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Pillars of the Mantle: Imaging the Interior of the Earth with Adjoint Tomography. In: PEARC17 Proceedings of the Practice and Experience in Advanced Research Computing 2017 on Sustainability, Success and Impact, Article No. 75

In this work, we investigate global seismic tomographic models obtained by spectral-element simulations of seismic wave propagation and adjoint methods. Global crustal and mantle models are obtained based on an iterative conjugate-gradient type of optimization scheme. Forward and adjoint seismic wave propagation simulations, which result in synthetic seismic data to make measurements and data sensitivity kernels to compute gradient for model updates, respectively, are performed by the SPECFEM3D_GLOBE package [1] [2] at the Oak Ridge Leadership Computing Facility (OLCF) to study the structure of the Earth at unprecedented levels. Using advances in solver techniques that run on the GPUs on Titan at the OLCF, scientists are able to perform large-scale seismic inverse modeling and imaging. Using seismic data from global and regional networks from global CMT earthquakes, scientists are using SPECFEM3D_GLOBE to understand the structure of the mantle layer of the Earth. Visualization of the generated data sets provide an effective way to understand the computed wave perturbations which define the structure of mantle in the Earth.

Pugmire, David↗

Sparse measurement medical CT reconstruction using multi-fused block matching denoising priors

A major challenge for medical X-ray CT imaging is reducing the number of X-ray projections to lower radiation dosage and reduce scan times without compromising image quality. However these under-determined inverse imaging problems rely on the formulation of an expressive prior model to constrain the solution space while remaining computationally tractable. Traditional analytical reconstruction methods like Filtered Back Projection (FBP) often fail with sparse measurements, producing artifacts due to their reliance on the Shannon-Nyquist Sampling Theorem. Consensus Equilibrium, which is a generalization of Plug and Play, is a recent advancement in Model-Based Iterative Reconstruction (MBIR), has facilitated the use of multiple denoisers are prior models in an optimization free framework to capture complex, non-linear prior information. However, 3D prior modelling in a Plug and Play approach for volumetric image reconstruction requires long processing time due to high computing requirement. Instead of directly using a 3D prior, this work proposes a BM3D Multi Slice Fusion (BM3D-MSF) prior that uses multiple 2D image denoisers fused to act as a fully 3D prior model in Plug and Play reconstruction approach. Our approach does not require training and are thus able to circumvent ethical issues related with patient training data and are readily deployable in varying noise and measurement sparsity levels. In addition, reconstruction with the BM3D-MSF prior achieves similar reconstruction image quality as fully 3D image priors, but with significantly reduced computational complexity. We test our method on clinical CT data and demonstrate that our approach improves reconstructed image quality.

Hossain, Maliha [ORNL]↗

Smoothing tool design and performance during subaperture glass polishing

During subaperture tool grinding and polishing, overlaps of the tool influence function can result in undesirable mid-spatial frequency (MSF) errors in the form of surface ripples, which are often corrected using a smoothing polishing step. Here, in this study, flat multi-layer smoothing polishing tools are designed and tested to simultaneously (1) reduce or remove MSF errors, (2) minimize surface figure degradation, and (3) maximize the material removal rate. A time-dependent convergence model in which spatial material removal varies with a workpiece-tool height mismatch, combined with a finite element mechanical analysis to determine the interface contact pressure distribution, was developed to evaluate various smoothing tool designs as a function of tool material properties, thicknesses, pad textures, and displacements. An improvement in smoothing tool performance is achieved when the gap pressure constant, $\overline{h}$ (which describes the inverse rate at which the pressure drops with a workpiece-tool height mismatch), is minimized for smaller spatial scale length surface features (namely, MSF errors) and maximized for large spatial scale length features (i.e., surface figure). Five specific smoothing tool designs were experimentally evaluated. A two-layer smoothing tool using a thin, grooved IC1000 polyurethane pad (with a high elastic modulus, E pad =360 MPa ), thicker blue foam (with an intermediate modulus, E foam =5.3 MPa ) underlayer, and an optimized displacement (d t =1 mm ) provided the best overall performance (namely, high MSF error convergence, minimal surface figure degradation, and high material removal rate).

47 OTHER INSTRUMENTATION↗

Integrating Natural Language Processing and Machine Learning Algorithms to Categorize Oncologic Response in Radiology Reports

A significant volume of medical data remains unstructured. Natural language processing (NLP) and machine learning (ML) techniques have shown to successfully extract insights from radiology reports. However, the codependent effects of NLP and ML in this context have not been well-studied. Between April 1, 2015 and November 1, 2016, 9418 cross-sectional abdomen/pelvis CT and MR examinations containing our internal structured reporting element for cancer were separated into four categories: Progression, Stable Disease, Improvement, or No Cancer. We combined each of three NLP techniques with five ML algorithms to predict the assigned label using the unstructured report text and compared the performance of each combination. The three NLP algorithms included term frequency-inverse document frequency (TF-IDF), term frequency weighting (TF), and 16-bit feature hashing. The ML algorithms included logistic regression (LR), random decision forest (RDF), one-vs-all support vector machine (SVM), one-vs-all Bayes point machine (BPM), and fully connected neural network (NN). The best-performing NLP model consisted of tokenized unigrams and bigrams with TF-IDF. Increasing N-gram length yielded little to no added benefit for most ML algorithms. With all parameters optimized, SVM had the best performance on the test dataset, with 90.6 average accuracy and F score of 0.813. The interplay between ML and NLP algorithms and their effect on interpretation accuracy is complex. The best accuracy is achieved when both algorithms are optimized concurrently.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations

Predictive modeling typically relies on Bayesian model calibration to provide uncertainty quantification. Variational inference utilizing fully independent (“mean-field”) Gaussian distributions are often used as approximate probability density functions. This simplification is attractive since the number of variational parameters grows only linearly with the number of unknown model parameters. However, the resulting diagonal covariance structure and unimodal behavior can be too restrictive to provide useful approximations of intractable Bayesian posteriors that exhibit highly non-Gaussian behavior, including multimodality. High-fidelity surrogate posteriors for these problems can be obtained by considering the family of Gaussian mixtures. Gaussian mixtures are capable of capturing multiple modes and approximating any distribution to an arbitrary degree of accuracy, while maintaining some analytical tractability. Unfortunately, variational inference using Gaussian mixtures with full-covariance structures suffers from a quadratic growth in variational parameters with the number of model parameters. The existence of multiple local minima due to strong nonconvex trends in the loss functions often associated with variational inference present additional complications, These challenges motivate the need for robust initialization procedures to improve the performance and computational scalability of variational inference with mixture models. In this work, we propose a method for constructing an initial Gaussian mixture model approximation that can be used to warm-start the iterative solvers for variational inference. The procedure begins with a global optimization stage in model parameter space. In this step, local gradient-based optimization, globalized through multistart, is used to determine a set of local maxima, which we take to approximate the mixture component centers. Around each mode, a local Gaussian approximation is constructed via the Laplace approximation. Finally, the mixture weights are determined through constrained least squares regression. The robustness and scalability of the proposed methodology is demonstrated through application to an ensemble of synthetic tests using high-dimensional, multimodal probability density functions. Here, the practical aspects of the approach are demonstrated with inversion problems in structural dynamics.

97 MATHEMATICS AND COMPUTING↗

Data-driven deconvolution for large eddy simulations of Kraichnan turbulence

In this article, we demonstrate the use of artificial neural networks as optimal maps which are utilized for convolution and deconvolution of coarse-grained fields to account for sub-grid scale turbulence effects. Here, we demonstrate that an effective eddy-viscosity is predicted by our purely data-driven large eddy simulation framework without explicit utilization of phenomenological arguments. In addition, our data-driven framework precludes the knowledge of true sub-grid stress information during the training phase due to its focus on estimating an effective filter and its inverse so that grid-resolved variables may be related to direct numerical simulation data statistically. The proposed predictive framework is also combined with a statistical truncation mechanism for ensuring numerical realizability in an explicit formulation. Through this, we seek to unite structural and functional modeling strategies for modeling non-linear partial differential equations using reduced degrees of freedom. Both a priori and a posteriori results are shown for a two-dimensional decaying turbulence case in addition to a detailed description of validation and testing. A hyperparameter sensitivity study also shows that the proposed dual network framework simplifies learning complexity and is viable with exceedingly simple network architectures. Our findings indicate that the proposed framework approximates a robust and stable sub-grid closure which compares favorably to the Smagorinsky and Leith hypotheses for capturing the theoretical k -3 scaling in Kraichnan turbulence.

42 ENGINEERING↗

Characterizing Stress Orientations in Southern Kansas

We repot that Induced seismicity predominantly occurs along faults that are optimally oriented to the local principal compressive stress direction, and the characterization of these stress orientations is an important component of understanding seismic hazards. The seismicity rate in southern Kansas rapidly increased in 2013 primarily due to the disposal of large volumes of wastewater into the Arbuckle Group. Previously, local stress orientations in this area were poorly constrained, which limited our understanding of the complex faulting and diverse earthquake mechanisms in this region. We use shear-wave splitting and focal mechanism inversion techniques to create multiple, independent estimates of maximum horizontal stress directions (S Hmax ) and their spatial variation across the study area. We then create an integrated model of stress orientations for southern Kansas and northern Oklahoma using our local results in conjunction with previous, regional stress orientation estimates. We find that S Hmax in both southern Kansas and central Oklahoma exhibits an east-northeast (~N78°E) orientation, and these regions bound a northeast (~N59°E) rotation within a ~20km area in northern Oklahoma near the Nemaha ridge.

58 GEOSCIENCES↗

Optimal Aerosol Parameterization for Remote Sensing Retrievals

We have developed a new algorithm for the retrieval of aerosol and gases from SAGE It1 solar transmission measurements. This algorithm improves upon the NASA operational algorithm in several key aspects, including solving the problem non-linearly and incorporating a new methodology for separating the contribution of aerosols and gases. In order to extract aerosol information we have built a huge database of aerosol models for both stratospheric and tropospheric aerosols, and polar stratospheric cloud particles. This set of models allows us to calculate a vast range of possible extinction spectra for aerosols. and from these, derive a set of eigenvectors which then provide the basis set used in our inversion algorithm. Our aerosol algorithm and retrievals are described in several articles (listed in References Section) published under this grant. In particular they allow us to analyze the spectral properties of aerosols and PSCs and ultimately derive their microphysical properties. We have found some considerable differences between our spectra and the ones derived from the SAGE III operational algorithm. These are interesting as they provide an independent check on the validity of published aerosol data and, in particular, on their associated uncertainties. In order to understand these differences, we are assembling independent aerosol data from other sources with which to make comparisons. We have carried out extensive comparisons of our ozone retrievals with both SAGE III and independent lidar, ozonesonde, and satellite measurements (Polyakov et al., 2004). These show very good agreement throughout the stratosphere and help to quantify differences which can be attributed to natural variation in ozone versus that produced by algorithmic differences. In the mid - upper stratosphere, agreement with independent data was generally within 5 - 20%. but in the lower stratosphere the differences were considerably larger. We believe that a large proportion of this discrepancy in the lower stratosphere is attributable to natural variation, and is also seen in comparisons between lidar and ozonesonde measurements. NO2 profiles obtained with our algorithm were compared to those obtained through the SAGE III operational algorithm and exhibited differences of 20 - 40%. Our retrieved profiles agree with the HALOE NO2 measurements significantly better than those of the operational retrieval. In other work (described below), we are extending our aerosol retrievals into the infrared regime and plan to perform retrievals from combined uv-visible-infrared spectra. This work will allow us to use the spectra to derive the size and composition of aerosols, and we plan to employ our algorithms in the analysis of PSC spectra. We are presently also developing a limb-scattering algorithm to retrieve aerosol data from limb measurements of solar scattered radiation.

Newchurch, Michael J.↗

Radar-Based Bayesian Estimation of Ice Crystal Growth Parameters within a Microphysical Model

The potential for polarimetric Doppler radar measurements to improve predictions of ice microphysical processes within an idealized model–observational framework is examined. In an effort to more rigorously constrain ice growth processes (e.g., vapor deposition) with observations of natural clouds, a novel framework is developed to compare simulated and observed radar measurements, coupling a bulk adaptive-habit model of vapor growth to a polarimetric radar forward model. Bayesian inference on key microphysical model parameters is then used, via a Markov chain Monte Carlo sampler, to estimate the probability distribution of the model parameters. The statistical formalism of this method allows for robust estimates of the optimal parameter values, along with (non-Gaussian) estimates of their uncertainty. To demonstrate this framework, observations from Department of Energy radars in the Arctic during a case of pristine ice precipitation are used to constrain vapor deposition parameters in the adaptive habit model. The resulting parameter probability distributions provide physically plausible changes in ice particle density and aspect ratio during growth. A lack of direct constraint on the number concentration produces a range of possible mean particle sizes, with the mean size inversely correlated to number concentration. Consistency is found between the estimated inherent growth ratio and independent laboratory measurements, increasing confidence in the parameter PDFs and demonstrating the effectiveness of the radar measurements in constraining the parameters. Furthermore, the combined Doppler and polarimetric observations produce the highest-confidence estimates of the parameter PDFs, with the Doppler measurements providing a stronger constraint for this case.

54 ENVIRONMENTAL SCIENCES↗

Pseudo-direct solution to the boundary-layer equations for separated flow

This paper describes a procedure for the automatic iteration of an inverse boundary-layer technique to a prescribed pressure distribution in a separated flow. The technique is demonstrated by computation of two transonic airfoil flows and two externally generated shock boundary-layer interaction flows. These results are compared to experimental data and to solutions of the full Navier-Stokes equations. These comparisons indicate that substantial economies can be obtained by applying methods like the present, in lieu of full Navier-Stokes methods, in zonal calculation schemes for design purposes. The optimization technique leading to convergence is described in detail and a table of typical computation time is presented.

Arieli, R.↗

Polarimetric Retrievals of Surface and Cirrus Clouds Properties in the Region Affected by the Deepwater Horizon Oil Spill

In 2010, the Goddard Institute for Space Studies (GISS) Research Scanning Polarimeter (RSP) performed several aerial surveys over the region affected by the oil spill caused by the explosion of the Deepwater Horizon offshore platform. The instrument was deployed on the NASA Langley B200 aircraft together with the High Spectral Resolution Lidar (HSRL), which provides information on the distribution of the aerosol layers beneath the aircraft, including an accurate estimate of aerosol optical depth. This work illustrates the merits of polarization measurements in detecting variations of ocean surface properties linked to the presence of an oil slick. In particular, we make use of the degree of linear polarization in the glint region, which is severely affected by variations in the refractive index but insensitive to the waviness of the water surface. Alterations in the surface optical properties are therefore expected to directly affect the polarization response of the RSP channel at 2264 nm, where both molecular and aerosol scattering are negligible and virtually all of the observed signal is generated via Fresnel reflection at the surface. The glint profile at this wavelength is fitted with a model which can optimally estimate refractive index, wind speed and direction, together with aircraft attitude variations affecting the viewing geometry. The retrieved refractive index markedly increases over oil-contaminated waters, while the apparent wind speed is significantly lower than in adjacent uncontaminated areas, suggesting that the slick dampens high-frequency components of the ocean wave spectrum. The constraint on surface reflectance provided by the short-wave infrared channels is a cornerstone of established procedures to retrieve atmospheric aerosol microphysical parameters based on the inversion of the RSP multispectral measurements. This retrieval, which benefits from the ancillary information provided by the HSRL, was in this specific case hampered by prohibitive variability in atmospheric conditions (very inhomogeneous aerosol distribution and cloud cover). Although the results presented for the surface are essentially unaffected, we discuss the results obtained by typing algorithms in sorting the complex mix of aerosol types, and show evidence of oriented ice in cirrus clouds present in the area. In this context, polarization measurements at 1880 nm were used to infer ice habit and cirrus optical depth, which was found in the subvisual/threshold-visible regime, confirming the utility of the aforementioned RSP channel for the remote sensing of even thin cold clouds.

Polarization↗

Radar-Based Bayesian Estimation of Ice Crystal Growth Parameters within a Microphysical Model

The potential for polarimetric Doppler radar measurements to improve predictions of ice microphysical processes within an idealized model–observational framework is examined. In an effort to more rigorously constrain ice growth processes (e.g., vapor deposition) with observations of natural clouds, a novel framework is developed to compare simulated and observed radar measurements, coupling a bulk adaptive-habit model of vapor growth to a polarimetric radar forward model. Bayesian inference on key microphysical model parameters is then used, via a Markov chain Monte Carlo sampler, to estimate the probability distribution of the model parameters. The statistical formalism of this method allows for robust estimates of the optimal parameter values, along with (non-Gaussian) estimates of their uncertainty. To demonstrate this framework, observations from Department of Energy radars in the Arctic during a case of pristine ice precipitation are used to constrain vapor deposition parameters in the adaptive habit model. The resulting parameter probability distributions provide physically plausible changes in ice particle density and aspect ratio during growth. A lack of direct constraint on the number concentration produces a range of possible mean particle sizes, with the mean size inversely correlated to number concentration. Consistency is found between the estimated inherent growth ratio and independent laboratory measurements, increasing confidence in the parameter PDFs and demonstrating the effectiveness of the radar measurements in constraining the parameters. The combined Doppler and polarimetric observations produce the highest-confidence estimates of the parameter PDFs, with the Doppler measurements providing a stronger constraint for this case.

Robert S. Schrom↗

Computational Investigation of Technetium(IV) Incorporation into Inverse Spinels: Magnetite (Fe 3 O 4 ) and Trevorite (NiFe 2 O 4 )

Iron oxides and oxyhydroxides play an important role in minimizing the mobility of redox-sensitive elements in engineered and natural environments. For the radionuclide technetium-99 (Tc), these phases hold promise as primary hosts for increasing Tc loading into glass waste form matrices, or as secondary sinks during the long-term storage of nuclear materials. Recent experiments show that the inverse spinel, magnetite [Fe(II)Fe(III)2O4], can incorporate Tc(IV) into its octahedral sub-lattice, and in that same class of materials, trevorite [Ni(II)Fe(III)2O4] is also being investigated for its ability to host Tc(IV). However, questions remain regarding the most energetically favorable charge-compensation mechanism for Tc(IV) incorporation in each structure, which will affect Tc behavior under changing waste processing or storage conditions. Here, quantum-mechanical methods were used to evaluate incorporation energies and optimized lattice bonding environments for three different, charge-balanced Tc(IV) incorporation mechanisms in magnetite and trevorite. In both cases, the removal of two octahedral Fe(II) or Ni(II) ions upon the addition of Tc(IV) to an octahedral site is the most stable mechanism, relative to the creation of octahedral Fe(III) defects or increasing octahedral Fe(II) content. Following hydration-energy corrections, Tc(IV) incorporation into magnetite is energetically favorable while an energy barrier exists for trevorite.

Environmental Molecular Sciences Laboratory↗

Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained “blind” ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

36 MATERIALS SCIENCE↗

Creating Optimal Fracture Networks

The primary goal of this project is the development of a multi-physics, multi-scale simulation capability to predict the initiation, propagation and maintenance of hydraulically driven fracture networks in heterogeneous geologic materials. The development and validation of integrated code capability, GEOS, that accurately captures the phenomenology of these complex physical processes across a wide range of time-­ (~10 -6 to ~10 8 s) and length- (~10 -3 to ~10 4 m) scales is the main scientific objective of the proposed initiative. GEOS constitutes a new analytical framework incorporating the underlying physics that drives fracture development – e.g. dynamically changing fracture network topologies, fluid/solid interactions taking place along discrete interfaces, and complex matrix/fracture transport processes. Enhanced seismic observational tools and inversion methods will also be developed. This initiative has positioned LLNL to play a leading role in the development of Enhanced Geothermal Systems, unconventional gas energy resources, risk assessment associated with geologic sequestration of CO 2 and the detection of radioactive gases from clandestine nuclear tests, impacting both energy and national security.

02 PETROLEUM↗

Probing Accuracy-Speedup Tradeoff in Machine Learning Surrogates for Molecular Dynamics Simulations

The performance promise of machine learning surrogates of molecular dynamics simulations of soft materials is significant but generally comes at the cost of acquiring large training datasets to learn the complex relationships between input soft material attributes and output properties. Under the constraint of limited high-performance computing resources, optimizing the size of the training datasets becomes paramount. Using an artificial neural network based surrogate for molecular dynamics simulations of confined electrolytes, we explore the tradeoff between surrogate accuracy and computational gains. Accuracy is assessed by computing the root-mean-square errors between the surrogate predictions and the ground truth results obtained via molecular dynamics simulations. The computational performance is judged by evaluating the speedup which incorporates the training dataset creation time. Improvement in accuracy occurs with a loss of speedup, which scales as the inverse of the training dataset size. Furthermore, the link between surrogate generalizability and the accuracy-speedup tradeoff is assessed by examining the errors incurred in surrogate predictions on unseen, interpolated input variables and developing a net speedup metric to capture the associated gains.

Anions↗

Evolution-guided engineering of small-molecule biosensors

Allosteric transcription factors (aTFs) have proven widely applicable for biotechnology and synthetic biology as ligand-specific biosensors enabling real-time monitoring, selection and regulation of cellular metabolism. However, both the biosensor specificity and the correlation between ligand concentration and biosensor output signal, also known as the transfer function, often needs to be optimized before meeting application needs. Here, we present a versatile and high-throughput method to evolve prokaryotic aTF specificity and transfer functions in a eukaryote chassis, namely baker's yeast Saccharomyces cerevisiae. From a single round of mutagenesis of the effector-binding domain (EBD) coupled with various toggled selection regimes, we robustly select aTF variants of the cis,cis-muconic acid-inducible transcription factor BenM evolved for change in ligand specificity, increased dynamic output range, shifts in operational range, and a complete inversion-of-function from activation to repression. Importantly, by targeting only the EBD, the evolved biosensors display DNA-binding affinities similar to BenM, and are functional when ported back into a prokaryotic chassis. The developed platform technology thus leverages aTF evolvability for the development of new host-agnostic biosensors with user-defined small-molecule specificities and transfer functions.

59 BASIC BIOLOGICAL SCIENCES↗

Magnetic excitations of the hybrid multiferroic (ND 4 ) 2 FeCl 5 ·D 2 O

We report a comprehensive inelastic neutron scattering study of the hybrid molecule-based multiferroic compound ( ND 4 ) 2 FeCl 5 · D 2 O in the zero-field incommensurate cycloidal phase and the high-field quasicollinear phase. The spontaneous electric polarization changes its direction concurrently with the field-induced magnetic transition, from mostly aligned with the crystallographic a axis to the c axis. To account for such a change in polarization direction, the underlying multiferroic mechanism was proposed to switch from the spin-current model induced via the inverse Dzyaloshinskii-Moriya interaction to the p - d hybridization model. We perform a detailed analysis of the inelastic neutron data of ( ND 4 ) 2 FeCl 5 · D 2 O using linear spin-wave theory to quantify magnetic interaction strengths and investigate the possible impact of different multiferroic mechanisms on the magnetic couplings. Overall our result reveals that the spin dynamics of both multiferroic phases can be well described by a Heisenberg Hamiltonian with easy-plane anisotropy. We do not find notable differences between the optimal model parameters of the two phases. The hierarchy of exchange couplings and the balance among frustrated interactions remain the same between two phases, suggesting that magnetic interactions in ( ND 4 ) 2 FeCl 5 · D 2 O are much more robust than the electric polarization in response to delicate reorganizations of the electronic degrees of freedom in an applied magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗