Intermediate Mixed State Research Articles

Pushing the limits of accessible length scales via a modified Porod analysis in small-angle neutron scattering on ordered systems.

Small-angle neutron scattering is a widely used technique to study large-scale structures in bulk samples. The largest accessible length scale in conventional Bragg scattering is determined by the combination of the longest available neutron wavelength and smallest resolvable scattering angle. A method is presented that circumvents this limitation and is able to extract larger length scales from the low-q power-law scattering using a modification of the well known Porod law connecting the scattered intensity of randomly distributed objects to their specific surface area. It is shown that in the special case of a highly aligned domain structure the specific surface area extracted from the modified Porod law can be used to determine specific length scales of the domain structure. The analysis method is applied to study the micrometre-sized domain structure found in the intermediate mixed state of the superconductor niobium. The analysis approach allows the range of accessible length scales to be extended from 1 µm to up to 40 µm using a conventional small-angle neutron scattering setup.

Microscopic description of intermediate mixed state in superconductors between the first and second types

Microscopic description of intermediate mixed state in superconductors between the first and second types

Collective dynamics of swarmalators with higher-order interactions

AbstractHigher-order interactions shape collective dynamics, but how they affect transitions between different states in swarmalator systems is yet to be determined. To that effect, we here study an analytically tractable swarmalator model that incorporates both pairwise and higher-order interactions, resulting in four distinct collective states: async, phase wave, mixed, and sync states. We show that even a minute fraction of higher-order interactions induces abrupt transitions from the async state to the phase wave and the sync state. We also show that higher-order interactions facilitate an abrupt transition from the phase wave to the sync state bypassing the intermediate mixed state. Moreover, elevated levels of higher-order interactions can sustain the presence of phase wave and sync state, even when pairwise interactions lean towards repulsion. The insights gained from these findings unveil self-organizing processes that hold the potential to explain sudden transitions between various collective states in numerous real-world systems.

Fully Microscopic Treatment of Magnetic Field Using Bogoliubov–De Gennes Approach

This work introduces an algorithm designed to solve the Bogoliubov–de Gennes equations of superconductivity theory. What sets this algorithm apart is its remarkable ability to precisely and consistently consider the impact of an external magnetic field, all within the microscopic approach. The computation scheme’s convergence is guaranteed by addressing the Biot–Savart equation for the field where the vector potential appears on both of its sides. To showcase the capabilities of this approach, we provide several key examples: the Abrikosov lattice, vortex core states, and the vortex structure in the intermediate mixed state of a superconductor. This method promises to offer valuable insights into the microscopic physics of intertype superconductivity.

Tracing Vortex Clustering in a Superconductor by the Magnetic Flux Distribution.

By investigating spatial configurations of the intermediate mixed state in an intertype superconductor, it is shown that vortex clustering can be characterized by the sample averaged distribution of the penetrating magnetic field. The clustering is manifested in the two-peak structure of the distribution. The second peak indicates a spot a material occupies in the phase diagram of superconductivity types. The conclusions are general and do not depend on details of the model.

Current-induced self-organisation of mixed superconducting states

Small-angle neutron scattering is used in combination with transport measurements to investigate the current-induced effects on the morphology of the intermediate mixed state (IMS) domains in the intertype superconductor niobium. We report the robust self-organisation of the vortex lattice domains to elongated parallel stripes perpendicular to the applied current in a steady-state. The experimental results for the formation of the superstructure are supported by theoretical calculations, which highlight important details of the vortex matter evolution. The investigation demonstrates a mechanism of a spontaneous pattern formation that is closely related to the universal physics governing the IMS in low-κ superconductors.

Observation of intermediate mixed state in high-purity cavity-grade Nb by magneto-optical imaging

Suppression of the occurrence of remanent vortices is necessary to improve the quality factor of superconducting resonators. In particular, the flux-expulsion dynamics in Nb during cooling has become of major interest to researchers focusing on superconducting cavities. To study the vortex states and their behavior in high-purity cavity-grade Nb, we used a magneto-optical imaging technique to perform real-space observations of the magnetic field distributions during the field-cooling and field-scanning processes. In the field-cooling process, the distributions were observed to undergo phase separation into vortex and Meissner regions, as would be expected in an intermediate mixed state (IMS). The vortex regions in the IMS, such as vortex bundles, tend to be larger in higher fields, in contrast to the Meissner regions, which experience shrinkage. In the field-scanning process, domelike field profiles, which indicate a geometrical barrier with very weak bulk pinning, were observed. The existence of the IMS suggests that cavity-grade Nb is in a type-II/1 superconductor regime, in which attractive interaction between vortices at a length scale of the penetration depth is crucial for the behavior of vortices.

Interhemispheric Auditory Cortical Synchronization in Asymmetric Hearing Loss.

Objectives:Auditory cortical activation of the two hemispheres to monaurally presented tonal stimuli has been shown to be asynchronous in normal hearing (NH) but synchronous in the extreme case of adult-onset asymmetric hearing loss (AHL) with single-sided deafness. We addressed the wide knowledge gap between these two anchoring states of interhemispheric temporal organization. The objectives of this study were as follows: (1) to map the trajectory of interhemispheric temporal reorganization from asynchrony to synchrony using magnitude of interaural threshold difference as the independent variable in a cross-sectional study and (2) to evaluate reversibility of interhemispheric synchrony in association with hearing in noise performance by amplifying the aidable poorer ear in a repeated measures, longitudinal study.Design:The cross-sectional and longitudinal cohorts were comprised of 49 subjects (AHL; N = 21; 11 male, 10 female; mean age = 48 years) and NH (N = 28; 16 male, 12 female; mean age = 45 years). The maximum interaural threshold difference of the two cohorts spanned from 0 to 65 dB. Magnetoencephalography analyses focused on latency of the M100 peak response from auditory cortex in both hemispheres between 50 msec and 150 msec following monaural tonal stimulation at the frequency (0.5, 1, 2, 3, or 4 kHz) corresponding to the maximum and minimum interaural threshold difference for better and poorer ears separately. The longitudinal AHL cohort was drawn from three subjects in the cross-sectional AHL cohort (all male; ages 49 to 60 years; varied AHL etiologies; no amplification for at least 2 years). All longitudinal study subjects were treated by monaural amplification of the poorer ear and underwent repeated measures examination of the M100 response latency and quick speech in noise hearing in noise performance at baseline, and postamplification months 3, 6, and 12.Results:The M100 response peak latency values in the ipsilateral hemisphere lagged those in the contralateral hemisphere for all stimulation conditions. The mean (SD) interhemispheric latency difference values (ipsilateral less contralateral) to better ear stimulation for three categories of maximum interaural threshold difference were as follows: NH (≤ 10 dB)—8.6 (3.0) msec; AHL (15 to 40 dB)—3.0 (1.2) msec; AHL (≥ 45 dB)—1.4 (1.3) msec. In turn, the magnitude of difference values were used to define interhemispheric temporal organization states of asynchrony, mixed asynchrony and synchrony, and synchrony, respectively. Amplification of the poorer ear in longitudinal subjects drove interhemispheric organization change from baseline synchrony to postamplification asynchrony and hearing in noise performance improvement in those with baseline impairment over a 12-month period.Conclusions:Interhemispheric temporal organization in AHL was anchored between states of asynchrony in NH and synchrony in single-sided deafness. For asymmetry magnitudes between 15 and 40 dB, the intermediate mixed state of asynchrony and synchrony was continuous and reversible. Amplification of the poorer ear in AHL improved hearing in noise performance and restored normal temporal organization of auditory cortices in the two hemispheres. The return to normal interhemispheric asynchrony from baseline synchrony and improvement in hearing following monoaural amplification of the poorer ear evolved progressively over a 12-month period.

Highly Cooperative Photoswitching in Dihydropyrene Dimers.

We present a strategy to achieve highly cooperative photoswitching, where the initial switching event greatly facilitates subsequent switching of the neighboring unit. By linking donor/acceptor substituted dihydropyrenes via suitable π‐conjugated bridges, the quantum yield of the second photochemical ring‐opening process could be enhanced by more than two orders of magnitude as compared to the first ring‐opening. As a result, the intermediate mixed switching state is not detected during photoisomerization although it is formed during the thermal back reaction. Comparing the switching behavior of various dimers, both experimentally and computationally, helped to unravel the crucial role of the bridging moiety connecting both photochromic units. The presented dihydropyrene dimer serves as model system for longer cooperative switching chains, which, in principle, should enable efficient and directional transfer of information along a molecularly defined path. Moreover, our concept allows to enhance the photosensitivity in oligomeric and polymeric systems and materials thereof.

Competition between vaccination and disease spreading.

We study the interaction between epidemic spreading and a vaccination process. We assume that, similar to the disease spreading, the vaccination process also occurs through direct contact, i.e., it follows the standard susceptible-infected-susceptible (SIS) dynamics. The two competing processes are asymmetrically coupled as vaccinated nodes can directly become infected at a reduced rate with respect to susceptible ones. We study analytically the model in the framework of mean-field theory finding a rich phase diagram. When vaccination provides little protection toward infection, two continuous transitions separate a disease-free immunized state from vaccinated-free epidemic state, with an intermediate mixed state where susceptible, infected, and vaccinated individuals coexist. As vaccine efficiency increases, a tricritical point leads to a bistable regime, and discontinuous phase transitions emerge. Numerical simulations for homogeneous random networks agree very well with analytical predictions.

Visualization of compensating currents in type-II/1 superconductor via high field cooling

The morphology of vortex lattice domains in bulk type-II/1 superconductors is of central interest for many areas such as fundamental condensed matter physics, engineering science, and the optimization of materials for high transport current superconductivity applications. Here, we present a comprehensive experimental study of a single crystal niobium in the intermediate mixed state and Shubnikov phase with two complementary neutron techniques: high resolution polarized neutron imaging and small-angle neutron scattering. In this way, we were able to identify and visualize the occurrence of compensating currents, the flux line closure, and the freezing of the vortex spacing during the process of field cooling and high field cooling. With the combination of complementary neutron techniques, it was possible to add insights into the quest for the understanding of the flux pinning and nucleation of vortices in type-II/1 superconductors during the process of field cooling and high field cooling.

Universal behavior of the intermediate mixed state domain formation in superconducting niobium

In the intermediate mixed state (IMS) of type-II/1 superconductors, vortex lattice (VL) and Meissner state domains coexist due to a partially attractive vortex interaction. Using a neutron-based multiscale approach combined with magnetization measurements, we study the continuous decomposition of a homogeneous VL into increasingly dense domains in the IMS in bulk niobium samples of varying purity. We find a universal temperature dependence of the vortex spacing, closely related to the London penetration depth and independent of the external magnetic field. The rearrangement of vortices occurs even in the presence of a flux freezing transition, i.e. pronounced pinning, indicating a breakdown of pinning at the onset of the vortex attraction.

The nature of voltage in superconductors with dynamic intermediate-mixed state

Aim: to describe scientific achievement providing the essence of the phenomenon; to confirm reliability of existence of DC electromagnetic induction using direct evidence.
 Methods: experimental research into magnetizing superconducting samples. Visualisation of intermediate and mixed state of superconductors and movement of quantised threads of magnetic flux, the beams of such threads. Development of mathematical theory on the basis of fractal geometry and functional analysis.
 Results: The essence of the scientific discovery consists in the proof that the direct consequence of the formation of an intermediate-mixed state of superconductors and the movement of quantum magnetic fluxes threads, beams of such filaments and macroscopic normal zones is the phenomenon of direct current electromagnetic induction.
 Conclusion: the discovery of DC electromagnetic induction has been made, superconducting topological electrical generators on the basis of DC electromagnetic induction have been built, that achieve high nominal parameters: 10-100 kA current, specific current load - 1 kA/kg.

Relative Ligand-Binding Free Energies Calculated from Multiple Short QM/MM MD Simulations.

We have devised a new efficient approach to compute combined quantum mechanical (QM) and molecular mechanical (MM, i.e. QM/MM) ligand-binding relative free energies. Our method employs the reference-potential approach with free-energy perturbation both at the MM level (between the two ligands) and from MM to QM/MM (for each ligand). To ensure that converged results are obtained for the MM → QM/MM perturbations, explicit QM/MM molecular dynamics (MD) simulations are performed with two intermediate mixed states. To speed up the calculations, we utilize the fact that the phase space can be extensively sampled at the MM level. Therefore, we run many short QM/MM MD simulations started from snapshots of the MM simulations, instead of a single long simulation. As a test case, we study the binding of nine cyclic carboxylate ligands to the octa-acid deep cavitand. Only the ligand is in the QM system, treated with the semiempirical PM6-DH+ method. We show that for eight of the ligands, we obtain well converged results with short MD simulations (1-15 ps). However, in one case, the convergence is slower (∼50 ps) owing to a mismatch between the conformational preferences of the MM and QM/MM potentials. We test the effect of initial minimization, the need of equilibration, and how many independent simulations are needed to reach a certain precision. The results show that the present approach is about four times faster than using standard MM → QM/MM free-energy perturbations with the same accuracy and precision.

Domain formation in the type-II/1 superconductor niobium: Interplay of pinning, geometry, and attractive vortex-vortex interaction

Vortex attraction which can cause a bundling of vortices has been observed in a multitude of type-II superconductors. While its underlying mechanisms have been extensively studied, the morphology of the emerging vortex superstructure has only been rarely considered. Here, we present a comprehensive experimental study on the type-II/1 superconductor niobium which focuses on the transformation of its homogeneous vortex lattice into an inhomogeneous domain structure at the onset of vortex attraction. By means of small-angle neutron scattering, ultra-small-angle neutron scattering, and neutron grating interferometry, the vortex lattice and the micrometer-scale vortex domain structure as well as its distribution could be investigated. In particular, we focus on the transformation of the vortex lattice at the transition to the intermediate mixed state, which is characterized by vortex attraction. We have found that the phase separation of the vortex lattice into an irregular domain structure takes place via a process showing strong similarity to spinodal decomposition. While pinning disorders the domain morphology, the characteristic length scale of the domain structure is governed by an interplay of field distortion energy and domain surface tension. Finally, geometric barriers in the disk-shaped samples provoke an inhomogeneous distribution of domains on the macroscopic scale.

Visualizing the morphology of vortex lattice domains in a bulk type-II superconductor.

Alike materials in the solid state, the phase diagram of type-II superconductors exhibit crystalline, amorphous, liquid and spatially inhomogeneous phases. The multitude of different phases of vortex matter has thence proven to act as almost ideal model system for the study of both the underlying properties of superconductivity but also of general phenomena such as domain nucleation and morphology. Here we show how neutron grating interferometry yields detailed information on the vortex lattice and its domain structure in the intermediate mixed state of a type-II niobium superconductor. In particular, we identify the nucleation regions, how the intermediate mixed state expands, and where it finally evolves into the Shubnikov phase. Moreover, we complement the results obtained from neutron grating interferometry by small-angle neutron scattering that confirm the spatially resolved morphology found in the intermediate mixed state, and very small-angle neutron scattering that confirm the domain structure of the vortex lattice.

Temperature dependence of clusters with attracting vortices in superconducting niobium studied by neutron scattering

We investigated the intermediate mixed state of a superconducting niobium sample using very small angle neutron scattering. We show that this state is stabilized through a sequence where a regular vortex lattice appears, which then coexists with vortex clusters before vanishing at low temperature. Vortices in clusters have a constant periodicity regardless of the applied field and exhibit a temperature dependence close to the one of the penetration depth. The clusters disappear in the high temperature limit. All the results agree with an explanation in terms of vortex attraction due to non-local effects and indicate a negligible role for pinning. Phase coexistence between the Abrikosov vortex lattice and vortex clusters is reported, showing the first-order nature of the boundary line.

Strong local lattice instability in hexagonal ferritesRFe2O4(R= Lu,Y,Yb) revealed by x-ray absorption spectroscopy

We present here an x-ray absorption study of the $R$Fe${}_{2}$O${}_{4}$ series (LuFe${}_{2}$O${}_{4}$, YFe${}_{2}$O${}_{4}$, YbFe${}_{2}$O${}_{4}$, and LuCoFeO${}_{4}$) at the Fe $K$-edge. Extended x-ray absorption fine structure (EXAFS) and x-ray absorption near-edge structure (XANES) spectra were measured at temperatures ranging from 100 K to 390 K crossing the charge ordering (CO) transition temperatures on both isotropic and oriented powder samples. Unpolarized and polarized x-ray absorption spectra with the x-ray polarization parallel and perpendicular to the hexagonal $c$ axis were obtained separately. The XANES spectra show almost no dependence with either polarization or temperature. This indicates that, in contrast to its average crystallographic structure, the local electronic and geometrical state of the Fe atom is barely anisotropic, and it remains the same above and below the proposed CO. Moreover, the linear combination of two spectra corresponding to the pure ionic states Fe${}^{2+}$ and Fe${}^{3+}$ does not fit to the experimental XANES of either LuFe${}_{2}$O${}_{4}$, YFe${}_{2}$O${}_{4}$, or YbFe${}_{2}$O${}_{4}$, discarding total ionic segregation in favor of an intermediate mixed valence state. The maximum charge disproportionation compatible with the XANES spectra is 0.5 \ifmmode\pm\else\textpm\fi{} 0.1 electrons in the whole temperature range. The polarized EXAFS spectra have allowed us to analyze the local structure separating the different contributions mixed up in the polycrystal. Best-fit results show that the five oxygen atoms of the first coordination shell are at nearly the same distance but with a large Debye-Waller factor. Neither the interatomic distances nor the Debye-Waller factors of the first oxygen coordination shell change with temperature, indicating that the dynamical structural distortion of the high-temperature symmetric hexagonal phase freezes upon cooling down. Thus, the local structure instability of the mixed valence is in the origin of the structural transitions.

Influence of ancillary ligands on the electronic structure and anion sensing features of ligand bridged diruthenium complexes

The present article deals with a newer class of ligand bridged asymmetric complexes incorporating ancillary ligands (AL) with varying electronic characteristics: [(bpy)2Ru(II)(μ-HL(2-)) Ru(II)(bpy)2](ClO4)2·([1](ClO4)2); [(pap)2Ru(II)(μ-HL(2-))Ru(II)(pap)2](ClO4)2 ([2](ClO4)2); [(bpy)2Ru(II)(μ-HL(2-))Ru(II)(pap)2](ClO4)2 ([3](ClO4)2); [(acac)2Ru(III)(μ-HL(2-))Ru(III)(acac)2] (4) and [(bpy)2Ru(II)(μ-HL(2-))Ru(III)(acac)2]ClO4 ([5]ClO4) (H3L: 5-(1H-benzo[d]imidazol-2-yl)-1H-imidazole-4-carboxylic acid, bpy = moderately π-accepting 2,2'-bipyridine, pap = strongly π-accepting 2-phenylazopyridine, acac(-) = σ-donating acetylacetonate). The molecular identity of [1](ClO4)2 was established by its single crystal X-ray structure. A large shift in Ru(II)/Ru(III) potential of 0.7-2.0 V took place on switching the ancillary ligands from AL = bpy to pap to acac(-), leading to the stabilisation of ruthenium(II) and ruthenium(III) states in 1(2+), 2(2+), 3(2+), 4 and 5(+), respectively. The detailed magnetic studies revealed that the paramagnetic Ru(III)Ru(III) state in 4 essentially behaves as a system with two independent S = 1/2 spins and it exhibits an anisotropic EPR at 77 K (<g> = 2.192, Δg = g1-g3 = 0.70) but without any half-field signal near g∼ 4. The isolated mixed valent Ru(II)Ru(III) state in 5(+) exhibits weak antiferromagnetic coupling of -0.25 cm(-1) and anisotropic EPR with <g> = 2.155, Δg = 0.704 but fails to show a Ru(II)→ Ru(III) IVCT (intervalence charge transfer) transition in the near-IR region up to 2000 nm. The complexes 1(2+), 2(2+) and 4 encompassing identical metal fragments, exhibited weak to moderate electrochemical coupling at the intermediate mixed valent states with Kc values of 10(2)-10(5). The coulometrically generated mixed valent Ru(II)Ru(III) state in 1(3+) or 4(-) also failed to display any prominent absorption in the near-IR region, but exhibited Ru(III) based rhombic EPR, implying valence localised situation with negligible intermetallic electronic coupling. The complexes 2(2+), 3(2+), 4 and 5(+) having one NH proton associated with the bridging ligand HL(2-) do not show any interaction with the anions F(-), Cl(-), Br(-), I(-), HSO4(-), H2PO4(-), OAc(-) and SCN(-) in CH3CN, though 1(2+) selectively recognises the fluoride ion.

Polyamorphic transitions in Ce-based metallic glasses by synchrotron radiation

We report here on a polyamorphic-phase transition upon application of pressure on a Ce-based metallic glass, Ce${}_{70}$Al${}_{10}$Ni${}_{10}$Cu${}_{10}$, investigated by x-ray diffraction and inelastic x-ray scattering. This alloy is found to display a strong hysteresis in volume per atom upon application and subsequent release of pressure. The observed structural changes are correlated with changes observed by inelastic x-ray scattering in the elastic constants, acoustic mode frequencies, and sound speed. The results reported here point toward three different amorphous phases for this alloy existing in the 0--25 GPa pressure region: low- and high-density states and an intermediate mixed state that displays a hysteresis behavior. Finally, we discuss the impact of Ce concentration on the polyamorphic transition for a series of Ce-based metallic glass alloys and link it to the phase transformation between $\ensuremath{\gamma}$-Ce and $\ensuremath{\alpha}$-Ce under pressure.