In principle, materials chemists should probably be looking to make fancy new solids that do new and wonderful things.

Manganese oxide, MnO, is neither particularly fancy nor very new. It is a solid, however, and it is wonderful in its own little way: it is the canonical example of an antiferromagnet, and its slightly-boring-sounding antiferromagnetic transition played a pretty pivotal role in the 1994 Physics Nobel. Cool MnO below about 110 K and the magnetic spins associated with all the Mn^{2+} ions line up in an alternating fashion: up, down, up, down… Of course this kind of magnetic order doesn’t give rise to a net magnetisation, which is why it took a fundamentally new type of experimental probe – neutron scattering – to detect. Ferromagnets (up, up, up, up…) are much more obvious because they produce a net magnetisation, and hence a bulk magnetic field.

With our own interest in order and disorder, we wanted to understand what the magnetic structure of systems like MnO looked like at temperatures just above the antiferromagnetic ordering temperature. In some ways this is a similar question to asking whether there are any parallels between the structure of a solid and its liquid phase. Sometimes the two are extremely similar, but sometimes the unbroken rotational symmetry of the liquid can allow local structures that are forbidden in solids: the (still controversial) icosahedral clusters of metallic liquids are one example.

For long-studied systems such as MnO, the prevailing view has always been that there is some similarity between the paramagnetic (high-temperature, liquid-like) structure and its antiferromagnetic states: locally, neighbouring spins still try and point in opposite directions, but the correlations between spin directions die out increasingly quickly at larger distances. But the symmetries of the two phases are different, and the constraints of periodic magnetic order are lifted in the paramagnet. So there could be fundamental differences once long-range order is lost. What also wasn’t at all clear was whether the paramagnetic state is magnetically homogeneous. In other words, does each spin find itself in effectively the same environment as its neighbours, or are some regions more ordered than others?

To answer these various questions, we turned to magnetic diffuse scattering measurements. It has long been known that the neutron scattering pattern of paramagnetic MnO contains diffuse scattering that contains information about local magnetic structure. Over the past ten years or so, we’ve been putting together a new set of computational tools to help to try and interpret this kind of scattering. And, because MnO is such a canonical magnet, it makes sense to apply these techniques to MnO.

To give some context, really this problem was one I was set whilst a PhD student at Cambridge. My then supervisor Martin Dove, together with Matt Tucker (who was a postdoc in the group at the time) and Dave Keen, had measured some powder neutron total scattering data for MnO at a range of different temperatures. At the time that team was developing RMCProfile, and one of my tasks was to extend the code to allow for refinement of magnetic structure. Anders Mellegård and Robert McGreevy had done this previously (and looked at MnO) for their RMCPOW code, based on an even earlier implementation that Robert and Dave had put together.

*(As an aside-with-an-aside, Dave tells the scientifically romantic story of the two of them working out how to implement Blech and Averbach’s equations whilst effectively trapped at Robert’s place during a particularly snowy winter’s day; Robert was then a JRF and Dave a DPhil student with Bill Hayes).*

Anyway, I did manage to magnetise up RMCProfile, and we even went on to publish a probably-still-slightly-controversial paper on the low-temperature mangetic structure of MnO. I tried to look at the paramagnetic phase as well – and even (way too ambitiously) – tried to pull out information about both the lattice dynamics and the local magnetic structure all at once. It was all too much to expect. Our data were powder-averaged and energy-integrated; our RMC analysis allowed these data to be interpreted in terms of both atomic displacements and spin reorientations. Too many degrees of freedom in our models, and too little information in our data! We (wisely) never published any of this at the time, instead holding off until we had a better way forward. One glimmer of hope was that Matthias Gutmann had measured some really beautiful single-crystal magnetic diffuse scattering patterns on SXD. If only we could analyse them!

The big break really came when Joe Paddison joined my group as a Part II – and later DPhil – student. Joe’s initial project was to code up an alternative to RMCProfile for magnetic systems that ignored the role of atomic displacements, hence reducing the number of degrees of freedom. The code that Joe developed – SPINVERT – worked really well, and he went on to use it to explore the magnetic structure of a whole range of different disordered magnets. But Joe is both a star coder and an excellent physicist, and he worked out a very efficient way of extending SPINVERT to be able to deal with the large volumes of data in single-crystal diffuse scattering measurements. Finally we had a way to model Matthias’s beautiful data, and so to try to understand paramagnetic MnO.

So what did we find? It turns out that paramgnetic MnO is not at all homogeneous. Its magnetic structure contains fairly large islands of crystalline-like magnetic order embedded within a substantially more disordered matrix. Each island breaks the crystal symmetry locally, and does so by picking out one of the body diagonals of the underlying cubic rocksalt structure. There are four different body diagonals, and each island chooses one of these essentially at random (these are shown by different colours in the image). Collectively the structure maintains cubic symmetry.

At low temperatures, where long-range antiferromagnetic order sets in, there is a strong coupling between magnetic order and the crystal lattice dimensions (something known as magnetostriction). We have intentionally ignored this coupling in our paramagnetic MnO study – because we wanted to reduce the number of degrees of freedom in our model. But now that we know this domain-like structure exists, it would be fascinating to find out whether it also couples to a local lattice relaxation. This would be important for two reasons. First, it may mean that the islands of local magnetic order persist for relatively long times. And, second, if they do hang around, then they may be able to support spin excitations that would be meaningfully related to the magnons of ordered magnetic phases. Indeed there some experimental hints that such excitations exist in paramagnetic MnO, and it would be great to be able to join the dots on these different aspects of the physics of paramagnetism. In many unconventional (high-*T*_{c}) superconductors, superconductivity is in competition with long-range antiferromagnetic order, and spin excitations have been proposed as a coupling mechanism.

Magnetic structure of paramagnetic MnO

J A M Paddison, M J Gutmann, J R Stewart, M G Tucker, M T Dove, D A Keen, and A L Goodwin

Physical Review B **97**, 014429 (2018)