Machine learning approach to muon spectroscopy analysis

In recent years, artificial intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised machine learning (ML) algorithm called principal component analysis (PCA) as a tool to analyse the data from muon spectroscopy experiments. Specifically, we apply the ML technique to detect phase transitions in various materials. The measured quantity in muon spectroscopy is an asymmetry function, which may hold information about the distribution of the intrinsic magnetic field in combination with the dynamics of the sample. Sharp changes of shape of asymmetry functions-measured at different temperatures-might indicate a phase transition. Existing methods of processing the muon spectroscopy data are based on regression analysis, but choosing the right fitting function requires knowledge about the underlying physics of the probed material. Conversely, PCA focuses on small differences in the asymmetry curves and works without any prior assumptions about the studied samples. We discovered that the PCA method works well in detecting phase transitions in muon spectroscopy experiments and can serve as an alternative to current analysis, especially if the physics of the studied material are not entirely known. Additionally, we found out that our ML technique seems to work best with large numbers of measurements, regardless of whether the algorithm takes data only for a single material or whether the analysis is performed simultaneously for many materials with different physical properties.

Wave Vector Difference of Magnetic Bragg Reflections and Low Energy Magnetic Excitations in Charge-stripe Ordered La2NiO4.11

We report on the magnetism of charge-stripe ordered La₂NiO_4.11±0.01 by neutron scattering and μSR. On going towards zero energy transfer there is an observed wave vector offset in the centring of the magnetic excitations and magnetic Bragg reflections, meaning the excitations cannot be described as Goldstone modes of the magnetic order. Weak transverse field μSR measurements determine the magnetically order volume fraction is 87% from the two stripe twins, and the temperature evolution of the magnetic excitations is consistent with the low energy excitations coming from the magnetically ordered volume of the material. We will discuss how these results contrast with the proposed origin of a similar wave vector offset recently observed in a La-based cuprate, and possible origins of this effect in La₂NiO_4.11.

Design and implementation of a low temperature, inductance based high frequency alternating current susceptometer

We report on the implementation of an induction based, low temperature, high frequency ac susceptometer capable of measuring at frequencies up to 3.5 MHz and at temperatures between 2 K and 300 K. Careful balancing of the detection coils and calibration allow a sample magnetic moment resolution of 5 × 10^-10 Am² at 1 MHz. We discuss the design and characterization of the susceptometer and explain the calibration process. We also include some example measurements on the spin ice material CdEr₂S₄ and iron oxide based nanoparticles to illustrate functionality.

Nuclear spin assisted quantum tunnelling of magnetic monopoles in spin ice

Extensive work on single molecule magnets has identified a fundamental mode of relaxation arising from the nuclear-spin assisted quantum tunnelling of nearly independent and quasi-classical magnetic dipoles. Here we show that nuclear-spin assisted quantum tunnelling can also control the dynamics of purely emergent excitations: magnetic monopoles in spin ice. Our low temperature experiments were conducted on canonical spin ice materials with a broad range of nuclear spin values. By measuring the magnetic relaxation, or monopole current, we demonstrate strong evidence that dynamical coupling with the hyperfine fields bring the electronic spins associated with magnetic monopoles to resonance, allowing the monopoles to hop and transport magnetic charge. Our result shows how the coupling of electronic spins with nuclear spins may be used to control the monopole current. It broadens the relevance of the assisted quantum tunnelling mechanism from single molecular spins to emergent excitations in a strongly correlated system.

Spin ice compounds have localised excitations that behave as magnetic monopoles which move by hopping from site to site, creating a chain of spins. Here the authors show that the hyperfine coupling between electron and nuclear spins is an important part of the mechanism underlying monopole motion.

Observation of a superconducting glass state in granular superconducting diamond

The magnetic field dependence of the superconductivity in nanocrystalline boron doped diamond thin films is reported. Evidence of a superconducting glass state is presented, as demonstrated by the observation of a quasi de Almeida-Thouless line in the phase diagram and a logarithmic time dependence of the magnetism. The position of the phase boundary in the H-T plane is determined from electrical transport data by detailed fitting to quasi-zero-dimensional fluctuation conductivity theory. This allows determination of the boundary between resistive and non-resistive behaviour to be made with greater precision than the standard ad hoc onset/midpoint/offset criterion. We attribute the glassy superconductivity to the morphological granularity of the diamond films.

Pauling Entropy, Metastability, and Equilibrium in Dy_{2}Ti_{2}O_{7} Spin Ice

Determining the fate of the Pauling entropy in the classical spin ice material Dy_{2}Ti_{2}O_{7} with respect to the third law of thermodynamics has become an important test case for understanding the existence and stability of ice-rule states in general. The standard model of spin ice-the dipolar spin ice model-predicts an ordering transition at T≈0.15  K, but recent experiments by Pomaranski et al. suggest an entropy recovery over long timescales at temperatures as high as 0.5 K, much too high to be compatible with the theory. Using neutron scattering and specific heat measurements at low temperatures and with long timescales (0.35  K/10^{6}  s and 0.5  K/10^{5}  s, respectively) on several isotopically enriched samples, we find no evidence of a reduction of ice-rule correlations or spin entropy. High-resolution simulations of the neutron structure factor show that the spin correlations remain well described by the dipolar spin ice model at all temperatures. Furthermore, by careful consideration of hyperfine contributions, we conclude that the original entropy measurements of Ramirez et al. are, after all, essentially correct: The short-time relaxation method used in that study gives a reasonably accurate estimate of the equilibrium spin ice entropy due to a cancellation of contributions.

Dipolar Spin Ice States with a Fast Monopole Hopping Rate in CdEr_{2}X_{4} (X=Se, S)

Excitations in a spin ice behave as magnetic monopoles, and their population and mobility control the dynamics of a spin ice at low temperature. CdEr_{2}Se_{4} is reported to have the Pauling entropy characteristic of a spin ice, but its dynamics are three orders of magnitude faster than the canonical spin ice Dy_{2}Ti_{2}O_{7}. In this Letter we use diffuse neutron scattering to show that both CdEr_{2}Se_{4} and CdEr_{2}S_{4} support a dipolar spin ice state-the host phase for a Coulomb gas of emergent magnetic monopoles. These Coulomb gases have similar parameters to those in Dy_{2}Ti_{2}O_{7}, i.e., dilute and uncorrelated, and so cannot provide three orders faster dynamics through a larger monopole population alone. We investigate the monopole dynamics using ac susceptometry and neutron spin echo spectroscopy, and verify the crystal electric field Hamiltonian of the Er^{3+} ions using inelastic neutron scattering. A quantitative calculation of the monopole hopping rate using our Coulomb gas and crystal electric field parameters shows that the fast dynamics in CdEr_{2}X_{4} (X=Se, S) are primarily due to much faster monopole hopping. Our work suggests that CdEr_{2}X_{4} offer the possibility to study alternative spin ice ground states and dynamics, with equilibration possible at much lower temperatures than the rare earth pyrochlore examples.

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.

Calculating electron momentum densities and Compton profiles using the linear tetrahedron method

A method for computing electron momentum densities and Compton profiles from ab initio calculations is presented. Reciprocal space is divided into optimally-shaped tetrahedra for interpolation, and the linear tetrahedron method is used to obtain the momentum density and its projections such as Compton profiles. Results are presented and evaluated against experimental data for Be, Cu, Ni, Fe3Pt, and YBa2Cu4O8, demonstrating the accuracy of our method in a wide variety of crystal structures.

Neutron scattering and μSR investigations of the low temperature state of LuCuGaO₄

LuCuGaO₄ has magnetic Cu(2+) and diamagnetic Ga(3+) ions distributed on a triangular bilayer and is suggested to undergo a spin glass transition at Tg ∼ 0.4 K. Using μSR (muon spin rotation) and neutron scattering measurements, we show that at low temperature the spins form a short range correlated state with spin fluctuations detectable over a wide range of timescales: at 0.05 K magnetic fluctuations can be detected in both the μSR time window and also extending beyond 7 meV in the inelastic neutron scattering response, indicating magnetic fluctuations spanning timescales between ∼10(-5) and ∼10(-10) s. The dynamical susceptibility scales according to the form χ″(ω)T(α), with α = 1, throughout the measured temperature range (0.05-50 K). These effects are associated with quantum fluctuations and some degree of structural disorder in ostensibly quite different materials, including certain heavy fermion alloys, kagome spin liquids, quantum spin glasses, and valence bond glasses. We therefore suggest that LuCuGaO₄ is an interesting model compound for the further examination of disorder and quantum magnetism.

Measurement of magnetic exchange in ferromagnet-superconductor La2/3Ca1/3MnO3/YBa2Cu3O7 bilayers

The existence of coherent magnetic correlations in the normal phase of cuprate high-temperature superconductors has proven difficult to measure directly. Here we report on a study of ferromagnetic-superconductor bilayers of La2/3Ca1/3MnO3/YBa2Cu3O7 (LCMO/YBCO) with varying YBCO layer thicknesses. Using x-ray magnetic circular dichroism, we demonstrate that the ferromagnetic layer induces a Cu magnetic moment in the adjacent high-temperature superconductor. For thin samples, this moment exists at all temperatures below the Curie temperature of the LCMO layer. However, for a YBCO layer thicker than 12 unit cells, the Cu moment is suppressed for temperatures above the superconducting transition, suggesting this to be a direct measurement of magnetic coherence in the normal state of a superconducting oxide.

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.

Bulk spin polarization of Co(1-x)Fe(x)S2

We report on a new method to determine the degree of bulk spin polarization in single crystal Co(1-x)Fe(x)S2 by modeling magnetic Compton scattering with ab initio calculations. Spin-dependent Compton profiles were measured for CoS2 and Co0.9Fe0.1S2. The ab initio calculations were then refined by rigidly shifting the bands to provide the best fit between the calculated and experimental directional profiles for each sample. The bulk spin polarizations, P, corresponding to the spin-polarized density of states at the Fermi level, were then extracted from the refined calculations. The values were found to be P=-72+/-6% and P=18+/-7% for CoS2 and Co0.9Fe0.1S2, respectively. Furthermore, determinations of P weighted by the Fermi velocity (v(F) or v(F)2) were obtained, permitting a rigorous comparison with other experimental data and highlighting the experimental dependence of P on v(F).

Static magnetic order in Tb2Sn2O7 revealed by muon spin relaxation with exterior muon implantation

Tb2Sn2O7 has been proposed as an ordered spin ice, but the precise nature of the low temperature magnetic state remains uncertain. Recent independent muon spin relaxation (microSR) investigations suggest the possibility of exotic ground states with static order precluded on time scales longer than 10(-6) s. Here the more conventional hypothesis of canted ferromagnetism is tested by means of microSR with the muons stopped outside the sample, as well as ultralow field bulk magnetization measurements. The field cooled state shows conventional static order, while the zero field cooled state may be interpreted in terms of conventional closed domains. These results rule out purely dynamical ground states and illustrate the value of exterior muon implantation as a complement to the conventional technique.

Muon spin rotation studies of spin dynamics at avoided level crossings in LiY0.998Ho0.002F4

We have studied the Ho3+ spin dynamics for LiY0.998Ho0.002F4 via the positive muon (mu+) transverse field depolarization rate lambdaTF as a function of temperature and magnetic field. We find sharp minima in lambdaTF(H) at fields for which the Ho3+ ion system has field-induced (avoided) level crossings. The reduction scales with calculated level repulsions, suggesting that mu+ depolarization by slow fluctuations of nonresonant Ho3+ spin states is partly suppressed when resonant tunneling opens new fluctuation channels at frequencies much greater than the muon precession frequency.