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DOE OSTI2022

Fragmentation analysis of a bar with the Lip-field approach

The Lip-field approach was introduced in Moës and Chevaugeon (2021) as a new way to regularize softening material models. It was tested in 1D quasistatic in Moës and Chevaugeon (2021) and 2D quasistatic in Chevaugeon and Moës (2021): this paper extends it to 1D dynamics, on the challenging problem of dynamic fragmentation. The Lip-field approach formulates the mechanical problem to be solved as an optimization problem, where the incremental potential to be minimized is the non-regularized one. Spurious localization is prevented by imposing a Lipschitz constraint on the damage field. Here, the displacement and damage field at each time step are obtained by a staggered algorithm, that is the displacement field is computed for a fixed damage field, then the damage field is computed for a fixed displacement field. Indeed, these two problems are convex, which is not the case of the global problem where the displacement and damage fields are sought at the same time. The incremental potential is obtained by equivalence with a cohesive zone model, which makes material parameters calibration simple. A non-regularized local damage equivalent to a cohesive zone model is also proposed. It is used as a reference for the Lip-field approach, without the need to implement displacement jumps. These approaches are applied to the brittle fragmentation of a 1D bar with randomly perturbed material properties to accelerate spatial convergence. Both explicit and implicit dynamic implementations are compared. Favorable comparison to several analytical, numerical and experimental references serves to validate the modeling approach.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Electric Field Effects on Water and Ion Structure and Diffusion at the Orthoclase (001)–Water Interface

Understanding the electrochemical properties of mineral–water interfaces tends to rely upon electrical double layer (EDL) models, but these models are based on the assumption that electrostatic equilibrium is constantly maintained. In reality, interfacial reactions, ion diffusion, and their electrochemical signatures are based in nonequilibrium conditions of locally or globally imbalanced electrical fields where current EDL models have limited purview. In this work, we performed molecular dynamics (MD) simulations of the orthoclase (001) surface in contact with a 1 M NaCl aqueous solution under various electric fields, to explore the interplay between EDL structure and dynamics when perturbed by electric fields of different direction and strength, by confinement, and by different distributions of structural surface charge. The simulations showed that confinement between two opposing (001) surfaces led to the development of an induced field when the applied field was perpendicular to the surfaces and, as a result, to ionic diffusion coefficients that were independent of electric field strength. In contrast, when the applied field was parallel to the surfaces, confinement resulted in ionic diffusion coefficients that were more strongly dependent on the magnitude of the electric field than in bulk water. Differences in the density and distribution of aluminol groups on the two surfaces had a significant impact on how the interfacial structure and dynamics varied in the presence of an electric field. Notably, these differences resulted in an electro-osmotic flow with opposite directions at the two surfaces under parallel applied electric field. Overall, the MD simulations highlighted the importance of considering atomic-level structure and heterogeneities when developing models of the electrochemical properties of mineral–water interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Theory of the Kitaev model in a [111] magnetic field

Recent numerical studies indicate that the antiferromagnetic Kitaev honeycomb lattice model undergoes a magnetic-field-induced quantum phase transition into a new spin-liquid phase. This intermediate-field phase has been previously characterized as a gapless spin liquid. By implementing a recently developed variational approach based on the exact fractionalized excitations of the zero-field model, we demonstrate that the field-induced spin liquid is gapped and belongs to Kitaev’s 16-fold way. Specifically, the low-field non-Abelian liquid with Chern number C = ±1 transitions into an Abelian liquid with C = ±4. The critical field and the field-dependent behaviors of key physical quantities are in good quantitative agreement with published numerical results. Furthermore, we derive an effective field theory for the field-induced critical point which readily explains the ostensibly gapless nature of the intermediate-field spin liquid.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Mapping the magnetic field in the Taurus/B211 filamentary cloud with SOFIA HAWC + and comparing with simulation

ABSTRACT Optical and infrared polarization mapping and recent Planck observations of the filametary cloud L1495 in Taurus show that the large-scale magnetic field is approximately perpendicular to the long axis of the cloud. We use the HAWC + polarimeter on SOFIA to probe the complex magnetic field in the B211 part of the cloud. Our results reveal a dispersion of polarization angles of 36°, about five times that measured on a larger scale by Planck. Applying the Davis–Chandrasekhar–Fermi (DCF) method with velocity information obtained from Institut de Radioastronomie Millimétrique 30 m C18O(1-0) observations, we find two distinct sub-regions with magnetic field strengths differing by more than a factor 3. The quieter sub-region is magnetically critical and sub-Alfv$\acute{\rm e}$nic; the field is comparable to the average field measured in molecular clumps based on Zeeman observations. The more chaotic, super-Alfv$\acute{\rm e}$nic sub-region shows at least three velocity components, indicating interaction among multiple substructures. Its field is much less than the average Zeeman field in molecular clumps, suggesting that the DCF value of the field there may be an underestimate. Numerical simulation of filamentary cloud formation shows that filamentary substructures can strongly perturb the magnetic field. DCF and true field values in the simulation are compared. Pre-stellar cores are observed in B211 and are seen in our simulation. The appendices give a derivation of the standard DCF method that allows for a dispersion in polarization angles that is not small, present an alternate derivation of the structure function version of the DCF method, and treat fragmentation of filaments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Low-energy magneto-optics of Tb 2 Ti 2 O 7 in a [111] magnetic field

The pyrochlore magnet Tb 2 Ti 2 O 7 shows a lack of magnetic order to low temperatures and is considered to be a quantum spin liquid candidate. Here we perform time-domain THz spectroscopy on high-quality Tb 2 Ti 2 O 7 crystals and study the low-energy excitations as a function of [111] magnetic field with high energy resolution. The low-energy crystal-field excitations change their energies anomalously under magnetic field. Despite several sharp field-dependent changes, we show that the material's spectrum can be described not by phase transitions but by field-dependent hybridization between the low-energy crystal-field levels. We highlight the strong coupling between spin and lattice degrees of freedom in Tb 2 Ti 2 O 7 as evidenced by the magnetic-field tunable crystal-field environment. Calculations based on single ion physics with field-induced symmetry reduction of the crystal-field environment can reproduce our data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Investigation of the effect of local atomic polarization on field-enhanced ion transport in insulating binary oxides: The case of CeO 2

Over the course of more than 70 years, several theoretical models for electric field-enhanced ion diffusion in crystalline insulators have been presented. However, there is no assessment of the validity of these models despite the urge to have a correct description of field-enhanced ion diffusion in several emerging technologies. Herein, an assessment of five models was carried out by computing the field-dependent migration enthalpy ΔH mig (E) for the oxide ion in CeO 2 . The input to these models is the zero-field and zero-temperature migration pathway and/or the activation barrier obtained from an interatomic potential. ΔH mig (E) from these models was compared with reference values obtained from a set of classical molecular-dynamics simulations in the temperature range of 1000 ≤ T ≤ 1600 K and the electric field range of 0 ≤ E ≤ 30 MV/cm. It is revealed that the most successful theoretical models are those that consider local polarization effects induced in the diffusing ion itself and its vicinity. However, all the models did not account for the effect of the electric field and finite temperature on the local polarization, leading to discrepancies between the predicted and the reference ΔH mig (E), particularly at high fields. By comparing results from a rigid-ion potential and a polarizable core-shell potential, it is concluded that an intraionic polarization degree of freedom in the polarizable potential is an important factor in predicting ΔH mig (E), regardless of the field-enhanced diffusion model particularly for low to moderate field. Finally, future more accurate treatments should consider the field- and temperature-dependent interionic and intraionic local polarization effects.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Artificial Soiling Replication of Field Losses on Commercial Photovoltaic Modules

Here, this study demonstrates the capabilities of an indoor artificial soiling approach developed to closely replicate the natural, cyclic soil accumulation processes in the field-dust suspension, deposition, and sedimentation/cementation-for a subtropical climate. In this work, a near-field environment is replicated in an artificial soiling cubic chamber through controlled regulation of humidity, temperature, dust type, and dust concentration, based on site-specific historical climate data. Two different models (MA and MB) of full-size commercial photovoltaic modules from a single manufacturer, installed side by side in the mid-Atlantic United States, were retrieved and subjected to artificial soiling experiments and various characterization measurements, including short-circuit current, colorimetry, reflectance, X-ray fluorescence, laser diffraction, and optical microscopy. Both in the field and in our improved field-representative artificial soiling tests, the MA model experienced roughly twice the soiling loss as the MB model. To closely replicate the field soiling losses for a site-specific climate, it is critical to include: 1) The use of field-collected dust with identical dust chemistry and particle distribution instead of standardized ISO 12103 Arizona Road dusts, 2) the use of only a small amount of field-collected dust inside the chamber during the deposition process (e.g., 0.15 g), and 3) the preconditioning of the surface coating for the partial/full dose of UV stress as experienced in the field during sunlight exposure and the abrasion as experienced in the field during regular module cleaning activities, if/as needed. The field-representative artificial soiling method developed here could potentially be adopted for rank ordering of various antisoiling coatings developed by researchers and industry stakeholders.

14 SOLAR ENERGY↗

NASA NTRS2014

Three-Dimensional MHD Simulation of FTEs Produced by Merging at an Isolated Point in a Sheared Magnetic Field Configuration

We present predictions for the evolution of FTEs generated by localized bursts of reconnection on a planar magnetopause that separates a magnetosheath region of high densities and weak magnetic field from a magnetospheric region of low densities and strong magnetic field. The magnetic fields present a shear angle of 105 degrees. Reconnection forms a pair of FTEs each crossing the magnetopause in the field reversal region and bulging into the magnetosphere and magnetosheath. At their initial stage they can be characterized as flux tubes since the newly reconnected magnetic field lines are not twisted. Reconnection launches Alfvenic perturbations that propagate along the FTEs generating high-speed jets, which move the pair of FTEs in opposite directions. As the FTE moves, it displaces the ambient magnetic field and plasma producing bipolar magnetic field and plasma velocity signatures normal to the nominal magnetopause in the regions surrounding the FTE. The combination of the ambient plasma with the FTE flows generates a vortical velocity pattern around the reconnected field lines. During its evolution the FTE evolves to a flux rope configuration due to the twist of the magnetic field lines. The alfvenic perturbations propagate faster along the part of the FTE bulging into the magnetosphere than in the magnetosheath, and due to the differences between the plasma and magnetic field properties the perturbations have slightly different signatures in the two regions. As a consequence, the FTEs have different signatures depending on whether the satellite encounters the part bulging into the magnetosphere or into the magnetosheath.

magnetopause↗

NASA NTRS2017

Static Electric Fields and Lightning Over Land and Ocean in Florida Thunderstorms

Natural cloud-to-ground (CG) lightning and the charge structure of the associated clouds behave differently over land and ocean. Existing literature has raised questions over the years on the behavior of thunderstorms and lightning over oceans, and there are still open scientific questions. We expand on the observational datasets by obtaining identical electric field observations over coastal land, near-shore, and deep ocean regions during both clear air and thunderstorm periods. Oceanic observations were obtained using two 3-meter NOAA buoys that were instrumented with Campbell Scientific electric field mills to measure the static electric fields. These data were compared to selected electric field records from the existing on-shore electric field mill suite of 31 sensors at Kennedy Space Center (KSC). CG lightning occurrence times, locations and peak current values for both on-shore and ocean were provided by the U.S. National Lightning Detection Network. The buoy instruments were first evaluated on-shore at the Florida coast, to calibrate field enhancements and to confirm proper behavior of the system in elevated-field environments. The buoys were then moored 20NM and 120NM off the coast of KSC in February (20NM) and August (120NM) 2014. Statistically larger CG peak currents were reported over the deep ocean for first strokes and for subsequent strokes with new contacts points. Storm-related static fields were significantly larger at both oceanic sites, likely due to decreased screening by nearby space charge. Time-evolution of the static field during storm development and propagation indicated weak or missing lower positive charge regions in most storms that initiated over the deep ocean, supporting one mechanism for the observed high peak currents in negative first strokes over the deep ocean. This project also demonstrated the practicality of off-shore electric field measurements for safety-related decision making at KSC.

Lightning↗

NASA NTRS2017

Static Electric Fields and Lightning Over Land and Ocean in Florida Thunderstorms

Electric Fields↗

NASA NTRS2016

Nongyrotropic Electrons in Guide Field Reconnection

We apply a scalar measure of nongyrotropy to the electron pressure tensor in a 2D particle-in-cell simulation of guide field reconnection and assess the corresponding electron distributions and the forces that account for the nongyrotropy. The scalar measure reveals that the nongyrotropy lies in bands that straddle the electron diffusion region and the separatrices, in the same regions where there are parallel electric fields. Analysis of electron distributions and fields shows that the nongyrotropy along the inflow and outflow separatrices emerges as a result of multiple populations of electrons influenced differently by large and small-scale parallel electric fields and by gradients in the electric field. The relevant parallel electric fields include large-scale potential ramps emanating from the x-line and sub-ion inertial scale bipolar electron holes. Gradients in the perpendicular electric field modify electrons differently depending on their phase, thus producing nongyrotropy. Magnetic flux violation occurs along portions of the separatrices that coincide with the parallel electric fields. An inductive electric field in the electron EB drift frame thus develops, which has the effect of enhancing nongyrotropies already produced by other mechanisms and under certain conditions producing their own nongyrotropy. Particle tracing of electrons from nongyrotropic populations along the inflows and outflows shows that the striated structure of nongyrotropy corresponds to electrons arriving from different source regions. We also show that the relevant parallel electric fields receive important contributions not only from the nongyrotropic portion of the electron pressure tensor but from electron spatial and temporal inertial terms as well.

Parallel Electric Fields↗

NASA NTRS2017

Field Exploration and Life Detection Sampling Through Planetary Analogue Sampling (FELDSPAR).

Exploration missions to Mars rely on rovers to perform analyses over small sampling areas; however, landing sites for these missions are selected based on large-scale, low-resolution remote data. The use of Earth analogue environments to estimate the multi-scale spatial distributions of key signatures of habitability can help ensure mission science goals are met. A main goal of FELDSPAR is to conduct field operations analogous to Mars sample return in its science, operations, and technology from landing site selection, to in-field sampling location selection, remote or stand-off analysis, in situ analysis, and home laboratory analysis. Lava fields and volcanic regions are relevant analogues to Martian landscapes due to desiccation, low nutrient availability, and temperature extremes. Operationally, many Icelandic lava fields are remote enough to require that field expeditions address several sampling constraints that are experienced in robotic exploration, including in situ and sample return missions. The Fimmvruhls lava field was formed by a basaltic effusive eruption associated with the 2010 Eyjafjallajkull eruption. Mlifellssandur is a recently deglaciated plain to the north of the Myrdalsjkull glacier. Holuhraun was formed by a 2014 fissure eruptions just north of the large Vatnajkull glacier. Dyngjusandur is an alluvial plain apparently kept barren by repeated mechanical weathering. Informed by our 2013 expedition, we collected samples in nested triangular grids every decade from the 10 cm scale to the 1 km scale (as permitted by the size of the site). Satellite imagery is available for older sites, and for Mlifellssandur, Holuhraun, and Dyngjusandur we obtained overhead imagery at 1 m to 200 m elevation. PanCam-style photographs were taken in the field by sampling personnel. In-field reflectance spectroscopy was also obtained with an ASD spectrometer in Dyngjusandur. All sites chosen were 'homogeneous' in apparent color, morphology, moisture, grain size, and reflectance spectra at all scales greater than 10 cm. Field lab assays were conducted to monitor microbial habitation, including ATP quantification, qPCR for fungal, bacterial, and archaeal DNA, and direct cell imaging using fluorescence microscopy. Home laboratory analyses include Raman spectroscopy and community sequencing. ATP appeared to be significantly more sensitive to small changes in sampling location than qPCR or fluorescence microscopy. Bacterial and archaeal DNA content were more consistent at the smaller scales, but similarly variable across more distant sites. Conversely, cell counts and fungal DNA content have significant local variation but appear relatively homogeneous over scales of 1 km. ATP, bacterial DNA, and archaeal DNA content were relatively well correlated at many spatial scales. While we have observed spatial variation at various scales and are beginning to observe how that variation fluctuates over time as biodiversity recovers after an eruption, we do not yet fully understand what parameters lead to the observed spatial variation. Home laboratory analyses will help us further understand the elemental and structural composition of the basaltic matrices, but further field analyses are vital for the understanding how temperature, moisture, incident radiation, and so forth influence the habitability of a microclimate.

Field↗

DOE OSTI2024

Machine learning the electric field response of condensed phase systems using perturbed neural network potentials

Abstract The interaction of condensed phase systems with external electric fields is of major importance in a myriad of processes in nature and technology, ranging from the field-directed motion of cells (galvanotaxis), to geochemistry and the formation of ice phases on planets, to field-directed chemical catalysis and energy storage and conversion systems including supercapacitors, batteries and solar cells. Molecular simulation in the presence of electric fields would give important atomistic insight into these processes but applications of the most accurate methods such as ab-initio molecular dynamics (AIMD) are limited in scope by their computational expense. Here we introduce Perturbed Neural Network Potential Molecular Dynamics (PNNP MD) to push back the accessible time and length scales of such simulations. We demonstrate that important dielectric properties of liquid water including the field-induced relaxation dynamics, the dielectric constant and the field-dependent IR spectrum can be machine learned up to surprisingly high field strengths of about 0.2 V Å −1 without loss in accuracy when compared to ab-initio molecular dynamics. This is remarkable because, in contrast to most previous approaches, the two neural networks on which PNNP MD is based are exclusively trained on molecular configurations sampled from zero-field MD simulations, demonstrating that the networks not only interpolate but also reliably extrapolate the field response. PNNP MD is based on rigorous theory yet it is simple, general, modular, and systematically improvable allowing us to obtain atomistic insight into the interaction of a wide range of condensed phase systems with external electric fields.

Science & Technology - Other Topics↗

DOE OSTI2024

Limiting current in a collisional crossed-field gap

Crossed-field devices are often used in pulsed power and high-power microwave applications. Previous studies derived closed-form solutions for the limiting current of a vacuum crossed-field system, corresponding to the maximum permissible current for laminar flow, below and above the Hull cutoff B H for magnetic insulation. We extend these studies by introducing collision frequency into the electron force law as a friction term to derive the limiting current in a collisional crossed-field gap. The resulting solution recovers the vacuum crossed-field case in the limit of no collisions and the collisional space-charge limited current with general initial velocity for magnetic field B → 0. In the limit of infinite collisions, we obtain a crossed-field equivalent to the Mott–Gurney law for the maximum current permissible in a collisional, nonmagnetic diode. When the collision frequency ν is less than the electron cyclotron frequency Ω, increasing initial velocity makes the critical current nonmonotonic with increasing ν with the critical current higher at B = B H for ν = Ω. As for a misaligned crossed-field gap where a component of the magnetic field was introduced parallel to the electric field across the gap, magnetic insulation is eliminated and the discontinuity at B = B H for limiting current observed in a vacuum crossed-field gap vanishes. As B → ∞, the limiting current approaches a constant that depends on the initial velocity and the collision frequency.

Breen, Lorin I.↗

DOE OSTI2022

Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO 4

We report results of low-temperature heat-capacity, magnetocaloric-effect, and neutron-diffraction measurements of TmVO 4 , an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially filled 4 f orbitals of the thulium (Tm 3 + ) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point by using a magnetic field oriented along the c axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase transition can be well described by using a semiclassical mean-field treatment of the transverse-field Ising model. However, in higher magnetic fields, closer to the field-tuned quantum phase transition, subtle deviations from this semiclassical behavior are observed, which are consistent with expectations of quantum fluctuations. Although the phase transition is driven by the local 4 f degrees of freedom, the crystal lattice still plays a crucial role, both in terms of mediating the interactions between the local quadrupoles and in determining the critical scaling exponents, even though the phase transition itself can be described via mean field. In particular, bilinear coupling of the nematic order parameter to acoustic phonons changes the spatial and temporal fluctuations of the former in a fundamental way, resulting in different critical behavior of the nematic transverse-field Ising model, as compared to the usual case of the magnetic transverse-field Ising model. Our results establish TmVO 4 as a model material and electronic nematicity as a paradigmatic example for quantum criticality in insulators.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Low-field magnetic anomalies in single crystals of the A-type square-lattice antiferromagnet EuGa 4

The body-centered-tetragonal antiferromagnet EuGa 4 was recently identified as a Weyl nodal-line semimetal that exhibits the topological Hall effect below its reported antiferromagnetic (AFM) ordering temperature T N = 15 – 16.5 K which we find to be T N = 16.4 ( 2 ) K. The Eu +2 ions are located at the corners and body centers of the unit cells. EuGa 4 exhibits A-type antiferromagnetic order below T N , where the Eu 2+ spin-7/2 moments are ferromagnetically aligned in the ab plane with the Eu moments in adjacent Eu planes along the c axis aligned antiferromagnetically. Low-field magnetization versus field M(H ab ) data at T = 2 K with the field aligned in the ab plane are reported that exhibit anomalous positive curvature up to a critical field H c1 at which a second-order transition occurs with H c1 ≈ 0.85 kOe for H∥ [1,1,0] and ≈ 4.8 kOe for H∥[1,0,0]. For larger fields, the linear behavior M ab = χ(T N ) H a b is followed until the critical field H c is reached at which all moments become aligned with the applied field. A theory is formulated for T = 0 K that fits the observed M(H ab ) behavior at T = 2 K well, where domains of A -type AFM order with fourfold rotational symmetry occur in the AFM state in zero field. The moments in the four domains reorient to become almost perpendicular to H ab at H c1 , followed by increasing canting of all moments toward the field with increasing field up to H c which is reported to be 71 kOe. A first-order transition in M(H ab ) at H ab = H c1 is predicted by the theory for T = 0 K when H ab is at a small angle from the [1,0,0] direction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Modeling iterative reconstruction and displacement field in the large scale structure

The next generation of galaxy surveys like the Dark Energy Spectroscopic Instrument and Euclid will provide datasets orders of magnitude larger than anything available to date. Our ability to model nonlinear effects in late time matter perturbations will be a key to unlock the full potential of these datasets, and the area of initial condition reconstruction is attracting growing attention. Iterative reconstruction developed by Marcel Schmittfull et al. is a technique designed to reconstruct the displacement field from the observed galaxy distribution. The nonlinear displacement field and initial linear density field are highly correlated. Therefore, reconstructing the nonlinear displacement field enables us to extract the primordial cosmological information better than from the late time density field at the level of the two-point statistics. This paper will test to what extent the iterative reconstruction can recover the true displacement field and construct a perturbation theory model for the postreconstructed field. We model the iterative reconstruction process with Lagrangian perturbation theory (LPT) up to third order for dark matter in real space and compare it with N-body simulations. Here we find that the simulated iterative reconstruction does not converge to the nonlinear displacement field, and the discrepancy mainly appears in the shift term, i.e., the term correlated directly with the linear density field. On the contrary, our 3LPT model predicts that the iterative reconstruction should converge to the nonlinear displacement field. We discuss the sources of discrepancy, including numerical noise/artifacts on small scales, and present an ad hoc phenomenological model that improves the agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Interplay of the Spin Density Wave and a Possible Fulde-Ferrell-Larkin-Ovchinnikov State in CeCoIn 5 in Rotating Magnetic Field

The d-wave superconductor CeCoIn 5 has been proposed as a strong candidate for supporting the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state near the low-temperature boundary of its upper critical field. Neutron diffraction, however, finds spin-density-wave (SDW) order in this part of the phase diagram for field in the a-b plane, and evidence for the SDW disappears as the applied field is rotated toward the tetragonal c axis. It is important to understand the interplay between the SDW and a possible FFLO state in CeCoIn 5 , as the mere existence of an SDW does not necessarily exclude an FFLO state. In this work, based on a model constructed on the basis of available experiments, we show that an FFLO state competes with an SDW phase. The SDW state in CeCoIn 5 is stabilized when the field is directed close to the a-b plane. When the field is rotated toward the c axis, the FFLO state emerges, and the SDW phase disappears. In the FFLO state, the nodal planes with extra quasiparticles (where the superconducting order parameter is zero) are perpendicular to the field, and in the SDW phase, the quasiparticle density of states is reduced. We test this model prediction by measuring heat transported by normal quasiparticles in the superconducting state. As a function of field, we observe a reduction of thermal conductivity for field close to the a-b plane and an enhancement of thermal conductivity when field is close to the c axis, consistent with theoretical expectations. Our modeling and experiments, therefore, indicate the existence of the FFLO state when field is parallel to the c axis.

36 MATERIALS SCIENCE↗