SANTA CRUZ, CA--Predicting the magnetic behavior of metallic compoundsis a surprisingly difficult problem for theoretical physicists. Whilethe properties of a common refrigerator magnet are not a great mystery,certain materials exhibit magnetic properties that do not fit withinexisting theories of magnetism. One such material inspired a recenttheoretical breakthrough by physicists at the University of California,Santa Cruz.
In a paper scheduled for publication in the August 26 issue of thejournal Physical Review Letters, Sriram Shastry, a professor of physicsat UCSC, and graduate student Jan Haerter describe "kineticantiferromagnetism," a new mechanism for metallic magnetism inmaterials with a particular type of atomic lattice structure. The papersolves a problem that has stumped theoretical physicists for decades.
"New materials tend to drive theoretical advances," Shastrysaid. "Metallic magnetism is a real frontier field in theoreticalphysics, and it has practical applications in materials science."
Superconductors, magnetic storage devices (such as computerhard drives), and other applications are among the areas in whichtheoretical advances in metallic magnetism could play an importantrole.
Shastry and Haerter were interested in the unusual magneticbehavior of sodium cobalt oxide, a material first described in 1997 andintensively studied in recent years. The material can be made withvariable amounts of sodium ions sandwiched between layers of cobaltoxide. The cobalt atoms form a triangular lattice structure that givesrise to "electronic frustration," which refers to the inability of theelectrons in the system to achieve a single state that minimizes theirtotal energy.
A landmark in the theoretical understanding of why certainmetals are ferromagnetic--known as the Nagaoka-Thouless theorem--wasachieved in the mid-1960s, but only applies to materials with anunfrustrated lattice structure. The frustrated case has remainedunsolved for the past 40 years.
"This problem has been a tough nut to crack. We were able tomake some progress and came up with a surprising result," Shastry said.
The magnetic properties of metals result from the configurationof the spins of electrons. Electron spin is a quantum mechanicalproperty that can be either "up" or "down." In a ferromagnetic metalthe electron spins tend to spontaneously align in the same direction.Ferromagnetism accounts for refrigerator magnets and most othermagnetic behavior encountered in daily life.
In antiferromagnetism, the spins align in a regular patternwith neighboring spins pointing in opposite directions, orantiparallel. For electrons living on a triangular lattice, however,this configuration is frustrated, because two of the three electrons ineach triangle must have the same spin.
"In physics, frustration is a good thing because it results ininteresting properties. There are many kinds of frustrated systems innature," Shastry said.
The kinetic antiferromagnetism in a triangular latticedescribed by Haerter and Shastry results from the movement of electronswhen there is a single "electron hole," or unoccupied site for anelectron, in the lattice. They used a theoretical model that enabledthem to study the spin configuration around the electron hole, andfound that the hole is surrounded by an unfrustrated hexagon in whichthe electron spins alternate in an antiferromagnetic pattern.
"The hole can be seen as a moving impurity around which spinstend to line up antiferromagnetically," the authors wrote in the paper.
Physicists use the concept of a moving electron hole tosimplify the analysis of the motions of large numbers of electrons. TheNagaoka-Thouless theorem shows how the motion of a single hole on anunfrustrated lattice leads to ferromagnetism. Haerter and Shastryshowed that the motion of a single hole on a frustrated lattice resultsin weak antiferromagnetism.
"It is surprising because the kinetic motion of electrons usually leads to ferromagnetism," Shastry said.
Sodium cobalt oxide is one of the first known metallic compoundswith a triangular lattice structure. The density of electron holes inthe lattice varies depending on the sodium content, and this hasdramatic effects on the material's magnetic behavior. Haerter andShastry's theory provides new insights into the physics of this unusualsystem.
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