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Materials Data on CrN4Cl(O2F)2 by Materials Project

Cr(NF)2N2ClO4 is Iron carbide-derived structured and crystallizes in the tetragonal I4_1md space group. The structure is zero-dimensional and consists of eight ammonia molecules, four ClO4 clusters, and four Cr(NF)2 clusters. In each ClO4 cluster, there are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a single-bond geometry to one Cl1- atom. The O–Cl bond length is 1.49 Å. In the second O2- site, O2- is bonded in a single-bond geometry to one Cl1- atom. The O–Cl bond length is 1.43 Å. Cl1- is bonded in a tetrahedral geometry to four O2- atoms. In each Cr(NF)2 cluster, Cr3+ is bonded in a distorted see-saw-like geometry to two equivalent N2+ and two equivalent F1- atoms. Both Cr–N bond lengths are 1.91 Å. Both Cr–F bond lengths are 1.79 Å. N2+ is bonded in a single-bond geometry to one Cr3+ atom. F1- is bonded in a single-bond geometry to one Cr3+ atom.

36 MATERIALS SCIENCE↗

Materials Data on INO4 by Materials Project

NO4I is Iron carbide-derived structured and crystallizes in the tetragonal I4_1/a space group. The structure is zero-dimensional and consists of four ammonia molecules and four IO4 clusters. In each IO4 cluster, O2- is bonded in a single-bond geometry to one I5+ atom. The O–I bond length is 1.81 Å. I5+ is bonded in a tetrahedral geometry to four equivalent O2- atoms.

36 MATERIALS SCIENCE↗

Controlling $T_c$ through Band Structure and Correlation Engineering in Collapsed and Uncollapsed Phases of Iron Arsenides

Recent observations of selective emergence (suppression) of superconductivity in the uncollapsed (collapsed) tetragonal phase of LaFe 2 As 2 has rekindled interest in understanding what features of the band structure control the superconducting $T_c$. In this work, we show that the proximity of the narrow Fe-$d_{xy}$ state to the Fermi energy emerges as the primary factor. In the uncollapsed phase this state is at the Fermi energy, and is most strongly correlated and a source of enhanced scattering in both single and two particle channels. The resulting intense and broad low energy spin fluctuations suppress magnetic ordering and simultaneously provide glue for Cooper pair formation. In the collapsed tetragonal phase, the $d_{xy}$ state is driven far below the Fermi energy, which suppresses the low-energy scattering and blocks superconductivity. A similar source of broad spin excitation appears in uncollapsed and collapsed phases of CaFe 2 As 2 . This suggests controlling coherence provides a way to engineer $T_c$ in unconventional superconductors primarily mediated through spin fluctuations.

36 MATERIALS SCIENCE↗

Rapid consolidation method for preparing bulk metastable iron-rich materials

Interstitially modified compounds of rare earth element-containing, iron-rich compounds may be synthesized with a ThMn 12 tetragonal crystal structure such that the compounds have useful permanent magnet properties. It is difficult to consolidate particles of the compounds into a bulk shape without altering the composition and magnetic properties of the metastable material. A combination of thermal analysis and crystal structure analysis of each compound may be used to establish heating and consolidation parameters for sintering of the particles into useful magnet shapes.

Zhou, Chen↗

In Situ Visualization of Local Distortions in the High- T c Molecule-Intercalated Li x (C 5 H 5 N) y Fe 2– z Se 2 Superconductor

A time-resolved synchrotron X-ray total scattering study sheds light on the evolution of the different structural length scales involved during the intercalation of the layered iron–selenide host by organic molecular donors, aiming at the formation of the expanded-lattice Li x (C 5 H 5 N) y Fe 2– z Se 2 hybrid superconductor. The intercalates are found to crystallize in the tetragonal ThCr 2 Si 2 -type structure at the average level, however, with an enhanced interlayer iron–selenide spacing ( d = 16.2 Å) that accommodates the heterocyclic molecular spacers. Quantitative atomic pair distribution function (PDF) analysis at variable times suggests distorted FeSe 4 tetrahedral local environments that appear swollen with respect to those in the parent β-FeSe. Simultaneously acquired in situ synchrotron X-ray powder diffraction data disclose that secondary phases (α-Fe and Li 2 Se) grow significantly when a higher lithium concentration is used in the solvothermal reaction or when the solution is aged. These observations are in line with the strongly reducing character of the intercalation medium’s solvated electrons that mediate the defect chemistry of the expanded-lattice superconductor. In the latter, intralayer correlated local distortions indicate electron-donating aspects that reflect in somewhat enlarged Fe–Se bonds. Additionally, they also reveal a degree of relief of chemical pressure associated with a large distance between Fe and Se sheets (“taller” anion height) and a stretched Fe–Fe square planar topology. The elongation of the latter, derived from the in situ PDF study, speaks for a plausible increase in the Fe-site vacancy concentration. The evolution of the local structural parameters suggests an optimum reaction window where kinetically stabilized phases resemble the distortions of the edge-sharing Fe–Se tetrahedra, required for a high- T c in expanded-lattice iron-chalcogenides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Coupling of fully symmetric As phonon to magnetism in Ba(Fe 1-x Au x ) 2 As 2

In this work, we study the coupling of the fully symmetric vibration mode of arsenic atoms to magnetism in a Ba ( Fe 1 - x Au x ) 2 As 2 system by polarization-resolved Raman spectroscopy and neutron diffraction. In this system, there are two phase transitions: a tetragonal-to-orthorhombic structural phase transition at temperature T S and a magnetic phase transition into collinear spin-density wave (SDW) state at temperature T N ( ≤ T S ). T S and T N almost coincide in the pristine compound, whereas they differ by as much as 8 K for compounds with dilute gold substitution for iron. Raman coupling to the A g (As) phonon is forbidden for the X Y scattering geometry in the tetragonal phase above T S , whereas it becomes allowed in the orthorhombic phase below T S : The emerging mode's intensity indicates the lattice orthorhombicity. Furthermore, we find that upon cooling below T S , first, weak A g (As) phonon mode intensity appears in the X Y scattering geometry spectra; however, the mode's intensity is significantly enhanced in the magnetic phase below T N . The A g (As) phonon also shows an asymmetric line shape below T N and an anomalous linewidth broadening upon Au doping. We describe the anomalous behavior of the A g (As) mode in the X Y scattering geometry using a Fano model involving the A g (As) phonon interacting with the B 2 g ( D 4 h )-symmetry-like electron-hole continuum. We conclude that the temperature dependence of light coupling amplitude to the A g (As) phonon follows the evolution of the magnetic order parameter M ( T ) . We propose that the intensity enhancement of the A g (As) phonon in the X Y scattering geometry below T N is due to electronic anisotropy induced by the collinear SDW order parameter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

In-plane uniaxial pressure-induced out-of-plane antiferromagnetic moment and critical fluctuations in BaFe 2 As 2

A small in-plane external uniaxial pressure has been widely used as an effective method to acquire single domain iron pnictide BaFe 2 As 2 , which exhibits twin-domains without uniaxial strain below the tetragonal-to-orthorhombic structural (nematic) transition temperature T s . Although it is generally assumed that such a pressure will not affect the intrinsic electronic/magnetic properties of the system, it is known to enhance the antiferromagnetic (AF) ordering temperature T N ( < T s ) and create in-plane resistivity anisotropy above T s . Here we use neutron polarization analysis to show that such a strain on BaFe 2 As 2 also induces a static or quasi-static out-of-plane ( c -axis) AF order and its associated critical spin fluctuations near T N / T s . Therefore, uniaxial pressure necessary to detwin single crystals of BaFe 2 As 2 actually rotates the easy axis of the collinear AF order near T N / T s , and such effects due to spin-orbit coupling must be taken into account to unveil the intrinsic electronic/magnetic properties of the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Optical and photoemission investigation of structural and magnetic transitions in the iron-based superconductor Sr 0.67 Na 0.33 Fe 2 As 2

We report the temperature-dependent optical conductivity and angle-resolved photoemission spectroscopy (ARPES) studies of the multiband iron-based superconductor Sr 0.67 Na 0.33 Fe 2 As 2 . Measurements were made in the high-temperature tetragonal paramagnetic phase, below the structural and magnetic transitions at $T_N$ $≃$ 125 K in the orthorhombic spin-density-wave (SDW)-like phase and $T_r$ $≃$42 K in the reentrant tetragonal double-Q magnetic phase where both charge and SDWorder exist, and below the superconducting transition at $T_c$ $≃$ 10 K. The free-carrier component in the optical conductivity is described by two Drude contributions: one strong and broad and the other weak and narrow. The broad Drude component decreases dramatically below TN and Tr , with much of its strength being transferred to a bound excitation in the midinfrared, while the narrow Drude component shows no anomalies at either of the transitions, actually increasing in strength at low temperature while narrowing dramatically. The behavior of an infrared-active mode suggests zone folding below Tr. Below Tc the dramatic decrease in the low-frequency optical conductivity signals the formation of a superconducting energy gap. ARPES reveals holelike bands at the center of the Brillouin zone (BZ), with both electron- and holelike bands at the corners. Below $T_N$, the hole pockets at the center of the BZ decrease in size, consistent with the behavior of the broad Drude component; however, below $T_r$ the electronlike bands shift and split, giving rise to a low-energy excitation in the optical conductivity at $≃$20 meV. The $C_2$ and $C_4$ magnetic states, with resulting spin-density-wave and charge-SDW order, respectively, lead to a significant reconstruction of the Fermi surface that has profound implications for the transport originating from the electron and hole pockets but appears to have relatively little impact on the superconductivity in this material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tuning superconductivity and spin-vortex instabilities in CaKFe 4 As 4 through in-plane antisymmetric strains

Lattice strains of appropriate symmetry have served as an excellent tool to explore the interaction of superconductivity in the iron-based superconductors with orthorhombic-nematic and stripe spin-density-wave (SSDW) order. In this Letter, we contribute to a broader understanding of the coupling of strain to superconductivity and competing normal-state orders by studying CaKFe 4 As 4 under large, in-plane strains of B 1 g and B 2 g symmetry. In contrast to the majority of iron-based superconductors, pure CaKFe 4 As 4 exhibits superconductivity with a relatively high transition temperature of T c ∼ 35 K in proximity of a noncollinear, tetragonal, hedgehog spin-vortex crystal (SVC) order. Through experiments and calculations, we demonstrate an anisotropic in-plane strain response of T c and the favored SVC configuration in CaKFe 4 As 4 . This supports a scenario, in which the change in spin fluctuations dominates the strain response of superconducting T c . Overall, by suggesting moderate B 2 g strains as an effective parameter to change the stability of SVC and SSDW, we outline a pathway to a unified phase diagram of iron-based superconductivity. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spin fluctuations in the 112-type iron-based superconductor Ca 0.82 La 0.18 Fe 0.96 Ni 0.04 As 2

Abstract We report time-of-flight inelastic neutron scattering (INS) investigations on the spin fluctuation spectrum in the 112-type iron-based superconductor (FeSC) Ca 0.82 La 0.18 Fe 0.96 Ni 0.04 As 2 (CaLa-112). In comparison to the 122-type FeSCs with a centrosymmetric tetragonal lattice structure (space group I 4 / m m m ) at room temperature and an in-plane stripe-type antiferromagnetic (AF) order at low temperature, the 112 system has a noncentrosymmetric structure (space group P 2 1 ) with additional zigzag arsenic chains between Ca/La layers and a magnetic ground state with similar wavevector Q A F but different orientations of ordered moments in the parent compounds. Our INS study clearly reveals that the in-plane dispersions and the bandwidth of spin excitations in the superconducting CaLa-112 closely resemble to those in 122 systems. While the total fluctuating moments ⟨ m 2 ⟩ ≈ 4.6 ± 0.2 μ B 2 /Fe are larger than 122 system, the dynamic correlation lengths are similar ( ξ ≈ 10 Å). These results suggest that superconductivity in iron arsenides may have a common magnetic origin under similar magnetic exchange couplings with a dual nature from local moments and itinerant electrons, despite their different magnetic patterns and lattice symmetries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High Performance Computing to Quantify the Evolution of Microscopic Concentration Gradients During Flash Processing

During the Flash process, the cross section of a plain-carbon or a low-alloy steel is austenitized through rapid heating and transformed on rapid cooling to a predominantly martensite + bainite structure with small amounts of retained austenite. Unlike conventional heat treating, homogeneity is intentionally avoided during Flash processing of steels. The Flash process assembly consists of a pair of rolls that transfer the steel sheets through the heating and cooling stage of the thermal cycle. The initial microstructure of the steel consists of ferrite (body-centered cubic iron) + carbide ((Fe,X)mCn) mixture. The heating rate through the peak temperature is a function of temperature and reaches a peak of about 300-400°C/s and the cooling rate has a maximum value of 3,000-4,000°C/s. The on-heating phase transformations include carbide dissolution, austenite (face-centered cubic iron) nucleation and growth, and diffusion of carbon and other substitutional elements in the steel. The on-cooling phase transformations include formation of martensite (body-centered tetragonal phase containing supersaturated solute) and bainite (ferrite plates with or without fine carbides). In this project, the focus is on Fe-C-Cr steels that are currently Flash processed for armor applications. The modeling effort proposed here will help optimize the Flash thermal cycle for these low alloy steels to achieve the target performance, which is an ongoing effort at SFP Works. A significant feature of Flash processed Fe-C-Cr steels is the presence of scatter in the through-thickness in the sheet. The variability in hardness results from a variability in the bainite + martensite microstructure that is sensitive to the local chemical concentration of C and Cr. Such a chemical inhomogeneity is intentionally obtained in the Flash process. Although such a microstructural gradient is presumably responsible for the exceptional properties of the Flash processed steel, it is very important to quantify the gradients as a function of Flash variabilities in processing parameters and the input microstructure. Understanding the mechanistic pathway that leads to microstructural gradients could be ground-breaking and instrumental for achieving better process control and optimized microstructural state to meet application-specific strength-ductility requirements. Since the final microstructure depends on setting up precise solute concentration gradients through a rapid heating process, and transforming these regions into various phases, it is important to understand how small changes in steel chemistry, input microstructure (carbide size and distribution), and process variables (Flash thermal cycle) will impact the solute concentration gradients.

97 MATHEMATICS AND COMPUTING↗

Orbital-Selective Instabilities and Spin Fluctuations at the Verge of Superconductivity in Interlayer-Expanded Iron Selenide

Understanding electron correlation-driven instabilities and their coupling to structural phases is essential for deciphering multiorbital pairing in unconventional superconductors. We investigate Li x (C 5 H 5 N) y Fe 2 Se 2 (x ∼ 0.6; y ∼ 0.7−0.9), a tetragonal β-FeSe intercalate with a superconducting transition temperature (T c = 39 K) closely tied to an expanded Fe-layer spacing (∼11.4 Å). High-resolution synchrotron Xray diffraction and core-level absorption spectroscopy reveal subtle lattice distortions on cooling without a symmetry-breaking transition. Instead, the material exhibits negative thermal expansion (NTE) in the two-dimensional Fe network below T S ∼ 70 K, and stiffening of local Se−Fe−Se bond dynamics near T c . The spatially incoherent rearrangement of FeSe 4 tetrahedra and the site-local fluctuations, signal reduced electron correlations compared to those of parent β-FeSe (T c = 8 K). Complementary X-ray emission spectroscopy, a fast local probe of Fe 3d valence states, detects persistent local Fe spin moments below T S , unlike quenching in related systems. These findings indicate that decoupling of Fe planes leads to an electronically driven lattice instability. The latter emerges as NTE induced from weak, orbital-selective localization of in-plane Fe 3d states rather than conventional transverse vibrations. Governed by Hund’s coupling, this selectivity permits coexistence of local spin fluctuations with itinerant d-electrons critical for enhancing T c . These results suggest that intercalation-driven d-orbital differentiation moderates electron correlations, providing a pathway to optimize the superconductivity in low-dimensional quantum materials.

36 MATERIALS SCIENCE↗

Strain-tunable microwave-resonance technique for quantum materials

By integrating a dielectric microwave resonator with a piezoelectric-based strain device, we develop an in situ strain-tunable microwave spectroscopy technique that enables contactless measurements of material properties under strain. To demonstrate the capability of this device, we measure the strain-dependent microwave surface impedance of the representative iron-based superconductor Ba⁢Fe 2 (As 1−𝑥 ⁢P 𝑥 ) 2 at the slightly overdoped composition. We successfully control and observe the suppression of superconductivity under both compressive and tensile anisotropic lattice distortions along the tetragonal [110] T direction, as manifested by changes in the quality factor and resonance frequency shifts of microwave resonance. Furthermore, strain-induced changes in microwave surface resistivity, an extension of conventional DC-limit transport elastoresistivity to the microwave regime, provide information on electronic anisotropy equivalent to that of DC elastoresistivity, while offering a contactless alternative. Furthermore, our strain-tunable cavity therefore serves as a powerful, contactless probe of fundamental material properties under strain and may also potentially facilitate the design of hybrid quantum systems with strain-engineered quantum degrees of freedom.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Microscopic origin of ultranodal superconducting states in spin- 1 2 systems

Several unconventional superconductors show indications of zero-energy excitations in the superconducting state consistent with the existence of a so-called Bogoliubov-Fermi surface (BFS). In particular, FeSe isovalently substituted with S seems to acquire a nonzero density of states at zero energy at low temperatures as the system goes into the tetragonal phase, consistent with a previously proposed phenomenological theory assuming an anisotropic spin singlet pairing gap coexisting with a nonunitary interband triplet component. Here we search for a microscopic model that can support the coexistence of singlet pairing with other orders, including interband nonunitary triplet pairing with magnetization, and discuss several candidates that indeed stabilize ground states with BFS. We show that with proper choice of the coupling strength of the various orders in our model, spontaneous breaking of C 4 rotational symmetry is realized at low temperatures. This feature resembles the findings of recent angle-resolved photoemission experiments in Fe(Se,S) in the tetragonal phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Short-Range Nematic Fluctuations in Sr 1-x Na x Fe 2 As 2 Superconductors

Interactions between nematic fluctuations, magnetic order and superconductivity are central to the physics of iron-based superconductors. Here we report on in-plane transverse acoustic phonons in hole-doped Sr 1-x Na x Fe 2 As 2 measured via inelastic x-ray scattering, and extract both the nematic susceptibility and the nematic correlation length. By a self-contained method of analysis, for the underdoped (x = 0.36) sample, which harbors a magnetically ordered tetragonal phase, we find it hosts a short nematic correlation length ξ ~ 10Å and a large nematic susceptibility Χ nem . The optimal-doped (x = 0.55) sample exhibits weaker phonon softening effects, indicative of both reduced xi and Χ nem . Overall, our results suggest short-range nematic fluctuations may favor superconductivity, placing emphasis on the nematic correlation length for understanding the iron-based superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Soft elastic constants from phonon spectroscopy in hole-doped Ba 1-x (K,Na) x Fe 2 As 2 and Sr 1-x Na x Fe 2 As 2

We report inelastic x-ray scattering measurements of the in-plane polarized transverse acoustic phonon mode propagating along q ∥ [ 100 ] in various hole-doped compounds belonging to the 122 family of iron-based superconductors. Additionally, the slope of the dispersion of this phonon mode is proportional to the square root of the shear modulus C 66 in the q → 0 limit and, hence, sensitive to the tetragonal to orthorhombic structural phase transition occurring in these compounds. In contrast to a recent report for Ba ( Fe 0.94 Co 0.06 ) 2 As 2 [Weber et al. , Phys. Rev. B 98 , 014516 (2018) ], we find qualitative agreement between values of C 66 deduced from our experiments and those derived from measurements of the Young modulus in Ba 1 - x ( K , Na ) x Fe 2 As 2 at optimal doping. These results provide an upper limit of about 50 Å for the nematic correlation length for the investigated optimally hole-doped compounds. Furthermore, we also studied compounds at lower doping levels exhibiting the orthorhombic magnetic phase, where C 66 is not accessible by volume probes, as well as the C 4 tetragonal magnetic phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Preferred Spin Excitations in the Bilayer Iron-Based Superconductor $CaK(Fe_{0.96}Ni_{0.04})_4As_4$ with Spin-Vortex Crystal Order

Spin-orbit coupling (SOC) is a key to understand the magnetically driven superconductivity in iron-based superconductors, where both local and itinerant electrons are present and the orbital angular momentum is not completely quenched. Here, we report a neutron scattering study on the bilayer compound CaK(Fe 0.96 Ni 0.04 ) 4 As 4 with superconductivity coexisting with a noncollinear spin-vortex crystal magnetic order that preserves the tetragonal symmetry of the Fe-Fe plane. In the superconducting state, two spin resonance modes with odd and even L symmetries due to the bilayer coupling are found similar to the undoped compound CaKFe 4 As 4 but at lower energies. Polarization analysis reveals that the odd mode is c-axis polarized, and the low-energy spin anisotropy can persist to the paramagnetic phase at high temperature, which closely resembles other systems with in-plane collinear and c-axis biaxial magnetic orders. Overall, these results provide the missing piece of the puzzle on the SOC effect in iron-pnictide superconductors, and also establish a common picture of c-axis preferred magnetic excitations below T c regardless of the details of magnetic pattern or lattice symmetry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Role of electromagnetic gauge-field fluctuations in the selection between chiral and nematic superconductivity

Motivated by the observation of nematic superconductivity in several systems, we revisit the problem of the leading pairing instability of two-component unconventional superconductors on the triangular lattice—such as (p x , p y )-wave and (d x 2 –y 2 , d xy )-wave superconductors. Such a system has two possible superconducting states: the chiral state (e.g., p + ip or d + id), which breaks time-reversal symmetry, and the nematic state (e.g., p + p or d + d), which breaks the threefold rotational symmetry of the lattice. Weak-coupling calculations generally favor the chiral over the nematic superconducting state, raising the question of what mechanism can stabilize the latter. Here, we show that the electromagnetic field fluctuations can play a crucial role in selecting between these two states. Specifically, we derive and analyze the effective free energy for the two-component superconducting order parameter after integrating out the gauge-field fluctuations, which is formally justified if the spatial order parameter fluctuations can be neglected. A nonanalytic cubic term arises, as in the case of a conventional s -wave superconductor. However, unlike the latter, the cubic term depends on the relative phase and on the relative amplitudes between the two order parameter components, in such a way that it generally favors the nematic state. This result is a direct consequence of the fact that the stiffness of the superconducting order parameter is not isotropic. Competition with the quartic term, which favors the chiral state, leads to a renormalized phase diagram in which the nematic state displaces the chiral state over a wide region in the parameter space. Here, we analyze the stability of the fluctuation-induced nematic phase, generalize our results to tetragonal lattices, and discuss their applicability to candidate nematic superconductors, including twisted bilayer graphene.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗