Domain-wall circulation gating and pinning via compositional engineering of cylindrical nanowires

The gist: Chemical modulations act as local potential wells that effectively pin domain walls due to their shared azimuthal curling, while the mechanism of propagation through such modulations is complex and depends on whether the circulation senses are parallel or antiparallel, with opposite circulations forcing a change in circulation before propagation can occur.

Domain Wall Interaction and Pinning Mechanisms

The interaction between domain walls (DWs) and chemical modulations involves a long-range moderate magnetostatic repulsion combined with a local energy well that depends on the respective circulation sense of magnetization in the domain wall and modulation The introduction of chemical modulations aims to modify the domain wall energy landscape, allowing controlled pinning sites to be established if the artificial pinning strength exceeds that related to material defects Micromagnetic simulations reveal that at long distances between the BPW and the modulation, both curves overlap and reveal a repulsive interaction At shorter distances, the magnetization textures of the BPW and the modulation overlap and interact directly via exchange This exchange interaction results in a decrease (resp. increase) of exchange energy depending on whether the circulations are parallel or antiparallel Experimental evidence shows BPW pinning at chemical modulations and TVW pinning next to them, highlighting the generality of the pinning potential regardless of modulation strength or DW type

Propagation with Identical Circulation Senses

When the BPW and the chemical modulation exhibit the same sign of circulation, smooth propagation occurs through a modulation The internal energy profile shows a well at the modulation and long-distance repulsion, consistent with previous findings The depinning field is reflected by the steepest slope of the internal energy, which is consistent with the Becker-Kondorsky model In this case, a BPW propagates smoothly through a chemical modulation when their circulation senses are parallel Experimental data confirmed the order of magnitude of pinning and depinning strength at the modulations for parallel circulations, showing controlled pinning stronger than intrinsic pinning on material defects

Propagation with Opposite Circulation Senses

The propagation of a BPW through a chemical modulation with initially antiparallel circulation is expected to behave differently, as the modulation should act as an energy barrier The internal energy profiles show an energy barrier due to magnetostatic-driven repulsion at distances larger than the BPW width However, at later stages, the situation changes drastically, and discontinuities of the internal energy are observed For short modulations of 20 nm length, the Bloch point reappears in the volume and pins onto the chemical modulation The larger depinning field reaches 32 mT for a 100 nm-long modulation, indicating a drastically different propagation mechanism than in the parallel circulation case

Topological Switching via Circulation Reversal

The opposite circulation situation forces the BPW to change its circulation before propagation can occur, effectively acting as a polarizing device This process involves the annihilation/re-nucleation of a Bloch point and a transient topology state of a transverse-vortex wall, which is reported here for the first time The phenomenon of BPW circulation switching upon crossing a chemical modulation under a magnetic field mirrors the mechanism reported in ref Riz et al. 29 for BPW switching in an homogeneous nanowire driven by an antiparallel Oersted field This suggests that chemical modulations can be utilized as a polarizing component to control the internal structure of domain walls

Experimental Probing and Characterization

The interaction between higher-magnetization chemical modulations and BPWs was experimentally outlined using X-ray Magnetic Circular Dichroism (XMCD) coupled to Transmission X-ray Microscopy (TXM) Images show BPW pinning at modulations or next to them, confirming the potential of modulations to pin DWs The combination of high spatial resolution and direct probing enables the extraction of unambiguous information about the DW type and inner structure The study utilized Permalloy (Fe20Ni80) nanowires with periodic Fe80Ni20 chemical modulations, providing informative magnetic images on their own

Methods and Simulation Details

Micromagnetic simulations were performed using the mumax3 code for a 90 nm diameter Permalloy nanowire with a 2 µm length and either a 20 nm or 100 nm-long Fe80Ni20 chemical modulation The system was studied under quasi-static conditions using a damping coefficient of α = 1 Material parameters included a single exchange stiffness for all materials and zero magnetocrystalline anisotropy The methodology involved monitoring the domain wall energy during slow drift under large damping or applying an axial external magnetic field to move the domain wall towards the chemical modulation The topological analysis was performed using a post-processing tool developed specifically for tetrahedron-based finite-elements

Conclusion

In summary, higher-magnetization chemical modulations act as local potential wells that effectively pin domain walls due to their shared azimuthal curling, lowering the total energy of the system While propagation through a modulation is complex, at distances larger than the BPW width, the interaction is primarily repulsive and magnetostatic For opposite circulations, the modulation forces the BPW to change its circulation before propagation can occur, acting as a polarizing device These findings open the possibility of utilizing chemical modulations as a polarizing component to control the internal structure of domain walls The mechanism observed is consistent with changes in domain wall type in homogeneous nanowires driven by field or Oersted-field

Methods

Permalloy (Fe20Ni80) cylindrical nanowires with Fe-rich chemical modulations were synthesized by single-bath template-assisted electrochemical deposition Nanoporous anodic aluminum oxide (AAO) templates were prepared by hard anodization of Al disks in a water-based solution of oxalic acid and ethanol The growth conditions were similar to those described in ref Ruiz-G´omez et al. 52 The wires were imaged with X-ray Magnetic Circular Dichroism (XMCD) coupled to Transmission X-ray Microscopy (TXM) Ptychographic reconstruction was carried out using the open-source PyNX software developed at the European Synchrotron Radiation Facility The system considered is a cylindrical Permalloy nanowire of 90 nm diameter and 2 µm length, with a 20 nmlong or 100 nm-long Fe80Ni20 chemical modulation at its center The mesh size used was 2 nm The following material parameters were used: spontaneous magnetization M1 = 8 × 10 5 A/m for the Permalloy segments, M2 = 14 × 10 5 A/m for the chemical modulation, single exchange stiffness for all materials A = 1.

1. Bold header: Control of Domain Wall Internal Structure

The improved AI system can reliably switch internal domain wall circulation by exploiting chemical modulations, as outlined in a modulation has the ability to switch the internal circulation of a DW upon its propagation, thereby acting as a polarizing component. This allows for controlling not only the position of walls but also their internal structure.

2. Bold header: Polarization Control via Chemical Modulations

The AI system can utilize chemical modulations as an engineered site to control domain wall motion by exploiting the interaction where the respective circulations of the wall and modulation, which can either be parallel (C + C+) or antiparallel (C + C−). This enables switching the circulation sense with an anti-parallel Œrsted field.

3. Bold header: Enhanced Pinning Site Identification

The AI system can identify optimal domain wall pinning sites by analyzing the energy landscape, specifically recognizing that chemical modulations act as local potential wells, that effectively pin domain walls due to their shared azimuthal curling, thereby lowering the total energy of the system. This allows for controlled pinning stronger than intrinsic pinning on material defects along the Permalloy segments.

4. Bold header: Topological State Tracking

The system can perform topological analysis to distinguish between wall types during modulation by tracking phenomena like the annihilation/re-nucleation of a Bloch point and a transient topology state of a transverse-vortex wall. This mimics the mechanism reported for BPW switching in an homogeneous nanowire driven by an antiparallel Oersted field.

Spintronic devices based on cylindrical magnetic nanowires have been proposed as a route toward three-dimensional information storage and processing by harnessing the controlled motion of domain walls (DWs). In this geometry, the Bloch-point wall (BPW) is the characteristic DW type. It features a curling of magnetization around a Bloch Point singularity, a topology that has been predicted to enable propagation at high speed without undergoing a Walker breakdown. We demonstrate that compositional modulations of larger magnetization, which host spontaneous curling states while the rest of the wire remains axial, fulfil a dual role: they act as deterministic pinning sites and as active gates for BPW circulation. Combining magnetic transmission X-ray microscopy and micromagnetic simulations, we reveal that DW-modulation interactions are the result of a superposition of long-range magnetostatic repulsion and short-range, circulation-dependent exchange contributions: parallel circulation produces an attractive well, while opposite circulation generates a repulsive barrier. This results in DW pinning at or near a compositional modulation. A DW's internal circulation can be inverted upon traversing a modulation, enabling on-demand switching of its circulation state. This dual mechanism demonstrates that both DW position and circulation can be tuned in a controlled manner, with potential implications for multistate spintronic devices.