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

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

Problem Statement
Bloch points are three-dimensional topological singularities in magnetization where the magnetic moment vanishes, playing a critical role in topological transformations such as skyrmion creation, annihilation, and vortex core reversal. While their existence is often enforced by topology in confined geometries like cylindrical nanowires, deterministic control over their nucleation—specifically their spatial position, polarity, circulation, and helicity—remains a significant challenge. Previous approaches have struggled to define the spin texture surrounding a Bloch point deterministically, as these configurations often emerge stochastically from symmetry or defects rather than being engineered through material design. The central problem addressed is whether the spin texture around a Bloch point can be uniquely defined through designed geometrical engineering rather than stochastic emergence.

Methodology
The authors address this challenge by engineering geometrical boundary conditions in three-dimensional nanomagnets. The core experimental strategy involves:

1. Nanostructure Fabrication: Using focused-electron beam-induced deposition (FEBID), the team fabricated free-standing magnetic cobalt (Co) double-helix nanowires. These structures consist of two segments with opposite geometric chirality (left-handed at the bottom, right-handed at the top) meeting at a "chirality interface." The segments are tilted by $\pm 15^\circ$ relative to the longitudinal axis to facilitate domain wall initialization.
2. Initialization Protocol: A saturating transverse magnetic field ($H_{ini} \parallel x$) is applied to nucleate either a head-to-head or tail-to-tail domain configuration at the chirality interface. Upon field relaxation, the competing topological constraints imposed by the opposing geometric chiralities stabilize a circulating Bloch point domain wall.
3. Characterization: The study employs a multi-modal imaging approach to resolve the 3D spin texture:
   • Magnetic Soft X-ray Nanotomography (XMCD): Performed at the ALBA Synchrotron (MISTRAL beamline) to reconstruct the vector magnetization with $\approx 50$ nm resolution.
   • Electron Holographic Tomography: Conducted in a transmission electron microscope (TEM) to map the electrostatic potential and magnetic induction ($B_z$) with higher spatial resolution, allowing for the visualization of internal magnetic structures and stray fields.
   • Micromagnetic Simulations: Finite-element simulations (using magnum.fe) were used to model the equilibrium states and validate experimental observations, incorporating parameters such as saturation magnetization ($M_{sat} = 700$ kA m$^{-1}$) and exchange stiffness ($A_{ex} = 10$ pJ m$^{-1}$).

Key Contributions and Results
The paper demonstrates the deterministic generation of Bloch points with fully controlled spin textures:

• Deterministic Control of Topological Parameters: By interfacing left- and right-handed helices, the authors uniquely define the Bloch point's polarity (head-to-head or tail-to-tail), circulation (clockwise or counter-clockwise), and helicity angle ($\gamma$). The polarity is set by the direction of the initial saturating field, while the circulation is dictated by the order of the geometric chirality segments (LH/RH vs. RH/LH).
• Experimental Verification: XMCD tomography directly visualized a head-to-head Bloch point with clockwise circulation, confirming the theoretical prediction that the geometric chirality interface acts as a robust nucleation site. The reconstructed magnetization showed a well-defined vortex-like circulation in the equatorial plane.
• Helicity and Hyperbolic Character: The experiments determined a helicity angle $\gamma \approx 100^\circ$, indicating that the spins not only circulate but also twist inward, creating a slightly hyperbolic Bloch point. This value aligns with micromagnetic simulations.
• Displacement and Pinning: The Bloch point was observed to be displaced from the exact chirality interface (by 60–140 nm) toward the segment with the same geometric chirality as the circulation (e.g., a head-to-head point moved toward the left-handed segment). This displacement is attributed to curvature-driven dynamics governed by the Landau-Lifshitz-Gilbert damping term, as well as local pinning effects arising from material inhomogeneities (variations in Co density) inherent to the FEBID growth process.
• Monopole-like Stray Fields: Both experimental and simulated stray field patterns exhibited high symmetry and a monopole-like character, distinct from the directional leakage seen in transverse domain walls, further confirming the presence of a Bloch point.

Significance and Claims
The authors claim that this work establishes a direct correspondence between geometrical topology (the reversal of geometric chirality) and magnetic topology (the emergence of Bloch point singularities). Unlike high-symmetry cylindrical nanowires or nanospheres where left- and right-handed circulations are energetically degenerate, this geometrical approach breaks this degeneracy, imprinting a well-defined circulation on the Bloch point.

The significance of this approach lies in its ability to provide full three-dimensional control over Bloch point domain walls, enabling the deterministic engineering of their spin texture and its selective coupling to current-induced Oersted fields. The authors posit that this capability is a prerequisite for future Bloch-point-based spintronic devices, such as racetrack memory and logic architectures, where the ability to selectively actuate domain walls based on their internal state is crucial. The paper concludes that by controlling geometric chirality in a tailored 3D geometry made from a single material, they have overcome the limitations of previous methods that relied on intrinsic defects or complex thin-film engineering with Dzyaloshinskii-Moriya interaction (DMI) tuning.