Emergence of long-range order in sheets of magnetic dimers

Edited by David D. Awschalom, The University of Chicago, Chicago, IL, and approved August 28, 2014 (received for review July 14, 2014)
September 22, 2014
111 (40) 14372-14377
Letter
Reply to Zayed: Interplay of magnetism and structure in the Shastry–Sutherland model
S. Haravifard, A. Banerjee [...] T. F. Rosenbaum

Significance

Magnetic materials are composed of individual spins that interact with each other and under suitable conditions can arrange themselves in an ordered array. When spins are confined to two-dimensional sheets, small perturbations can disrupt their order and destroy the magnetic state. We show how a set of interacting, quantum-mechanical spins placed on the corners of a square array evolves from a set of locally bonded entities to a globally ordered structure. The system stabilizes itself against fluctuations through subtle local contractions, elongations, and tilts. The combination of neutron and X-ray scattering at pressures up to 60,000 atmospheres reveals the complex interplay of structural distortions and spin alignments that permit long-range order to emerge in this model quantum magnet.

Abstract

Quantum spins placed on the corners of a square lattice can dimerize and form singlets, which then can be transformed into a magnetic state as the interactions between dimers increase beyond threshold. This is a strictly 2D transition in theory, but real-world materials often need the third dimension to stabilize long-range order. We use high pressures to convert sheets of Cu2+ spin 1/2 dimers from local singlets to global antiferromagnet in the model system SrCu2(BO3)2. Single-crystal neutron diffraction measurements at pressures above 5 GPa provide a direct signature of the antiferromagnetic ordered state, whereas high-resolution neutron powder and X-ray diffraction at commensurate pressures reveal a tilting of the Cu spins out of the plane with a critical exponent characteristic of 3D transitions. The addition of anisotropic, interplane, spin–orbit terms in the venerable Shastry–Sutherland Hamiltonian accounts for the influence of the third dimension.

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Acknowledgments

We are grateful to B. H. Toby for assistance in data refinement using the General Structure Analysis System (GSAS) and to A. Dabkowski for help in preparing the single-crystal sample for high-pressure neutron scattering experiment. The work at the University of Chicago was supported by National Science Foundation Grant DMR-1206519. The work performed at the Advanced Photon Source was supported by the US Department of Energy (DOE) Office of Basic Energy Sciences under Contract DE-AC02-06CH11357 and that at the Spallation Neutron Source by the DOE Office of Basic Energy Sciences.

Supporting Information

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Information & Authors

Information

Published in

Go to Proceedings of the National Academy of Sciences
Go to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
Vol. 111 | No. 40
October 7, 2014
PubMed: 25246541

Classifications

Submission history

Published online: September 22, 2014
Published in issue: October 7, 2014

Keywords

  1. condensed matter physics
  2. quantum magnetism
  3. phase transition
  4. dimensional cross-over
  5. neutron and X-ray scattering

Acknowledgments

We are grateful to B. H. Toby for assistance in data refinement using the General Structure Analysis System (GSAS) and to A. Dabkowski for help in preparing the single-crystal sample for high-pressure neutron scattering experiment. The work at the University of Chicago was supported by National Science Foundation Grant DMR-1206519. The work performed at the Advanced Photon Source was supported by the US Department of Energy (DOE) Office of Basic Energy Sciences under Contract DE-AC02-06CH11357 and that at the Spallation Neutron Source by the DOE Office of Basic Energy Sciences.

Notes

This article is a PNAS Direct Submission.

Authors

Affiliations

S. Haravifard
The James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637;
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439;
A. Banerjee
The James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637;
Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, TN 37831;
J. van Wezel
School of Physics, The University of Bristol, Bristol BS8 1TL, United Kingdom; and
D. M. Silevitch
The James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637;
A. M. dos Santos
Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, TN 37831;
J. C. Lang
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439;
E. Kermarrec
Department of Physics and Astronomy and Brockhouse Institute for Material Research, McMaster University, Hamilton, ON, Canada L8S 4M1
G. Srajer
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439;
B. D. Gaulin
Department of Physics and Astronomy and Brockhouse Institute for Material Research, McMaster University, Hamilton, ON, Canada L8S 4M1
J. J. Molaison
Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, TN 37831;
H. A. Dabkowska
Department of Physics and Astronomy and Brockhouse Institute for Material Research, McMaster University, Hamilton, ON, Canada L8S 4M1
T. F. Rosenbaum2 [email protected]
The James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637;
Present address: Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125.

Notes

2
To whom correspondence should be addressed. Email: [email protected].
Author contributions: S.H. and T.F.R. designed research; S.H., A.B., A.M.d.S., J.C.L., E.K., G.S., B.D.G., and J.J.M. performed research; S.H., B.D.G., and H.A.D. contributed new reagents/analytic tools; S.H., J.v.W., D.M.S., and T.F.R. analyzed data; and S.H., J.v.W., D.M.S., and T.F.R. wrote the paper.

Competing Interests

The authors declare no conflict of interest.

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    Emergence of long-range order in sheets of magnetic dimers
    Proceedings of the National Academy of Sciences
    • Vol. 111
    • No. 40
    • pp. 14309-14636

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