The material at the heart of the work is strontium ruthenate, SrRuO3, a perovskite oxide that is both a good metal and a ferromagnet below its Curie temperature. The team, led by Yingzhuo Lun, Xinxin Hu and Qi Ren, with senior authors Gustau Catalan, Jordi Arbiol and Jiawang Hong, grew single-crystal SrRuO3 films about ten nanometers thick and then released them from their substrates using a water-soluble sacrificial layer. This freed the membranes so that one could be picked up, rotated and laid back down on another, forming a twisted bilayer. The technique is the same twistronics playbook that revolutionized graphene research, where stacking two carbon sheets at a magic angle produced unconventional superconductivity. Here, however, the twist is not tuning electronic bands but sculpting the mechanical strain landscape inside an oxide metal.

When two identical crystals are overlaid at a twist angle, their lattices fall in and out of registry across the plane, producing a long-wavelength moiré superlattice. In regions where the atomic columns align perfectly, known as AA stacking, the local environment differs sharply from the mismatched AB regions. The result is a spatially periodic pattern of shear strain concentrated near the bilayer interface. Crucially, strain gradients in solids can generate electric fields through the flexoelectric effect, a phenomenon in which deformation itself polarizes a material, even a centrosymmetric one. Because flexoelectricity scales with strain gradients rather than strain, it becomes exceptionally powerful at the nanoscale, and the moiré pattern provides exactly the kind of periodic shear gradients needed to organize polarization into extended textures.

To see what those gradients actually do to the atoms, the researchers turned to state-of-the-art electron microscopy. Using aberration-corrected scanning transmission electron microscopy combined with ptychographic reconstruction, a computational technique that can push spatial resolution to the limits set by lattice vibrations, they mapped the positions of ruthenium atoms with picometer precision, layer by layer through the thickness of the bilayer. What emerged were vortices: the tiny displacements of ruthenium ions relative to their surrounding oxygen cage rotated continuously around each moiré unit cell, forming dipolar whirlpools whose handedness and magnitude followed the moiré periodicity. In unannealed control samples, the displacements were random and minimal, averaging only about 1.6 picometers, confirming that the ordered vortices are a genuine consequence of the twisted, relaxed bilayer geometry rather than an artifact of preparation.

The vortex strength proved exquisitely tunable. By fabricating bilayers with twist angles ranging from roughly three to ten degrees, the team showed that the magnitude of the polar displacements depends systematically on the twist angle, and also on depth: the effect is strongest near the twisted interface, where the shear strain gradients are largest, and decays into the interior of each membrane. Density functional theory calculations reproduced and explained these observations, showing that the moiré-induced shear strain gradients generate flexoelectric fields that periodically polarize the metal despite the screening action of its free carriers. The calculations provided the microscopic link between the mechanical moiré pattern and the observed dipolar texture, closing the loop between experiment and theory.

Perhaps the most intriguing twist is magnetic. Below the ferromagnetic Curie temperature of SrRuO3, the films retain their magnetic order, so the vortices live inside a metal that is simultaneously polar and ferromagnetic, a combination physicists call a polar metal or, when both orders coexist, a multiferroic-like state. The measurements revealed that the dipolar order and the ferromagnetic order appear to compete: their magnitudes show opposite dependencies on the twist angle, so conditions that strengthen the polar vortices weaken the magnetization, and vice versa. Magnetic and electrical transport characterizations supported this picture of two order parameters jostling for dominance within the same ten-nanometer membranes. This competition is scientifically valuable because magnetoelectric coupling of any kind is rare, and controllable coupling in a metallic system could open routes to devices where electric and magnetic information interconvert.

The result is notable for what it says about screening. The textbook argument against ferroelectricity in metals holds that free electrons rearrange to cancel any polarization field within roughly a lattice constant. The new work demonstrates that flexoelectrically driven polar textures can nevertheless persist in a metal, because the driving force is a strain gradient that continuously re-polarizes the lattice rather than a static depolarizing field that charges can simply erase. Earlier theoretical work had predicted that polar metals could be switched and stabilized by strain gradients, and previous experiments had flexoelectrically polarized ferromagnetic metals, but the present study is the first to image extended, moiré-programmed polarization vortices inside a metallic ferromagnet directly at atomic resolution.

The study also builds on a rapid sequence of advances in twisted oxide membranes. In 2024, researchers observed a two-dimensional ferroelectric vortex pattern in twisted bilayers of the insulating ferroelectric barium titanate, and later that year a polar vortex was reported hiding in twisted bilayers of the paraelectric strontium titanate. Those experiments established that twist could impose topology on polar order in dielectrics. The new result answers the obvious next question: does the same physics survive in a metal, where free charge should destroy it? The answer, remarkably, is yes, provided the polar texture is flexoelectric in origin and spatially modulated so that screening currents cannot fully neutralize it.

Methodologically, the paper showcases how far electron ptychography has come as a tool for buried interfaces. Because the vortices live at the hidden interface between two membranes, conventional imaging struggles to separate the overlapping lattices. The team used multislice ptychographic reconstructions to resolve the structure depth-resolved through the bilayer, tracking how the lattice reconstruction and the ruthenium displacement field evolve with distance from the interface, and released the underlying ptychographic dataset and reconstruction software openly. Quantitative strain analysis of the images mapped the shear strain gradients that feed the flexoelectric fields, allowing a direct, atom-by-atom comparison between the measured displacement field and the predicted flexoelectric response.

The implications reach toward future technologies. Polar vortices and related topological textures such as skyrmions are attractive for ultradense, low-energy memory and logic because they are robust, mobile and switchable. Extending such textures into metals adds electrical conductivity, which is essential for reading and writing signals quickly, and adds magnetism, which is the currency of spintronics. A material in which twist angle sets the strength of electric whirlpools that in turn compete with magnetization suggests devices in which geometry alone programs coupled electric and magnetic states, without external fields. Much work remains, from clarifying the dynamics of the polar-magnetic competition to integrating twisted oxide membranes onto device platforms, but the demonstration that a simple rotation of two metallic films can conjure ordered polarization vortices marks a genuine expansion of the twistronics frontier, from electronic bands to the very dipoles inside a magnet.

Subject of Research: Flexoelectric polarization vortices induced by twistronics in ferromagnetic metallic SrRuO3 bilayers

Article Title: Polarization vortices in a ferromagnetic metal via twistronics

Article References: Lun, Y., Hu, X., Ren, Q., Saeed, U., Gupta, K., Mundet, B., Pinto-Huguet, I., Santiso, J., Padilla-Pantoja, J., Caicedo Roque, J. M., Eriksen, M. B., Merino, G., Ma, Y., Li, Q., Zhu, B., Tang, G., Pesquera, D., Wang, X., Hong, J., … Catalan, G. (2026). Polarization vortices in a ferromagnetic metal via twistronics. Nature Materials. https://doi.org/10.1038/s41563-026-02755-8

Image Credits: AI Generated

DOI: 10.1038/s41563-026-02755-8

Keywords: twistronics, polarization vortices, flexoelectricity, SrRuO3, ferromagnetic metal, polar metal, moiré superlattice, multiferroics, oxide membranes, electron ptychography, topological polarization, strain gradients