Page 73 - ILLS Annual Report 2018

SCIENTIFIC HIGHLIGHTS
70-71
Figure 2
Comparison between ordering wave-vectors for experiment and theory.
The keys to answering this question lie in both the extremely detailed measurements and the theoretical modelling, which allow us to make real comparisons
of different hypotheses. Earlier experiments favoured multipolar order [1]. New measurements [2] of both static and dynamical correlations were carried out at
low temperatures, in order to isolate quantum from thermal fluctuations, and high magnetic fields, to alter the balance of frustration to order. The theoretical modelling required us to take into account the fact that even
order in the dipoles can occur at wave-vectors that are incommensurable with the underlying lattice, so that the magnetic unit cell is in principle infinitely larger than the structural. In practice, this means that we need tools to calculate and compare the stabilities of new unit cells, hundreds, or even, thousand times larger than would suffice for a simple periodic structure. In fact, what allows us to say ultimately that the order is based on dipoles and not multipoles is that the calculated wave-vector
changes as a function of external magnetic field, which is compatible with this interpretation and incompatible with multi-polar order. The different phases are illustrated in figure 1. Furthermore, the calculations show that
a surprisingly small but biaxial exchange anisotropy
is necessary and sufficient to stabilise a sequence of phases: cycloid to cone to fan, in the easy-axis direction (see figure 2 on the left-hand side), with the correct dependence on external field; and cycloid to canted- collinear to fan in the intermediate direction (right-hand side). The multipolar state does not appear.
In conclusion, while detailed experiments with neutrons provide a wealth of information that can distinguish competing complex, but subtly different, quantum phases, theoretical work is needed to provide the details on which comparisons can be made and to make plausible the relation between the small additional interactions and the consequent stability.
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