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# Tuning spin excitations in magnetic films by confinement

## Abstract

Spin excitations of magnetic thin films are the founding element for magnetic devices in general. While spin dynamics have been extensively studied in bulk materials, the behaviour in mesoscopic films is less known due to experimental limitations. Here, we employ resonant inelastic X-ray scattering to investigate the spectrum of spin excitations in mesoscopic Fe films, from bulk-like films down to three unit cells. In bulk samples, we find isotropic, dispersive ferromagnons consistent with previous neutron scattering results for bulk single crystals. As the thickness is reduced, these ferromagnetic spin excitations renormalize to lower energies along the out-of-plane direction while retaining their dispersion in the in-plane direction. This thickness dependence is captured by simple Heisenberg model calculations accounting for the confinement in the out-of-plane direction through the loss of Fe bonds. Our findings highlight the effects of mesoscopic scaling on spin dynamics and identify thickness as a knob for fine tuning and controlling magnetic properties.

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## Data availability

Data that support the findings of this study are available upon reasonable request from the corresponding authors.

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## Acknowledgements

We are indebted to J. Hill, C. Mazzoli, J. Tranquada, T. Ziman, M. Stiles, P. Bruno, M. Hybertsen and E. Vescovo for fruitful discussions. J.P. thanks A. Pelliciari for his lifelong support. This work was supported by the US Department of Energy (DOE) Office of Science, Early Career Research Program. Work at Yale University was supported by the US DOE, Office of Science, Office of Basic Energy Sciences under award no. DE-SC0019211. K.G. was supported by the US DOE, Office of Science, Basic Energy Sciences as part of the Computational Materials Science Program. This research used beamline 2-ID of NSLS-II, a US DOE Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under contract no. DE-SC0012704. Surface X-ray diffraction measurements were performed at beamline 33-ID-D of the Advanced Photon Source, a US DOE Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357.

## Author information

Authors

### Contributions

V.B. conceived the project. J.P., S.L., J.L., Y.G., A.B., I.J. and V.B. performed the RIXS experiments. S.L., C.H.A. and F.J.W. prepared the Fe/MgO thin films and characterized them using SQUID and X-ray reflectometry. V.B. analysed and interpreted the data, with the help of J.P.; K.G. performed the theory calculations. J.P. and V.B. wrote the manuscript with input from all the authors.

### Corresponding authors

Correspondence to Jonathan Pelliciari or Valentina Bisogni.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Materials thanks Eiji Saitoh and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–11, Tables 1–2 and Notes 1–4.

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Pelliciari, J., Lee, S., Gilmore, K. et al. Tuning spin excitations in magnetic films by confinement. Nat. Mater. 20, 188–193 (2021). https://doi.org/10.1038/s41563-020-00878-0

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