Surfing the (mag)net
Thu, Sep 12, 2024A net is a periodic (repeating) series of connected points. This concept is at the heart of solid state science because we often think of the chemical structures of materials as comprising atoms connected by bonds, which therefore form a net. The underlying net of a material allows for classification—is this structure related to that structure—but also prediction of its properties, e.g. is it likely to be stiff or soft. Although there are an infinite number of possible nets, the best estimate is that there are only twenty nets with only one kind of vertex and edge.^{1} Most of these will be familiar, at least to chemists, like the simple cubic pcu net beloved of scaffolders or the facecentred cubic fcu net that emerges in pyramidal stacks of oranges. There’s a particular interest in the nets which are not bipartite (i.e. the points of the net can’t be coloured in red and blue such that no red neighbours another red and no blue a blue, normally containing a triangle), because these can very have unusual magnetic properties. In these nonbipartite nets, if a magnetic spin is put at every node and they interact such that the spins prefer to point in opposite directions, that is, they are antiferromagnetically coupled, there are very many states there are nearly equal in energy: they are frustrated.
This has been recognised for a very long time (since at least the 1950s), when it was discovered that some of these very simple nonbipartite nets are so frustrated that they will never freeze into a unique ordered state, no matter how much they are cooled (they have “spin liquid” ground states). There are seven of these frustrated high symmetry nets, and to our surprise, not all of these nets had been previously investigated for their frustrated magnetic properties. In this paper, we investigate all seven nets, and find three new spin liquids. Because structures can be relatively easily classified according to their net we are also able to suggest materials that might realise these predicted spin liquid states.
Our interest in this sprang from the field of metalorganic frameworks: solids made from metal atoms (or clusters of metal atoms) joined by organic molecules into extended networks. This modularity means there structures are readily classified according to their topologies, and so MOF chemists very often use topology to design structures for particular applications. As magnetic interactions in MOFs will typically have to be carried along the ligand, the structural and magnetic topologies will be the same. We therefore hope that this work will help MOF chemists find some of the new magnetic phases we predict!
Here’s a fun video showing the nets and the diffuse scattering: https://www.youtube.com/shorts/XKCg_OHj0YI

Where the nearestneighbour to every point is the one it is connected to by an edge in its highest symmetry form. It’s possible to generate an arbitrarily large number of nets where distant points are connected, but this produces some very weird nets that seem extremely unlikely to ever exist in the physical world. ↩︎
Paper
Discovering Classical Spin Liquids by Topological Search of High Symmetry Nets
J A M Paddison and M J Cliffe
ACS Cent. Sci., ,  (2024).