A Quantum Perspective on Bloch Point Topological Singularities

AbstractBloch points represent singularities within magnetic materials. From a macroscopic viewpoint, their cores are points where the magnetization vector is undefined, resulting in unique topological characteristics that influence the magnetic behavior of their hosts. The picture is very different at the microscopic level, where quantum effects enter the scene. The spin variables' quantum dynamics effect on the BP's stability is revealed. Zero‐point fluctuations, intrinsic fluctuations within the quantum mechanical ground state originating from the uncertainty principle, play a fundamental role. It is found that quantum fluctuations bloom in the vicinity of the singularity, thereby reducing the effective magnetic moment in its neighborhood. This increases the overall stability of the BP. These methods also allow for a characterization of the magnonic eigenmodes surrounding and bound to the singularity. The latter leads to predict on quite general grounds several features of the magnonic spectra, its degeneration structure, and its splitting response under a magnetic field. The last result is coherent with the association of a magnetic moment to the orbital angular momentum of the magnons. This approach allows integration with multiscale algorithms to provide a realistic description of generic topological singularities.

Control of a twisted domain wall motion supported by topology

We report the topology-mediated modulation of a twisted domain wall speed in a thick perpendicularly magnetized system. By exploiting the topological robustness of the direction of the Bloch wall component in the twisted domain wall, we show that the domain wall speed either increases or decreases depending on whether the transverse magnetic field is parallel or antiparallel to the Bloch wall component. The decrease in the speed is maintained until the antiparallel transverse reaches ∼0.3 T, indicating that the twisted domain wall can offer wide controllability supported by the topological robustness which involves an injection of a Bloch point. We also demonstrate that the transverse magnetic field suppresses the Walker breakdown, allowing high mobility domain wall motion for a wide range of perpendicular driving fields.

Dynamics of chiral domain walls in bent cylindrical magnetic nanowires

Cylindrical magnetic nanowires (NWs) constitute a viable component of 3D nanoscale magnetic devices and engineering their response to external stimuli is necessary for their future functionalization. Here, by means of micromagnetic simulations, we study the dynamical response of vortex–antivortex and Bloch point domain walls under the action of an applied magnetic field in curved arc-shaped NWs varying the saturation magnetization value. Our results provide evidence that, in the range considered in this work, the curvature has no influence on the critical diameters, delimiting different domain wall types. However, it has a relevant effect on the domain wall dynamics. Specifically, the vortex–antivortex domain wall oscillates back and forth while rotating around the nanowire, and the frequency and amplitude can be tuned by curvature and applied field. On the contrary, Bloch point domain wall dynamics does not show any oscillatory behavior, and the domain wall is rapidly expelled from the nanowire with velocities similar to that of the straight cylindrical nanowires. These results allow engineering magnetic response of cylindrical nanowires with curvature.

Bloch Point Quadrupole Constituting Hybrid Topological Strings Revealed with Electron Holographic Vector Field Tomography.

Topological magnetic (anti)skyrmions are robust string-like objects heralded as potential components in next-generation topological spintronics devices due to their low-energy manipulability via stimuli such as magnetic fields, heat, and electric/thermal current. While these 2D topological objects are widely studied, intrinsically 3D electron-spin real-space topology remains less explored despite its prevalence in bulky magnets. 2D-imaging studies reveal peculiar vortex-like contrast in the core regions of spin textures present in antiskyrmion-hosting thin plate magnets with S4 crystal symmetry, suggesting a more complex 3D real-space structure than the 2D model suggests. Here, holographic vector field electron tomography captures the 3D structure of antiskyrmions in a single-crystal, precision-doped (Fe0.63Ni0.3Pd0.07)3P (FNPP) lamellae at room temperature and zero field. These measurements reveal hybrid string-like solitons composed of skyrmions with topological number W = -1 on the lamellae's surfaces and an antiskyrmion (W = + 1) connecting them. High-resolution images uncover a Bloch point quadrupole (four magnetic (anti)monopoles that are undetectable in 2D imaging) which enables the observed lengthwise topological transitions. Numerical calculations corroborate the stability of hybrid strings over their conventional (anti)skyrmion counterparts. Hybrid strings result in topological tuning, a tunable topological Hall effect, and the suppression of skyrmion Hall motion, disrupting existing paradigms within spintronics.

Universal scalefree non-Hermitian skin effect near the Bloch point

Universal scalefree non-Hermitian skin effect near the Bloch point

Giant supermagnonic Bloch point velocities in cylindrical ferromagnetic nanowires.

Achieving high velocities of magnetic domain walls is a crucial factor for their use as information carriers in modern nanoelectronic applications. In nanomagnetism and spintronics, these velocities are often limited either by internal domain wall instabilities, known as the Walker breakdown phenomenon, or by spin wave emission, known as the magnonic regime. In the rigid domain wall model, the maximum magnon velocity acts as an effective "speed of light", providing a relativistic analogy for the domain wall speed limitation. Cylindrical magnetic nanowires are an example of systems without the Walker breakdown phenomenon. Here we demonstrate that the magnonic limit could be outstandingly surpassed in cylindrical nanowires with high magnetization, such as iron. Our numerical modeling shows the Bloch point domain wall velocities as high as 14 km s-1, well above the magnonic limit estimated in the interval 1.7-2.0 km s-1. The key ingredient is the three-dimensional conical shape of the domain wall, which elongates and breaks during the dynamics, expelling backwards pairs of Bloch points. This leads to domain wall acceleration, the effect, which resembles the "jet propulsion". This effect will be very important for three-dimensional networks based on cylindrical magnetic nanowires.

Controlling stable Bloch points with electric currents

The Bloch point is a point singularity in the magnetisation configuration, where the magnetisation vanishes. It can exist as an equilibrium configuration and plays an important role in many magnetisation reversal processes. In the present work, we focus on manipulating Bloch points in a system that can host stable Bloch points—a two-layer FeGe nanostrip with opposite chirality of the two layers. We drive Bloch points using spin-transfer torques and find that Bloch points can move collectively without any Hall effect and report that Bloch points are repelled from the sample boundaries and each other. We study pinning of Bloch points at wedge-shaped constrictions (notches) in the nanostrip and demonstrate that arrays of Bloch points can be moved past a series of notches in a controlled manner by applying consecutive current pulses of different strength. Finally, we simulate a T-shaped geometry and demonstrate that a Bloch point can be moved along different paths by applying current between suitable strip ends.

Sewing skyrmion and antiskyrmion by quadrupole of Bloch points

Sewing skyrmion and antiskyrmion by quadrupole of Bloch points

Bloch point nanospheres for the design of magnetic traps

Through micromagnetic simulations, this work analyzes the possibility of using an array of magnetic nanospheres hosting Bloch points (BPs) to compose a system with the features of a magnetic trap (MT). We show that a BP can be nucleated as a metastable configuration in a wide range of the nanosphere radius compared to a quasi-uniform and vortex state. We also show that the stabilized BP generates a quadrupolar magnetic field outside the nanosphere. Based on this fact, we analyze the field profile of different arrays of these nanospheres, showing that the obtained magnetic field profiles share the needed features to compose MTs. Some highlights of using an array of Bloch point nanospheres in MTs rely on the magnetic field gradients achieved, which are orders of magnitude higher than similar standard systems, and allow three-dimensional trapping. Our results could be useful in trapping particles through the intrinsic magnetization of ferromagnetic nanoparticles while avoiding the commonly used mechanisms associated with Joule heating.

Harmonic oscillations of point soliton (Bloch point) in cylindrical ferromagnetic nanowire

Harmonic oscillations of a point magnetic soliton (Bloch point) located in a domain wall (DW) of a cylindrical ferromagnetic nanowire along the spatial directions of a primitive vortex cell formed by the magnetization vectors at the boundary between the core and the transition zone of the soliton are considered. The possibility of experimental implementation of Bloch point resonant oscillations excited by external alternating magnetic field is shown. In the case of weak attenuation, the maximum values of the resonant frequencies of Bloch points in iron and nickel nanowires are determined, which are 10 and 3 GHz, respectively. These results can be applied in the modern nanotechnologies based on the use of the magnetic properties of ferromagnetic nanowires whose DWs contain Bloch points.

Dynamics and Reversible Control of the Bloch-Point Vortex Domain Wall in Short Cylindrical Magnetic Nanowires

Fast and efficient switching of nanomagnets is one of the main challenges in the development of future magnetic memories. We numerically investigate the evolution of static and dynamic spin-wave (SW) magnetization in short (50--400 nm in length and 120 nm in diameter) cylindrical ferromagnetic nanowires, where competing magnetization configurations of a single vortex (SV) and a Bloch-point vortex domain wall (BP-DW) can be formed. For a limited nanowire length range (between 150 and 300 nm), we demonstrate reversible transitions induced by a microwave field (forwards) and by opposite spin currents (backwards) between topologically different SV and BP-DW states. By tuning the nanowire length, the excitation frequency, the microwave pulse duration, and the spin-current value, we show that the optimum (low-power) manipulation of the BP-DW can be achieved with a microwave excitation tuned to the main SW mode for nanowire lengths around 230--250 nm, where single-vortex domain-wall magnetization reversal via nucleation and propagation of a SV-DW transition takes place. An analytical model of the dynamics of the Bloch point provides an estimate of the gyrotropic mode frequency close to that obtained via micromagnetic simulations. A practical implementation of the method in a device is proposed, involving microwave excitation and the generation of opposite spin currents via the spin-orbit torque. Our findings open up an alternative pathway for the creation of topological magnetic memories.

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.

Bloch points in nanostrips

Complex magnetic materials hosting topologically non-trivial particle-like objects such as skyrmions are under intensive research and could fundamentally change the way we store and process data. One important class of materials are helimagnetic materials with Dzyaloshinskii-Moriya interaction. Recently, it was demonstrated that thin nanodisks consisting of two layers with opposite chirality can host a single stable Bloch point of two different types at the interface between the layers. Using micromagnetic simulations we show that FeGe nanostrips consisting of two layers with opposite chirality can host multiple coexisting Bloch points in an arbitrary combination of the two different types. We show that the number of Bloch points that can simultaneously coexist depends on the strip geometry and the type of the individual Bloch points. Our simulation results allow us to predict strip geometries suitable for an arbitrary number of Bloch points. We show an example of an 80-Bloch-point configuration verifying the prediction.