At low enough temperature, most magnetic materials form a periodic magnetic order which minimises the energy of magnetic interactions. However, in so-called “frustrated” magnets, the geometry of the crystal structure prevents magnetic interactions from being fully satisfied — imagine three spins on a triangle, which can never be mutually antiparallel. Frustrated materials can remain in a paramagnetic phase down to very low temperatures. But these are not paramagnets in a conventional sense: spins remain correlated over short length scales, and these local correlations are thought to be implicated in phenomena as diverse as as emergent magnetic monopoles in spin ice and spin fluctuations in high-Tc superconductors.
We have now used neutron scattering measurements to try to understand magnetic frustration in a sample of β-Mn doped with a small quantity of Co. Pure β-Mn is of fundamental interest as the only element thought to exhibit a “quantum spin liquid” phase, but the availability of single-crystal samples makes closely-related β-MnCo a much better candidate for experiments.
Our polarised neutron scattering measurements, carried out on the ILL spectrometer D7 at a temperature of just 50 mK, confirmed that β-MnCo showed no sign of long-range magnetic order. The highly-structured magnetic diffuse scattering patterns we measured (themselves a key experimental signature of frustrated magnetism) were fitted using two techniques. First, reverse Monte Carlo (RMC) refinement was used in order to identify the strongest magnetic correlations. Second, we used a mean-field approximation to fit a magnetic Hamiltonian to the data, identifying the strongest magnetic interactions. We found that the data can be well described using an effective Heisenberg model with just two interaction parameters: an antiferromagnetic nearest-neighbour J1 and a ferromagnetic 5th-neighbour J5.
These two types of interaction help us understand both the local spin correlations and the absence of long-range magnetic order in β-MnCo. The ferromagnetic J5 interactions couple Mn atoms into helical chains that run parallel to the <111> crystal axes. Representing these chains as rods oriented along the helical axis maps the entire structure onto a set of four intersecting rod lattices. Spin correlations along these rods are always ferromagnetic — this means that it is possible to interpret each rod as behaving like a single collective object. Neighbouring rods then interact via the antiferromagnetic J1. The resulting pattern strongly resembles that found in the canonical antiferromagnetic Heisenberg model on the simple triangular lattice. The identification of strong magnetic frustration and emergent spin structures in such a chemically-simple system provides a valuable experimental reference point against which to benchmark developments in the theory of unconventional metals.
An obvious avenue for future research on this specific system is to identify nesting vectors of the Fermi surface in order to determine the origin of the interactions we have identified empirically. However, perhaps our key result is to show how typical behaviour — the emergence of complexity from simple building blocks — can be reversed in a structurally-complex system such as β-MnCo. There may be hints here of a more general phenomenon: the emergence of simple collective states within complex networks has also been observed in fields as diverse as neural signalling and the dynamics of amorphous materials. Hence a focus on structural complexity may prove an important experimental strategy for realising novel states of condensed matter.