Emergence of long-range order in sheets of magnetic dimers

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 dimensio...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2014-10, Vol.111 (40), p.14372-14377
Main Authors: Haravifard, S., Banerjee, A., van Wezel, J., Silevitch, D. M., dos Santos, A. M., Lang, J. C., Kermarrec, E., Srajer, G., Gaulin, B. D., Molaison, J. J., Dabkowska, H. A., Rosenbaum, T. F.
Format: Article
Language:English
Subjects:
Anisotropy
Chemistry
condensed matter physics
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Crystal lattices
Diffraction
dimensional cross-over
Dimers
Geometric planes
Ground state
High pressure
Magnetism
neutron and X-ray scattering
Neutron diffraction
Neutron scattering
Neutrons
phase transition
Physical Sciences
quantum magnetism
Quantum theory
Two dimensional modeling
Wave diffraction
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Summary: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 Cu ²⁺ spin 1/2 dimers from local singlets to global antiferromagnet in the model system SrCu ₂(BO ₃) 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. 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.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1413318111