For newly discovered 'quantum spin liquid', the beauty is in its simplicity

Dec 20, 2012
For newly discovered 'quantum spin liquid', the beauty is in its simplicity
This image depicts magnetic effects within Herbertsmithite crystals, where green regions represent higher scattering of neutrons from NIST's Multi-Angle Crystal Spectrometer (MACS). Scans of typical highly-ordered magnetic materials show only isolated spots of green, while disordered materials show uniform color over the entire sample. The in-between nature of this data shows some order within the disorder, implying the unusual magnetic effects within a spin liquid. Credit: NIST

(—A research team including scientists from the National Institute of Standards and Technology (NIST) has confirmed long-standing suspicions among physicists that electrons in a crystalline structure called a kagome (kah-go-may) lattice can form a "spin liquid," a novel quantum state of matter in which the electrons' magnetic orientation remains in a constant state of change.

The research shows that a spin liquid state exists in Herbertsmithite—a mineral whose atoms form a kagome lattice, named for a simple weaving pattern of repeating triangles well-known in Japan. Kagome are one of the simplest structures believed to possess a spin liquid state, and the new findings, revealed by neutron scattering, indeed show striking evidence for a fundamental prediction of spin liquid physics.

Generally, magnetism results from the , also called spin, of electrons within atoms. Rather than aligning in a stable, repetitive up-down pattern as they do in most magnetic solids at low temperatures, the electrons in a spin liquid are frustrated by mutual interactions from settling into a permanent alignment, so the electron spins constantly change direction, even at temperatures close to .

Named after a mineralogist, Herbertsmithite was proposed to be a quantum spin liquid by Daniel Nocera and Young Lee of the Massachusetts Institute of Technology (MIT) in 2007. Herbertsmithite has a peculiar crystal structure in which its copper atoms lie at the corners of triangles with interactions that favor having the up-down alignment pattern of electronic spins on each corner. However, while electrons on two of the corners of a triangle can align, one up and one down, their alignment produces a quandary for the electron on the third corner, which cannot align with both.

"The electronic spin on the third copper atom essentially doesn't know what to do with itself," says Collin Broholm, a physicist at NIST and Johns Hopkins University, who was also part of the team that previously characterized a different material with a spin-liquid-like state.** "The locations of copper atoms in Herbertsmithite suggest the material might not be able to order itself magnetically, which is interesting because it is so unusual. But testing the hypothesis of a quantum spin liquid required the right instrument and very pure crystals of Herbertsmithite, and until recently, we had neither."

The MIT group provided the crystals after managing to grow them artificially in their lab, a painstaking process that took years. To determine the behaviors of the electronic spins in the crystals' , the team used the Multi-Axis Crystal Spectrometer (MACS) at the NIST Center for Neutron Research. MACS, which scatters a beam of neutrons off a sample of material, showed that Herbertsmithite scattered neutrons in a highly unusual way: Instead of all the scattered neutrons possessing identical energies at a given momentum, as they do with most magnetic materials, the neutrons had a wide spectrum of energies. This is hard evidence that Herbertsmithite indeed has spin-liquid properties.

The apparent simplicity of Herbertsmithite belies the complexity of the spin that it apparently supports, Broholm says, which could make it useful someday.

"The structural simplicity of Herbertsmithite is valuable if we are to put the quantum spin liquid to use—as proposed for information processing, for example," he says. "Complex chemistry usually brings disorder, but this material is relatively simple, so it realizes the quantum spin liquid with higher fidelity."

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More information: T.-H. Han, J.S. Helton, S. Chu, D.G. Nocera, J.A. Rodriguez-Rivera, C. Broholm and Y.S. Lee. Fractionalized excitations in the spin liquid state of a kagome lattice antiferromagnet. Nature, 492, Dec. 20, 2012, doi: 10.1038/nature11659

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3 / 5 (2) Dec 20, 2012
The picture tells the story. The electrons have found a larger pattern--beyond their triangle--within which they can align, thus creating "some order" within the disorder. The regularity of the kagome pattern yields a larger shape (larger than the basic triangle). There is a plentiful supply of this larger shape, and each larger shape is located at regular spacing from its siblings.

Importantly, the larger shape is an orderly period--360 degrees. The electrons can organize their spins within this 360 degree period. Each spin will have the same proportional orientation to its neighbors as every other spin within the 360 degree period. Helimagnetism is one such form of order.

A two electron system that is ordered behaves the same way--360 divided by two results in 0 and 180 order. A three part system could be 0, 120, 240, but that does not work for electrons.

Unavoidably, the rest of this kagome system remains disordered as far as their electrons are concerned. Order, disorder.
3 / 5 (2) Dec 20, 2012
Assuming the hexagonal overlay is properly positioned in relation to the blue spots, the result is predictable. A triangle is incommensurate with the order desired by the electrons. The hexagon is commensurate. The hexagon solves the frustration. Two and three are both factors of six.
1 / 5 (2) Dec 20, 2012
Herbertsmithite - a model of a two dimensional universe?. String-net liquid model has become popular before few years. I do consider it a conceptual intermediate between topological string field (SFT) and loop quantum gravity (LQG) theories. In AWT it corresponds the fact, the density fluctuations inside of dense gases (typically condensing supercritical fluids) have character of mutually entangled strings and fibers.
1 / 5 (2) Dec 20, 2012
The kagome lattice has its Coulomb force analogy in hexagonal Wigner crystals inside of Mott insulators, which are precursor of high-temperature superconductors. It illustrates the duality of elektromagnetic and elektrostatic interactions: whereas in the Wigner's lattice the charges of electrons cannot move at all, inside of kagome lattice their spins reach the highest mobility under given conditions.
1 / 5 (1) Dec 27, 2012
We can find a hexagonal phase at another places of solid state physics, like at the surface of so-called topological insulators. It's not accidental, because the principle remains always the same: it's the tightest arrangement of mutually repulsing particles (magnets, charged electrons) constrained to 2D plane.

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