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At least 361 records · Page 20

Exploring Functional Materials by Understanding Beam‐Sample Interactions

Abstract Ultra‐low‐dose electron diffraction is performed with a double metal cyanide catalyst (DMC) to understand how electron irradiation stimulates structural alterations in functional materials. The commonly fading diffraction patterns with dose accumulation depend on the irradiated area and the beam current even when below 50 femto Amperes. Heat generation is observed and modeled by statistical, inelastic scattering events to describe how phonon excitations modulate radiation hardness. Specifically, the characteristic 1/e‐decay of Bragg intensities from DMC is delayed from 6 to 30 eÅ −2 at room temperature, which is comparable to the effect of embedding radiation soft matter in ice. DMC's radiation hardness is enhanced by a latency dose that forms during a phase transformation. This unifying model predicts that a critical dose rate exists for any material that varies between 0.1 and 10 4 eÅ −2 s −1 because of a material dependent competition of heat generation and spread. It shows that Brillouin scattering causes time dependent perturbations in electron irradiated solids that trigger time‐temperature‐transformations on a time scale of nanoseconds to microseconds at room temperature, which is not included in traditional models describing the decay of Bragg intensities by radiolysis.

Kisielowski, Christian↗

Isotropic nature of the metallic Kagome ferromagnet Fe 3 Sn 2 at high temperatures.

Anisotropy and competing exchange interactions have emerged as two central ingredients needed for centrosymmetric materials to exhibit topological spin textures. Fe 3 Sn 2 is thought to have these ingredients as well, as it has recently been discovered to host room temperature skyrmionic bubbles with an accompanying topological Hall effect. We present small-angle inelastic neutron scattering measurements that unambiguously show that Fe3Sn2 is an isotropic ferromagnet below TC ≈ 660 K to at least 480 K – the lower temperature threshold of our experimental configuration. Fe 3 Sn 2 is known to have competing magnetic exchange interactions, correlated electron behavior, weak magnetocrystalline anisotropy, and lattice anisotropy; all of these features are thought to play a role in stabilizing skyrmions in centrosymmetric systems. Our results reveal that at elevated temperatures, there is an absence of significant magnetocrystalline anisotropy and that the system behaves as a nearly ideal isotropic exchange interaction ferromagnet, with a spin stiffness D(T = 480 K) = 168 meV Å2, which extrapolates to a ground state spin stiffness D(T = 0 K) = 231 meV Å2.

36 MATERIALS SCIENCE↗

Entanglement Witness for Indistinguishable Electrons Using Solid-State Spectroscopy

Characterizing entanglement in quantum materials is crucial for advancing next-generation quantum technologies. Despite recent strides in witnessing entanglement in magnetic materials with distinguishable spin modes, quantifying entanglement in systems formed by indistinguishable electrons remains a formidable challenge. To solve this problem, we introduce a method to extract various four-fermion correlations by analyzing the nonlinearity in resonant inelastic x-ray scattering spectra. These correlations constitute the primary components of the cumulant two-particle reduced density matrix. We further derive bounds for its eigenvalues and demonstrate the linear scaling with fermionic entanglement depth, providing a reliable witness for entanglement. Using the material-relevant strongly correlated models as examples, we show how this entanglement witness can efficiently quantify multipartite entanglement across different phase regions, highlighting its advantage over quantum Fisher information. Published by the American Physical Society 2025

Liu, Tongtong (ORCID:0000000295324061)↗

Neutral Pion Electroproduction and development of a Neutral Particle Spectrometer

Protons and neutrons, i.e. nucleons, are the basic building blocks of the matter in the visible universe. The strong force binds the nucleons to form nuclei. The electromagnetic force forms the atoms by binding the electrons with the nuclei. The electromagnetic interaction is well understood by Quantum Electrodynamics (QED), which shows the most precise predictability amongst all the theories in physics. In QED, charges interact with each other by exchanging photons. The Quantum Chromodynamics (QCD) describes the strong interaction. Its degrees of freedom are quarks and gluons, the fundamental constituents of the nucleons. The quarks interact with each other by exchanging gluons. However, unlike QED, the gluons interact amongst themselves. This feature of self bindings of the gluons confines the quarks and gluons in the nucleons/hadrons, never to be seen as free. In order to study some of the features of QCD, such as confinement or the structure of the nucleon, one usually needs to rely on experiments. Electromagnetic probes, governed by the well-understood QED, are excellent tools to probe the nucleon. In general, different scales, e.g. electron beam energies, probe different regions of the nucleon. At low energy, of the order of a few GeV, the electron probes the nucleon in the valence quark region. As its energy increases, the electron probes the sea quark and gluon regions. The study of the nucleon structure in all these regions is needed to fully understand QCD. Form factors and parton distribution functions measured from elastic scattering and deep inelastic scattering of leptons off nucleons have provided a partial view of the internal structure of the nucleon. In the mid-1990s, Generalized Parton Distributions (GPDs) were developed. These new objects are a generalization of the form factors and parton distribution functions, but contain richer information on the nucleon internal structure. GPDs are accessible experimentally by deep exclusive reactions. Deeply virtual Compton scattering (DVCS) and deeply virtual meson production (DVMP) are some examples. The first dedicated DVCS/DVMP experiment took place in 2004 in Hall A at The Thomas Jefferson National Accelerator Facility, i.e. Jefferson Lab, in Virginia, U.S.A. A new DVCS/DVMP experiment, after the beam energy upgrade of Jefferson Lab, was carried out in Hall A in a wider kinematic range. Its data were taken from 2014 to 2016. In Hall C at Jefferson Lab, the next DVCS/DVMP experiment will take place. The Hall C experiment will further exploit the kinematic range with higher precision. A Neutral Particle Spectrometer (NPS) is in development to measure DVCS/DVMP events under high background conditions. Jefferson Lab will provide the highest precision data in the valence quark region for various exclusive reactions. The Electron-Ion Collider (EIC) is a future experimental facility currently planned to start operations around 2030 in the U.S.A. Its high energy and high luminosity will probe the sea quark and gluon regions providing answers to the outstanding questions of QCD, in particular in the region where matter is dominated by gluons. First of all, this document describes the data analysis and results of the Hall A neutral pion electroproduction off the proton, from the data taken in 2014-2016. Later, some of the developments towards the construction of the electromagnetic calorimeter of the NPS for the upcoming DVCS/DVMP experiment in Hall C are presented. Finally, one of the candidate materials for the EIC calorimeter, a glass scintillator, will be briefly introduced. I have participated to all these projects, in collaboration with many colleagues. I present in this thesis my contributions to each of these projects. My contributions to the neutral pion data analysis were focused on background subtractions on the calorimeter, acceptance calculations, and the estimation of the systematic uncertainty associated to the event selection cuts. Some necessary information on calibrations of the detectors and data analysis methods are also described. In the NPS project, I performed background dose calculations and energy and position resolution studies of the calorimeter, all using Monte Carlo simulations, with realistic geometries of the experimental apparatus. Characterization of the crystals of the calorimeter was also done. Additionally, I measured the radiation hardness of some glass scintillator in its early stage of development. In order to have a future reference when the glass calorimeter prototype will be tested, I simulated the energy resolution of the prototype.

Ko, Ho-San↗

Lattice dynamics, sound velocities, and atomic environments of szomolnokite at high pressure

Complex mixtures of sulfates, silicates, and ice have been observed in a variety of planetary environments on Earth, Mars and the icy satellites of the solar system. Characterizing the properties of the corresponding compositional endmembers is important for understanding the interiors of a range of planetary bodies in which these phases are observed. To measure the electronic and vibrational properties of the pure ferrous iron endmember of the kieserite group, szomolnokite, (FeSO 4 ∙H 2 O), we have performed synchrotron 57 Fe nuclear resonant inelastic and forward scattering experiments in the diamond-anvil cell up to 14.5 GPa. This pressure range covers depths within Earth’s interior relevant to sulfur cycling in subduction zones and the range of pressures expected within icy satellite interiors. We find evidence of crystal lattice softening, changes in elastic properties, and changes in the electric field gradients of iron atoms associated with two structural transitions occurring within the experimental pressure range. Here we apply these findings to icy satellite interiors, including discussion of elastic properties, modeling of ice-sulfate aggregates, and implications for tidal observations.

58 GEOSCIENCES↗

Magnetically propagating Hund’s exciton in van der Waals antiferromagnet NiPS3

Abstract Magnetic van der Waals (vdW) materials have opened new frontiers for realizing novel many-body phenomena. Recently NiPS 3 has received intense interest since it hosts an excitonic quasiparticle whose properties appear to be intimately linked to the magnetic state of the lattice. Despite extensive studies, the electronic character, mobility, and magnetic interactions of the exciton remain unresolved. Here we address these issues by measuring NiPS 3 with ultra-high energy resolution resonant inelastic x-ray scattering (RIXS). We find that Hund’s exchange interactions are primarily responsible for the energy of formation of the exciton. Measuring the dispersion of the Hund’s exciton reveals that it propagates in a way that is analogous to a double-magnon. We trace this unique behavior to fundamental similarities between the NiPS 3 exciton hopping and spin exchange processes, underlining the unique magnetic characteristics of this novel quasiparticle.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tuning anisotropic bonding via chemistry and pressure in layered pnictides and chalcogenides (Final Report)

The overarching goal of this research program, as originally delineated in the proposal “Tuning anisotropic bonding via chemistry and pressure in layered pnictides and chalcogenides” was to develop a predictive, chemistry-driven understanding of the impact of the phonon behavior on thermal properties of bulk layered materials. At finite temperatures, atomic vibrations (phonons) strongly impact the thermodynamics, thermal and electrical transport, and phase-switching properties of functional materials. In particular, soft phonon modes and strongly anharmonic potentials can have spectacular consequences, including structural phase transitions (for example in ferroelectrics and phase-change memory materials), metal-insulator transitions, and extreme thermal resistance preventing heat propagation. Bulk materials with highly-anisotropic bonding may provide unique strategies to induce soft-phonon modes and lattice instabilities. Recently, increasingly detailed investigations of the lattice dynamics in layered materials have been made possible by the advent of first-principles phonon calculations and advanced characterization techniques based on neutron and X-ray scattering. However, due to the lack of studies in which composition and bonding character are systematically varied, there are still fundamental questions regarding the impacts of anisotropic bonding and anharmonicity on lattice stability and thermal transport. One of the major goals of this research program is therefore to address this gap by coherently tuning bonding anisotropy and anharmonicity across families of related compounds. Such approaches have revealed new strategies for exploiting structural anisotropy in quasi-1D and 2D bulk materials to obtain tailored functional properties. This project systematically explored the lattice dynamics, phase stability, and transport properties in bulk layered materials by using both composition and applied pressure to tune the degree of bonding anisotropy and anharmonicity. To accomplish this work, we combined i) single-crystal growth of key material systems with tunable anisotropy, ii) in-situ high-temperature/high-pressure characterization of structure and phonons to probe bonding anisotropy and anharmonicity, including state-of-the-art inelastic X-ray scattering (IXS) and inelastic neutron scattering (INS), and iii) first-principles simulations leveraging large-scale computing to identify the fundamental origins of the observed effects, by relating atomic structure and dynamics to electronic orbital interactions. Finally, we modeled and verified the impact of the phonon behavior on thermal transport to identify new strategies for a-priori design of thermal conductivity. Our integrated collaborative approach helped to systematically unravel the effects of anisotropy and bonding anharmonicity on phonon transport, thermodynamics, and thermal properties of complex anisotropic materials.

30 DIRECT ENERGY CONVERSION↗

Tuning anisotropic bonding via chemistry and pressure in layered pnictides and chalcogenides. Final Report

The overarching goal of this research program, as originally delineated in the proposal “Tuning anisotropic bonding via chemistry and pressure in layered pnictides and chalcogenides” was to develop a predictive, chemistry-driven understanding of the impact of the phonon behavior on thermal properties of bulk layered materials. At finite temperatures, atomic vibrations (phonons) strongly impact the thermodynamics, thermal and electrical transport, and phase-switching properties of functional materials. In particular, soft phonon modes and strongly anharmonic potentials can have spectacular consequences, including structural phase transitions (for example in ferroelectrics and phase-change memory materials), metal-insulator transitions, and extreme thermal resistance preventing heat propagation. Bulk materials with highly-anisotropic bonding may provide unique strategies to induce soft-phonon modes and lattice instabilities. Recently, increasingly detailed investigations of the lattice dynamics in layered materials have been made possible by the advent of first-principles phonon calculations and advanced characterization techniques based on neutron and X-ray scattering. However, due to the lack of studies in which composition and bonding character are systematically varied, there are still fundamental questions regarding the impacts of anisotropic bonding and anharmonicity on lattice stability and thermal transport. One of the major goals of this research program is therefore to address this gap by coherently tuning bonding anisotropy and anharmonicity across families of related compounds. Such approaches have revealed new strategies for exploiting structural anisotropy in quasi-1D and 2D bulk materials to obtain tailored functional properties. This project systematically explored the lattice dynamics, phase stability, and transport properties in bulk layered materials by using both composition and applied pressure to tune the degree of bonding anisotropy and anharmonicity. To accomplish this work, we combined i) single-crystal growth of key material systems with tunable anisotropy, ii) in-situ high-temperature/high-pressure characterization of structure and phonons to probe bonding anisotropy and anharmonicity, including state-of-the-art inelastic X-ray scattering (IXS) and inelastic neutron scattering (INS), and iii) first-principles simulations leveraging large-scale computing to identify the fundamental origins of the observed effects, by relating atomic structure and dynamics to electronic orbital interactions. Finally, we modeled and verified the impact of the phonon behavior on thermal transport to identify new strategies for a-priori design of thermal conductivity. Our integrated collaborative approach helped to systematically unravel the effects of anisotropy and bonding anharmonicity on phonon transport, thermodynamics, and thermal properties of complex anisotropic materials.

36 MATERIALS SCIENCE↗

Anomalous Electrical Transport in the Kagome Magnet YbFe 6 ⁢Ge 6

Two-dimensional (2D) kagome metals offer a unique platform for exploring electron correlation phenomena derived from quantum many-body effects. Here, in this study, we report a combined study of electrical magnetotransport and neutron scattering on YbFe 6 ⁢Ge 6 , where the Fe moments in the 2D kagome layers exhibit an 𝐴-type collinear antiferromagnetic order below 𝑇 N ≈ 500 K. Interactions between the Fe ions in the layers and the localized Yb magnetic ions in between reorient the 𝑐-axis-aligned Fe moments to the kagome plane below 𝑇 SR ≈ 63 K. Our magnetotransport measurements show an intriguing anomalous Hall effect (AHE) that emerges in the spin-reorientated collinear state, accompanied by the closing of the spin anisotropy gap as revealed from inelastic neutron scattering. The gapless spin excitations and the Yb-Fe interaction are able to support a dynamic scalar spin chirality, which explains the observed AHE. Therefore, our Letter demonstrates that spin fluctuations may provide an additional scattering channel for the conduction electrons and give rise to AHE even in a collinear antiferromagnet.

Yao, Weiliang [Rice Univ., Houston, TX (United Sta↗

Surface science insight note: Optimizing XPS instrument performance for quantification of spectra

X-ray photoelectron spectroscopy (XPS) provides quantitative information from photoemission peaks and shapes observed within the background due to the inelastic scattering of photoelectrons. To quantify the signal, both photoemission peaks and background in spectra must be adjusted for instrumental transmission variations that are a consequence of changes in efficiency when recording electrons with different kinetic energy. While it is generally assumed that correcting spectroscopic data for transmission is a necessary part of quantification by XPS, there are consequences for the quantification of spectra measured using an instrument for which transmission has significant curvature. In this Insight, the implications of curvature in transmission characteristics are discussed and a method based on XPS microscopy is proposed that ensures the transmission response of an instrument is free from significant curvature. An example of an instrument for which a flat transmission response is presented is achieved through collecting spectra using lens modes designed to measure stigmatic images.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SMEFT probes in future precision DIS experiments

We analyze the potential of future high-energy deep-inelastic scattering (DIS) experiments to probe new physics within the framework of the Standard Model effective field theory (SMEFT). We perform a detailed study of SMEFT probes at a future Large Hadron-electron Collider (LHeC) and a Future Circular lepton-hadron Collider (FCC-eh) machine, and extend previous simulations of the potential of an electron-ion collider (EIC) to include 𝑍-boson vertex corrections. Precision 𝑍-pole constraints on vertex corrections suffer from numerous degeneracies in the Wilson-coefficient parameter space. We find that both the LHeC and the FCC-eh can help remove these degeneracies present in the existing global fits of precision 𝑍-pole observables and LHC data. The FCC-eh and LHeC will in many cases improve upon the existing precision electroweak bounds on the SMEFT parameter space. This highlights the important role of precision DIS measurements for new physics studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Spin excitations in the kagome-lattice metallic antiferromagnet Fe 0.89 Co 0.11 Sn

Kagome-lattice materials have attracted tremendous interest due to the broad prospect for seeking superconductivity, quantum spin liquid states, and topological electronic structures. Among them, the transition-metal kagome lattices are high-profile objects for the combination of topological properties, rich magnetism, and multiple-orbital physics. Here we report an inelastic neutron scattering study on the spin dynamics of a kagome-lattice antiferromagnetic metal Fe 0.89 Co 0.11 Sn. Although the magnetic excitations can be observed up to ~250 meV, well-defined spin waves are only identified below ~90 meV and can be modeled using Heisenberg exchange with ferromagnetic in-plane nearest-neighbor coupling J 1 , in-plane next-nearest-neighbor coupling J 2 , and antiferromagnetic (AFM) interlayer coupling J c under linear spin-wave theory. Above ~90 meV, the spin waves enter the itinerant Stoner continuum and become highly damped particle-hole excitations. At the K point of the Brillouin zone, we reveal a possible band crossing of the spin wave, which indicates a potential Dirac magnon. Finally, our results uncover the evolution of the spin excitations from the planar AFM state to the axial AFM state in Fe 0.89 Co 0.11 Sn, solve the magnetic Hamiltonian for both states, and confirm the significant influence of the itinerant magnetism on the spin excitations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Polarized TMD fragmentation functions for 𝐽/𝜓 production

We calculate the matching, at leading order, of the transverse momentum-dependent fragmentation functions (TMDFFs) for light quarks and gluons fragmenting to a 𝐽/𝜓 onto polarized nonrelativistic QCD (NRQCD) TMDFFs. The NRQCD TMDFFs have an operator product expansion in terms of nonperturbative NRQCD production matrix elements. Using the results we obtain, we make predictions for the light quark fragmentation contribution to the production of polarized 𝐽/𝜓 in semi-inclusive deep inelastic scattering (SIDIS) both for unpolarized and longitudinally polarized beams. These results are an important contribution to polarized 𝐽/𝜓 production in SIDIS and thus are needed for comparison with experiments at the future Electron-Ion Collider.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Spectator Proton Detection and Reconstruction in Deep Inelastic D(E,EPS) Scattering

A Radial Time Projection Chamber (RTPC) was designed and installed in Jefferson Lab's Hall B as part of the BONuS12 (Barely Off-shell Nucleon Structure) experiment. The goal of BONuS12 is to accurately measure the structure function of the neutron by scattering 11 GeV electrons and detecting them with the CLAS12 spectrometer. Deuterium gas was used as an effective neutron target, and the new RTPC was used to detect low momentum spectator protons. Protons follow a curved path in the 5 Tesla solenoid that is part of CLAS12, ionizing the He-CO2 gas in an annular drift region surrounding the target. These ionization electrons are radially drifted outwards, amplified using cylindrical GEM (Gaseous Electron Multiplication) foils and recorded using readout pads located along the entire outer face of the cylindrical detector. The particle track reconstruction software discussed in detail in this thesis uses the signals from these pads to build tracks, which are reconstructed into the drift region using the arrival times of the signals and the positions of the pads. The proton momentum is measured from the track?s curvature and thus used to extract information about the struck neutron. This thesis introduces the theory of spectator tagging as an effective strategy for measuring neutron structure, by minimizing nuclear effects in the absence of a free neutron target. Along with discussing the many detectors that make up the CLAS12 spectrometer, the RTPC will be covered in detail, along with the tracking software designed to interpret the electronic signals to rebuild the low-momentum particle tracks, and fit them to extract the relevant kinematics. The results of the software, and preliminary analysis will be shown in the final chapter, as well as the discussion of possible improvements which could be made to the tracking software.

Payette, David↗

Work function measurements of clean and modified carbon nanospikes

Carbon surfaces incorporating densely packed spikes with nanometer sharpness have shown exceptional electrocatalytic properties attributed to the enhanced electric field from the topography of the spikes. In this article, the composition of nanospike surfaces is identified by x-ray photoelectron spectroscopy (XPS) and their absolute work function determined using ultraviolet photoemission spectroscopy (UPS). Low temperature annealing of as-grown samples above 275 °C is required to produce a clean surface which has a 4.13 eV work function, a half volt lower than that of flat graphite. Treatments that contaminate the spiked surface, including exposure to air, oxidation at elevated temperature, or immersion in water or hydrocarbons, all increase the work function. Processing that blunts the spikes, including exposure to an oxygen plasma, argon sputtering, or high temperature annealing (800 °C) result in a work function close to that of flat graphite. An unusual double onset in the UPS secondary electron intensity is observed on as-grown nanospike samples and is reproduced by absorbing hydrocarbons on the surface. In conclusion, this double onset appears to be unique to carbon substrates and may originate in inelastic scattering of photoelectrons.

36 MATERIALS SCIENCE↗

New reflections on hard X-ray photon-in/photon-out spectroscopy

Analysis of the electronic structure and local coordination of an element is an important aspect in the study of the chemical and physical properties of materials. This is particularly relevant at the nanoscale where new phases of matter may emerge below a critical size. X-ray emission spectroscopy (XES) at synchrotron radiation sources and free electron lasers has enriched the field of X-ray spectroscopy. Additionally, the spectroscopic techniques derived from the combination of X-ray absorption and emission spectroscopy (XAS–XES), such as resonant inelastic X-ray scattering (RIXS) and high energy resolution fluorescence detected (HERFD) XAS, are an ideal tool for the study of nanomaterials. New installations and beamline upgrades now often include wavelength dispersive instruments for the analysis of the emitted X-rays. With the growing use of XAS–XES, scientists are learning about the possibilities and pitfalls. We discuss some experimental aspects, assess the feasibility of measuring weak fluorescence lines in dilute, radiation sensitive samples, and present new experimental approaches for studying magnetic properties of colloidal nanoparticles directly in the liquid phase.

47 OTHER INSTRUMENTATION↗

The solenoidal large intensity device (SoLID) for JLab 12 GeV

The solenoidal large intensity device (SoLID) is a new experimental apparatus planned for Hall A at the Thomas Jefferson National Accelerator Facility (JLab). SoLID will combine large angular and momentum acceptance with the capability to handle very high data rates at high luminosity. With a slate of approved high-impact physics experiments, SoLID will push JLab to a new limit at the QCD intensity frontier that will exploit the full potential of its 12 GeV electron beam. In this paper, we present an overview of the rich physics program that can be realized with SoLID, which encompasses the tomography of the nucleon in 3D momentum space from semi-inclusive deep inelastic scattering, expanding the phase space in the search for new physics and novel hadronic effects in parity-violating DIS, a precision measurement of J/ψ production at threshold that probes the gluon field and its contribution to the proton mass, tomography of the nucleon in combined coordinate and momentum space with deep exclusive reactions, and more. To meet the challenging requirements, the design of SoLID described here takes full advantage of recent progress in detector, data acquisition and computing technologies. In addition, we outline potential experiments beyond the currently approved program and discuss the physics that could be explored should upgrades of CEBAF become a reality in the future.

3D imaging↗

Magnetic and quadrupole coupling emerging in NdB 4 with geometrically frustrated orthogonal antiferromagnetic dimer

Unusual successive order in NdB 4 with the frustrated Shastry-Sutherland lattice was investigated by means of inelastic neutron scattering. Here, we found that the pseudoquartet with |±5/2⟩ and |±7/2⟩ in the paramagnetic state splits into four levels in the magnetically ordered states. The observed spectra are in good agreement with the 𝑓-electron states obtained from the on-site Hamiltonian with the magnetic interaction ⟨𝐽 𝑥 ⟩ ⁢𝐽 𝑥 , the coupling of 𝐽 𝑥 with quadrupole 𝑂 𝑧⁢𝑥 , and the crystalline electric field potential. The 𝑓-electron states reproduce the temperature dependences of the in-plane moment 𝑚 ⊥ = ⟨𝐽 𝑥 ⟩, which is the primary order parameter, and a weakly induced 𝑚 𝑐 = ⟨𝐽 𝑧 ⟩ as the secondary order parameter. The magnetic-quadrupole coupling emerges and plays an essential role under the geometrical frustration, where the Heisenberg interactions are canceled out.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗