In science frustration can become part of everyday life: the experiment doesn’t work the way you wanted, someone else booked the instrument you needed, and of course the fact the paper (or your thesis) won’t write itself. Most people try to avoid frustration; it is generally thought to be bad for your health. However, for some condensed matter physicists frustration—specifically frustrated magnetism—is something to be sought out. Magnetic frustration arises from an incompatibility between the arrangement of magnetic atoms in the crystal structure, and the type of magnetic interaction between those atoms. The classic example is that of the 2D triangular Ising antiferromagnet: magnetic spins that must be antiparallel on a triangle will never all be satisfied.
There are two beautiful things about the general family of geometrically frustrated materials. The first is that the diffraction patterns obtained are highly complex, incorporating Bragg reflections and diffuse scattering arising from the ordered and disordered parts of the structure respectively. Secondly, frustrated systems can give rise to collective ’emergent’ structures, large-scale assemblies that are much larger than the simple particle-particle interaction driving them. Magnetic vortices in the skyrmion phase of chiral ferromagnets and spin-ice magnetic monopoles are two topical examples.
Theoreticians love coming up with exotic combinations of lattice geometry and magnetic interactions (of which there are many) and calculating properties. A fundamental challenge is finding real materials harbouring such unusual states. In particular, canonical examples of low-dimensional frustrated magnets can be very difficult to realise due to interactions between planes or chains of magnetic atoms persisting.
Systems chemistry meets magnetism
Emergent states are also of great interest in systems chemistry, but here arising from combinations of supramolecular, rather than magnetic, interactions. Here a complementary challenge exists: rather than finding real examples, developing general approaches to control the emergent states becomes the problem. So we ask, can combining approaches from these conceptually-related fields help to address the challenges of each?
In our recent study, we interpret the solid phases of gold(I)/silver(I) cyanides as mimics of known, and previously unrealised, frustrated magnets. AuCN and AgCN have well known structures: in each the metal coordinatively bonds to two cyanides in a linear arrangement, and these inorganic polymer chains pack on a triangular lattice. The key structural degree of freedom is the relative vertical shifts of these chains. AuCN adopts a structure based on alignment of chains, whereas AgCN is based on displacements of one third of the unit cell height — a difference rationalised by considering competing inter-chain interactions. A switch from stronger metallophilic (AuCN) to stronger electrostatic (AgCN) interactions qualitatively explains this difference; quantitively these states can be mapped onto the ground states of the 2D triangular XY (anti)ferromagnet using quantum mechanical calculations. Critically the system can be thought of as truly 2D in nature as each chain acts as a self-interacting entity with its neighbours.
(For AgCN the dominant electrostatic interactions lead to a frustrated system as the lowest energy state is where chains are displaced by one half but this is not realisable on the triangular lattice. Rather, the lowest-energy compromise (i.e. displacements by 1/3) is adopted throughout this structure.)
The real fun results when we consider the mixed-metal cyanide Ag1/2Au1/2(CN). Inter-chain interactions now include both the electrostatic and metallophilic interactions as before, but also the difference in strength between aurophilic (Au…Au) and argentophilic (Ag…Ag) interactions. It transpires that the analogous magnetic system (the 2D triangular bilinear-biquadratic system) is known from theory, but had never been realised. By calculating structural models from the theoretical phase diagram of the system, we are able to pinpoint the correct combination of interactions that accounts for the atypical diffraction pattern of Ag1/2Au1/2(CN). Moreover, we find the presence of emergent screw dislocations (related to the spin vortices for the magnetic system) that are encoded for by the self-interaction potential of an individual Au–CN–Ag–CN–Au chain.
Mappings between magnetic and structural states are not new, but here we demonstrate a path to realising exotic 2D magnetic states in chemical analogues that are difficult (if not impossible) to make when considering magnetic interactions alone. Probing excitations and/or the response to external stimuli are exciting avenues of further research. Are the screw dislocations static or mobile? Can temperature or pressure be used to vary the strength of exchange parameters?
Encoding complexity within supramolecular analogues of frustrated magnets
A B Cairns, M J Cliffe, J A M Paddison, D Daisenberger, M G Tucker, F-X Coudert and A L Goodwin
Nature Chemistry (2016, in press) DOI: 10.1038/NCHEM.2462