Generation of Bloch Points with Controlled Spin Texture Using Geometrical Boundary Conditions

The gist: This work demonstrates deterministic control over Bloch point nucleation by engineering geometrical boundary conditions via a chirality interface between 3D printed helical nanowires, allowing for precise control over the Bloch point's polarity, circulation, and helicity

How it works

The core mechanism involves introducing a chirality interface between two three-dimensional double-helix nanowires of opposite handedness to impose competing topological constraints that uniquely define the magnetization configuration surrounding the Bloch point This geometrical approach enables full three-dimensional control of Bloch point domain walls allowing deterministic engineering of their spin texture and its selective coupling to current-induced Oersted fields The structure consists of double helices of opposite geometric chirality where a left-handed segment is at the bottom and a right-handed segment is at the top, meeting at a chirality interface marked with (∗) Each segment is tilted by an angle of ±θtilt away from the longitudinal z axis, which allows for initialization of head-to-head or tail-to-tail domain wall configurations when subjected to a sufficiently strong transverse magnetic field Hini x

Controlling Bloch Point Parameters

The geometrical interface at (∗) acts as a topological structural defect that imprints opposite geometric chirality χG across the interface, which corresponds to a corresponding opposite magnetic handedness χM This mechanism enables simultaneous control over the Bloch point polarity (head-to-head or tail-to-tail, set by the direction of the initially applied field), its circulation (set by the RH/LH or LH/RH order of the helical segments), and its position (localized close to the chirality interface) The sign of Hini in this system dictates whether a tail-to-tail counter-clockwise or a head-to-head clockwise Bloch point domain wall is stabilized, as shown in Figs. 1(f,g)

Experimental Verification and Characterization

The existence of these controlled Bloch points is confirmed using advanced nanotomography techniques such as transmission electron microscopy (TEM) and magnetic soft X-ray transmission microscopy Magnetic soft X-ray tomography at the ALBA synchrotron allows for volume-resolved reconstruction of the vector character of local magnetic moments down to a spatial resolution limit of about 50 nm Electron holographic tomography reconstructs the three-dimensional distribution of components of the magnetic induction B within and outside a nanostructure at nanometer resolution These methods confirm that Bloch point domain walls are reliably nucleated with predefined polarity, circulation, and helicity angle

Spin Texture Analysis

The micromagnetic state near an axially symmetric Bloch point is described by parameters p (polarity), v (vorticity), and γ (helicity angle) The continuous angle γ describes how moments at the equator point either inward or outward for a hedge-hog-like Bloch point, or rotate around the central axis in a twisted configuration Experimental data from XMCD tomography found a helicity angle γ ≈ 100◦, which is in good agreement with simulations and indicates that spins in the equatorial plane of the Bloch point not only circulate but also twist inwards, creating a Bloch point of slightly hyperbolic character

Dynamics and Pinning Effects

The displacement of a Bloch point domain wall from a region of high curvature is predicted to depend on its polarity Analytical arguments and micromagnetic simulations show that upon initialization from a saturated state, a head-to-head (tail-to-tail) Bloch point moves towards the left-handed (right-handed) chiral section However, higher-resolution TEM measurements reveal that the Bloch point position is also strongly influenced by local pinning sites and microstructural inhomogeneities, leading to deviations from this idealized behavior The superior spatial resolution of TEM holography allows to discern effects of the local structural environment on the location and behavior of a Bloch point

Conclusion

This geometrical approach establishes a direct correspondence between geometrical topology, namely the reversal of geometric chirality, and magnetic topology, namely the emergence of Bloch point singularities The deterministic relation between Bloch-point polarity and circulation achieved here provides direct control over the coupling of the domain wall to current-induced Oersted fields, holding strong potential for future spintronic devices This geometrical selection and control of Bloch points holds strong potential for future Bloch-point based spintronic devices, including racetrack memory and logic architectures

Methods Summary

1. Sample Growth involved using focused electron beam-induced deposition (FEBID) to grow 3D nano-printed free-standing magnetic Co helical nanowires The individual helix strands have a diameter of 85 nm, while the helix is characterized by a periodicity of 250 nm and a nominal gyration radius of 34 nm

2. Magnetic Soft X-ray Nanotomography was performed at the MISTRAL beamline of the ALBA synchrotron using x-rays tuned to the Co L2 absorption edge Data acquisition involved recording images from two tilt series, one for rotations around the main axis and one for tilts around the y axis

3. Transmission Electron Microscopy was used to obtain a three-dimensional reconstruction of the electrostatic potential via off-axis electron holography This technique allows for quantitative separation of the electrostatic and magnetic phase shifts, providing access to both the structural information and the magnetic induction component Bz(r)

4. Micromagnetic simulations were run using custom code magnum.pi to obtain a remanent spin state of a Bloch point by evolving the LLG equation from a saturated state The simulation analysis derives quantities like magnetostatic volume charge and emergent vorticity field omega(r)

Supporting Information Summary

The supporting information details the extensive data processing pipeline, including image registration techniques using edge-filters and Fourier-based cross-correlation algorithms to correct for drifts The reconstruction of 3D magnetization involves a Simultaneous Iterative Reconstruction Technique (SIRT) evolved from previous methods The determination of the helicity angle γ is achieved by relating the spin angle ϕm to the real-space polar angle ϕ, yielding an experimental value of γ′exp ≈ 99.6◦ The alternative two-step initialization protocol uses a transverse field Hx to switch axial magnetization and circulation in one segment after an initial Hz field sets the axially magnetized state The analysis of the LLG damping term predicts a deterministic shift of a Bloch point domain wall relative to a curved section, although pinning at local inhomogeneities may dominate The determination of the helicity angle γ can also be obtained by an approximate formula involving the magnetostatic charge and divergence along the main axis z′ The electron holographic tomography reconstructs Bz(r) by removing stray field outside the nanowire by setting Bz values to zero where V falls below a threshold value of 15 V representing the nanowire surface The final triangulation of the Bloch point position is achieved by comparing experimental projections with magnetic-induction maps calculated from remanent Bloch-point states obtained via micromagnetic simulations The results show that Bloch point domain walls exhibit a symmetric magnetic phase contrast that does not depend on the projection direction, supporting the presence of a Bloch point

References

(1) Feldtkeller, E. Continuous and Singular Micromagnetic Configurations. IEEE Transactions on Magnetics 2017, 53, 1–8

(2) Hermosa-Muñoz, J.; Hierro-Rodríguez, A.; Sorrentino, A.; Martín, J. I.; Alvarez-Prado, L. M.; Pereiro, E.; Quirós, C.; Vélez, M.; Ferrer, S. Bloch Points and Topological Dipoles Observed by X-ray Vector Magnetic Tomography in a Ferromagnetic Microstructure. Communications Physics 2023

(3) Ruiz-Gómez, S. et al. Tailoring the Energy Landscape of a Bloch Point Domain Wall with Curvature. Nature Communications 2025

(4) Hermosa, J.; Hierro-Rodríguez, A.; Quirós, C.; Martín, J. I.; Sorrentino, A.; Aballe, L.; Pereiro, E.; Vélez, M.; Ferrer, S. Bloch Points and Topological Dipoles Observed by X-ray Vector Magnetic Tomography in a Ferromagnetic Microstructure. Communications Physics 2023

(5) Fullerton, J.; Leo, N.; Jurczyk, J.; Donnelly, C.; Sanz-Hernández, D.; Skoric, L.; Mille, N.; Stanescu, S.; MacLaren, D. A. Fractional Skyrmion Tubes in Chiral-Interfaced 3D Magnetic Nanowires. Advanced Functional Materials 2025

(6) Hermosa-Muñoz, J.; Hierro-Rodríguez, A.; Sorrentino, A.; Martín, J. I.; Alvarez-Prado, L. M.; Pereiro, E.; Quirós, C.; Vélez, M.; Ferrer, S. Hyperbolic Bloch Points in Ferrimagnetic Exchange Spring. Results in Physics 2024

(7) Tonomura, A.; Matsuda, T.; Endo, J.; Arii, T.; Mihama, K.

1. Enhanced Topological Defect Control in Materials Design (Atomic Scale)

This system can deterministically engineer Bloch points with controlled spin texture by engineering geometrical boundary conditions, allowing for the design of materials where the spin texture surrounding the Bloch point is uniquely defined.

2. Deterministic Spintronic Device Architectures

The improved AI can enable the design of devices containing Bloch points, as this approach provides a pathway towards 3D spintronic device architectures containing Bloch points by controlling Bloch point polarity (head-to-head or tail-to-tail, set by the direction of the initially applied field), its circulation (set by the RH/LH or LH/RH order of the helical segments) and its position.

3. Novel Field Protocols for In-Situ Characterization

The system can utilize an alternative field protocol using lower field magnitudes that is suitable for in-situ studies, enabling researchers to probe Bloch point physics, including their high-frequency response [13, 42, 45] and non-reciprocal interactions with current-generated Oersted fields [10, 14, 21, 23].

4. High-Resolution Spin Texture Mapping

The AI can perform three-dimensional spin order mapping by combining various techniques like transmission electron microscopy (TEM) and magnetic soft X-ray transmission microscopy, allowing for the visualization of the local magnetic configuration down to the spatial resolution limit of about 50 nm.

5. Triangulation of Singularity Position

The system can accurately determine the location of topological defects by employing a method where Combining the determined coordinates from three or more different viewing angles allows triangulation of the Bloch point position in three dimensions using data from electron holography and X-ray tomography.

Bloch points are three-dimensional topological singularities in magnetization that play a key role in topological transformations of spin textures, such as skyrmion creation or annihilation. While topology often enforces the existence of Bloch points in confined geometries like cylindrical nanowires, deterministic control over their position and magnetic configuration remains challenging. Here we demonstrate the generation of Bloch points with controlled spin texture by engineering geometrical boundary conditions in three-dimensional nanomagnets. By introducing a chirality interface between two three-dimensional double-helix nanowires of opposite handedness, forming a kinked, non-collinear structure, we impose competing topological constraints that uniquely define the magnetization configuration surrounding the Bloch point. A saturating magnetic field nucleates head-to-head or tail-to-tail domain configurations at the chirality interface, producing a Bloch-point domain wall with deterministic polarity, circulation and helicity. This geometrical approach enables full three-dimensional control of Bloch point domain walls allowing deterministic engineering of their spin texture and its selective coupling to current-induced Oersted fields.