# Three-dimensionality of field-induced magnetism in a high-temperature superconductor

## Abstract

Many physical properties of high-temperature superconductors are two-dimensional phenomena derived from their square-planar CuO2 building blocks. This is especially true of the magnetism from the copper ions. As mobile charge carriers enter the CuO2 layers, the antiferromagnetism of the parent insulators, where each copper spin is antiparallel to its nearest neighbours1, evolves into a fluctuating state where the spins show tendencies towards magnetic order of a longer periodicity. For certain charge-carrier densities, quantum fluctuations are sufficiently suppressed to yield static long-period order2,3,4,5,6, and external magnetic fields also induce such order7,8,9,10,11,12. Here we show that, in contrast to the chemically controlled order in superconducting samples, the field-induced order in these same samples is actually three-dimensional, implying significant magnetic linkage between the CuO2 planes. The results are important because they show that there are three-dimensional magnetic couplings that survive into the superconducting state, and coexist with the crucial inter-layer couplings responsible for three-dimensional superconductivity. Both types of coupling will straighten the vortex lines, implying that we have finally established a direct link between technical superconductivity, which requires zero electrical resistance in an applied magnetic field and depends on vortex dynamics, and the underlying antiferromagnetism of the cuprates.

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## Acknowledgements

We thank N. H. Andersen, B. M. Andersen, A. B. Abrahamsen and S. Kivelson for discussions. Experiments at the Berlin Neutron Scattering Centre were made possible by the support of the European Community—Access to Research Infrastructure action of the Improving Human Potential Programme. Work in London was supported by Royal Society Wolfson Merit Awards.

## Author information

Correspondence to B. Lake.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary Information

Supplementary material and supplementary figures 1-7 (PDF 283 kb)

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Reprints and Permissions

Lake, B., Lefmann, K., Christensen, N. et al. Three-dimensionality of field-induced magnetism in a high-temperature superconductor. Nature Mater 4, 658–662 (2005) doi:10.1038/nmat1452

• #### DOI

https://doi.org/10.1038/nmat1452

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