Research News
A lot of natural shapes are based on the principle of the golden ratio, a certain harmonic ratio of numbers, distances or areas, whereby the larger quantity relates to the smaller quantity in the same manner as the sum of both quantities relates to the larger quantity. These proportions are also inherent in the spiral shape of the Nautilus cephalopods, shown here in cross section. Photo: iStock/Phil Cardamone
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www.helmholtz.de/eurekalert-top-story-2010
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HZB's "Golden Ratio" Top Story 2010
With 130,000 hits, the HZB press release on the "Golden Ratio in a Quantum World" constituted the absolute top story in EurekAlert!, the American science information service. Together with British colleagues, HZB researchers around Prof. Dr Alan Tennant for the first time discovered hidden symmetry properties in a magnetic crystal corresponding to the "golden ratio". This 1 to 1.618 ratio of two quantities is considered an aesthetic ideal since antiquity and features also mathematically interesting characteristics. The examined material was cobalt niobate, a material possessing special magnetic properties. The existing spins align to form chains which in conjunction behave like a thin rod magnet.
However, the chain is only one atomic layer thick. When applying a magnetic field at right angles to an aligned spin, the magnetic chain will transform into a new state. In doing so, the researchers were able to observe how the chain of atoms behaves. "Like a nanoscale guitar string", says Dr Radu Coldea from Oxford University. "Here the tension comes from the interaction between spins causing them to magnetically resonate," says Coldea. As with a guitar string, resonances are created. The first two notes of the observed resonance frequencies show a perfect golden ratio relationship with each other. "It is noteworthy that in a quantum system one finds perfect harmony instead of disorder", says Alan Tennant.
