🔬 materials science

Quasi-1D Spin Textures: From Chiral Soliton Lattice to Fan State

Using resonant elastic X-ray scattering and micromagnetic simulations, researchers demonstrate that in the anisotropic chiral magnet Mn $_{1.4}$ PtSn, applying a magnetic field perpendicular to the crystallographic propagation axis stabilizes a unique fan-like state where quasi-one-dimensional spin textures transform from a chiral soliton lattice while maintaining a transverse propagation direction.

Original authors: M. Winter, A. Pignedoli, A. S. Sukhanov, M. Azhar, A. Tahn, B. Achinuq, J. R. Bollard, V. Ukleev, C. Luo, F. Radu, S. Wintz, M. Weigand, A. Mistonov, P. Vir, J. Geck, C. Felser, G. van der Laan, T. He

Published 2026-06-23

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CC BY 4.0

Original authors: M. Winter, A. Pignedoli, A. S. Sukhanov, M. Azhar, A. Tahn, B. Achinuq, J. R. Bollard, V. Ukleev, C. Luo, F. Radu, S. Wintz, M. Weigand, A. Mistonov, P. Vir, J. Geck, C. Felser, G. van der Laan, T. Hesjedal, K. Everschor-Sitte, B. Rellinghaus, M. C. Rahn

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a crowd of people (the atoms in a crystal) who naturally want to hold hands and form a spiral line, twisting in a specific direction. In most materials, if you push this crowd with a magnetic "wind" (a magnetic field), they simply stand up straighter, turning the spiral into a cone shape. It's a predictable, smooth change.

However, the scientists in this paper studied a special material called Mn1.4PtSn. In this material, the rules are different. The crystal structure acts like a set of train tracks that forces the spiral to stay on a specific path, no matter what.

Here is the story of what they discovered, using simple analogies:

1. The Setup: The "Train Tracks"

In this material, the magnetic "spirals" (called Chiral Soliton Lattices) are stuck on a track running along one specific direction.

The Normal Scenario: Usually, if you blow a magnetic wind from the side, the spiral tries to turn into a cone to face the wind.
The Twist: Because of the material's internal "train tracks," the spiral cannot turn to face the wind. It must keep running sideways, perpendicular to the wind.

2. The Experiment: Blowing the Wind

The researchers used a powerful X-ray camera (Resonant Elastic X-ray Scattering) to watch what happens when they apply a magnetic field from the side (perpendicular to the spiral's track). They slowly increased the strength of this "wind."

They observed two distinct phases:

Phase A (The Spiral): At low wind speeds, the material has two types of spirals running in different directions. One runs parallel to the wind, the other runs perpendicular.
Phase B (The Fan): As the wind gets stronger, something surprising happens. The spiral that was running perpendicular to the wind suddenly "unwinds." It stops twisting all the way around and instead starts oscillating back and forth like a fan blade.

3. The "Fan State" Explained

Think of the original spiral like a corkscrew. It twists 360 degrees over and over.
The new "Fan State" is like a swinging pendulum or a folding fan. The spins (the people in the crowd) no longer make a full circle. Instead, they swing left and right around the direction of the wind, but they never complete a full loop.

Why is this special? In most magnetic materials, a fan shape is unstable because the material "prefers" to twist in one specific direction (like a right-handed screw). A fan requires the spins to swing symmetrically, which usually costs too much energy.
The Secret Ingredient: The paper reveals that the shape of the sample (it's a very thin slice, like a piece of paper) creates a "magnetic pressure" (magnetostatic interactions) that forces the material to accept this fan shape. It's like a tightrope walker who, under specific conditions, finds it easier to balance on a flat board than to twist.

4. The "One-Way Street"

The most dramatic finding is that this change is irreversible.

When they turned the magnetic field off, the material did not go back to being a spiral. It stayed as a fan.
It's as if the material walked through a door that locked behind it. Once the wind blew hard enough to turn the corkscrew into a fan, the corkscrew was gone forever (at least until they reset the material in a different way).

5. The Two Domains

The material had two groups of spirals:

Group 1: Running with the wind. This group just got squashed and disappeared.
Group 2: Running across the wind. This group transformed into the Fan State and took over the whole material.

Summary

The paper shows that by changing the direction of the magnetic field, you can force a magnetic material to switch between two completely different "modes":

A twisting spiral (topologically complex).
A swinging fan (topologically simple).

This happens because the material's internal "train tracks" prevent it from doing the usual thing (turning into a cone), and the thin shape of the sample provides the extra push needed to stabilize the fan. The scientists proved that you can use the direction of a magnetic field as a switch to fundamentally change the shape of magnetic patterns in a material.

Technical Summary: Quasi-1D Spin Textures: From Chiral Soliton Lattice to Fan State

Problem Statement
In most helimagnets, applying a magnetic field aligns the propagation direction of helical spin textures with the field, resulting in a conical state that obscures the unwinding process. While two-dimensional textures like skyrmions are well-studied, one-dimensional (1D) modulations offer a simpler setting to track field-driven transformations. However, in the anisotropic chiral magnet Mn $_{1.4}$ PtSn (Heusler compound, $D_{2d}$ symmetry), the response to in-plane magnetic fields has remained largely unexplored. Previous studies, primarily using Lorentz transmission electron microscopy (LTEM) with out-of-plane fields, focused on antiskyrmions and multi-q states. The experimental limitations of LTEM (requiring fields perpendicular to the electron beam) prevented the separation of in-plane and out-of-plane responses in this highly anisotropic material. Specifically, it was unclear whether a fan-like state—a topologically trivial texture where spins oscillate about the field direction—could be stabilized as a stable equilibrium phase in a Dzyaloshinskii–Moriya interaction (DMI)-active system, given that DMI typically penalizes such non-chiral configurations.

Methodology
The authors employed a combination of experimental and computational techniques to investigate spin textures in high-quality Mn $_{1.4}$ PtSn single crystals:

Sample Preparation: Lamellae (~80 nm thick) were prepared via focused ion beam (FIB) milling with the crystallographic $c$ -axis as the surface normal.
Resonant Elastic X-ray Scattering (REXS): Experiments were conducted at the Diamond Light Source (beamline I10) using a portable octupole magnet (POMS). This setup allowed for vector magnetic field application, specifically sweeping an in-plane field (parallel to the $a$ -axis) from 0 to 450 mT while measuring momentum transfers in the $a$ – $b$ plane.
Scanning Transmission X-ray Microscopy (STXM): Used to visualize real-space domain reorganization at selected field values.
Micromagnetic Simulations: Two approaches were utilized:
1. Multi-domain simulations: Modeling a finite slab ( $2 \times 2 \times 0.1$ $\mu$ m $^3$ ) with free boundary conditions to simulate domain redistribution and irreversible collapse.
2. Single-domain simulations: Modeling a periodic slab (100 nm thick) with periodic boundary conditions to determine intrinsic equilibrium modulation lengths and energy competition between $\pi$ -chiral soliton lattice ( $\pi$ -CSL) and fan states.

Key Contributions and Results
The study reveals a distinct transformation pathway for 1D spin textures in Mn $_{1.4}$ PtSn under in-plane fields, contrasting with the behavior observed under out-of-plane fields.

Field-Induced Phase Transition:
- At zero field, the ground state is a mixed-domain $\pi$ -CSL with orthogonal propagation directions ( $\text{dom}_{\parallel}$ along the field, $\text{dom}_{\perp}$ perpendicular to the field).
- Upon applying an in-plane field, the system undergoes a sequence of changes:
  - $H < H_1$ (~90 mT): The modulation lengths remain constant.
  - $H_1 < H < H_2$ (~190 mT): A first-order phase transition occurs in the $\text{dom}_{\perp}$ domain. The $\pi$ -CSL (topological winding number $Q \neq 0$ ) abruptly unwinds into a fan state ( $Q = 0$ ), where spins oscillate symmetrically about the field direction without completing a full rotation. This is evidenced by a discontinuous jump in magnetization and a shift in the Bragg peak intensity.
  - $H_2 < H < H_3$ (~240 mT): The $\text{dom}_{\parallel}$ domain (propagating along the field) collapses, transferring phase volume to the $\text{dom}_{\perp}$ fan state. This process is irreversible; upon reducing the field to zero, the sample remains in a single-domain fan state.
  - $H > H_3$ : The system reaches a single-domain fan state that continuously contracts (modulation length decreases) as the field increases, eventually approaching the field-polarized state.
Modulation Length Dynamics:
- Unlike the conical state formation in conventional helimagnets (which typically involves expanding modulation lengths or specific commensurate-incommensurate transitions), the fan state in this geometry exhibits a continuous contraction of the modulation length with increasing field.
- In the mixed-domain regime ( $H < H_1$ ), the modulation lengths of both domains remain locked, likely due to the continuous connection of stripes across domain boundaries, which frustrates the opposing tendencies of the conically distorted $\text{dom}_{\parallel}$ (contracting) and the $\pi$ -CSL $\text{dom}_{\perp}$ (expanding).
Role of Magnetostatic Interactions:
- Simulations indicate that while DMI in the bulk penalizes the fan configuration (which lacks a single rotational sense), magnetostatic interactions in finite-thickness films are crucial for stabilizing the fan state.
- Surface flux-closure domains reduce the energy cost of the fan configuration, allowing it to become the energetically favorable ground state above $H_1$ .

Significance
The paper provides experimental evidence for a fan-like regime in a chiral magnet with DMI, a state previously uncertain in such systems. The work highlights that field orientation acts as a switch between fundamentally different transformation pathways:

Out-of-plane fields drive a continuous, topology-preserving condensation of $\pi$ -solitons into higher-order 2 $\pi$ -CSLs.
In-plane fields drive a discontinuous, topology-destroying unwinding into a topologically trivial fan state.

The authors conclude that this mechanism—magnetostatic stabilization of a non-chiral modulated state in a finite film of a chiral magnet—is likely applicable to other symmetry classes hosting 1D modulations (e.g., $C_{nv}$ helimagnets like FeGe and CrNb $_3$ S $_6$ ). The ability to irreversibly toggle between topologically distinct 1D states using moderate in-plane fields suggests potential for field-programmable control of spin-polarized state topology in spintronic and magnonic devices.