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. Rosenbauma1,2
- 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
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Edited by David D. Awschalom, The University of Chicago, Chicago, IL, and approved August 28, 2014 (received for review July 14, 2014)
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Fig. 1.Crystallographic structure of SrCu2(BO3)2 (SCBO). (Upper) Low-temperature structure of SCBO projected into the a–b plane. (Lower) a–c plane. Solid, dashed, and dotted blue lines show the interactions between the dimerized Cu2+ ions, representing the intradimer (J = 84 K), in-plane interdimer (J' = 54 K), and out-of-plane interdimer (J′′ = 8 K) (6) interactions, respectively. This hierarchy of direct exchange interactions underlies the effectively 2D nature of the system in the absence of global magnetic order.
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Fig. 2.Signature of the antiferromagnetic ordered phase in SCBO. Single-crystal neutron diffraction intensities of SCBO at T = 90 K (blue) and T = 290 K (red) at P ∼ 5.5 GPa vs. reciprocal lattice units (r.l.u). A high-temperature (T = 290 K) background has been subtracted from these data sets. Solid lines are Voigt fits to the data. (Left) Structural Bragg peak at Q = (0 4 0). The intensity stays constant with changing temperature. The height of the peak is normalized to unity. (Right) Emergence of the magnetic Bragg peak at the structurally forbidden reflection (0 3 0) at lower temperature. The intensity of the (0 3 0) peak is normalized to the intensity of the (0 4 0) structural Bragg peak.
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Fig. 3.Symmetry reduction with decreasing temperature at high pressure in SCBO. (A) Powder neutron diffraction intensity vs. lattice spacing for SCBO at T = 90 K (blue) and 120 K (red) at P = 5.5 GPa. A forbidden peak emerges at the lower T. Data at T = 120, 160, and 180 K all behave similarly. (B) Simulation of neutron powder diffraction cross-section for antiferromagnetic SCBO (black) in its high-pressure, low-temperature phase compared with actual data collected at T = 90 K and P = 5.5 GPa (blue). Scattering from the pressure cell gasket occurs at d ∼ 2.7 Å. (C) SCBO lattice parameters as a function of temperature extracted from powder neutron diffraction data collected at P = 5.5 GPa. Data at temperatures below T = 120 K are refined using a P121 symmetry; data collected for T > 120 K are refined using a C121 model.
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Fig. 4.Onset of antiferromagnetic order. Temperature dependence of the integrated intensity of X-ray single-crystal diffraction data (black solid squares) times 100 and of neutron powder diffraction data (open blue triangles) for (0 3 0) reflection at P = 5.5 GPa. The integrated intensity of the (0 3 0) peak in antiferromagnetic SCBO was calculated from a simulation of structural and magnetic neutron cross-sections (red dashed line). All integrated intensities at (0 3 0) are normalized to the integrated intensities of their corresponding (2 0 0) reflection. (Inset) Single-crystal X-ray diffraction data collected at the emergence of the forbidden (0 3 0) reflection. The solid line is a power-law fit to I = Io [(Tc − T)/Tc]2β, with Tc = 122 ± 0.2 K and a critical exponent, β = 0.36 ± 0.04, associated with a 3D universality class.
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Fig. 5.Schematic of local dimer rearrangements at the onset of global order. (A) Magnetic structure of SCBO based on the Shastry–Sutherland model’s prediction of an antiferromagnetic ground state. The solid lines show the intradimer Cu2+ (S = 1/2) interactions (J) and the dashed lines represent the interdimer Cu2+ (S = 1/2) interactions (J'). (B) Proposed magnetic structure of SCBO extracted from neutron powder diffraction data collected at P = 5.5 GPa and temperatures below T ∼ 120 K. The dashed lines show the in-plane dimer–dimer (S = 1) interactions (JAF) and the interplane dimer–dimer (S = 1) interactions (J'AF). The no longer equivalent red and blue Cu–Cu dimers are elongated and compressed, respectively, and tilt out of the a–b plane.
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Fig. 6.Schematic view of magnetic planes of SCBO in the unit cell. A and B show the schematic views of the projections of the spin orientations of Cu2+ ions of SCBO along the (A) a–b and (B) a–c crystallographic planes according to the 2D antiferromagnetically ordered Shastry–Sutherland model. (C and D) Schematic views of the projections of the spin orientations of Cu2+ ions of SCBO along the (C) a–b and (D) a–c crystallographic planes according to the modified model described in the text. The effects of the anisotropic DM interaction in the 3D long-range ordered phase results in the slight divergence of the projections of the spin orientations from exactly parallel–perpendicular to the dimer axes alignments. B and D show that in the proposed 3D compared with the pure Shastry–Sutherland 2D ordering, the dimers are tilted with respect to the a–b plane and their bonds are expanded (red) and contracted (blue).
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Fig. 7.Dimensional cross-over reflected in changed angle and length of dimers. The temperature dependence of Cu–Cu bond lengths and tilt angles with respect to the a–b plane derived from neutron powder diffraction at high pressure. A symmetry change from C121 to P121 occurs at Tc = 122 K. (A) The relative ratio of the bond lengths of the red to the blue Cu–Cu dimers of Fig. 5B (solid squares) diverges from 1 for T < Tc, where all Cu–Cu dimers are no longer equivalent. (B) Tilting of the red and blue dimers out of the a–b plane below Tc.
