Field-Tunable Berezinskii-Kosterlitz-Thouless Correlations in a Heisenberg Magnet.

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}](PF_{6})_{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^{'}/k_{B}≈1 mK. Because of the moderate intralayer exchange coupling of J/k_{B}=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}](PF_{6})_{2} is determined by the field-tuned XY anisotropy and the concomitant BKT physics.

Intrinsic Nature of Spontaneous Magnetic Fields in Superconductors with Time-Reversal Symmetry Breaking.

We present a systematic investigation of muon-stopping states in superconductors that reportedly exhibit spontaneous magnetic fields below their transition temperatures due to time-reversal symmetry breaking. These materials include elemental rhenium, several intermetallic systems, and Sr_{2}RuO_{4}. We demonstrate that the presence of the muon leads to only a limited and relatively localized perturbation to the local crystal structure, while any small changes to the electronic structure occur several electron volts below the Fermi energy, leading to only minimal changes in the charge density on ions close to the muon. Our results imply that the muon-induced perturbation alone is unlikely to lead to the observed spontaneous fields in these materials, whose origin is more likely intrinsic to the time-reversal symmetry-broken superconducting state.

Information and Decoherence in a Muon-Fluorine Coupled System.

The unitary evolution of a quantum system preserves its coherence, but interactions between the system and its environment result in decoherence, a process in which the quantum information stored in the system becomes degraded. A spin-polarized positively charged muon implanted in a fluoride crystal realizes such a coherent quantum system, and the entanglement of muon and nearest-neighbor fluorine nuclear spins gives rise to an oscillatory time dependence of the muon polarization that can be detected and measured. Here we show that the decohering effect of more distant nuclear spins can be modelled quantitatively, allowing a very detailed description of the decoherence processes coupling the muon-fluorine "system" with its "environment," and allowing us to track the system entropy as the quantum information degrades. These results show how to precisely quantify the spin relaxation of muons implanted into quantum entangled states in fluoride crystals.

Observation of a neutron spin resonance in the bilayered superconductor CsCa2Fe4As4F2.

We report inelastic neutron scattering (INS) investigations on the bilayer Fe-based superconductor CsCa2Fe4As4F2 above and below its superconducting transition temperature T c ≈ 28.9 K to investigate the presence of a neutron spin resonance. This compound crystallises in a body-centred tetragonal lattice containing asymmetric double layers of Fe2As2 separated by insulating CaF2 layers and is known to be highly anisotropic. Our INS study clearly reveals the presence of a neutron spin resonance that exhibits higher intensity at lower momentum transfer (Q) at 5 K compared to 54 K, at an energy of 15 meV. The energy E R of the observed spin resonance is broadly consistent with the relationship E R = 4.9k B T c, but is slightly enhanced compared to the values observed in other Fe-based superconductors. We discuss the nature of the electron pairing symmetry by comparing the value of E R with that deduced from the total superconducting gap value integrated over the Fermi surface.

Probing magnetic order and disorder in the one-dimensional molecular spin chains CuF2(pyz) and [Ln(hfac)3(boaDTDA)] n (Ln = Sm, La) using implanted muons.

We present the results of muon-spin relaxation ([Formula: see text]SR) measurements on antiferromagnetic and ferromagnetic spin chains. In antiferromagnetic CuF2(pyz) we identify a transition to long range magnetic order taking place at [Formula: see text] K, allowing us to estimate a ratio with the intrachain exchange of [Formula: see text] and the ratio of interchain to intrachain exchange coupling as [Formula: see text]. The ferromagnetic chain [Sm(hfac)3(boaDTDA)] n undergoes an ordering transition at [Formula: see text] K, seen via a broad freezing of dynamic fluctuations on the muon (microsecond) timescale and implying [Formula: see text]. The ordered radical moment continues to fluctuate on this timescale down to 0.3 K, while the Sm moments remain disordered. In contrast, the radical spins in [La(hfac)3(boaDTDA)] n remain magnetically disordered down to T = 0.1 K suggesting [Formula: see text].

Local magnetism, magnetic order and spin freezing in the 'nonmetallic metal' FeCrAs.

We present the results of x-ray scattering and muon-spin relaxation ([Formula: see text]SR) measurements on the iron-pnictide compound FeCrAs. Polarized non-resonant magnetic x-ray scattering results reveal the 120° periodicity expected from the suggested three-fold symmetric, non-collinear antiferromagnetic structure. [Formula: see text]SR measurements indicate a magnetically ordered phase throughout the bulk of the material below [Formula: see text] K. There are signs of fluctuating magnetism in a narrow range of temperatures above [Formula: see text] involving low-energy excitations, while at temperatures well below [Formula: see text] behaviour characteristic of freezing of dynamics is observed, likely reflecting the effect of disorder in our polycrystalline sample. Using density functional theory we propose a distinct muon stopping site in this compound and assess the degree of distortion induced by the implanted muon.

Unconventional Field-Induced Spin Gap in an S=1/2 Chiral Staggered Chain.

We investigate the low-temperature magnetic properties of the molecule-based chiral spin chain [Cu(pym)(H_{2}O)_{4}]SiF_{6}·H_{2}O (pym=pyrimidine). Electron-spin resonance, magnetometry and heat capacity measurements reveal the presence of staggered g tensors, a rich low-temperature excitation spectrum, a staggered susceptibility, and a spin gap that opens on the application of a magnetic field. These phenomena are reminiscent of those previously observed in nonchiral staggered chains, which are explicable within the sine-Gordon quantum-field theory. In the present case, however, although the sine-Gordon model accounts well for the form of the temperature dependence of the heat capacity, the size of the gap and its measured linear field dependence do not fit with the sine-Gordon theory as it stands. We propose that the differences arise due to additional terms in the Hamiltonian resulting from the chiral structure of [Cu(pym)(H_{2}O)_{4}]SiF_{6}·H_{2}O, particularly a uniform Dzyaloshinskii-Moriya coupling and a fourfold periodic staggered field.

A.C. susceptibility as a probe of low-frequency magnetic dynamics.

The experimental technique of a.c. susceptibility can be used as a probe of magnetic dynamics in a wide variety of systems. Its use is restricted to the low-frequency regime and thus is sensitive to relatively slow processes. Rather than measuring the dynamics of single spins, a.c. susceptibility can be used to probe the dynamics of collective objects, such as domain walls in ferromagnets or vortex matter in superconductors. In some frustrated systems, such as spin glasses, the complex interactions lead to substantial spectral weight of fluctuations in the low-frequency regime, and thus a.c. susceptibility can play a unique role. We review the theory underlying the technique and magnetic dynamics more generally and give applications of a.c. susceptibility to a wide variety of experimental situations.

Room-temperature helimagnetism in FeGe thin films.

Chiral magnets are promising materials for the realisation of high-density and low-power spintronic memory devices. For these future applications, a key requirement is the synthesis of appropriate materials in the form of thin films ordering well above room temperature. Driven by the Dzyaloshinskii-Moriya interaction, the cubic compound FeGe exhibits helimagnetism with a relatively high transition temperature of 278 K in bulk crystals. We demonstrate that this temperature can be enhanced significantly in thin films. Using x-ray scattering and ferromagnetic resonance techniques, we provide unambiguous experimental evidence for long-wavelength helimagnetic order at room temperature and magnetic properties similar to the bulk material. We obtain α intr = 0.0036 ± 0.0003 at 310 K for the intrinsic damping parameter. We probe the dynamics of the system by means of muon-spin rotation, indicating that the ground state is reached via a freezing out of slow dynamics. Our work paves the way towards the fabrication of thin films of chiral magnets that host certain spin whirls, so-called skyrmions, at room temperature and potentially offer integrability into modern electronics.

Muon-spin relaxation study of the double perovskite insulators Sr2 BOsO6 (B = Fe, Y, ln).

We present the results of zero-field muon-spin relaxation measurements made on the double perovskite insulators Sr2 BOsO6 (B = Fe,Y, In). Spontaneous muon-spin precession indicative of quasistatic long range magnetic ordering is observed in Sr2FeOsO6 within the AF1 antiferromagnetic phase for temperatures below [Formula: see text] K. Upon cooling below T2≈67 K the oscillations cease to be resolvable owing to the coexistence of the AF1 and AF2 phases, which leads to a broader range of internal magnetic fields. Using density functional calculations we identify a candidate muon stopping site within the unit cell, which dipole field simulations show to be consistent with the proposed magnetic structure. The possibility of incommensurate magnetic ordering is discussed for temperatures below TN = 53 K and 25 K for Sr2YOsO6 and Sr2InOsO6, respectively.

Anisotropic local modification of crystal field levels in Pr-based pyrochlores: a muon-induced effect modeled using density functional theory.

Although muon spin relaxation is commonly used to probe local magnetic order, spin freezing, and spin dynamics, we identify an experimental situation in which the measured response is dominated by an effect resulting from the muon-induced local distortion rather than the intrinsic behavior of the host compound. We demonstrate this effect in some quantum spin ice candidate materials Pr(2)B(2)O(7) (B=Sn, Zr, Hf), where we detect a static distribution of magnetic moments that appears to grow on cooling. Using density functional theory we show how this effect can be explained via a hyperfine enhancement arising from a splitting of the non-Kramers doublet ground states on Pr ions close to the muon, which itself causes a highly anisotropic distortion field. We provide a quantitative relationship between this effect and the measured temperature dependence of the muon relaxation and discuss the relevance of these observations to muon experiments in other magnetic materials.

Low-field superconducting phase of (TMTSF)2ClO4.

The low-field phase of the organic superconductor (TMTSF)(2)ClO(4) is studied by muon-spin rotation. The zero temperature limit of the magnetic penetration depth within the TMTSF layers is obtained to be λ(ab)(0) = 0.86(2) µm. Temperature dependence of the muon-spin relaxation shows no indication of gap nodes on the Fermi surface nor of any spontaneous fields due to time-reversal-symmetry breaking. The weight of evidence suggests that the symmetry of this low-field phase is odd-frequency p-wave singlet, a novel example of odd-frequency pairing in a bulk superconductor.

Spin waves and revised crystal structure of honeycomb iridate Na2IrO3.

We report inelastic neutron scattering measurements on Na2IrO3, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zigzag magnetic order. The onset of long-range magnetic order below T(N)=15.3 K is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90° Ir-O-Ir bonds required for dominant Kitaev exchange.

Chemical engineering of molecular qubits.

We show that the electron spin phase memory time, the most important property of a molecular nanomagnet from the perspective of quantum information processing, can be improved dramatically by chemically engineering the molecular structure to optimize the environment of the spin. We vary systematically each structural component of the class of antiferromagnetic Cr(7)Ni rings to identify the sources of decoherence. The optimal structure exhibits a phase memory time exceeding 15 µs.

Design and commissioning of a high magnetic field muon spin relaxation spectrometer at the ISIS pulsed neutron and muon source.

The high magnetic field (HiFi) muon instrument at the ISIS pulsed neutron and muon source is a state-of-the-art spectrometer designed to provide applied magnetic fields up to 5 T for muon studies of condensed matter and molecular systems. The spectrometer is optimised for time-differential muon spin relaxation studies at a pulsed muon source. We describe the challenges involved in its design and construction, detailing, in particular, the magnet and detector performance. Commissioning experiments have been conducted and the results are presented to demonstrate the scientific capabilities of the new instrument.

Observation of a level crossing in a molecular nanomagnet using implanted muons.

We have observed an electronic energy level crossing in a molecular nanomagnet (MNM) using muon spin relaxation. This effect, not observed previously despite several muon studies of MNM systems, provides further evidence that the spin relaxation of the implanted muon is sensitive to the dynamics of the electronic spin. Our measurements on a broken ring MNM [H(2)N(t)Bu(is)Pr][Cr(8)CdF(9)(O(2)CC(CH(3))(3))(18)], which contains eight Cr ions, show clear evidence for the S = 0 --> S = 1 transition that takes place at B(c) = 2.3 T. The crossing is observed as a resonance-like dip in the average positron asymmetry and also in the muon spin relaxation rate, which shows a sharp increase in magnitude at the transition and a peak centred within the S = 1 regime.

Magnetic and non-magnetic phases of a quantum spin liquid.

A quantum spin-liquid phase is an intriguing possibility for a system of strongly interacting magnetic units in which the usual magnetically ordered ground state is avoided owing to strong quantum fluctuations. It was first predicted theoretically for a triangular-lattice model with antiferromagnetically coupled S = 1/2 spins. Recently, materials have become available showing persuasive experimental evidence for such a state. Although many studies show that the ideal triangular lattice of S = 1/2 Heisenberg spins actually orders magnetically into a three-sublattice, non-collinear 120° arrangement, quantum fluctuations significantly reduce the size of the ordered moment. This residual ordering can be completely suppressed when higher-order ring-exchange magnetic interactions are significant, as found in nearly metallic Mott insulators. The layered molecular system κ-(BEDT-TTF)(2)Cu(2)(CN)(3) is a Mott insulator with an almost isotropic, triangular magnetic lattice of spin-1/2 BEDT-TTF dimers that provides a prime example of a spin liquid formed in this way. Despite a high-temperature exchange coupling, J, of 250 K (ref. 6), no obvious signature of conventional magnetic ordering is seen down to 20 mK (refs 7, 8). Here we show, using muon spin rotation, that applying a small magnetic field to this system produces a quantum phase transition between the spin-liquid phase and an antiferromagnetic phase with a strongly suppressed moment. This can be described as Bose-Einstein condensation of spin excitations with an extremely small spin gap. At higher fields, a second transition is found that suggests a threshold for deconfinement of the spin excitations. Our studies reveal the low-temperature magnetic phase diagram and enable us to measure characteristic critical properties. We compare our results closely with current theoretical models, and this gives some further insight into the nature of the spin-liquid phase.

Tuning the interlayer spacing of high-T_{c} Bi-based superconductors by intercalation: measuring the penetration depth and the two-dimensional superfluid density.

Substantial control of the interlayer spacing in Bi-based high temperature superconductors has been achieved through the intercalation of guest molecules between the superconducting layers. Measurements using implanted muons reveal that the penetration depth increases with increasing layer separation while T_{c} does not vary appreciably, demonstrating that the bulk superfluid density is not the determining factor controlling T_{c}. Our results strongly suggest that for Bi-based high temperature superconductors the superfluid density appearing in the Uemura scaling relation rho_{s} proportional, variantT_{c} should be interpreted as the two-dimensional density within the superconducting layers, which we find to be constant for each class of system investigated.

Coexistence of static magnetism and superconductivity in SmFeAsO(1-x)F(x) as revealed by muon spin rotation.

The recent observation of superconductivity with critical temperatures (Tc) up to 55 K in the pnictide RFeAsO(1-x)F(x), where R is a lanthanide, marks the first discovery of a non-copper-oxide-based layered high-Tc superconductor. It has raised the suspicion that these new materials share a similar pairing mechanism to the cuprate superconductors, as both families exhibit superconductivity following charge doping of a magnetic parent material. In this context, it is important to follow the evolution of the microscopic magnetic properties of the pnictides with doping and hence to determine whether magnetic correlations coexist with superconductivity. Here, we present a muon spin rotation study on SmFeAsO(1-x)F(x), with x=0-0.30 that shows that, as in the cuprates, static magnetism persists well into the superconducting regime. This analogy is quite surprising as the parent compounds of the two families have rather different magnetic ground states: itinerant spin density wave for the pnictides contrasted with the Mott-Hubbard insulator in the cuprates. Our findings therefore suggest that the proximity to magnetic order and associated soft magnetic fluctuations, rather than strong electronic correlations in the vicinity of a Mott-Hubbard transition, may be the key ingredients of high-Tc superconductors.

Muon-fluorine entanglement in fluoropolymers.

We present the results of muon spin relaxation measurements on the fluoropolymers polytetrafluoroethylene (PTFE), poly(vinylidene fluoride) (PVDF) and poly(vinyl fluoride) (PVF). Entanglement between the muon spin and the spins of the fluorine nuclei in the polymers allows us to identify the different muon stopping states that occur in each of these materials and provides a method of probing the local environment of the muon and the dynamics of the polymer chains.