Probabilistic Programming in Python using PyMC

Probabilistic programming (PP) allows flexible specification of Bayesian statistical models in code. PyMC3 is a new, open-source PP framework with an intutive and readable, yet powerful, syntax that is close to the natural syntax statisticians use to describe models. It features next-generation Markov chain Monte Carlo (MCMC) sampling algorithms such as the No-U-Turn Sampler (NUTS; Hoffman, 2014), a self-tuning variant of Hamiltonian Monte Carlo (HMC; Duane, 1987). Probabilistic programming in Python confers a number of advantages including multi-platform compatibility, an expressive yet clean and readable syntax, easy integration with other scientific libraries, and extensibility via C, C++, Fortran or Cython. These features make it relatively straightforward to write and use custom statistical distributions, samplers and transformation functions, as required by Bayesian analysis

Nuclear magnetic resonance studies of magnetic fluctuations and nematic order in iron-based superconductors

This thesis illustrates the use of the nuclear magnetic resonance (NMR) technique as a local probe for the study of static and dynamic magnetism in the iron-based superconductors. First, a Korringa ratio analysis of 59Co and 75As NMR data reveals the existence of ferromagnetic (FM) spin fluctuations in SrCo2As2 and the hole- and electron-doped BaFe2As2 families of iron-pnictide superconductors. The analysis further shows that the FM fluctuations compete with AFM fluctuations to suppress superconductivity in these materials. The FM fluctuations are thus a crucial ingredient to understanding the variability of the superconducting transition temperature (Tc) and the shape of the superconducting dome in these and other iron-pnictide families. Secondly, a study of KFe2As2 under pressures up to 2.1 GPa reveals a crossover between a high-temperature incoherent, local-moment behavior and a low-temperature coherent behavior at a crossover temperature, T*. The T* is found to increase monotonically with pressure, consistent with increasing hybridization between localized 3d orbital-derived bands with the itinerant electron bands. No anomaly in T* is seen at the critical pressure where a change of slope of Tc(p) has been observed. In the superconducting state, two-component nuclear spin-lattice relaxation is observed at low temperatures, suggesting the existence of two distinct local electronic environments. Finally, 77Se-NMR studies of FeSe subjected to external pressure and sulfur doping are presented. In pure FeSe under pressure, the NMR spectra reveal the existence of a short-range, local nematic ordered state above the bulk nematic ordering temperature. Furthermore, this local nematic order does not compete with low-energy AFM spin fluctuations. In sulfur-doped FeSe(1−x)Sx, the observed behavior of the magnetic fluctuations parallels the Tc, providing strong evidence for the primary importance of magnetic fluctuations for superconductivity, despite the presence of nematic quantum criticality in this system

Competing Magnetic Fluctuations in Iron Pnictide Superconductors: Role of Ferromagnetic Spin Correlations Revealed by NMR

In the iron pnictide superconductors, theoretical calculations have consistently shown enhancements of the static magnetic susceptibility at both the stripe-type antiferromagnetic (AFM) and in-plane ferromagnetic (FM) wavevectors. However, the possible existence of FM fluctuations has not yet been examined from a microscopic point of view. Here, using $^{75}$As NMR data, we provide clear evidence for the existence of FM spin correlations in both the hole- and electron-doped BaFe$_2$As$_2$ families of iron-pnictide superconductors. These FM fluctuations appear to compete with superconductivity and are thus a crucial ingredient to understanding the variability of $T_{\rm c}$ and the shape of the superconducting dome in these and other iron-pnictide families.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Let

NMR evidence for static local nematicity and its cooperative interplay with low-energy magnetic fluctuations in FeSe under pressure

We present $^{77}$Se-NMR measurements on single-crystalline FeSe under pressures up to 2 GPa. Based on the observation of the splitting and broadening of the NMR spectrum due to structural twin domains, we discovered that static, local nematic ordering exists well above the bulk nematic ordering temperature, $T_{\rm s}$. The static, local nematic order and the low-energy stripe-type antiferromagnetic spin fluctuations, as revealed by NMR spin-lattice relaxation rate measurements, are both insensitive to pressure application. These NMR results provide clear evidence for the microscopic cooperation between magnetism and local nematicity in FeSe.Comment: 5 pages, 5 figures, accepted for publication in Phys. Rev. B rapid communicatio