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.

Abstract:

In most superconductors electrons form Cooper pairs in a spin-singlet state mediated by either phonons or by long-range interactions such as spin fluctuations. The superconductor UTe₂ is a rare material wherein electrons are believed to form pairs in a unique spin-triplet state with potential topological properties. While spin-triplet pairing may be mediated by ferromagnetic or antiferromagnetic fluctuations, experimentally, the magnetic properties of UTe₂ are unclear. By way of muon spin rotation/relaxation (μSR) measurements on independently grown UTe₂ single crystals we demonstrate the existence of magnetic clusters that gradually freeze into a disordered spin frozen state at low temperatures. Our findings suggest that inhomogeneous freezing of magnetic clusters is linked to the ubiquitous residual linear term in the temperature dependence of the specific heat (C) and the low-temperature upturn in C/T versus T. The omnipresent magnetic inhomogeneity has potential implications for experiments aimed at establishing the intrinsic low-temperature properties of UTe₂.

Abstract:

We study magnetism in the κ-(ET)2X family of charge-transfer salts using implanted muon spectroscopy in conjunction with detailed ab initio electronic structure calculations using density functional theory (DFT). ET stands for the electron donor molecule bis(ethylendithio)tetrathiafulvalene and X is an anion. The DFT calculations are used to establish molecular spin distributions, muon stopping sites, and dipolar field parameters, that allow us to make a quantitative interpretation of the experimental results. Materials in the κ-(ET)2X family with X = Ag2(CN)3 and X = Cu2(CN)3 have attracted particular interest, as they have the attributes of quantum spin liquids, showing no magnetic ordering down to 30 mK in zero field μSR and in NMR, despite having exchange couplings of order 200-250 K. In contrast, the material with X = Cu[N(CN)2]Cl has an antiferromagnetic (AF) ordering transition with TN in the region of 23-30 K. In order to better understand the muon spectroscopy signature of magnetism in this whole family of compounds at both low and high magnetic fields, we look in detail at the case X = Cu[N(CN)2]Cl. As the first step in our study, the spin density distribution for the ET dimer is calculated using DFT and used to simulate the 3.7 T H1-NMR spectrum of this salt, with the spectrum showing good agreement with that measured previously [K. Miyagawa, A. Kawamoto, Y. Nakazawa, and K. Kanoda, Phys. Rev. Lett. 75, 1174 (1995)0031-900710.1103/PhysRevLett.75.1174]. Best match to the data is found for antiferromagnetic interlayer ordering and an ordered moment per dimer of 0.25μB. DFT is also used to explore muon stopping sites for this salt, finding one set of sites resulting from muonium addition to C=C double bonds in the ET layer, with muons stopping in the anion layer forming another group of sites. The dipolar fields associated with each of the stopping sites is computed and these are compared with the precession frequencies observed in the ZF-μSR spectrum [M. Ito, T. Uehara, H. Taniguchi, K. Satoh, Y. Ishii, and I. Watanabe, J. Phys. Soc. Jpn. 84, 053703 (2015)0031-901510.7566/JPSJ.84.053703]. Best match to the ZF-μSR spectrum is obtained with the mode of interlayer ordering having FM character and an ordered moment per dimer of 0.31μB for muon sites in the anion layer and 0.36μB for muonium sites in the ET layer. New measurements of TF-μSR spectra for fields up to 8 T are reported and analyzed to obtain the best estimate of the magnetic order parameter under different measurement conditions, allowing us to observe the variation of TN with applied field and the field-induced transverse canting of the moments.