# Moiré engineering of electronic phenomena in correlated oxides

## Abstract

Moiré engineering has recently emerged as an effective approach to control quantum phenomena in condensed matter systems1,2,3,4,5,6. In van der Waals heterostructures, moiré patterns can be formed by lattice misorientation between adjacent atomic layers, creating long-range electronic order. Moiré engineering has so far been executed solely in stacked van der Waals multilayers. Here we describe electronic moiré patterns in films of a prototypical magnetoresistive oxide, La0.67Sr0.33MnO3, epitaxially grown on LaAlO3 substrates. Using scanning probe nanoimaging, we observe microscopic moiré profiles attributed to the coexistence and interaction of two distinct incommensurate patterns of strain modulation within these films. The net effect is that both the electronic conductivity and ferromagnetism of La0.67Sr0.33MnO3 are modulated by periodic moiré textures extending over mesoscopic scales. Our work provides a potential route to achieving spatially patterned electronic textures on demand in strained epitaxial materials.

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## Data availability

The data represented in Figs. 1–4 are available as Source Data 14. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

Stony Brook University authors acknowledge support from the National Science Foundation under grant no. DMR-1904576. This work was partly supported by the RISE2 node of NASA’s Solar System Exploration Research Virtual Institute under NASA Cooperative Agreement 80NSSC19MO2015. USTC authors acknowledge support from the National Natural Science Foundation of China (grants nos 11974324, 11804326, U1832151, 11675179 and 51627901), the Strategic Priority Research Program of Chinese Academy of Sciences (grant no. XDC07010000), the National Key Research and Development Programme of China (grants nos 2017YFA0403600 and 2017YFA0402903), the Anhui Initiative in Quantum Information Technologies (grant no. AHY170000), Hefei Science Centre CAS (grant no. 2018HSC-UE014) and the Fundamental Research Funds for the Central Universities (grant no. WK2030040087). A.J.M. was supported by the Basic Energy Sciences programme of the Department of Energy under grant no. DE-SC 0012375. D.N.B. was supported by ARO under grant no. W911NF-17-1-0543. This work was partially carried out at the USTC Centre for Micro and Nanoscale Research and Fabrication.

## Author information

Authors

### Contributions

M.L., C.Z. and D.N.B. designed and supervised the work. X.C. and X.F. performed the s-SNOM measurements with assistance from Z.N., S.X., D.W. and H.Z.; L.L., N.Z. and H.X. fabricated the samples and performed the XRD, magnetic and transport characterizations; T.G. and Q.L. performed the MFM measurements; X.C., L.L., X.F., D.N.B., M.L. and C.Z. analysed the data and wrote the manuscript. A.S.M., A.J.M. and Z.L. contributed to data interpretation and presentation. All authors contributed to the scientific discussion and manuscript revisions.

### Corresponding authors

Correspondence to Lin Li or D. N. Basov or Mengkun Liu or Changgan Zeng.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Maria Calderon and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Structure characterizations of LSMO thin film grown on LAO substrate.

a, X-ray diffraction spectrum of a 20-nm-thick LSMO/LAO film. The LSMO thin films are clearly single-crystalline and coherently epitaxial on the LAO (001) substrates. The LSMO film’s out-of-plane lattice constant as determined by the XRD peak is c=3.90 Å, which slightly exceeds the bulk value of 3.87 Å. The out-of-plane expansion, or tensile strain, proceeds from the compressive in-plane strain from the LAO substrates (pseudo-cubic structure with a lattice constant of 3.79 Å). b, The rocking curve of the (002) reflection of LSMO thin film. The data can be well fitted with the sum of two Gaussian peaks, one (red) originates from LSMO film and the other (blue) is due to a contribution of the substrate. c, Atomically resolved cross-sectional TEM image of a 20-nm LSMO/LAO film, showing that the film has good epitaxial quality with a sharp interface structure. The interface between LSMO and LAO is indicated by white arrows. Inset: low magnification TEM image. d, Energy dispersive spectroscopy (EDS) elemental mapping images across the interface.

### Extended Data Fig. 2 Twin structures in LAO substrates.

a, Optical image of a LAO substrate with the surface partially covered by LSMO thin films. Twin structure fringes of the LAO substrate are visible across the LSMO film edge, lying parallel to the guiding black dashed line. b,c, AFM image and corresponding height profile of the twin structures in the LAO substrate.

### Extended Data Fig. 3 Rhombohedral domains in the LSMO films on LAO substrates.

Large-scale OC-SEM image of a LSMO thin film showing surface rhombohedral domains. The inset demonstrates that the direction of rhombohedral domains in LSMO is identical to that of the LAO twins, running along the LAO [100] direction.

### Extended Data Fig. 4 Miscut stripes (MS)-induced electronic pattern in LSMO.

a, AFM image of a LSMO/LAO sample showing surface steps due to miscuts on the LAO substrate. b, Corresponding near-field image obtained simultaneously with the AFM image in a, showing spatially alternating values of IR near-field signal. c, Line profiles along the dashed lines in a and b show that near-field signal is positively correlated to the topography of miscut steps.

### Extended Data Fig. 5 Variation of electronic moiré patterns across the LSMO film.

a, Optical image of a LSMO thin film on LAO substrate. b, The concurrent variations of periodicity d and angle θ for moiré patterns obtained from different regions (numbered and marked in a by red circles). c, IR near-field images taken from different regions (1 to 12) marked in a.

### Extended Data Fig. 6 Simulation of moiré pattern.

The moiré pattern can be simulated by multiplying two periodic striped patterns representing DS and MS and then imposing a Gaussian average filter with radius ~100 nm. The simulation details are described in Supplementary Note 4.

### Extended Data Fig. 7 A display of near-field images of a variety of moiré patterns.

Different manifestations of moiré patterns observed across the film with vastly distinctive periodicities.

### Extended Data Fig. 8 Simulations of the curved moiré patterns.

ac, Typical manifestations of curved moiré patterns (right panel) and how they are simulated (left panel). White dashed lines indicate the directions of MS and DS. Curved MS was achieved via adding a spatially varying phase ϕ(y) into εMS (the MS-induced strain field) during the simulation (see Supplementary Note 4 and 5). Red dashed lines indicate the LAO twin boundaries.

### Extended Data Fig. 9 Diversity of miscut steps in the LAO substrates.

AFM image of a LAO substrate revealing that the miscut steps change their orientations (traced by the white dashed lines) and periodicities across the twin boundary of LAO (indicated by the red dashed line). This is common in commercially available LAO substrates.

### Extended Data Fig. 10 Evidence of the fine structures.

a, Near-field image taken across the LAO twin boundary (indicated by the red dashed line). On the non-moiré region (left), DS-induced electronic pattern can be faintly identified in the nano-IR contrast. b, Line profile of the white dashed line in a. The period is ~540 nm, consistent with the OC-SEM image of DS. c, Near-field image taken on the moiré region in a and filtered with a Fourier filter for $${\mathrm{k}} < \frac{1}{{250{\mathrm{nm}}}}$$.Fine structures of the electronic pattern corresponding to MS (or DS) can be observed. d, Line profile across the fine structure. The period is ~610 nm, qualitatively consistent with the typical MS (or DS) periodicity.

## Supplementary information

### Supplementary Information

Supplementary Notes 1–6.

## Source data

### Source Data Fig. 1

Source data for Fig. 1.

### Source Data Fig. 2

Source data for Fig. 2.

### Source Data Fig. 3

Source data for Fig. 3.

### Source Data Fig. 4

Source data for Fig. 4.

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