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General Approach to Solving Spin Moiré Superstructures

Paul M. Neves1,*, Takashi Kurumaji2, Joshua P. Wakefield1, Arno Hiess3,4, Paul Steffens3, Navid Qureshi3, Robert Cubitt3, Lisa M. DeBeer-Schmitt5, Johanna C. Palmstrom6 et al.

Satoru Hayami7, Marek Bartkowiak8, Markus Zolliker8, Jonathan S. White8, and Joseph G. Checkelsky1

  • *Contact author: pmneves@mit.edu
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Phys. Rev. X 16, 021054 – Published 11 June, 2026

DOI: https://doi.org/10.1103/bjq3-py7l

Abstract

Recently, a host of exciting magnetic textures such as topologically protected skyrmion lattices has been discovered in several bulk metallic lanthanide compounds. In addition to hosting skyrmion phases, a hallmark of this class of materials is the appearance of numerous spin textures characterized by superposition of multiple magnetic modulations: spin moiré superlattices. In order to understand the multitude of complex phases often present in these materials, we require a general-purpose experimental and theoretical framework. Here, we demonstrate such an approach in EuAg4Sb2 by comprehensively characterizing and modeling its three complex zero-field magnetic textures. Systematic symmetry-breaking experiments using uniaxial strain determine that the ground-state incommensurate magnetic phase (ICM1) is single q, meaning the magnetic moments modulate along one magnetic propagation vector. In contrast, ICM2 and ICM3 are both double q, meaning they are formed from the superposition of two sinusoidal spin modulations, i.e., spin moiré superlattices. Further, through application of polarized small-angle neutron scattering and spherical neutron polarimetry, we demonstrate that ICM1 is a single-q cycloid and ICM2 and ICM3 are double-q vortex lattices. Despite the quasi-two-dimensional nature of EuAg4Sb2, the modulations propagate out of the ab plane, leading to a shift of the spin texture between triangular lattice planes. Further, the ICM3 to ICM2 transition includes an unusual 45° rotation of the magnetic vortex lattice. Motivated by the coexistence of such drastically different phases in this compound, we conclude by developing a phenomenological model that sheds light on the energetic origins of these varied phases. Our experimental probes and theoretical modeling definitively characterize three different and tunable phases in one material and provide insight for the design of topological spin-texture materials.

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Popular Summary

Determining the stability and identity of complex spin textures in layered magnetic materials is a persistent challenge because multiple competing patterns often coexist and transform under subtle external conditions. We addressed this by mapping the magnetic ground states of the layered metal EuAg4Sb2 using strain-controlled and polarization-resolved neutron scattering. We identified three distinct zero-field phases, including a single-q cycloid and two double-q vortex lattices, which emerge from the superposition of spin waves and exhibit quasi-three-dimensional modulations across layers. Our measurements revealed that one vortex lattice rotates by 45° during phase evolution, providing a sharp signature of textural reorganization, while small magnetic fields introduce a uniform ferromagnetic component that tips the phase balance. A phenomenological model captures these transitions and confirms that the coexistence of these textures arises from free-energy tunability. These results establish EuAg4Sb2 as a platform for manipulating spin states and demonstrate a general method for characterizing complex magnetic patterns in quantum materials.

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Phys. Rev. X 16, 021054– Published 11 June, 2026
  • Received 14 September 2025
  • Revised 23 February 2026
  • Accepted 29 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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