Muons and magnets

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.