Control of helix orientation in chiral magnets via lateral confinement

TL;DR

This work demonstrates that lateral confinement in a DMI-driven helimagnet (FeGe) induces a chiral surface twist that acts as an effective surface anisotropy, governing the in-plane orientation of the helix propagation vector $\bm{q}$ in confined geometries. The authors develop an analytical boundary-condition–based model and validate it with micromagnetic simulations and MFM experiments on FeGe nanostructures, showing that $\bm{q}$ reorients continuously with aspect ratio and matches predictions for large systems. The results establish geometry-induced anisotropy as a general mechanism to steer DMI-stabilized spin-spiral states, with direct implications for device-level control in helimagnets and potential extensions to multilayers and synthetic chiral heterostructures.

Abstract

Helimagnetic materials offer a versatile platform for spin-based device concepts owing to their long-range, tunable spiral order. Here, we demonstrate controlled manipulation of the helimagnetic propagation vector q by geometrical confinement, using FeGe as a model DMI-driven chiral magnet. Micromagnetic simulations based on the nonlinear sigma model reveal that open boundaries give rise to a chiral surface twist acting as an effective surface anisotropy, which dictates the preferred helix orientation in the absence of magnetostatic shape effects. This geometry-induced anisotropy is quantitatively captured by an analytical model derived from the DMI boundary condition. Magnetic force microscopy measurements on focused-ion-beam structured FeGe confirm the predicted orientation behavior and establish geometry-controlled helimagnetic order as a robust, tunable mechanism for steering DMI-stabilized spin-spiral states. The concept provides a general route toward device-level control of chiral magnetic order in of non-centrosymmetric systems.

Figures (5)

• Figure 1: Helical spin order in FeGe. (a) Schematic illustration of the helical ground state showing the wavelength $\lambda$ and propagation direction $\bm{q}$. (b) Micromagnetic simulation of the helical state with the magnetization shown as arrows and color-coded according to the local magnetization direction (black = down, white = up, red = right, cyan = left). (c) Corresponding color-map representation of the same state as in (b).
• Figure 2: Shape anisotropy in a rectangular magnet with an aspect ratio of 2:1. (a) Simulated ferromagnetic state including dipolar interactions, showing alignment of $\bm{M}$ along the long axis due to conventional shape anisotropy. (b) Simulated helical state without demagnetization energy, where the propagation vector $\bm{q}$ aligns diagonally to minimize the boundary energy through the chiral surface twist. (c) Corresponding energy landscapes as a function of orientation angle $\theta$. Orange stars mark the energy minima. The inset shows the calculated surface-twist contribution.
• Figure 3: Dependence of the helix orientation on the aspect ratio of the confined region. (a) Color-coded phase diagram of the equilibrium orientation angle $\theta$ between $\bm{q}$ and $\hat{e}_x$, plotted as a function of lateral dimensions $L_x$ and $L_y$. Blue and red correspond to $\theta=0^{\circ}$ and $90^{\circ}$, respectively. Black squares mark data points for which the corresponding real-space textures are shown in (b). (b) Representative relaxed helical states for selected aspect ratios. (c) Orientation angle $\theta$ as a function of the aspect ratio $L_x/L_y$. Dots show numerical results colored by the total circumference; the black line represents the analytical model derived from the DMI boundary condition. Dashed segments denote the range outside the model’s validity ($6^{\circ} \lesssim\theta \lesssim 84^{\circ}$). The inset illustrates the restricted Fourier transform used to extract $\theta$, shown here for $(L_x,L_y) = (10.5\lambda,2.5\lambda)$, corresponding to the orange box in panels (a,b).
• Figure 4: Experimental observation of helimagnetic order under lateral confinement. (a) SEM image of a 1 µ m thick FeGe lamella with an aspect ratio of approximately 1:2. (b) Corresponding MFM image revealing helimagnetic order, with propagation vector $\bm{q}$ tilted relative to the long axis. (c) Fast Fourier transform (FFT) of the MFM image used to determine the orientation angle $\theta$ between $\bm{q}$ and the long axis, yielding $23.7 \pm 1.4^{\circ}$.
• Figure 5: Influence of lateral confinement on the helix orientation. (a–c) SEM images of rectangular FIB-cut regions with aspect ratios of about 1:1, 2:1, and 7:1, respectively. Overlaid MFM scans show the corresponding helimagnetic stripe patterns. White arrows indicate the direction of the helical propagation vector $\bm{q}$ inside each confined region, and the extracted orientation angle $\theta$ relative to the long side of the rectangle. The comparison between interior and exterior orientations demonstrates the predictable geometry-dependent reorientation of $\bm{q}$ in agreement with simulation results.