Pressure-Tuning the Quantum Phase Transition in a Model 2-D Magnet

APRIL 11, 2012

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Argonne and University of Chicago physicist Sara Haravifard with the instrument on XSD beamline 6-ID-B at the APS used for the high-resolution, high-pressure structural measurements of SCBO at cryogenic temperatures.

The fundamental interactions that determine how spins arrange themselves in a material play a critical role in a wide variety of physical phenomena that have wide-ranging real and potential technological applications, such as magnetism, electronic ordering, and superconductivity. Researchers utilizing the U.S. Department of Energy Office of Science’s Advanced Photon Source at Argonne National Laboratory have recently used high-resolution x-ray scattering to demonstrate how pressure can be used to dial-in different magnetic states in a two-dimensional magnetic material. This research offers new insights into the behavior of quantum magnets with competing low-temperature ground states, a possible path to undiscovered exotic materials with a range of controllable properties.

One of the first basic problems encountered in elementary quantum mechanics involves the description (energy and momentum states) of a system containing two identical particles. When these particles possess a magnetic moment or “spin,” the relative orientation of these spins can determine the energetics of the system. A “singlet” quantum mechanical state describes the system when the particle’s spins are anti-aligned yielding a total spin of zero, while the “triplet” state encompasses the three spin combinations which produce a nonzero net spin. The helium atom, which involves two identical electrons with spin ½, orbiting a nucleus, is a classic example of such a system, where such spin-coupled states can be used to explain the fine structure of the electronic energy levels.

Similar systems involving identical spin ½ particles can also be found in certain solid materials, where their collective interactions can lead to a variety of exotic and useful phenomena such as spin liquid behavior, electronic ordering, and superconductivity. Compounds where such particles are confined on one-dimensional chains or two-dimensional (2-D) sheets within a crystalline lattice are particularly intriguing because they are simple enough to be exactly soluble, yet sufficiently rich to capture a wealth of physics that can be extended to understand more complicated systems. A prototypical example of a 2-D spin material is the copper compound SrCu2(BO3)2 (SCBO), where spin ½ Cu2+ions couple with each other within an atomic plane but have only weak interactions between adjacent planes. At low enough temperatures, the Cu ions form “dimers,” coupled pairs of atoms in singlet or triplet states, which are arranged on square lattice with adjacent dimers rotated by 90˚. The behavior of such a system can be described using the Shastry-Sutherland model, where the magnetic ordering and excitations are determined by the relative strength of the magnetic interactions within (J) and between (J’) the dimers (Here J is the “magnetic coupling constant”, which describes how tightly the spins are bound to each other). In SBCO, the ratio of these intra-dimer to inter-dimer interactions (J/J’) is believed to be just below a critical value between two magnetic states. So the application of pressure (chemical or hydrostatic) is expected to transform SCBO into new, magnetically ordered states. At low temperatures these changes in state are referred to as “quantum phase transitions” since they are driven by quantum rather than thermal fluctuations.

Recently, a research team from The University of Chicago, Argonne National Laboratory, and McMaster University used high-pressure, single-crystal synchrotron x-ray scattering on X-ray Science Division beamlines 4-ID-D and 6-ID-B at the Advanced Photon Source to probe the low-temperature magnetic states in SCBO. They found that the magnetic state of the material could be determined by precise measurements of the crystal lattice parameters as SBCO was driven through the quantum phase transition. Prior experiments probing the quantum phase transition in SCBO had used chemical doping to drive the change in state. Chemical doping, however, necessarily introduces a significant degree of disorder into the system, disturbing the formation of long-range order and possibly altering the quantum critical response. The application of hydrostatic-pressure in this study provided a clean mechanism to change the exchange-coupling ratio (J/J’) by varying the atomic bond lengths without the introduction of additional disorder. X-ray studies provide one of the few methods for understanding the high-pressure magnetic states in a material because applying pressure at cryogenic temperatures requires a source of extreme pressure such as a diamond anvil cell (DAC), which limits the sample size to dimensions that will fit in the DAC, on the order of 100 µm. These conditions make magnetization measurements and neutron scattering studies that directly probe the magnetism difficult if not impossible. Using a DAC cooled down to cryogenic temperatures, the research team was able to track the suppression of the singlet-triplet energy gap at a second-order quantum phase transition at P~2 gigapascals (GPa), followed at higher pressure (~4.5 GPa) by a first-order structural/magnetic transition into an antiferromagnetic state.

The results of this study were published in the February 14, 2012, issue of the Proceedings of the National Academy of Science of the United States of America. The study’s lead author, Argonne and University of Chicago physicist Sara Haravifard explained that the research experimentally proved a result that had heretofore only been expected theoretically. "It’s important for us to understand how spins interact with each other so we can get a picture of the behavior of more complicated systems," she said. In the long term, this research on spin-states in SBCO could bridge the gap to new classes of exotic materials with a range of tunable, or controllable, properties. Similar behaviors have been shown in high-temperature superconductors, and the manipulations performed in the new study "supplement our strong theoretical understanding of these materials," Haravifard said.

See: S. Haravifard1,2, A. Banerjee2, J. C. Lang1, G. Srajer1, D. M. Silevitch2, B. D. Gaulin3,4, H. A. Dabkowska3, and T. F. Rosenbaum2*, “Continuous and discontinuous quantum phase transitions in a model two-dimensional magnet,” Proc. Natl. Acad. Sci. USA 109 (7), 2286-2289 (2012). DOI:10.1073/pnas.1114464109

Author affiliations: 1Argonne National Laboratory, 2The University of Chicago, 3McMaster University, 4Canadian Institute for Advanced Research

Correspondence: * E-mail:

The work at the University of Chicago was supported by National Science Foundation Grant DMR-0907025. D.M.S. acknowledges support from the U.S. Department of Energy (DOE) Office of Science Grant DEFG02-99ER45789. e of the Advanced Photon Source at Argonne National Laboratory was supported by the U.S. Department of Energy Office (DOE) of Science under Contract No. DE-AC02-06CH11357.

An Argonne press release on this work can be found here.

Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U.S. Department of Energy Office of Science under Contract No. DE-AC02-06CH11357.

The Advanced Photon Source at Argonne National Laboratory is one of five national synchrotron radiation light sources supported by the U.S. Department of Energy’s Office of Science to carry out applied and basic research to understand, predict, and ultimately control matter and energy at the electronic, atomic, and molecular levels, provide the foundations for new energy technologies, and support DOE missions in energy, environment, and national security. To learn more about the Office of Science x-ray user facilities, visit

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