Researchers Say "Frustrated Magnets" Hint At Broader Organizing Principle In Nature

These and other important phenomena ---including high-temperature superconductivity --- suggest that there are "higher-order organizing principles that are intrinsic to nature," explains lead author Seung-Hun Lee, NCNR staff physicist.

The team discovered that self-organized "spin clusters" emerge out of competing interactions in a geometrically frustrated magnet. Though involving interactions on a very tiny scale -- measured in nanometers (billionths of a meter)-- the team says its discovery may provide a new model for exploring "emergent structure in complex interacting systems" on different levels. They singled out research on protein folding as a potential beneficiary. In protein folding, cells assemble units called amino acids into complex three-dimensional shapes that dictate the function of the resulting protein.

Lee and colleagues set out to determine how atoms arrayed in the lattice--like geometry of frustrated magnets resolve an apparent predicament: how to align their spins -- the sources of magnetism --- when faced with a bewildering number of options.

As a conventional magnet cools, atoms pair up with their neighbors and line up their spins, so that they spin in parallel or in opposition (antiparallel). At a temperature unique to the type of material, the magnet undergoes a phase transition, at which a highly symmetrical, long-range ordering of spins is achieved. The material and each spin are said to be in their ground state, a condition of equilibrium, or ultimate stability.

For illustration, this spin-ordering is accomplished easily in materials with squares as a structural building block. An atom can spin antiparallel to the spins of the atoms in the two adjacent corners.

This is not the case for a geometrically frustrated magnet, which is assembled from triangular units. If atoms at two corners spin antiparallel, the atom in the third is left with a no-win situation. Whichever orientation it chooses, the third atom will be out of sync with one of its two neighbors. As a result, the entire system is "geometrically frustrated" and all spins can fluctuate among a range of potential ground states. Long-range order is not attainable, raising the question as to how spins organize locally to cope with a seemingly confusing array of alignment options.

At the NCNR, researchers used neutrons, which are sensitive to magnetic spins, to probe magnetic interactions in zincochromite, a mineral whose crystal structure consists of tetrahedral building blocks with four triangular faces. Beams of neutrons can serve as a high-power magnetic microscope that reveals the geometric arrangement of spins in a solid and how this arrangement evolves as temperature changes. Patterns of neutrons that scattered after they were beamed at zincochromite samples revealed orderly groupings of spins.

The researchers determined that, at low temperatures, the spins organize into six-sided, or hexagonal, structures that repeat throughout the material. Six neighboring tetrahedra contribute one side each to the hexagon. In turn, six spins, one at each corner, are arranged so that each one is antiparallel to its two nearest neighbors --- a highly stable organization.

The patterns of scattered neutrons also suggest that the six hexagon spins act in concert, bunching all spins into one and creating what Lee and his colleagues call a "spin director." Each hexagon achieves local magnetic order and its spin director is largely confined, interacting only weakly with the spin directors of neighboring hexagons.

As a result, the researchers say, geometrically frustrated magnets are not, as suspected, a system of strongly interacting spins, but rather a "protectorate of weakly interacting" composite spins.

In addition to Lee, collaborators include Collin Broholm of Johns Hopkins University and the NCNR; William Ratcliff of Rutgers University; Goran Gasparovic of Johns Hopkins; Qing Zhen Huang of the NCNR; Tae Hee Kim of Rutgers; and Sang-Wook Cheong of Rutgers.

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