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At least 721 records · Page 40

M-Edge Spectroscopy of Transition Metals: Principles, Advances, and Applications

M-edge X-ray absorption spectroscopy (XAS), which probes 3p→3d transitions in first-row transition metals, provides detailed insights into oxidation states, spin-states, and local electronic structure with high element and orbital specificity. Operating in the extreme ultraviolet (XUV) region, this technique provides sharp multiplet-resolved features with high sensitivity to ligand field and covalency effects. Compared to K- and L-edge XAS, M-edge spectra exhibit significantly narrower full widths at half maximum (typically 0.3–0.5 eV versus >1 eV at the L-edge and >1.5–2 eV at the K-edge), owing to longer 3p core-hole lifetimes. M-edge measurements are also more surface-sensitive due to the lower photon energy range, making them particularly well-suited for probing thin films, interfaces, and surface-bound species. The advent of tabletop high-harmonic generation (HHG) sources has enabled femtosecond time-resolved M-edge measurements, allowing direct observation of ultrafast photoinduced processes such as charge transfer and spin crossover dynamics. This review presents an overview of the fundamental principles, experimental advances, and current theoretical approaches for interpreting M-edge spectra. We further discuss a range of applications in catalysis, materials science, and coordination chemistry, highlighting the technique’s growing impact and potential for future studies.

M-edge XANES↗

Relativistic dynamics, Green function and pseudodifferential operators

The central role played by pseudodifferential operators in relativistic dynamics is known very well. In this work, operators like the Schrodinger one (e.g., square root) are treated from the point of view of the non-local pseudodifferential Green functions. Starting from the explicit construction of the Green (semigroup) theoretical kernel, a theorem linking the integrability conditions and their dependence on the spacetime dimensions is given. Relativistic wave equations with arbitrary spin and the causality problem are discussed with the algebraic interpretation of the radical operator and their relation with coherent and squeezed states. Also we perform by means of pure theoretical procedures (based in physical concepts and symmetry) the relativistic position operator which satisfies the conditions of integrability: it is a non-local, Lorentz invariant and does not have the same problems as the “local”position operator proposed by Newton and Wigner. Physical examples, as zitterbewegung and rogue waves, are presented and deeply analyzed in this theoretical framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Transverse-momentum-dependent quark distribution functions of spin-one targets: Formalism and covariant calculations

In this paper, we present a covariant formulation and model calculations of the leading-twist time-reversal even transverse-momentum-dependent quark distribution functions (TMDs) for a spin-one target. Emphasis is placed on a description of these three-dimensional distribution functions which is independent of any constraints on the spin quantization axis. We apply our covariant spin description to all nine leading-twist time-reversal even ρ meson TMDs in the framework provided by the Nambu–Jona-Lasinio model, incorporating important aspects of quark confinement via the infrared cutoff in the proper-time regularization scheme. In particular, the behaviors of the three-dimensional TMDs in a tensor polarized spin-one hadron are illustrated. Sum rules and positivity constraints are discussed in detail. Our results do not exhibit the familiar Gaussian behavior in the transverse momentum, and other results of interest include the finding that the tensor polarized TMDs—associated with spin-one hadrons—are very sensitive to quark orbital angular momentum, and that the TMDs associated with the quark operator γ + γ T γ 5 would vanish were it not for dynamical chiral symmetry breaking. In addition, we find that 44% of the ρ meson's spin is carried by the orbital angular momentum of the quarks, and that the magnitude of the tensor polarized quark distribution function is about 30% of the unpolarized quark distribution. Finally, a qualitative comparison between our results for the tensor structure of a quark-antiquark bound state is made to existing experimental and theoretical results for the two-nucleon (deuteron) bound state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Spin-EPR-pair separation by conveyor-mode single electron shuttling in Si/SiGe

Long-ranged coherent qubit coupling is a missing function block for scaling up spin qubit based quantum computing solutions. Spin-coherent conveyor-mode electron-shuttling could enable spin quantum-chips with scalable and sparse qubit-architecture. Its key feature is the operation by only few easily tuneable input terminals and compatibility with industrial gate-fabrication. Single electron shuttling in conveyor-mode in a 420 nm long quantum bus has been demonstrated previously. Here we investigate the spin coherence during conveyor-mode shuttling by separation and rejoining an Einstein-Podolsky-Rosen (EPR) spin-pair. Compared to previous work we boost the shuttle velocity by a factor of 10000. We observe a rising spin-qubit dephasing time with the longer shuttle distances due to motional narrowing and estimate the spin-shuttle infidelity due to dephasing to be 0.7% for a total shuttle distance of nominal 560 nm. Shuttling several loops up to an accumulated distance of 3.36 μm, spin-entanglement of the EPR pair is still detectable, giving good perspective for our approach of a shuttle-based scalable quantum computing architecture in silicon.

42 ENGINEERING↗

CPHASE gate with Rydberg atoms (CPHAR)

We demonstrate a controlled phase gate approach to entangling neutral atoms using a tunable, Rydberg-dressed interaction. Previous approaches utilize a “dipole blockade” or a “spin-flip blockade” and thereby lack arbitrary phase control, and are less extensible to simultaneous entangling operations in many-atom systems. We systematically study major error mechanisms that limit the fidelity of the entangling interaction and find the dominant error mechanism to be phase noise in the coherent control of the single spins. Our work charts a definitive path to high fidelity entanglement using Rydberg-state-mediated interactions in neutral atoms.

74 ATOMIC AND MOLECULAR PHYSICS↗

Lindblad many-body scars

Quantum many-body scars have received much recent attention for being both intriguing nonergodic states in otherwise quantum chaotic systems and promising candidates to encode quantum information efficiently. So far, these studies have mostly been restricted to Hermitian systems. Here, we study many-body scars in many-body quantum chaotic systems coupled to a Markovian bath, which we term Lindblad many-body scars. They are defined as simultaneous eigenvectors of the Hamiltonian and dissipative parts of the vectorized Liouvillian. Importantly, because their eigenvalues are purely real, they are not related to revivals. The number and nature of the scars depend on both the symmetry of the Hamiltonian and the choice of jump operators. For a dissipative four-body Sachdev-Ye-Kitaev (SYK) model with 𝑁 fermions, either Majorana or complex, we construct analytically some of these Lindblad scars while others could only be obtained numerically. As an example of the former, we identify 𝑁/2+1 scars for complex fermions due to the 𝑈⁡(1) symmetry of the model and two scars for Majorana fermions as a consequence of the parity symmetry. Similar results are obtained for a dissipative XXZ spin chain. We also characterize the physical properties of Lindblad scars. First, the operator size is independent of the disorder realization and has a vanishing variance. By contrast, the operator size for nonscarred states, believed to be quantum chaotic, is well described by a distribution centered around a specific size and a finite variance, which could be relevant for a precise definition of the eigenstate thermalization hypothesis in dissipative quantum chaos. Moreover, the entanglement entropy of these scars has distinct features such as a strong dependence on the partition choice and, in certain cases, a large entanglement.

Eigenstate thermalization↗

Surface Radiation Budget (SRB) Release 2.5 Longwave Monthly Data in Native Format (SRB_REL2.5_LW_MONTHLY)

The Surface Radiation Budget Data include upward and downward fluxes averaged at monthly intervals for the entire globe between 07/01/1983 and 06/30/2005. These parameters were derived using the Longwave algorithm of the NASA World Climate Research Programme/Global Energy and Water-Cycle Experiment (WCRP/GEWEX) Surface Radiation Budget (SRB) Project. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2005-06-30] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=1 degree; Longitude_Resolution=Ranges from 1 degree (tropics and subtropics) to 120 degrees (the poles).; Temporal_Resolution=3 hourly; Temporal_Resolution_Range=3 hourly].

SURFACE UPWARD LONGWAVE FLUX↗

Controlling the helicity of light by electrical magnetization switching

Controlling the intensity of emitted light and charge current is the basis of transferring and processing information. By contrast, robust information storage and magnetic random-access memories are implemented using the spin of the carrier and the associated magnetization in ferromagnets. In this study, the missing link between the respective disciplines of photonics, electronics and spintronics is to modulate the circular polarization of the emitted light, rather than its intensity, by electrically controlled magnetization. Here we demonstrate that this missing link is established at room temperature and zero applied magnetic field in light-emitting diodes through the transfer of angular momentum between photons, electrons and ferromagnets. With spin-orbit torque a charge current generates also a spin current to electrically switch the magnetization. This switching determines the spin orientation of injected carriers into semiconductors, in which the transfer of angular momentum from the electron spin to photon controls the circular polarization of the emitted light. The spin-photon conversion with the nonvolatile control of magnetization opens paths to seamlessly integrate information transfer, processing and storage. Our results provide substantial advances towards electrically controlled ultrafast modulation of circular polarization and spin injection with magnetization dynamics for the next-generation information and communication technology, including space-light data transfer. The same operating principle in scaled-down structures or using two-dimensional materials will enable transformative opportunities for quantum information processing with spin-controlled single-photon sources, as well as for implementing spin-dependent time-resolved spectroscopies.

74 ATOMIC AND MOLECULAR PHYSICS↗

SPECTRAL ENERGY DISTRIBUTIONS OF YOUNG STARS IN IC 348: THE ROLE OF DISKS IN ANGULAR MOMENTUM EVOLUTION OF YOUNG, LOW-MASS STARS

Theoretical work suggests that a young star's angular momentum content and rotation rate may be strongly influenced by magnetic interactions with its circumstellar disk. A generic prediction of these 'disk-locking' theories is that a disk-locked star will be forced to co-rotate with the Keplerian angular velocity of the inner edge of the disk; that is, the disk's inner-truncation radius should equal its co-rotation radius. These theories have also been interpreted to suggest a gross correlation between young stars' rotation periods and the structural properties of their circumstellar disks, such that slowly rotating stars possess close-in disks that enforce the star's slow rotation, whereas rapidly rotating stars possess anemic or evacuated inner disks that are unable to brake the stars and instead the stars spin up as they contract. To test these expectations, we model the spectral energy distributions (SEDs) of 33 young stars in IC 348 with known rotation periods and infrared excesses indicating the presence of circumstellar disks. For each star, we match the observed SED, typically sampling 0.6-8.0 {mu}m, to a grid of 200,000 pre-computed star+disk radiative transfer models, from which we infer the disk's inner-truncation radius. We then compare this truncation radius to the disk's co-rotation radius, calculated from the star's measured rotation period. We do not find obvious differences in the disk truncation radii of slow rotators versus rapid rotators. This holds true both at the level of whether close-in disk material is present at all, and in analyzing the precise location of the inner disk edge relative to the co-rotation radius among the subset of stars with close-in disk material. One interpretation is that disk locking is unimportant for the IC 348 stars in our sample. Alternatively, if disk locking does operate, then it must operate on both the slow and rapid rotators, potentially producing both spin-up and spin-down torques, and the transition from the disk-locked state to the disk-released state must occur more rapidly than the stellar contraction timescale.

79 ASTRONOMY AND ASTROPHYSICS↗

Operator product expansion beyond leading order for two-component fermions

Here, we consider a homogeneous, balanced gas of strongly interacting fermions in two spin states interacting through a large scattering length. Finite-range corrections are needed for a quantitative description of data which experiments and numerical simulations have provided. We use a perturbative field-theoretical framework and a tool called the operator product expansion (OPE), which together allow for the expression of finite-range corrections to the universal relations and momentum distribution. By using the OPE, we derive the 1/k 6 part of the momentum tail, which is related to the sum of the derivative of the energy with respect to the finite range and the averaged kinetic energy of opposite spin pairs. By comparing the 1/k 4 term and the 1/k 6 correction in the momentum distribution to provided quantum Monte Carlo (QMC) data, we show that including the 1/k 6 part offers marked improvements. Our field-theoretical approach enables for a clear understanding of the role of the scattering length and finite effective range in the universal relations and the momentum distribution.

74 ATOMIC AND MOLECULAR PHYSICS↗

Distributed Wind Controls: A Research Roadmap for Microgrids, Infrastructure Resilience, and Controls Launchpad (MIRACL)

The Microgrids, Infrastructure Resilience, and Advanced Controls Launchpad (MIRACL) project’s controls research area aims to expand the benefits from distributed wind (DW) generation assets beyond solely providing low cost power directly to consumers. To make distributed wind turbines operate more effectively there is a need for more advanced ways to control them, allowing power companies, businesses, and energy consumers to take advantage of the unique characteristics of wind energy. DW can contribute to the safe and secure operation of grid by providing services such as voltage regulation, frequency regulation, spinning reserves, and even black start capabilities. In the larger DER context where much of the research has focused around solar technologies, the inertia available in wind technologies has generally not been considered. For wind turbines to provide these services in an optimal and expanded way, development and demonstration of control methods and communication interfaces within a grid and microgrid framework are required. In this document, NREL led the literature review in collaboration with SNL, of DER controls-focused integration research to establish a baseline for the controls research under the MIRACL project to identify specific control functions to be focused on throughout this project. This literature review focused primarily on the control functions of variable distributed generation, largely pulling from past solar PV and battery controls works, with a specific focus on applicability for distributed wind energy systems. The goal of this document is to identify a research roadmap based on the open literature and past national laboratory works to inform advanced wind turbine and power electronics control functions for four use cases: 1) distributed wind in isolated systems, 2) grid-connected microgrids (wind-hybrid systems and islanded operation), 3) behind-the-meter distributed wind applications in the power distribution systems, and 4) front-of-the-meter distributed wind applications in the power distribution systems.

17 WIND ENERGY↗

Violation of Bell’s inequality in a spin 1/2 quantum magnet

Violation of Bell’s inequality test has been established as an efficient tool to determine the presence of entanglement in quantum spin 1/2 magnets. Herein, macroscopic thermodynamic quantities, namely, magnetic susceptibility and specific heat have been employed to perform Bell’s inequality test for [NH{sub 4}CuPO{sub 4}, H{sub 2}O], a spin 1/2 antiferromagnet with nearest neighbor interactions. The mean value of the Bell operator is quantified and plotted as a function of temperature. The threshold temperature is determined above which the Bell’s inequality is not violated and a good consistency is found between the analyses done on magnetic and thermal data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Behavior of Spinning Space Vehicles with Onboard Liquids, 2nd Edition, Technical Report B8030

Although the fundamental principles of spin stabilization are well established, uncertainty regarding the potential for rapid nutation growth caused by onboard liquids is a continuing concern. NASA and other organizations regularly encounter the issue of rapid nutation growth due to energy dissipation by liquids on spinning vehicles. Of concern is the stability of spinning upper stages and of spacecraft that spin for part or all of their missions. Several missions have required last-minute hardware or operational changes to deal with rapid nutation divergences that were identified late in the program. In some instances, major schedule slips were barely averted. In at least two cases, it was determined that a spinning upper stage was not a viable option. Historically, the "slosh" issue has been addressed by each space vehicle project individually, if it has been addressed at all. Due to budgetary and programmatic constraints, individual projects are unable to address the problem globally. Hence, there has been little effort to collect available test and flight data and use that data to make a coherent, unified picture of the "slosh" effect and how to deal with it. To some extent, each project has had to "reinvent the wheel", which can be both costly and risky. This study is a step toward correcting the situation. Specifically, the goal was to identify and collect available flight and test data for spinning vehicles with onboard liquid propellants. A total of 149 flight data points and 1,692 test points were collected as part of this study. This data was analyzed, correlated, and is presented here in a normalized form. In most cases, the normalization involves a dimensionless nutation time constant that can be used to predict performance of other vehicles with the same type of tank. For some configurations, it was also possible to identify conditions that can lead to resonance between nutational motion and liquid modes. Gaps in the knowledge base are identified and approaches to filling those gaps are outlined. The data presented here has two different but related uses. First, it can be applied directly to current and future spacecraft programs. Second, it can provide truth models for testing analytical techniques. Experience has shown that purely analytical models of the liquid "slosh" effect on spinning vehicles are unreliable unless they are validated against flight or test data. To the author's knowledge, this report contains the most extensive and varied data set available. As such, it should be a good resource for anyone seeking to develop and validate improved analytical techniques. All of the original digital data sets have been archived on disk, with copies provided to NASA/KSC. With some restrictions, many of these data sets can be made available to researchers within the United States. Whenever possible, spacecraft are identified by name in this report. However, several organizations provided access to data with the explicit proviso that their programs not be identified and that parameters be presented only in normalized form. These constraints have been respected.

Hubert, Carl↗

Multidimensional effective field theory analysis for direct detection of dark matter

The scattering of dark matter particles off nuclei in direct detection experiments can be described in terms of a multidimensional effective field theory (EFT). Here a new systematic analysis technique is developed using the EFT approach and Bayesian inference methods to exploit, when possible, the energy-dependent information of the detected events, experimental efficiencies, and backgrounds. Highly dimensional likelihoods are calculated over the mass of the weakly interacting massive particle (WIMP) and multiple EFT coupling coefficients, which can then be used to set limits on these parameters and choose models (EFT operators) that best fit the direct detection data. Expanding the parameter space beyond the standard spin-independent isoscalar cross section and WIMP mass reduces tensions between previously published experiments. Combining these experiments to form a single joint likelihood leads to stronger limits than when each experiment is considered on its own. Simulations using two nonstandard operators ($\mathscr{O}$ 3 and $\mathscr{O}$ 8 ) are used to test the proposed analysis technique in up to five dimensions and demonstrate the importance of using multiple likelihood projections when determining constraints on WIMP mass and EFT coupling coefficients. In particular, this shows that an explicit momentum dependence in dark matter scattering can be identified.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

STOCHASTIC OPTIMAL POWER FLOW FOR REAL-TIME MANAGEMENT OF DISTRIBUTED RENEWABLE GENERATION AND DEMAND RESPONSE (Final Report)

To meet the grand challenge of a sustainable energy future, there has been a surge of interest in renewable energy. Today, the uncertainty associated with renewable resources is handled by using operating reserves. The high penetration of renewable resources, however, introduces difficult-to-control dynamics and challenges for power system operation. Decision support tools are necessary at the bulk system operational level to recognize and efficiently utilize renewable resources and distributed demand response products in concert with traditional grid resources. It is envisaged that responsive load can potentially have very significant cost advantages over either spinning or non-spinning ramping reserve. Critical decisions are made during hour(s)-ahead and real-time power system operation regarding the commitment and dispatch of generators to ensure power delivery is both reliable and economic. These decisions are typically made by a security constrained optimal flow, which determines future generator commitments, dispatches, and ensures adequate reserves are available in the event of a contingency (unexpected outage) or if future system conditions deviate from forecasts. However, security has been always based on a pre-specified subset of contingency constraints whose enforcement does not guarantee security under all possible future possibilities while also giving little or no weight to the likelihood of each contingent event or the severity of its consequences. Existing tools, which are based exclusively on deterministic optimization models, do not yield optimal operational decisions to address these new challenges, in terms of both reliability and cost-effectiveness. This project has focused on developing a stochastic optimal power flow (SOPF) framework, which integrates renewable resource uncertainty, load uncertainty, distributed storage (DS), demand response (DR) products, in a holistic manner to address the uncertainty associated with ever-increasing renewable resources, along with the inclusion of distributed demand response products in future power systems. A proof-of-concept problem was created using the Pennsylvania-Jersey-Maryland (PJM) power system network. Synthetic wind generation was added to the system to simulate 50% wind penetration. A 1-hour test of SOPF operation indicated more than 6% operational cost savings. The project continued by adding the Midwestern Independent System Operator (MISO) as a partner, with focus shifting from SOPF to Stochastic Look-Ahead Unit Commitment (SLAC). Unlike PJM, MISO is faced with significant renewable energy resources within its footprint and is challenged with substantial uncertainty in its operations. The SLAC distinguishes itself from existing tools that operators use. At best, today’s tools solve two to three cases independently, where one or two system parameters, such as forecasted load level (e.g., a low, base, and high forecast), are varied and the resulting scenarios are analyzed independently. The stochastic-based optimization of SLAC leverages statistical information from an ensemble of potential operational scenarios and their respective likelihood. The SLAC output can be translated into valuable information to the operator such as suggested commitments, optimal scheduling and dispatch of resources, reserve requirements at both locational and zonal resolutions, ramping availability and requirements, availability of demand response including operational guidance concerning the near-term and real-time coordination between distributed energy resources, and utilization of distributed storage resources. The developed SOPF/SLAC tool, a stand-alone tool compatible with existing EMSs, will provide system operators with unprecedented visibility, flexibility and predictability to these resources and operational guidance concerning the real-time coordination between DERs and DR/DS products. The game changing and practical impact of this disruptive technology will be dramatic and will usher in a new era in the electric power industry, wherein green energy concepts are fully embraced, and electric power costs are lowered throughout the nation.

42 ENGINEERING↗

Regional Real-Time PV Spinning Reserve Estimator

Curtailed photovoltaic (PV) generation is a zero-marginal-cost spinning reserve that can be used for a number of active power control services. Unlike traditional spinning reserve providers, however, i.e., fossil-fueled generators, which have well-defined operating characteristics, e.g., available headroom or potential high limit (PHL), PV plants have by nature variable and uncertain operating characteristics. To ensure the effective coordination between PV plants and the system operator during an active power control event, accurate knowledge of the PV PHL is essential. It ensures that enough headroom is reserved by the PV plants to deliver the award services in real time and informs feasible dispatch decisions made by the market operator. To tackle this challenge, a novel reference-control grouping-based PV plant reserve estimation method has been proposed by the National Renewable Energy Laboratory under past projects funded by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Solar Energy Technologies Office. The estimation method separates inverters within a plant into two groups: a control group and a reference group. While the reference group is reserved to operate at its PHL, the control group can be curtailed to provide the grid services. Real-time outputs from the reference inverters are used to estimate the PHL for the whole plant based on the ratio between capacities of the reference group and of the plant. This work further enhances the methodology by (1) improving the model accuracy through machine learning; (2) automating the reference inverter selection through correlation analysis; (3) considering estimation look-ahead windows; and (4) applying to regional spinning reserve estimation. Significant performance improvement has been observed based on real-world data collected by CAISO, Southern Company, and Terabase Energy. Compared with the original scaling method, the newly proposed machine learning-based approach reduces the estimation errors by 30% and 13% at the plant level and region level, respectively. Results obtained from this project are intended to be used by grid operators, market operators, balancing authorities, and PV plant owners and operators to facilitate PV participation in ancillary service markets. Regulators, policymakers, and system planners can also consider the results of this work in their decision-making processes. In addition to the performance improvement on the existing reference-control based grouping method, we also investigated how the variability of PV generation from a single PV inverter can be used to represent the variability of PV generation at the plant level.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Matrix diagonalization algorithm and its applicability to the nuclear shell model

An importance-sampling iterative algorithm for diagonalizing shell model Hamiltonian matrices is reviewed and implemented in a spin uncoupled basis. Shell model spaces of dimensions up to N < or approx.10{sup 9} are considered. The analysis shows that about 10% of the basis states are enough to bring the eigenvalues to convergence. This fraction of states, however, is insufficient to lead to convergence of the transition strengths, thereby limiting the applicability of the method to not too large spaces. In its domain of validity, the method yields a large number of eigensolutions and can be usefully adopted for rather complete studies of low-energy spectroscopy. This is done here for {sup 132,134}Xe isotopes. The calculation yields spectra and electromagnetic responses in fairly good agreement with the available experimental data and unveils the properties of the low-energy states of these isotopes, including their proton-neutron symmetry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Magnetic and ferroelectric ordering in BiMn{sub 2}O{sub 5} oxide

A group-theoretical analysis of the magnetic phase of BiMn{sub 2}O{sub 5} oxide is performed using the space symmetry group of the compound. Using the projection operator method, we determine the basis functions of the irreducible representation of the space group, which are expressed in terms of the magnetic vector components. This representation can govern two phase transitions from the paramagnetic state to the antiferromagnetic phase with close temperatures and ordering of the spins of manganese ions in two crystallographic positions. It is found from renorm group analysis of these transitions that when these transitions occur as second- order transitions, the electric polarization does not appear in the system because spin fluctuations in this case elevate the symmetry of the system. Polarization appears when at least one of these transitions becomes a first-order transition as a result of spin fluctuations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗