# Complex magnetic order in nickelate slabs

## Abstract

Magnetic ordering phenomena have a profound influence on the macroscopic properties of correlated-electron materials, but their realistic prediction remains a formidable challenge. An archetypical example is the ternary nickel oxide system RNiO3 (R = rare earth), where the period-four magnetic order with proposals of collinear and non-collinear structures and the amplitude of magnetic moments on different Ni sublattices have been subjects of debate for decades1,2,3,4,5,6. Here we introduce an elementary model system—NdNiO3 slabs embedded in a non-magnetic NdGaO3 matrix—and use polarized resonant X-ray scattering (RXS) to show that both collinear and non-collinear magnetic structures can be realized, depending on the slab thickness. The crossover between both spin structures is correctly predicted by density functional theory and can be qualitatively understood in a low-energy spin model. We further demonstrate that the amplitude ratio of magnetic moments in neighbouring NiO6 octahedra can be accurately determined by RXS in combination with a correlated double cluster model. Targeted synthesis of model systems with controlled thickness and synergistic application of polarized RXS and ab initio theory thus provide new perspectives for research on complex magnetism, in analogy to two-dimensional materials created by exfoliation7.

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## Acknowledgements

We thank G. Khaliullin, I. Elfimov, Y. Lu, C. Dietl, F. Wrobel, H.-U. Habermeier and P. Wochner for fruitful discussions. Financial support from the DFG under grant no. SFB/TRR80 G1 and from the European Union Seventh Framework Program [FP/2007–2013] under grant agreement no. 312483 (ESTEEM2) is acknowledged. Part of this work has been funded by the Max Planck-UBC Centre for Quantum Materials. Further, this work was supported by the Swiss National Science Foundation through Division II. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Program (FP7/2007–2013)/ERC grant agreement no. 319286 (Q-MAC). The Canadian Light Source (CLS) is funded by the Canada Foundation for Innovation, NSERC, the National Research Council of Canada, the Canadian Institutes of Health Research, the Government of Saskatchewan, Western Economic Diversification Canada, and the University of Saskatchewan.

## Author information

M.H., R.J.G. and E.B. conceived the project, performed the experiments, and analysed the data together with M.L.T., G.A.S. and B.K. Assistance in the experiments and contributions to the data analysis were made by M.B., S.M. and A.F. STEM investigations were performed by Y.E.S. under the supervision of Y.W. and P.A.v.A. The DFT + U calculations were carried out by Z.Z. and P.H. The RXS experiments were supported by R.S. and F.H. The PLD samples were grown by G.C. and G.L. The sputtered sample was grown and characterized by S.C. under the supervision of M.G. and J-M.T. M.H., B.K. and E.B. wrote the manuscript with contributions from all authors.

Correspondence to E. Benckiser.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary Figures 6–12, Supplementary Tables 1–4, Supplementary References 1–15

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• #### DOI

https://doi.org/10.1038/s41567-018-0218-5

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