Muons and magnets

Abstract:

The fluorinated ionomer Nafion, first discovered by the Du Pont company, is a material that provides efficient proton conducting membranes for application in important technological areas such as hydrogen fuel cells. Although many aspects of the polymer have been studied in relation to these applications, the microscopic mechanisms for proton transport in this polymer are still only poorly understood. We have therefore applied implanted muon techniques to the study of Nafion, aiming to gain information about these mechanisms via the muon acting as a local spin probe. Our results indicate that the muon is highly sensitive to the hydration state of the polymer and to the dynamical processes of the various sub-phases within the material. A three component model is found to describe the data well. This model has one F-µ-F component, reflecting muons in the PTFE-like polymer matrix, a second component representing quasi-static environments dominated by a single close proton and a third component encompassing highly dynamic proton-coupled environments. The properties have been studied within this modelling framework as a function of temperature for both dehydrated and fully hydrated samples.

Abstract:

LF-µSR studies have previously been used to study the diffusive 1D motion of solitons and polarons in conducting polymers. This type of study was also applied to investigating the diffusive motion of spinons in spin-1/2 antiferromagnetic chains. Recently the method has been extended to examples of 2D layered triangular spin lattices which can support quantum spin liquid states, such as 1T-TaS₂ and YbZnGaO₄. These systems are found to show spin dynamics that matches well to 2D spin diffusion, such a model being found to provide a much better fit to the data than previously proposed models for spin correlations in such systems. In YbZnGaO₄ the diffusion rate shows a clear crossover between classical and quantum regimes as T falls below the exchange coupling J. That the spin diffusion approach works well in the high T classical region might be expected, but it is found that it also works equally well in the low T quantum region where quantum entanglement controls the spin dynamics. Measurement of the diffusion rate allows a T dependent length scale to be derived from the data that can be assigned to a quantum entanglement length ξ_E. Another entanglement measure, the Quantum Fisher Information F_Q can also be obtained from the data and its T dependence is compared to that of ξ_E.

Abstract:

A positively charged muon implanted in copper sits at an octahedral interstitial site and experiences a magnetic dipolar coupling with six nearest-neighbour quadrupolar I = 3/2 copper nuclei. The resulting avoided level crossing resonance observed as a function of magnetic field provides a means of studying these interactions and understanding the effect of the electric-field gradient due to the muon acting on the quadrupolar nuclei. The effect is usually modelled by considering the interaction between the positive muon and a single copper nucleus, but the other five copper nuclei are equally important. By solving the problem in the full 2(2I + 1)⁶ = 8192-dimensional Hilbert space, we demonstrate the effect of these additional interactions.

Abstract:

Most muon spin rotation (µSR) experiments are based on the coupling between a muon (a quantum, spin-½ particle) and a macroscopic magnetic field, either applied externally (as is often the case for experiments on superconductors) or produced internally (due to, for example, the alignment of spins in an ordered magnet). This article will review some experiments which have exploited this, essentially classical, interaction, but then will consider cases in which a more intrinsically quantum mechanical approach is needed. In these cases, one cannot ignore the back reaction of the muon's effect on the system it is probing. It can be profitable to consider the muon as a qubit, evaluating the decoherence of quantum information injected by the muon into the environmental spin system. Experiments focussed on this approach are underpinned by DFT+µ calculations (density functional theory with an included muon) and give rise to an excellent agreement between theory and experiment and open up new ways of using the muon as a probe.

Abstract:

We report the manifestation of field-induced Berezinskii-Kosterlitz-Thouless (BKT) correlations in the weakly coupled spin-1/2 Heisenberg layers of the molecular-based bulk material [Cu(pz)2(2−HOpy)2](PF6)2. At zero field, a transition to long-range order occurs at 1.38 K, caused by a weak intrinsic easy-plane anisotropy and an interlayer exchange of J′/kB≈1  mK. Because of the moderate intralayer exchange coupling of J/kB=6.8  K, the application of laboratory magnetic fields induces a substantial XY anisotropy of the spin correlations. Crucially, this provides a significant BKT regime, as the tiny interlayer exchange J′ only induces 3D correlations upon close approach to the BKT transition with its exponential growth in the spin-correlation length. We employ nuclear magnetic resonance measurements to probe the spin correlations that determine the critical temperatures of the BKT transition as well as that of the onset of long-range order. Further, we perform stochastic series expansion quantum Monte Carlo simulations based on the experimentally determined model parameters. Finite-size scaling of the in-plane spin stiffness yields excellent agreement of critical temperatures between theory and experiment, providing clear evidence that the nonmonotonic magnetic phase diagram of [Cu(pz)2(2−HOpy)2](PF6)2 is determined by the field-tuned XY anisotropy and the concomitant BKT physics.