Search NASA⌕ Search

SEARCH · Search NASA

Results for “specific correlation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33

Holographic flows from CFT to the Kasner universe

The Schwarzschild singularity is known to be classically unstable. We demonstrate a simple holographic consequence of this fact, focusing on a perturbation that is uniform in boundary space and time. Deformation of the thermal state of the dual CFT by a relevant operator triggers a nonzero temperature holographic renormalization group flow in the bulk. This flow continues smoothly through the horizon and, at late interior time, deforms the Schwarzschild singularity into a more general Kasner universe. We show that the deformed near-singularity, trans-horizon Kasner exponents determine specific non-analytic corrections to the thermal correlation functions of heavy operators in the dual CFT, in the analytically continued ‘near-singularity’ regime.

79 ASTRONOMY AND ASTROPHYSICS↗

Quantitative analysis of Raman spectral parameters for carbon fibers: practical considerations and connection to mechanical properties

Although the literature on the Raman spectra of carbon fibers is vast, no consistent, robust predictive relationship between mechanical properties of carbon fibers and spectral parameters exists. This shortcoming is due to the use of numerous fitting functions to evaluate Raman spectra of carbon fibers and the inconsistencies in establishing the best fitting models in a statistically robust fashion. To address this gap, we present a comprehensive work on the Raman spectra of carbon fibers that combines a vast library of experimental data with a robust numerical analysis and a statistical evaluation of a wide range of suggested fitting models. This manuscript begins with a brief review of the commonly applied fitting models. Then, the Raman spectra of 32 commercially available polyacrylonitrile-based carbon fibers collected at excitation wavelengths 532, 633, and 785 nm are presented and the best fit for all fibers is evaluated based on several statistical criteria in conjunction with numerical calculations and physical arguments. The results suggest that high-performance fibers must be fit with at least five peaks, whereas high-tensile modulus fibers are best fit with at least six distinct peaks. Finally, we employ simultaneous fitting of the Raman spectra of specific fibers and wavelengths and demonstrate that strong correlations exist between mechanical properties and the D1 peak position and shape across the range of evaluated mechanical properties. Finally, we suggest straightforward improvements in fitting analysis procedures that can be implemented to increase coherency in the understanding of the underlying carbon fiber microstructure intuited from Raman spectroscopy.

36 MATERIALS SCIENCE↗

Cerebral Cortex Regions Selectively Vulnerable to Radiation Dose-Dependent Atrophy

Purpose and Objectives: Neurologic deficits after brain radiation therapy (RT) typically involve decline in higher-order cognitive functions such as attention and memory rather than sensory defects or paralysis. We sought to determine whether areas of the cortex critical to cognition are selectively vulnerable to radiation dose-dependent atrophy. Methods and Materials: We measured change in cortical thickness in 54 primary brain tumor patients who underwent fractionated, partial brain RT. The study patients underwent high-resolution, volumetric magnetic resonance imaging (T1-weighted; T2 fluid-attenuated inversion recovery, FLAIR) before RT and 1 year afterward. Semiautomated software was used to segment anatomic regions of the cerebral cortex for each patient. Cortical thickness was measured for each region before RT and 1 year afterward. Two higher-order cortical regions of interest (ROIs) were tested for association between radiation dose and cortical thinning: entorhinal (memory) and inferior parietal (attention/memory). For comparison, 2 primary cortex ROIs were also tested: pericalcarine (vision) and paracentral lobule (somatosensory/motor). Linear mixed-effects analyses were used to test all other cortical regions for significant radiation dose-dependent thickness change. Statistical significance was set at α = 0.05 using 2-tailed tests. Results: Cortical atrophy was significantly associated with radiation dose in the entorhinal (P=.01) and inferior parietal ROIs (P=.02). By contrast, no significant radiation dose-dependent effect was found in the primary cortex ROIs (pericalcarine and paracentral lobule). In the whole-cortex analysis, 9 regions showed significant radiation dose-dependent atrophy, including areas responsible for memory, attention, and executive function (P≤.002). Conclusions: Areas of cerebral cortex important for higher-order cognition may be most vulnerable to radiation-related atrophy. This is consistent with clinical observations that brain radiation patients experience deficits in domains of memory, executive function, and attention. Correlations of regional cortical atrophy with domain-specific cognitive functioning in prospective trials are warranted.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Persistent Protein Motions in a Rugged Energy Landscape Revealed by Normal Mode Ensemble Analysis

Proteins are allosteric machines that couple motions at distinct, often distant, sites to control biological function. Low-frequency structural vibrations are a mechanism of this long-distance connection and are often used computationally to predict correlations, but experimentally identifying the vibrations associated with specific motions has proved challenging. Spectroscopy is an ideal tool to explore these excitations, but measurements have been largely unable to identify important frequency bands. The result is at odds with some previous calculations and raises the question what methods could successfully characterize protein structural vibrations. Here we show the lack of spectral structure arises in part from the variations in protein structure as the protein samples the energy landscape. However, by averaging over the energy landscape as sampled using an aggregate 18.5 μs of all-atom molecular dynamics simulation of hen egg white lysozyme and normal-mode analyses, we find vibrations with large overlap with functional displacements are surprisingly concentrated in narrow frequency bands. These bands are not apparent in either the ensemble averaged vibrational density of states or isotropic absorption. However, in the case of the ensemble averaged anisotropic absorption, there is persistent spectral structure and overlap between this structure and the functional displacement frequency bands. We systematically lay out heuristics for calculating the spectra robustly, including the need for statistical sampling of the protein and inclusion of adequate water in the spectral calculation. The results show the congested spectrum of these complex molecules obscures important frequency bands associated with function and reveal a method to overcome this congestion by combining structurally sensitive spectroscopy with robust normal mode ensemble analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

Here, we analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call “complexity reduction”. In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature T g of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2–6 nm at T g . Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

cancer↗

Chemical Framework to Design Linear-like Relaxors toward Capacitive Energy Storage

ABO 3 -type perovskite relaxor ferroelectrics (RFEs) have emerged as the preferred option for dielectric capacitive energy storage. However, the compositional design of RFEs with high energy density and efficiency poses significant challenges owing to the vast compositional space and the absence of general rules. Here, we present an atomic-level chemical framework that captures inherent characteristics in terms of radius and ferroelectric activity of ions. By categorizing A/B-site ions as host framework, rattling, ferroelectrically active, and blocking ions and assembling these four types of ions with specific criteria, linear-like relaxors with weak locally correlated and highly extendable unit-cell polarization vectors can be constructed. As example, we demonstrate two new compositions of Bi 0.5 K 0.5 TiO 3- based and BaTiO 3- based relaxors, showing extremely high recoverable energy densities of 17.3 and 12.1 J cm –3 , respectively, both with a high efficiency of about 90%. Further, the role of different types of ions in forming heterogeneous polar structures is identified through element-specific local structure analysis using neutron total scattering combined with reverse Monte Carlo modeling. Further, our work not only opens up new avenues toward rational compositional design of high energy storage performance lead-free RFEs but also sheds light on atomic-level manipulation of functional properties in compositionally complex ferroelectrics.

25 ENERGY STORAGE↗

Using Machine Learning to Predict Cloud Turbulent Entrainment–Mixing Processes

Different turbulent entrainment–mixing mechanisms between clouds and environment are essential to cloud–related processes; however, accurate representation of entrainment–mixing in weather/climate models still poses a challenge. This study exploits the use of machine learning (ML) to address this challenge. Four ML (Light Gradient Boosting Machine [LGB], eXtreme Gradient Boosting, Random Forest, and Support Vector Regression) are examined and compared. It is found that LGB performs best, and thus is selected to understand the impact of entrainment–mixing on microphysics using simulation data from Explicit Mixing Parcel Model. Compared with traditional parameterizations, the trained LGB provides more accurate microphysical properties (number concentration and cloud droplet spectral dispersion). The partial dependences of predicted microphysics on features exhibit a strong alignment with physical mechanisms and expectations, as determined by the interpreting method, thus overcoming the limitations of the “black box” scheme. The underlying mechanisms are that the smaller number concentration and larger spectral dispersion correspond to more inhomogeneous entrainment–mixing. Specifically, number concentration after entrainment–mixing is positively correlated with adiabatic number concentration and liquid water content affected by entrainment–mixing, and inversely correlated with adiabatic volume mean radius. Spectral dispersion after entrainment–mixing is negatively correlated with liquid water content affected by entrainment–mixing, turbulent dissipation rate and relative humidity of entrained air. Sensitivity analysis further suggests that number concentration is mainly determined by cloud microphysical properties whereas spectral dispersion is influenced by both cloud microphysical properties and environmental variables. The results indicate that the LGB scheme has the potential to enhance the representation of entrainment–mixing in weather/climate models.

54 ENVIRONMENTAL SCIENCES↗

Airborne observations reveal elevational gradient in tropical forest isoprene emissions

Terrestrial vegetation emits vast quantities of volatile organic compounds (VOCs) to he atmosphere1-3, which influence oxidants and aerosols leading to complex feedbacks on air quality and climate4-6. Isoprene dominates global non-methane VOC emissions with tropical regions contributing ~80% of global isoprene emissions2. Isoprene emission rates vary over several orders of magnitude for different plant species, and characterizing this immense biological chemodiversity is a challenge for estimating isoprene emission from tropical forests. Here we present the isoprene emission estimates from aircraft direct eddy covariance measurements over the pristine Amazon forest. We report isoprene emission rates that are 3 times higher than satellite top-down estimates and 35% higher than model predictions based on satellite land cover and vegetation specific emission factors (EFs). The results reveal strong correlations between observed isoprene emission rates and terrain elevations which are confirmed by similar correlations between satellite-derived isoprene emissions and terrain elevations. We propose that the elevational gradient in the Amazonian forest isoprene emission capacity is determined by plant species distributions and can explain a substantial degree of isoprene emission variability in tropical forests. Finally, we apply this approach over the central Amazon and use a model to demonstrate the impacts on regional air quality.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Direct observation of a dynamical glass transition in a nanomagnetic artificial Hopfield network

Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those describing brain function, error-correcting codes5 or stock-market dynamics. This wide interest in spin glasses provides strong motivation to generate an artificial spin glass within the framework of artificial spin ice systems. Here we present the experimental realization of an artificial spin glass consisting of dipolar coupled single-domain Ising-type nanomagnets arranged onto an interaction network that replicates the aspects of a Hopfield neural network. Using cryogenic X-ray photoemission electron microscopy (XPEEM), we performed temperature-dependent imaging of thermally driven moment fluctuations within these networks and observed characteristic features of a two-dimensional Ising spin glass. Specifically, the temperature dependence of the spin glass correlation function follows a power-law trend predicted from theoretical models on two-dimensional spin glasses. As a result, we observe clear signatures of the hard-to-observe rugged spin glass free energy in the form of sub-aging, out-of-equilibrium autocorrelations and a transition from stable to unstable dynamics.

36 MATERIALS SCIENCE↗

Predictions of delafossite-hosted honeycomb and kagome phases

Delafossites, typically denoted by the formula ABO 2 , are a class of layered materials that exhibit a wide range of electronic and optical properties. Recently, the idea of modifying these delafossites into ordered kagome or honeycomb phases via strategic doping has emerged as a potential way to tailor these properties. In this study, we use high-throughput density functional theory calculations to explore many possible candidate kagome and honeycomb phases by considering dopants selected from the parent compounds of known ternary delafossite oxides from the inorganic crystal structure database. Here our results indicate that while A-site in existing delafossites can host a limited range of elemental specifies, and display a low propensity for mixing or ordering, the oxide sub-units in the BO 2 much more readily admit guest species. Our study identifies four candidate B-site kagome and fifteen candidate B-site honeycombs with a formation energy more than 50 meV f.u. −1 below other competing phases. The ability to predict and control the formation of these unique structures offers exciting opportunities in materials design, where innovative properties can be engineered through the selection of specific dopants. A number of these constitute novel correlated metals, which may be of interest for subsequent efforts in synthesis. These novel correlated metals may have significant implications for quantum computing, spintronics, and high-temperature superconductivity, thus inspiring future experimental synthesis and characterization of these proposed materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reduction of on-resistance and current crowding in quasi-vertical GaN power diodes

This paper studies the key parameters affecting on-resistance and current crowding in quasi-vertical GaN power devices by experiment and simulation. The current distribution in the drift region, n−-GaN, was found to be mainly determined by the sheet resistance of the current spreading layer, n+-GaN. The actual on-resistance of the drift region significantly depends on this current distribution rather than the intrinsic resistivity of the drift layer. As a result, the total specific on-resistance of quasi-vertical diodes shows a strong correlation with the device area and sheet resistance of the current spreading layer. By reducing the sheet resistance of the current spreading layer, the specific on-resistance of quasi-vertical GaN-on-Si power diodes has been reduced from ∼10 mΩ·cm2 to below 1 mΩ·cm2. Design space of the specific on-resistance at different breakdown voltage levels has also been revealed in optimized quasi-vertical GaN power diodes.

Zhang, Yuhao (ORCID:0000000228495653)↗

Communication: A mean field platform for excited state quantum chemistry

We present a mean field theory for excited states that is broadly analogous to ground state Hartree-Fock theory. Like Hartree-Fock, our approach is deterministic, state-specific, applies a variational principle to a minimally correlated ansatz, produces energy stationary points, relaxes the orbital basis, has a Fock-build cost-scaling, and can serve as the foundation for correlation methods such as perturbation theory and coupled cluster theory. To emphasize this last point, we pair our mean field approach with an excited state analog of second order Møller-Plesset theory and demonstrate that in water, formaldehyde, neon, and stretched lithium fluoride, the resulting accuracy far exceeds that of configuration interaction singles and rivals that of equation of motion coupled cluster.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Controlling morphology in hybrid isotropic/patchy particle assemblies

Brownian dynamics is used to study self-assembly in a hybrid system of isotropic particles (IPs), combined with anisotropic building blocks that represent special “designer particles.” Those are modeled as spherical patchy particles (PPs) with binding only allowed between their patches and IPs. In this study, two types of PPs are considered: Octahedral PPs (Oh-PPs) and Square PPs (Sq-PPs), with octahedral and square arrangements of patches, respectively. The self-assembly is additionally facilitated by the simulated annealing procedure. Here, the resultant structures are characterized by a combination of local correlations in cubatic ordering and a symmetry-specific variation of bond orientation order parameters (SymBOPs). By varying the PP/IP size ratio, we detected a sharp crossover between two distinct morphologies in both types of systems. High symmetry phases, NaCl crystal for Oh-PP and square lattice for Sq-PP, are observed for larger size ratios. For the smaller ones, the dominant morphologies are significantly different, e.g., Oh-PPs form a compact amorphous structure with predominantly face-to-face orientation of neighboring PPs. Unusually, for a morphology without a long-range order, it is still possible to identify well organized coherent clusters of this structure, thanks to the adoption of our SymBOP-based characterization.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra

Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light–matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori–Nakajima–Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method’s capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.

Chemistry↗

Understanding Interfacial Electrochemical Reactions through in situ ec-STEM and IL-Cryo-STEM

A major criterion in the design of next generation materials for electrical energy storage applications is a comprehensive understanding of interfacial electrochemical reactions as well as correlating the structure and chemistry across site-specific electrode/electrolyte interfaces with electron, charge, and mass transport processes as they govern performance characteristics. Scanning transmission electron microscopy (STEM) based techniques have emerged as an indispensable materials characterization tool that provides high spatial resolution imaging and chemical analysis and has been effectively utilized to obtain an atomic to nanoscale view of the interfacial structure before and after electrochemical cycling. More recently, there have been several advances that now allows us to obtain more detailed mechanistic insight into evolving reactions through in situ ec-STEM and electrical biasing platforms such as in the understanding of the mechanisms of solid electrolyte interphase formation, lithium dendrite nucleation and growth mechanisms and ionic transport mechanisms within intercalation, conversion, and alloying electrode materials. Several major advantages of the in situ ec-STEM approach is the quantitative electrochemical measurement of charge passed during cycling with simultaneous analysis of the electrochemical processes with STEM imaging and diffraction. Here, while spectroscopic analysis of the electrochemical reactions products has been performed, there is the issue of beam sensitivity and therefore, Cryo-STEM imaging combined with electron energy loss spectroscopy (EELS) techniques have been employed to analyze the chemistry of the SEI and Li dendrites. In this talk, we discuss the potential for combining identical location (IL) STEM techniques with Cryo-EM. The advantage of using this approach is that the sample is placed on a conventional TEM grid and the exact same location of the specimen can be analyzed before and after quantitative electrochemical measurements. Moreover, since the sample is on the TEM grid, the grid itself can be prepared for further Cryo-TEM experiments by plunge freezing in liquid nitrogen then transferred to the Cryo-TEM under liquid nitrogen. Results obtain from these experiments can be used to enhance our scientific understanding of interfacial chemistry at electrode/electrolyte interfaces and may be useful in the design of new materials.

36 MATERIALS SCIENCE↗

Crystal and magnetic structures of magnetic topological insulators MnBi 2 Te 4 and MnBi 4 Te 7

Using single-crystal neutron diffraction, we present a systematic investigation of the crystal structure and magnetism of the van der Waals topological insulators MnBi 2 Te 4 and MnBi 4 Te 7 , where rich topological quantum states have been recently predicted and observed. Structural refinements reveal that considerable Bi atoms occupied on the Mn sites in both materials, distinct from the previously reported antisite disorder. We show unambiguously that MnBi 2 Te 4 orders antiferromagnetically below 24 K, featured by a magnetic symmetry R I - 3 c , while MnBi 4 Te 7 is antiferromagnetic below 13 K with a magnetic space group P c - 3 c 1 . They both present antiferromagnetically coupled ferromagnetic layers with spins along the c axis. We put forward a stacking rule for the crystal structure of an infinitely adaptive series MnBi 2 n Te 3 n + 1 ( n ≥ 1 ) with a building unit of [ Bi 2 Te 3 ] . Overall, by comparing the magnetic properties between MnBi 2 Te 4 and MnBi 4 Te 7 , together with recent density-functional theory calculations, we concluded that a two-dimensional magnetism limit might be realized in the derivatives. Our work may promote theoretical studies of topological magnetic states in the series of MnBi 2 n Te 3 n + 1 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantifying multipoint ordering in alloys

A central problem in multicomponent lattice systems is to systematically quantify multipoint ordering. Ordering in such systems is often described in terms of pairs, even though this is not sufficient when three-point and higher-order interactions are included in the Hamiltonian. Current models and parameters for multipoint ordering are often only applicable for very specific cases or require approximating a subset of correlated occupational variables on a lattice as being uncorrelated. In this paper, cluster order parameters are introduced to systematically quantify arbitrary multipoint ordering motifs in substitutional systems through direct calculations of normalized cluster probabilities. These parameters can describe multipoint chemical ordering in crystal systems with multiple sublattices, multiple components, and systems with reduced symmetry. These are defined in this paper and applied to quantify four-point chemical ordering motifs in platinum/palladium alloy nanoparticles that are of practical interest to the synthesis of catalytic nanocages. Impacts of chemical ordering on nanocage stability are discussed. It is demonstrated that approximating four-point probabilities from superpositions of lower-order pair probabilities is not sufficient in cases where three- and four-body terms are included in the energy expression. Furthermore, conclusions about the formation mechanisms of nanocages may change significantly when using common pair approximations.

36 MATERIALS SCIENCE↗

Itinerant G-type antiferromagnet SrCr 2 As 2 studied by magnetization, heat capacity, electrical resistivity, and NMR measurements

Here, the physical properties of itinerant antiferromagnetic (AFM) SrCr 2 As 2 with body-centered tetragonal ThCr 2 Si 2 structure were investigated in single crystalline and polycrystalline forms by electrical resistivity ρ, heat capacity C p , magnetic susceptibility χ versus temperature T, and magnetization M versus applied magnetic field H isotherm measurements as well as 75 As and 53 Cr nuclear magnetic resonance (NMR) measurements in the wide temperature range T = 1.6–900 K. From the χ(T) and 75 As NMR measurements, the G-type AFM state below T N = 615(15) K has been determined, consistent with the previous neutron-diffraction measurements. Direct evidence of magnetic ordering of the Cr spins was shown by the observation of the 53 Cr NMR spectrum under H = 0. From the χ( T) measurements on single-crystal SrCr 2 As 2 under the two different magnetic field directions H|| ab and H || c in the AFM state, the Cr ordered moments are shown to align along the c axis in the G-type AFM state. The metallic state is directly evidenced by the ρ, C p , and NMR measurements, and the density of states at the Fermi energy $\mathscr{D}$(E F ) in the AFM state is estimated to be 7.53 states/eV f.u. for both spin directions which is almost twice the bare $\mathscr{D}$(E F ) estimated from first-principles calculations, suggesting an enhancement of the conduction-carrier mass by a factor of two in the AFM state. The $\mathscr{D}$(E F ) is found to be nearly constant below at least 100 K and is independent of H. The ρ(T) is found to show T-linear behavior above T N and exhibits positive curvature below T N where significant loss of spin-disorder scattering upon magnetic ordering is observed. The resistivity anisotropy of the compound remains moderate ρ c /ρ a ~ 9 through most of the magnetically ordered phase but shows a rapid increase below 50 K.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗