Link found between golden ratio and atomic symmetry

(Nanowerk News) Researchers in Germany and the UK have discovered symmetry hidden in solid state matter at very small scales. The findings, published in the journal Science ("Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry"), indicate that symmetry involves the golden ratio famous from art and architecture. The research was supported in part by the NMI3 ('Integrated infrastructure initiative for neutron scattering and muon spectroscopy') project, which was funded under the 'Coordination of research activities' Thematic area of the EU's Sixth Framework Programme (FP6) to the tune of EUR 21 million.

Scientists say unexpected and even irrational behaviour goes hand in hand with particles at the atomic, or quantum, scale. The emergence of new properties is triggered by what experts call 'Heisenberg's uncertainty principle', which basically states that it is impossible to know both the exact position and exact velocity of an object at the same time. The effect, however, is just noticeable on a subatomic scale.

For this latest study, the researchers investigated the magnetic material cobalt niobate, which is made up of linked magnetic atoms that form chains just one atom wide. According to them, cobalt niobate comes in handy when someone wants to describe ferromagnetism at tiny scales in solid state matter.

The magnetic chain changes into a new state called 'quantum critical' when a magnetic field is applied at right angles to an aligned spin, the team said. The quantum critical, experts say, can be considered as being a quantum version of a fractal pattern.

'The system reaches a quantum uncertain - or a Schrödinger cat state [composed of two diametrically opposed conditions at the same time],' explained Professor Alan Tennant of Helmholtz-Zentrum Berlin für Materialien und Energie (HZB) in Germany, who co-authored the study. 'This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical.'

The researchers discovered that when they tuned the system and artificially introduced more quantum uncertainty, the chain of atoms acted like a nanoscale guitar string. They used a special probe, 'neutron scattering', which enabled them to see the actual atomic scale vibrations of a system.

'Here the tension comes from the interaction between spins causing them to magnetically resonate,' said lead author Dr Radu Coldea of Oxford University in the UK. 'For these interactions we found a series (scale) of resonant notes: the first 2 notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618..., which is the golden ratio famous from art and architecture.'

Scientists say that in mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is the same as the ratio of the larger quantity to the smaller one.

Dr Coldea underlined that there is nothing coincidental about that. 'It reflects a beautiful property of the quantum system - a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material.'

Mathematical theories developed for particle physics could find a niche in nanoscale science, and could fuel technology in future, according to the researchers.

'Such discoveries are leading physicists to speculate that the quantum, atomic scale world may have its own underlying order,' Professor Tennant, who led the HZB team, said, adding that 'similar surprises may await researchers in other materials in the quantum critical state.'