Long-Range Magnetic Order in Structurally Embedded Mesospin Metamaterials

TL;DR

The study tackles the difficulty of achieving intrinsic long-range magnetic order in mesoscale metamaterials with minimal lithographic disorder. It introduces Fe$^{+}$-ion implantation into Pd to create embedded mesospins that spontaneously order into a Type-I antiferromagnetic ground state, as demonstrated by resonant X-ray scattering and real-space microscopy. The magnetic order is evidenced by sharp magnetic Bragg peaks and extended AFM domains, with the magnetic unit cell enlarged by $\sqrt{2} ext{ and rotated by }45^ ext{o}$ relative to the island lattice, indicating strong coherence across large areas. This scalable, structurally coherent architecture enables exploration of spin–photon coupling and functional X-ray scattering in metamaterials, with potential for graded 3D architectures and reconfigurable magnetic functionality beyond conventional lithographic approaches.

Abstract

Engineered assemblies of interacting magnetic elements-magnetic metamaterials-provide a powerful route to tailor collective magnetic order and dynamics. By structuring matter at the mesoscale, they bridge atomic magnetism and macroscopic functionality, enabling emergent behaviour inaccessible in conventional materials. However, realizing large-area metamaterials that combine high morphological uniformity with intrinsic long-range order has remained challenging, largely due to the structural disorder inherent to lithographic fabrication. Here we demonstrate a scalable route to structurally and magnetically coherent metamaterials by embedding iron-ions to form mesospins within a non-magnetic thin film palladium host matrix. Using controlled implantation, we realize morphologically uniform arrays that spontaneously develop extended antiferromagnetic order in the as-fabricated state - without the need of external annealing or field cycling. Resonant X-ray scattering and microscopy reveal sharp magnetic Bragg peaks modulated by the mesospin form factor, evidencing long-range antiferromagnetic order coupled to structural coherence. This embedded architecture establishes a platform for exploring coherent spin-photon interactions and functional X-ray scattering in magnetic metamaterials free from lithographic topography and disorder.

Figures (13)

• Figure 1: Implanted magnetic metamaterial. Scanning electron microscopy image of a square artificial spin ice patterned via ion implantation, illustrating the high uniformity of ion-implanted mesospins. The surface morphology of the array reflects the patterned implantation mask, and a slight surface swelling of the implanted regions is visible due to the local lattice expansion induced by Fe incorporation. The mesospins of Fe-implanted regions in a paramagnetic Pd matrix, have lateral dimensions of $L=$470nm, $W=$170nm and an edge-to-edge gap of $g=$170nm. Details of the sample fabrication are presented in Methods.
• Figure 2: Resonant X-ray reflectivity and magnetic moment profiles.a X-ray reflectivity curve. b Asymmetry obtained from the subtraction of XRR signals acquired with opposite in-plane magnetic fields with a beam energy of 707eV, sensitive to Fe. c Electron density (black line) and magnetic moment density (green line) extracted from simultaneously fitting the reflectivity and asymmetry data for different X-ray photon energies. The depth profiles originate at the MgO substrate ($z = 0$), followed by the V adhesion layer, Pd film, and Fe-implanted region. These layer positions are indicated in the panel for clarity.
• Figure 3: Real-space magnetic imaging and vertex populations.a Representative PEEM - XMCD image of the implanted square ASI lattice in the as-implanted state. The black and white colors indicate a magnetization component parallel and antiparallel to the X-ray beam, respectively. b Vertex types for the square ASI lattice. Type-I has the lowest energy state, followed by Type-II, III and IV. c Vertex population for the implanted square ASI lattice. A dominant Type-I configuration of the ASI lattice is observed, enabling the use of these samples as benchmarks in X-ray scattering studies.
• Figure 4: X-ray scattering from implanted ASIs.a Ewald construction illustrating the scattering geometry in the soft X-ray diffraction experiments on the implanted artificial spin ice lattices. The reciprocal lattice of the ASI gives rise to a series of intensity rods (schematically depicted as cones) extending along the out-of-plane direction. The intensity modulation along these rods encodes information about the vertical structure of the mesospins. The incident beam vector $\mathbf{k}_i$, reflected beam $\mathbf{k}_r$, and scattered beam $\mathbf{k}_f$ define the scattering geometry, with the end of $\mathbf{k}_f$ lying on the surface of the Ewald sphere. A constructive scattering condition is satisfied whenever the Ewald sphere intersects an intensity rod. The recorded diffraction intensities are determined not only by the structural contribution but also by the detector position (gray box), the form factor of the implanted mesospins, and the specific magnetization textures within the elements. b Side view ($yz$ plane) of the Ewald construction, showing the intersection of the Ewald sphere with the Bragg rods and the resulting mapping of diffraction peaks onto the detector plane.
• Figure 5: Off- and on-resonance scattering.a Diffraction pattern of the implanted ASI lattice, shown after corrections for the Ewald sphere curvature. Only charge scattering contributes at this energy, resulting in weak peak intensities and a narrow dynamic range due to the low electron density contrast between Fe-implanted regions and the Pd matrix. The characteristic “×”-shaped envelope reflects the structural form factor of the mesospin basis. The white shaded area corresponds to the beam stop covering the specular reflection. b The integrated intensity along $K$ as a function of $H$ for a region of interest centred on $K=3$ and marked with the red dash-dotted line in panel a. c Resonant enhancement increases the structural Bragg peak intensity and reveals additional reflections associated with long-range antiferromagnetic order. The clearer “×”-shaped modulation highlights the coherent mesospin basis form factor, while the emergence of mixed-parity peaks evidences the magnetic contribution to the scattering. d The integrated intensity as a function of $H$ for a region of interest centred on $K=3$ and marked with the red dash-dotted line in panel c. Gray-shaded areas denote the positions of the reflections arising due to the antiferromagnetic order on the ASI lattice (Fig. \ref{['PEEM-XMCD']}a).