5 minute read
Frustrated systems
In physics, frustration refers to a situation where competing interactions prevent a system’s potential energy from being minimised. As in life, the solution is compromise. Mansfield’s Professorial Fellow in Physics, Professor Stephen Blundell, shares insight into his groundbreaking research.
When hammering out a compromise, each side never gets exactly what it wants, but ideally the pain of giving up something wanted is shared between the parties. This situation is not just the preserve of industrial disputes or international relations but is also found in magnetic materials. Sometimes it’s easy and all the individual atomic magnetic moments that comprise a magnetic material want the same thing. No compromise is needed, and they all point in the same direction (as with metallic iron). Another solution, in fine Mansfield tradition, is the nonconformist scenario, where every magnetic moment refuses to conform to the behaviour of its immediate neighbour, and instead prefers to do the precise opposite. In this case, the magnetic moments align in an up – down – up – down – up – down… arrangement.
But just as in human negotiations, the situation can get more complicated. Think of three magnetic moments, arrows pointing in different directions, arranged on the three corners of a triangle, each one hell-bent on doing the precise opposite of its neighbour. The first one points up, so the second one points down, and the third one is left with no good options. Pointing oppositely to either one of its neighbours, as it wants to, leads it to align with the other neighbour. The only solution is a compromise, with each magnetic moment pointing at 120 degrees to its neighbour. The triangular geometry is said to be ‘frustrated’, the same terminology that would be used to describe a three-way negotiation where no party feels fully satisfied.
Throw quantum mechanics into the mix and you have a further complication: now those magnetic moments need not to be in definite states of pointing up or down or left or right, but can exist in strange superposition states, just like Schrödinger’s cat. This sounds like science fiction, but it’s exactly what is found in various magnetic materials studied by my research group in the Department of Physics. How do we do this?
One of our main experimental techniques involves implanting ‘magnetic spies’ into these magnetic materials, tiny secret agents that can bury themselves into the interstitial spaces between the atoms and report back on what they find. These undercover operatives are muons, radioactive particles that are produced in particle accelerators, and which turn out to be a wonderful means of detecting microscopic magnetic fields inside materials. My group has pioneered techniques in identifying where these particles hide inside the material (a method called density functional theory – a familiar term to physicists). We’re developing a new method to control how these experiments work using pulses of radiofrequency and/ or microwave radiation, which we hope will provide a new method of learning about frustrated magnetic materials.
An intriguing feature of frustrated systems is that they don’t stay still for long. Because any solution is based on compromise, each of the magnetic moments is perpetually straining at the bit, attempting to find an improvement in its local conditions. But each little wobble or nudge of a magnetic moment produces a knock-on effect on its neighbours, as each tries to get more comfortable, or less uncomfortable, as its environment slowly changes. This produces low frequency dynamics in the arrangement of magnetic moments, something we can detect in our experiments, both with muons and also using a noise-detection system that has been developed by one of my colleagues.
These slow dynamics of frustrated systems have analogues in the world of human negotiations, where hammered-out compromises can unravel over time, and contested and unresolved issues can lead to dynamics that persist, rather than subside. Characterising and fully understanding the persistent dynamics in magnetic materials is one of the aims of my research.
A single human being is a difficult enough object of study, but it’s the complexity of the interactions between millions of individuals that makes the behaviour of an entire society and the compromises within it such an intractable problem for research at an entirely different level. In just the same way, physicists started their study of the world by solving problems involving relatively few components, such as the motion of the Earth around the Sun, or the splitting of a single atom. But some of the most challenging, and fascinating, problems involve the interactions between not one, two, or three, but huge numbers of atoms. This is just the type of situation we encounter in frustrated magnets, and it’s what makes the problem so difficult but also so exciting.
Stephen’s research is supported by a major European Research Council grant, funded by UK Research and Innovation.
