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Stanford Report, March 6, 2002

'Quantum magnets' help scientists understand physical limits of matter

Physicists create unusual insulator that 'eludes physical description,' serves as model magnet for experiments


In superconductors, electrons zip around with virtually no resistance or energy loss. In insulators, however, they barely move, lacking the energy to overcome high resistance. Strangely, scientists can turn certain unusual insulators into high-temperature superconductors by adding the right impurities. Conventional theories predict that these insulators should actually be ordinary conductors. Researchers are still working to understand the exotic magnetic properties of these materials, which are strongly influenced by their quantum nature.

"These materials have extremely exotic properties that really have eluded physical description," says Martin Greven, an assistant professor in Stanford's Department of Applied Physics and at the Stanford Synchrotron Radiation Laboratory. "We are interested in arriving at a quantitative understanding of their magnetic properties."

With Stanford graduate students Owen Vajk and Patrick Mang and physicists Peter Gehring and Jeffrey Lynn at the National Institute of Standards and Technology (NIST), Greven has been trying to understand the complex magnetic behavior of the insulators as magnetic atoms are randomly replaced with nonmagnetic impurity atoms. Instead of yielding a superconductor, the introduction of nonmagnetic impurities creates a novel model magnet.

From left, physicists Owen Vajk, Martin Greven and Patrick Mang display exotic crystals they've made in the Geballe Laboratory for Advanced Materials on campus. Layered in the crystals are 'quantum magnets.' Photo: L.A. Cicero

The scientists used a powerful technique called neutron scattering to take "snapshots" of the magnetic behavior within crystals of the insulator. In the March 1 issue of the journal Science, they report that they have been able to reach the point at which the random impurities disrupt the long-range magnetic order of the crystals. While tomorrow's quantum magnets may find applications in technology, today's materials provide models with which scientists can test theoretical predictions, as well as the physical limits of matter.

The art of growing exotic crystals

Making materials to study quantum magnetism is no easy task. It takes manual dexterity and long hours to monitor the crystal growth. While the United States lags behind Japan in this field, Greven's group has built a world-class crystal growth facility with funding provided by the U.S. Department of Energy, the National Science Foundation and the Alfred P. Sloan Foundation. Says Greven: "Clearly, if the students can grow their own samples, then they can go on and do their own science. If you have to ask others, perhaps far away, for samples, they may or may not be able to give them to you. They may have different interests. So growing your own crystals helps you define your own research. It helps you to be at the forefront of new discoveries."

Vajk, a fifth-year graduate student, led the crystal-growing effort at Stanford's new Geballe Laboratory for Advanced Materials. With help from Mang, a fourth-year graduate student, he was the first to succeed at something other researchers have been attempting for more than a decade. Starting with the building blocks of a classic high-temperature superconductor -- lanthanum copper oxide -- he added zinc and magnesium and melted the material in a special furnace using focused, high-powered light. "If you don't get it right, then the crystal isn't stable," Vajk says, "and you end up with a crystal that will disintegrate."

It took more than a week to grow each of the 2-inch crystals used in their experiments. The crystals are formed from alternating magnetic copper-oxide and nonmagnetic lanthanum-oxide layers, making the individual magnetic layers act as model two-dimensional systems. The nonmagnetic zinc and magnesium atoms are randomly interspersed in the magnetic layers, replacing magnetic copper atoms.

Electrons in atoms have electronic properties as a consequence of their charge, and magnetic properties as a consequence of their orientation, or "spin." In a magnetic sheet of copper and oxygen atoms, the electron spins tend to alternate between "up" and "down" in a pattern like the black and red squares on a checkerboard. Matter in such a configuration is referred to as an antiferromagnet. This arrangement of billions of atoms on the checkerboard, or two-dimensional lattice, does not simply result from the individual copper atoms themselves, but from the interaction of neighboring electron spins with each other. Quantum mechanical effects play a much stronger role in antiferromagnets than in ferromagnets, such as refrigerator magnets, where spins tend to align parallel to each other.

Neutron scattering detects quantum fluctuations

After the crystals were grown, the researchers took them to Maryland for analysis. At the NIST Center for Neutron Research, the physicists probed the magnetic structure of the crystals with a technique -- neutron scattering -- that is not available on the West Coast. "The neutron beams we use are produced in a research nuclear reactor," explains Vajk. "Electric charge doesn't matter to neutrons, but neutrons interact with the magnetic moments of electrons. So neutrons can 'see' magnetic structure and magnetic fluctuations."

Says Greven: "What we have been measuring with this technique is a snapshot of the spins on these checkerboards." NIST physicist Lynn adds, "We could not have attacked this problem without neutrons." The important role of neutron scattering in modern research was recognized with the 1994 Nobel Prize in physics, which was awarded to Clifford G. Shull and Bertram N. Brockhouse for their pioneering work in developing this technique.

The distance over which magnetic spins "talk" to each other depends on the temperature, Greven says. "At room temperature, in the crystals we were looking at, they don't talk over a distance larger than four or five neighbors. But when you cool these crystals, the distance over which the magnetic moments can exchange information -- talk to each other -- increases in a nontrivial fashion due to both their quantum nature as well as the presence of the impurities, and eventually exceeds hundreds of neighbors."

The NIST measurements also enabled the physicists to track the low-temperature long-range magnetic order as magnetic atoms were replaced with nonmagnetic ones. They found that quantum fluctuations lead to an erosion of magnetic order with increased dilution, and that when approximately 40 percent of the magnetic atoms were replaced with nonmagnetic atoms, the spins of neighboring atoms were no longer connected, or ordered, throughout the system.

Back at Stanford, Vajk uses computer simulations to perform so-called "Monte Carlo" calculations of these randomly diluted quantum magnets. This technique lets him simulate properties of a two-dimensional model without having to solve the problem exactly, and compare the results to the experimental data. The numerical results confirm the scientists' understanding of the properties of these crystals. The combined experimental and numerical data should help guide physicists in developing a theoretical description of these quantum magnets.

"Once we truly understand these and related materials and their magnetic properties as a function of impurity content, we can hope to design better materials in the lab that then have better properties from a technological point of view," says Greven.

Each two-inch crystal takes more than a week to grow. To study quantum magnetism, scientists replace magnetic with nonmagnetic atoms. Photo: L.A. Cicero