PkANN - I. Non-linear matter power spectrum interpolation through artificial neural networks

We investigate the interpolation of power spectra of matter fluctuations using Artificial Neural Network (PkANN). We present a new approach to confront small-scale non-linearities in the power spectrum of matter fluctuations. This ever-present and pernicious uncertainty is often the Achilles' heel in cosmological studies and must be reduced if we are to see the advent of precision cosmology in the late-time Universe. We show that an optimally trained artificial neural network (ANN), when presented with a set of cosmological parameters (Omega_m h^2, Omega_b h^2, n_s, w_0, sigma_8, m_nu and redshift z), can provide a worst-case error <=1 per cent (for z<=2) fit to the non-linear matter power spectrum deduced through N-body simulations, for modes up to k<=0.7 h/Mpc. Our power spectrum interpolator is accurate over the entire parameter space. This is a significant improvement over some of the current matter power spectrum calculators. In this paper, we detail how an accurate interpolation of the matter power spectrum is achievable with only a sparsely sampled grid of cosmological parameters. Unlike large-scale N-body simulations which are computationally expensive and/or infeasible, a well-trained ANN can be an extremely quick and reliable tool in interpreting cosmological observations and parameter estimation. This paper is the first in a series. In this method paper, we generate the non-linear matter power spectra using HaloFit and use them as mock observations to train the ANN. This work sets the foundation for Paper II, where a suite of N-body simulations will be used to compute the non-linear matter power spectra at sub-per cent accuracy, in the quasi-non-linear regime 0.1 h/Mpc <= k <= 0.9 h/Mpc. A trained ANN based on this N-body suite will be released for the scientific community.Comment: 12 pages, 9 figures, 2 tables, updated to match version accepted by MNRA

Magnetic excitations in the spinel compound Lix_x[Mn1.96_{1.96}Li0.04_{0.04}]O4_4 (x= 0.2, 0.6, 0.8, 1.0): how a classical system can mimic quantum critical scaling

We present neutron scattering results on the magnetic excitations in the spinel compounds Li$_x$[Mn$_{1.96}$Li$_{0.04}$]O$_4$ (x= 0.2, 0.6, 0.8, 1.0). We show that the dominant excitations below T ~ 70 K are determined by clusters of Mn^4+ ions, and that these excitations mimic the E/T-scaling found in quantum critical systems that also harbor magnetic clusters, such as CeRu$_{0.5}$Fe$_{1.5}$Ge$_2$. We argue that our results for this classical spinel compound show that the unusual response at low temperatures as observed in quantum critical systems is (at least) partially the result of the fragmentation of the magnetic lattice into smaller units. This fragmentation in quantum critical systems is the direct and unavoidable result of intrinsic disorder.Comment: 8 pages, 8 figures; to be submitted to PR

AC susceptibility of the quantum critical point mimicking series Lix[Mn1.96Li0.04]O4 (x = 0.0,0.1,0.2,0.35,0.5,0.6,0.8,1.0)

doi:10.1063/1.3367976The present work elucidates the series of magnetic phase transitions present in the series of spinel compounds Lix Mn1.96Li0.04 O4 x=0.0, 0.1, 0.2, 0.35, 0.5, 0.6, 0.8, 1.0 . These systems display dynamical scaling originating from the presence of magnetic clusters that form below 70 K. This scaling is similar to what has been observed in the 122 quantum critical point materials containing intrinsic disorder. We study this system using ac susceptibility in order to understand how disorder leads to fragmentation of the magnetic lattice. The Li doped system's antiferromagnetic AF ordering sets in below 70 K; however, for x=1 this ordering is limited to clusters of Mn4+ ions that are weakly coupled to each other. For the intermediate Li concentrations we observe the formation of individual spin clusters consistent with neutron scattering experiments and we find evidence for the coaligning of these clusters for T 20 K. A maximum in the peak of the susceptibility versus Li content between x=0.5 and x=0.35 indicates a crossover from a regime dominated by the cluster dynamics to one in which the long- range order of the delithiated -MnO2 phase begins to emerge. We discuss the magnetic phase diagram pertaining to short-range order in relationship to the dynamic response of these systems as measured by inelastic neutron scattering experiments. [copyright] 2010 American Institute of Physics.This research is supported by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Grant No. DE-FG02-07ER46381

Quantum Magnetic Properties in Perovskite with Anderson Localized Artificial Spin-1/2

Quantum magnetic properties in a geometrically frustrated lattice of spin-1/2 magnet, such as quantum spin liquid or solid and the associated spin fractionalization, are considered key in developing a new phase of matter. The feasibility of observing the quantum magnetic properties, usually found in geometrically frustrated lattice of spin-1/2 magnet, in a perovskite material with controlled disorder is demonstrated. It is found that the controlled chemical disorder, due to the chemical substitution of Ru ions by Co-ions, in a simple perovskite CaRuO3 creates a random prototype configuration of artificial spin-1/2 that forms dimer pairs between the nearest and further away ions. The localization of the Co impurity in the Ru matrix is analyzed using the Anderson localization formulation. The dimers of artificial spin-1/2, due to the localization of Co impurities, exhibit singlet-to-triplet excitation at low temperature without any ordered spin correlation. The localized gapped excitation evolves into a gapless quasi-continuum as dimer pairs break and create freely fluctuating fractionalized spins at high temperature. Together, these properties hint at a new quantum magnetic state with strong resemblance to the resonance valence bond system.Comment: 8 pages, 6 figure

Magnetic Excitations in the Spinel Compound Liₓ [Mn₁.₉₆ Li₀.₀₄] O₄ (x=0.2,0.6,0.8,1.0 ): How a Classical System can Mimic Quantum Critical Scaling

We present neutron-scattering results on the magnetic excitations in the spinel compounds Lix [Mn1.96 Li0.04] O4 (x=0.2,0.6,0.8,1.0). We show that the dominant excitations below T~70K are determined by Mn ions located in clusters, and that these excitations mimic the dynamic scaling found in quantum critical systems that also harbor magnetic clusters, such as CeRu0.5 Fe1.5 Ge2. We argue that our results for this classical spinel compound suggest that the unusual response at low temperatures as observed in quantum critical systems that have been driven to criticality through substantial chemical doping is (at least) partially the result of the fragmentation of the magnetic lattice into smaller units

Synthesis and characterization of Ca-doped LaMnAsO

We report on our attempt to hole-dope the antiferromagnetic semiconductor LaMnAsO by substitution of the La3+ site by Ca2+. We use neutron and x-ray diffraction, magnetic susceptibility, and transport techniques to characterize polycrystalline (La1−xCax)MnAsO samples prepared by solid-state reaction and find that the parent compound is highly resistant to substitution with an upper limit x≤0.01. Magnetic susceptibility of the parent and the x=0.002(xnom=0.04) compounds indicate a negligible presence of magnetic impurities (i.e., MnO or MnAs). Rietveld analysis of neutron and x-ray diffraction data shows the preservation of both the tetragonal (P4/nmm) structure upon doping and the antiferromagnetic ordering temperature, TN=355±5 K