Emergence of long-range order in sheets of magnetic dimers
- S. Haravifarda,b,
- A. Banerjeea,c,
- J. van Wezeld,
- D. M. Silevitcha,
- A. M. dos Santosc,
- J. C. Langb,
- E. Kermarrece,
- G. Srajerb,
- B. D. Gauline,
- J. J. Molaisonc,
- H. A. Dabkowskae, and
- T. F. Rosenbauma,1,2
- aThe James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637;
- bAdvanced Photon Source, Argonne National Laboratory, Argonne, IL 60439;
- cNeutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, TN 37831;
- dSchool of Physics, The University of Bristol, Bristol BS8 1TL, United Kingdom; and
- eDepartment of Physics and Astronomy and Brockhouse Institute for Material Research, McMaster University, Hamilton, ON, Canada L8S 4M1
-
Edited by David D. Awschalom, The University of Chicago, Chicago, IL, and approved August 28, 2014 (received for review July 14, 2014)
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.
- condensed matter physics
- quantum magnetism
- phase transition
- dimensional cross-over
- neutron and X-ray scattering
Footnotes
-
↵1Present address: Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125.
- ↵2To whom correspondence should be addressed. Email: tfr{at}caltech.edu.
-
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.
-
The authors declare no conflict of interest.
-
This article is a PNAS Direct Submission.
-
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1413318111/-/DCSupplemental.
