Bloch Lines Research Articles

Bloch lines in thin films with perpendicular magnetic anisotropy and intermediate quality factor

Bloch lines (BLs) are linear topological defects of magnetic domain walls structure, studied well for bubble domain materials. We investigate its structure and role in magnetization reversal for thin ferromagnetic films with perpendicular magnetic anisotropy and intermediate quality factor. We observe vertical BLs with Bloch points and U-shaped structures with vertical and horizontal parts in three-dimensional micromagnetic simulations for Q = 0.34. Also we suggest analytical model functions, describing 3D magnetization distribution in domain walls with BLs.

Topological Magnetic-Spin Textures in Two-Dimensional van der Waals Cr2Ge2Te6.

Two-dimensional (2D) van der Waals (vdW) materials show a range of profound physical properties that can be tailored through their incorporation in heterostructures and manipulated with external forces. The recent discovery of long-range ferromagnetic order down to atomic layers provides an additional degree of freedom in engineering 2D materials and their heterostructure devices for spintronics, valleytronics, and magnetic tunnel junction switches. Here, using direct imaging by cryo-Lorentz transmission electron microscopy we show that topologically nontrivial magnetic-spin states, skyrmionic bubbles, can be realized in exfoliated insulating 2D vdW Cr2Ge2Te6. Due to the competition between dipolar interactions and uniaxial magnetic anisotropy, hexagonally packed nanoscale bubble lattices emerge by field cooling with magnetic field applied along the out-of-plane direction. Despite a range of topological spin textures in stripe domains arising due to pair formation and annihilation of Bloch lines, bubble lattices with single chirality are prevalent. Our observation of topologically nontrivial homochiral skyrmionic bubbles in exfoliated vdW materials provides a new avenue for novel quantum states in atomically thin insulators for magneto-electronic and quantum devices.

Biskyrmion lattices in centrosymmetric magnetic films

Abstract Theoretical framework is developed that explains biskyrmion lattices observed in non-chiral magnetic films. We study films of finite thickness containing up to $1000\times1000\times100$ spins. Hexatic biskyrmion lattices in a pure 2D exchange model are naturally described by the Weierstrass $\wp$ and $\zeta$ elliptic functions. Starting with such a lattice as an initial state we investigate how it evolves towards the minimum-energy state in the presence of perpendicular magnetic anisotropy and dipole-dipole interaction. In accordance with experiments, we find that the final state is a triangular lattice of biskyrmion bubbles containing Bloch lines.

Formation of Zero‐Field Magnetic Bubbles and Magnetic Phase Transitions in PbFe12O19 via In Situ Lorentz Microscopy

Understanding the magnetic transitions between different noncollinear spin textures under external stimuli is an important topic in modern magnetism. Here, the stripe‐to‐bubble transition is investigated in hexaferrite PbFe12O19 (001) thin plates with a magnetocrystalline anisotropy constant of Ku = 22 × 105 erg cm−3 at room temperature by in situ Lorentz transmission electron microscopy (LTEM) with varying specimen temperature and magnetic field. The LTEM observations reveal that the application and subsequent reduction of a parallel field to the specimen plane at room temperature results in the formation of zero‐field metastable magnetic bubbles. However, the application of an external field perpendicular to the specimen plane did not transform magnetic stripes to bubbles. This is in stark contrast to most perpendicularly magnetized materials that host magnetic bubbles. It is also found that the presence of Bloch lines in stripes induced by the parallel field is crucial for bubble formation. Moreover, in situ heating and cooling experiments for different initial states of magnetic stripes revealed a facilitating role of Bloch lines in the stripe‐to‐bubble transition and the metastable nature of zero‐field bubbles in PbFe12O19 thin films.

Three-Dimensional Numerical Modeling and Visualization of the Domain Structure in Films with Perpendicular Anisotropy

Three-dimensional numerical modeling of static domain structures in a Co(0001) film is performed for different values of an external magnetic field perpendicular to the surface of the film or lying in the plane of the film. Changes in the fine structure of domain walls, associated with the appearance, motion, and disappearance of Bloch lines and Bloch points, are considered in detail.

Multistep Bloch-line-mediated Walker breakdown in ferromagnetic strips

A well-known feature of magnetic field driven dynamics of domain walls in ferromagnets is the existence of a threshold driving force at which the internal magnetization of the domain wall starts to precess -- a phenomenon known as the Walker breakdown -- resulting in an abrupt drop of the domain wall propagation velocity. Here, we report on micromagnetic simulations of magnetic field driven domain wall dynamics in thin ferromagnetic strips with perpendicular magnetic anisotropy which demonstrate that in wide enough strips Walker breakdown is a multistep process: It consists of several distinct velocity drops separated by short linear parts of the velocity vs field curve. These features originate from the repeated nucleation, propagation and annihilation of an increasing number of Bloch lines within the domain wall as the driving field magnitude is increased. This mechanism arises due to magnetostatic effects breaking the symmetry between the two ends of the domain wall.

Magnetic domain wall skyrmions

It is well established that the spin-orbit interaction in heavy metal/ferromagnet heterostructures leads to a significant interfacial Dzyaloshinskii-Moriya Interaction (DMI) that modifies the internal structure of magnetic domain walls (DWs) to favor N\'{e}el over Bloch type configurations. However, the impact of such a transition on the structure and stability of internal DW defects (e.g., vertical Bloch lines) has not yet been explored. We present a combination of analytical and micromagnetic calculations to describe a new type of topological excitation called a DW Skyrmion characterized by a $360^\circ$ rotation of the internal magnetization in a Dzyaloshinskii DW. We further propose a method to identify DW Skyrmions experimentally using Fresnel mode Lorentz TEM; simulated images of DW Skyrmions using this technique are presented based on the micromagnetic results.

One through the other tunneling of the “kink” – Type solitons in domain wall of ferromagnetic film

Abstract The sub-barrier quantum passing through one another of length segments of two nanosized magnetic solitons (kink – type) in the form of unipolar vertical Bloch lines is considered. Solitons located in a domain wall of a magnetic stripe domain formed in a uniaxial ferromagnetic film. It is shown that this effect occurs due to the quantum oscillations of vertical Bloch lines excited by an external magnetic field at subhelium temperatures. It has been established that tunneling of “whole” Bloch lines requires stronger magnetic fields than in the case of tunneling of small segments of soliton’s length.

Barkhausen Noise from Precessional Domain Wall Motion.

The jerky dynamics of domain walls driven by applied magnetic fields in disordered ferromagnets-the Barkhausen effect-is a paradigmatic example of crackling noise. We study Barkhausen noise in disordered Pt/Co/Pt thin films due to precessional motion of domain walls using full micromagnetic simulations, allowing for a detailed description of the domain wall internal structure. In this regime the domain walls contain topological defects known as Bloch lines which repeatedly nucleate, propagate, and annihilate within the domain wall during the Barkhausen jumps. In addition to bursts of domain wall propagation, the in-plane Bloch line dynamics within the domain wall exhibits crackling noise and constitutes the majority of the overall spin rotation activity.

Microscopic magnetization distribution of Bloch lines in a uniaxial magnet

Bloch lines are formed to reduce the magnetostatic energy generated by the Bloch walls in uniaxial magnets. Recently, it is reported that Bloch lines play important roles in the emergence and helicity reversal of magnetic bubbles in Sc-substitute M-type hexaferrites (BaFe12–x–0.05ScxMg0.05O19). Although Bloch lines have been discussed on the basis of micromagnetic simulations, the detailed structure was not observed directly. In this study, we investigated the microscopic structures of Bloch lines in BaFe10.35Sc1.6Mg0.05O19 uniaxial magnets. Differential-phase contrast scanning transmission microscopy directly revealed that the edges of the Bloch walls were misaligned in the Bloch lines of BaFe10.35Sc1.6Mg0.05O19. From the micromagnetic simulations based on the Monte-Carlo technique, we showed that the misaligned Bloch walls were caused by the dipole-dipole interactions in the hexaferrite. Our results will help to understand the microstructures of Bloch lines at a nanometer scale.

Stabilization and control of topological magnetic solitons via magnetic nanopatterning of exchange bias systems

Stabilizing and manipulating topological magnetic quasiparticles in thin films is of great interest for potential applications in data storage and information processing. Here, we present a strategy for stabilizing magnetic vortices and Bloch lines with controlled position, vorticity, and chirality in a continuous exchange bias system. By tailoring vectorially the unidirectional anisotropy of the system at the nanoscale, via thermally assisted magnetic scanning probe lithography, we show experimentally and via micromagnetic simulations the non-volatile creation of vortex-antivortex pairs. In addition, we demonstrate the deterministic stabilization of cross and circular Bloch lines within patterned Néel magnetic domain walls. This work enables the implementation of complex functionalities based on the control of tailored topological spin-textures in spintronic and magnonic nanodevices.

Spontaneous nanometric magnetic bubbles with various topologies in spin-reoriented La1−xSrxMnO3

Topological zero-field nanometric domains and their capability to be manipulated by external fields show potential applications in spintronics. Here, the spontaneous magnetic bubbles (≈100 nm in diameter) are observed at zero field in a ferromagnetic manganite La1−xSrxMnO3 (0.15 < x < 0.2) by using Lorentz transmission electron microscopy. The spin reorientation as a function of temperature drives the magnetic domain transition from traditional 180° in-plane domains to helical stripes and bubbles, resulting in rich magnetic configurations with various topologies. It directly demonstrates that the dynamic motion of Bloch lines in bubbles introduces the topologic transition under the application of magnetic fields.

Stable Mixed-Valent Complexes Formed by Electron Delocalization Across Hydrogen Bonds of Pyrimidinone-Linked Metal Clusters.

Electron transfer across a mixed-valent hydrogen-bonded self-dimer of oxo-centered triruthenium clusters bridged by a pair of 4(3 H)-pyrimidinones is reported. Spectroelectrochemical studies in methylene chloride reveal that 1 rapidly self-dimerizes upon one-electron reduction, forming the strongly coupled mixed-valent hydrogen-bonded dimer (12)-. In the mixed-valent state, significantly broadened, partially coalesced ν(CO) bands are observed, allowing estimation of the electron transfer rate ( kET) by an optical Bloch line shape analysis. Simulation of the FTIR line shapes provides an estimate of kET on the order of 1011 s-1, indicating a highly delocalized electronic structure across the hydrogen bonds. These findings are supported by the determination of the formation constant ( KMV) for (12)-, which is found to be on the order of 106 M-1, or nearly 4 orders of magnitude higher than that for the neutral isovalent dimer (12). This represents a stabilization of approximately 5.7 kcal/mol (1980 cm-1) arising from electron exchange across the hydrogen bonds in the mixed-valent state. Significantly, an enormous intensity enhancement of the amide ν(NH) band (3300 cm-1) of (12)- is observed, supporting strong mixing of the bridging ligand vibrational modes with the electronic wave function of the mixed-valent state. These findings demonstrate strong donor-bridge-acceptor coupling and that highly delocalized electronic structures can be attained in hydrogen-bonded systems, which are often considered to be too weakly bound to support strong electronic communication.

Optical investigations of the perturbations of Bloch lines stimulated by an electric field in ferrite garnets films

We revealed the magnetoelectric activity effect of vertical Bloch lines of ferrite garnets film in external electric AC field. Effect visually manifested as a broadening of the regions of their localizations. These perturbations are revealed without additional impact of the magnetic field. Magneto-optical measurements and method of optical dark field microscopy with the direct visual observations were used for the investigations.

Quantum colliding of nanoscale solitons in a domain wall of magnetic stripe domain

The possibility of sub-barrier mutual passage of two nanosized solitons in the form of vertical Bloch lines located in a domain wall of a magnetic stripe domain formed in a uniaxial magnetic film with a strong magnetic anisotropy is shown. The conditions for this effect are determined.

Dynamics and morphology of chiral magnetic bubbles in perpendicularly magnetized ultra-thin films

We study bubble domain wall dynamics using micromagnetic simulations in perpendicularly magnetized ultra-thin films with disorder and Dzyaloshinskii-Moriya interaction. Disorder is incorporated into the material as grains with randomly distributed sizes and varying exchange constant at the edges. As expected, magnetic bubbles expand asymmetrically along the axis of the in-plane field under the simultaneous application of out-of-plane and in-plane fields. Remarkably, the shape of the bubble has a ripple-like part which causes a kink-like (steep decrease) feature in the velocity versus in-plane field curve. We show that these ripples originate due to the nucleation and interaction of vertical Bloch lines. Furthermore, we show that the Dzyaloshinskii-Moriya interaction field is not constant but rather depends on the in-plane field. We also extend the collective coordinate model for domain wall motion to a magnetic bubble and compare it with the results of micromagnetic simulations.

Motion and Interaction of Magnetic Dislocations in Alternating Magnetic Field

The behavior of magnetic dislocations (MDs) in an alternating harmonic magnetic field in iron garnets has been experimentally investigated. The results are presented for single-crystal plates in which the drift of domain walls is observed in fields of sound frequencies. It is found that MDs in a stripe domain structure are able to move not only along but also across domain walls. A pairwise interaction between magnetic dislocations when they approach each other to distances on the order of the sizes of the cores of MDs is revealed. The processes of the annihilation, mutual passing of magnetic dislocations through each other and overtaking are found. The features of the dynamic behavior of MDs are explained using a mechanism based on the presence of vertical Bloch lines in a structure of domain walls. MDs are formed at nucleation centers, and their nucleation field is lower than the drift-starting field, which corresponds to previously proposed dislocational mechanism of the drift. The dependencies of quantitative parameters of the drift and MDs on amplitude and frequency of the pumping field are determined. The behavior of MDs should be considered when analyzing the mechanisms for magnetization and temperature-dependent phase transitions in magnetic layers.

Bloch-line dynamics within moving domain walls in 3D ferromagnets

We study field-driven magnetic domain wall dynamics in garnet strips by large-scale three-dimensional micromagnetic simulations. The domain wall propagation velocity as a function of the applied field exhibits a low-field linear part terminated by a sudden velocity drop at a threshold field magnitude, related to the onset of excitations of internal degrees of freedom of the domain wall magnetization. By considering a wide range of strip thicknesses from 30 nm to 1.89 $\mu$m, we find a non-monotonic thickness dependence of the threshold field for the onset of this instability, proceeding via nucleation and propagation of Bloch lines within the domain wall. We identify a critical strip thickness above which the velocity drop is due to nucleation of horizontal Bloch lines, while for thinner strips and depending on the boundary conditions employed, either generation of vertical Bloch lines, or close-to-uniform precession of the domain wall internal magnetization takes place. For strips of intermediate thicknesses, the vertical Bloch lines assume a deformed structure due to demagnetizing fields at the strip surfaces, breaking the symmetry between the top and bottom faces of the strip, and resulting in circulating Bloch line dynamics along the perimeter of the domain wall.

Skyrmion clusters from Bloch lines in ferromagnetic films

Conditions under which various skyrmion objects emerge in experiments on thin magnetic films remain largely unexplained. We investigate numerically centrosymmetric spin lattices in films of finite thickness with ferromagnetic exchange, magnetic anisotropy, and dipole-dipole interaction. Evolution of labyrinth domains into compact topological structures on application of the magnetic field is found to be governed by the configuration of Bloch lines inside domain walls. Depending on the combination of Bloch lines, the magnetic domains evolve into individual skyrmions, biskyrmions, or more complex topological objects. While the geometry of such objects is sensitive to the parameters, their topological charge is uniquely determined by the topological charge of Bloch lines inside the magnetic domain from which the object emerges.

Quantum vibrations of a pair of vertical Bloch lines in the domain wall of a magnetic stripe domain

It is demonstrated that quantum oscillations of a pair of interacting vertical Bloch lines occur in the domain wall of a magnetic stripe domain. It is established that this effect corresponds to the sub-helium temperature range.