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DOE OSTI2022

Absence of precursor incommensurate charge order in electronic nematic Ba 0.35 Sr 0.65 Ni 2 As 2

Recent discoveries of charge order and electronic nematic order in the iron-based superconductors and cuprates have pointed towards the possibility of nematic and charge fluctuations playing a role in the enhancement of superconductivity. The Ba 1–x Sr x Ni 2 As 2 system, closely related in structure to the BaFe 2 As 2 system, has recently been shown to exhibit both types of ordering without the presence of any magnetic order. We report single-crystal x-ray diffraction experiments on Ba 0.35 Sr 0.65 Ni 2 As 2 , providing evidence that the previously reported incommensurate charge order with wave-vector (0, 0.28, 0) tet in the tetragonal state of BaNi 2 As 2 vanishes by 65% Sr substitution together with nematic order. Furthermore, our measurements suggest that the nematic and incommensurate charge orders are closely tied in the tetragonal state and show that the (0, 0.33, 0) tri charge ordering in the triclinic phase of BaNi 2 As 2 evolves to become (0, 0.5, 0) tri charge ordering at x = 0.65 before vanishing at x = 0.71.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Dual-stage structural response to quenching charge order in magnetite

The Verwey transition in magnetite (Fe 3 O 4 ) is the prototypical metal-insulator transition and has eluded a comprehensive explanation for decades. A major element of the challenge is the complex interplay between charge order and lattice distortions. Here we use ultrafast electron diffraction (UED) to disentangle the roles of charge order and lattice distortions by tracking the transient structural evolution after charge order is melted via ultrafast photoexcitation. A dual-stage response is observed in which X 3 , X 1 and Δ 5 type structural distortions occur on markedly different timescales of 0.7-3.2 ps and longer than 3.2 ps. We propose that these distinct timescales arise because X 3 -type distortions strongly couple to the trimeron charge order whereas the Δ 5 -distortions are more strongly associated with monoclinic to cubic distortions of the overall lattice. Our work aids in clarifying the charge-lattice interplay using UED method and illustrates the disentanglement of the complex phases in magnetite.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

High Resolution Polar Kerr Effect Studies of CsV 3 Sb 5 : Tests for Time-Reversal Symmetry Breaking below the Charge-Order Transition

We report high resolution polar Kerr effect measurements on CsV 3 Sb 5 single crystals in search for signatures of spontaneous time reversal symmetry breaking below the charge order transition at T * = 94 K. Utilizing two different versions of zero-area loop Sagnac interferometers operating at 1550 nm wavelength, each with the fundamental attribute that without a time reversal symmetry breaking sample at its path, the interferometer is perfectly reciprocal, we find no observable Kerr effect to within the noise floor limit of the apparatus at 30 nanoradians. Simultaneous coherent reflection ratio measurements confirm the sharpness of the charge order transition in the same optical volume as the Kerr measurements. At finite magnetic field we observe a sharp onset of a diamagnetic shift in the Kerr signal at T *, which persists down to the lowest temperature without change in trend. Since 1550 nm is an energy that was shown to capture all features of the optical properties of the material that interact with the charge order transition, we are led to conclude that it is highly unlikely that time reversal symmetry is broken in the charge ordered state in CsV 3 Sb 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

51 V NMR evidence for interlayer-modulated charge order and a first-order low-temperature transition in CsV 3 ⁢Sb 5

Charge order in the kagome superconductor CsV 3 ⁢Sb 5 exhibits a complex three-dimensional organization and intermediate-temperature anomalies whose bulk character has remained unsettled. We use orientation-dependent 51 V NMR as a site-selective probe to determine the stacking of the charge density wave (CDW) state and its thermal evolution. Below 𝑇 CDW ≈ 94K, the field-linear splitting of the 51 V central transition together with the anisotropy of the Knight shift tensor identify an interlayer-modulated 3⁢𝑞 CDW whose local environments are consistent with a four-layer 2 × 2 × 4 stacking with mixed trihexagonal/Star-of-David distortions, in agreement with synchrotron x-ray determinations. For comparison, RbV 3 ⁢Sb 5 serves as a reference exhibiting a uniform trihexagonal 2 × 2 × 2 stacking, allowing us to isolate features unique to the 2 × 2 × 4 state in CsV 3 ⁢Sb 5 . With 𝐻 0 ∥ 𝑐, the 51 V quadrupolar satellites through the intermediate temperature scale near 𝑇 CO ≈ 65K reorganize into two well-resolved electric-field-gradient manifolds that coexist over a finite interval; their relative spectral weights interchange on cooling while the total integrated satellite intensity remains conserved and 𝜈 𝑄 within each manifold is nearly temperature independent. The coexistence without critical broadening, together with conserved intensity, provides bulk evidence consistent with a first-order charge-order transition near 𝑇 CO . Our measurements do not resolve whether this lower-temperature transition corresponds to a distinct in-plane order or a reorganization of the 3⁢𝑞 state; rather, they delimit this window and provide bulk, site-resolved constraints that connect prior reported anomalies to a thermodynamic first-order transition.

Wang, Xiaoling [California State Univ., East Bay, ↗

DOE OSTI2020

Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate

Copper oxide high-T C superconductors possess a number of exotic orders that coexist with or are proximal to superconductivity. Quantum fluctuations associated with these orders may account for the unusual characteristics of the normal state, and possibly affect the superconductivity. Yet, spectroscopic evidence for such quantum fluctuations remains elusive. Here in this paper, we use resonant inelastic X-ray scattering to reveal spectroscopic evidence of fluctuations associated with a charge order in nearly optimally doped Bi 2 Sr 2 CaCu 2 O 8+δ . In the superconducting state, while the quasielastic charge order signal decreases with temperature, the interplay between charge order fluctuations and bond-stretching phonons in the form of a Fano-like interference increases, an observation that is incompatible with expectations for competing orders. Invoking general principles, we argue that this behaviour reflects the properties of a dissipative system near an order–disorder quantum critical point, where the dissipation varies with the opening of the pseudogap and superconducting gap at low temperatures, leading to the proliferation of quantum critical fluctuations, which melt charge order.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Discovery of charge order above room-temperature in the prototypical kagome superconductor La(Ru1−xFex)3Si2

Abstract The kagome lattice is an intriguing and rich platform for discovering, tuning and understanding the diverse phases of quantum matter, crucial for advancing modern and future electronics. Despite considerable efforts, accessing correlated phases at room temperature has been challenging. Using single-crystal X-ray diffraction, we discovered charge order above room temperature in La(Ru 1−x Fe x ) 3 Si 2 (x= 0, 0.01, 0.05), where charge order related to out-of-plane Ru atom displacements appears belowT CO,I ≃ 400 K. The secondary charge ordered phase emerges belowT CO,II ≃ 80–170 K. Furthermore, first principles calculations reveal both the kagome flat band and the van Hove point near the Fermi energy in LaRu 3 Si 2 , driven by Ru-dz 2 orbitals. Our results identify LaRu 3 Si 2 as the kagome superconductor with the highest known charge ordering temperature, offering a promising avenue for researching room temperature quantum phases and developing related technologies.

Physics↗

DOE OSTI2023

Tunable unconventional kagome superconductivity in charge ordered RbV 3 Sb 5 and KV 3 Sb 5

Unconventional superconductors often feature competing orders, small super fluid density, and nodal electronic pairing. While unusual superconductivity has been proposed in the kagome metals AV 3 Sb 5 , key spectroscopic evidence has remained elusive. Here we utilize pressure-tuned and ultra-low temperature muon spin spectroscopy to uncover the unconventional nature of super conductivity in RbV 3 Sb 5 and KV 3 Sb 5 . At ambient pressure, we observed time reversal symmetry breaking charge order below ${T}_{1}^{*}$ ≃ 110 K in RbV 3 Sb 5 with an additional transition at ${T}_{2}^{*}$ ≃ 50 K. Remarkably, the superconducting state displays a nodal energy gap and a reduced superfluid density, which can be attributed to the competition with the charge order. Upon applying pressure, the charge-order transitions are suppressed, the superfluid density increases, and the superconducting state progressively evolves from nodal to nodeless. Once optimal superconductivity is achieved, we find a superconducting pairing state that is not only fully gapped, but also spontaneously breaks time-reversal symmetry. Our results point to unprecedented tunable nodal kagome super conductivity competing with time-reversal symmetry-breaking charge order and offer unique insights into the nature of the pairing state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Pressure-induced charge orders and their postulated coupling to magnetism in hexagonal multiferroic LuFe 2 O 4

Hexagonal LuFe 2 O 4 is a promising charge order (CO) driven multiferroic material with high charge and spin-ordering temperatures. The coexisting charge and spin orders on Fe 3+ /Fe 2+ sites result in magnetoelectric behaviors, but the coupling mechanism between the charge and spin orders remains elusive. Here, by tuning external pressure, we reveal three charge-ordered phases with suggested correlation to magnetic orders in LuFe 2 O 4 : (i) a centrosymmetric incommensurate three-dimensional CO with ferrimagnetism, (ii) a non-centrosymmetric incommensurate quasi-two-dimensional CO with ferrimagnetism, and (iii) a centrosymmetric commensurate CO with antiferromagnetism. Experimental in situ single-crystal X-ray diffraction and X-ray magnetic circular dichroism measurements combined with density functional theory calculations suggest that the charge density redistribution caused by pressure-induced compression in the frustrated double-layer [Fe 2 O 4 ] cluster is responsible for the correlated spin-charge phase transitions. The pressure-enhanced effective Coulomb interactions among Fe-Fe bonds drive the frustrated (1/3, 1/3) CO to a less frustrated (1/4, 1/4) CO, which induces the ferrimagnetic to antiferromagnetic transition. Our results not only elucidate the coupling mechanism among charge, spin, and lattice degrees of freedom in LuFe 2 O 4 , but also provide a new way to tune the spin-charge orders in a highly controlled manner.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Charge order induced Dirac pockets in the nonsymmorphic crystal TaTe 4

The interplay between charge order (CO) and nontrivial band topology has spurred tremendous interest in understanding topological excitations beyond the single-particle description. In a quasi-one-dimensional nonsymmorphic crystal TaTe 4 , the (2a×2b×3c) charge ordered ground state drives the system into a space group where the symmetry indicator features the emergence of Dirac fermions and unconventional double Dirac fermions. In this study, using angle-resolved photoemission spectroscopy and first-principles calculations, we provide evidence of the CO induced Dirac fermion-related bands near the Fermi level. Furthermore, the band folding at the Fermi level is compatible with the new periodicity dictated by the CO, indicating that the electrons near the Fermi level follow the crystalline symmetries needed to host double Dirac fermions in this system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Charge order textures induced by non-linear couplings in a half-doped manganite

Abstract The self-organization of strongly interacting electrons into superlattice structures underlies the properties of many quantum materials. How these electrons arrange within the superlattice dictates what symmetries are broken and what ground states are stabilized. Here we show that cryogenic scanning transmission electron microscopy (cryo-STEM) enables direct mapping of local symmetries and order at the intra-unit-cell level in the model charge-ordered system Nd 1/2 Sr 1/2 MnO 3 . In addition to imaging the prototypical site-centered charge order, we discover the nanoscale coexistence of an exotic intermediate state which mixes site and bond order and breaks inversion symmetry. We further show that nonlinear coupling of distinct lattice modes controls the selection between competing ground states. The results demonstrate the importance of lattice coupling for understanding and manipulating the character of electronic self-organization and that cryo-STEM can reveal local order in strongly correlated systems at the atomic scale.

42 ENGINEERING↗

DOE OSTI2020

Nonlocal Coulomb interaction and spin-freezing crossover as a route to valence-skipping charge order

Abstract Multiorbital systems away from global half-filling host intriguing physical properties promoted by Hund’s coupling. Despite increasing awareness of this regime dubbed Hund’s metal, effect of nonlocal interaction is still elusive. Here we study a three-orbital model with 1/3 filling (two electrons per site) including the intersite Coulomb interaction ( V ). Using the G W plus extended dynamical mean-field theory, the valence-skipping charge order transition is shown to be driven by V . Most interestingly, the instability to this transition is significantly enhanced in the spin-freezing crossover regime, thereby lowering the critical V to the formation of charge order. This behavior is found to be closely related to the population profile of the atomic multiplet states in the spin-freezing regime. In this regime, maximum spin states are dominant in each total charge subspace with substantial amount of one- and three-electron occupations, which leads to almost equal population of one- and the maximum spin three-electron state. Our finding unveils another feature of the Hund’s metal and has potential implications for the broad range of multiorbital systems as well as the recently discovered charge order in iron pnictides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Electronic structures, charge transfer, and charge order in twisted transition metal dichalcogenide bilayers

Moiré superlattices of transition metal dichalcogenide (TMD) bilayers have been shown to host correlated electronic states, which arise from the interplay of long wavelength moiré potential and long-range Coulomb interaction. Here, we theoretically investigate structural relaxation and single-particle electronic structure of twisted TMD homobilayer. From the large-scale density functional theory calculation and continuum model with layer degrees of freedom, we find that the out-of-plane gating field creates a tunable charge transfer gap at the Dirac point between the first and second moiré valence bands. We further study the charge orders at the fractional band fillings. In the flat band limit, we find from Monte Carlo simulations a series of charge-ordered insulating states at various fillings $n = \frac{1}{4}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, 1$. Further, we predict that gating field induces a phase transition between different electron crystals at fixed filling $n = \frac{1}{2}$ or $\frac{2}{3}$. At half-filling $\textit{n} = 1$, the ground state is a Mott insulator with electronically driven ferroelectricity. This work demonstrates that TMD homobilayer provides a powerful platform for the investigation of tunable charge transfer insulator and charge orders.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Isotropic parallel antiferromagnetism in the magnetic field induced charge-ordered state of $\mathrm{Sm Ru_4 P_{12}}$ caused by $p - f$ hybridization

Nature of the field-induced charge-ordered phase (phase II) of SmRu 4 P 12 has been investigated by resonant x-ray diffraction (RXD) and polarized neutron diffraction (PND), focusing on the relationship between the atomic displacements and the antiferromagnetic (AFM) moments of Sm. From the analysis of the interference between the nonresonant Thomson scattering and the resonant magnetic scattering, combined with the spectral function obtained from x-ray magnetic circular dichroism, it is shown that the AFM moment of Sm prefers to be parallel to the field (m AF ∥ H), giving rise to large and small moment sites around which the P 12 and Ru cage contract and expand, respectively. This is associated with the formation of the staggered ordering of the Γ 7 -like and Γ 8 -like crystal-field states, providing a strong piece of evidence for the charge order. PND was also performed to obtain complementary and unambiguous conclusion. In addition, isotropic and continuous nature of phase II is demonstrated by the field-direction invariance of the interference spectrum in RXD. Finally, crucial role of the p-f hybridization is shown by resonant soft x-ray diffraction at the P K edge (1s↔3p), where we detected a resonance due to the spin polarized 3p orbitals reflecting the AFM order of Sm.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Coexistence and Coupling of Multiple Charge Orderings and Spin States in Hexagonal Ferrite

The coupling between charge and spin orderings in strongly correlated systems plays a crucial role in fundamental physics and device applications. As a candidate of multiferroic materials, LuFe 2 O 4 with a nominal Fe 2.5+ valence state has the potential for strong charge–spin interactions; however, these interactions have not been fully understood until now. Here, combining complementary characterization methods with theoretical calculations, two types of charge orderings with distinct magnetic properties are revealed. The ground states of LuFe 2 O 4 are decided by the parallel/antiparallel coupling of both charge and spin orderings in the adjacent FeO double layers. Whereas the ferroelectric charge ordering remains ferrimagnetic below 230 K, the antiferroelectric ordering undergoes antiferromagnetic–ferrimagnetic–paramagnetic transitions from 2 K to room temperature. This study demonstrates the unique aspects of strong spin-charge coupling within LuFe 2 O 4 . Our results shed light on the coexistence and competing nature of orderings in quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Observation of novel charge ordering and spin reorientation in perovskite oxide PbFeO 3

Pb M O 3 ( M = 3 d transition metals) family shows systematic variations in charge distribution and intriguing physical properties due to its delicate energy balance between Pb 6 s and transition metal 3 d orbitals. However, the detailed structure and physical properties of PbFeO 3 remain unclear. Herein, we reveal that PbFeO 3 crystallizes into an unusual 2 a p × 6 a p × 2 a p orthorhombic perovskite super unit cell with space group Cmcm . The distinctive crystal construction and valence distribution of Pb 2+ 0.5 Pb 4+ 0.5 FeO 3 lead to a long range charge ordering of the -A-B-B- type of the layers with two different oxidation states of Pb (Pb 2+ and Pb 4+ ) in them. A weak ferromagnetic transition with canted antiferromagnetic spins along the a -axis is found to occur at 600 K. In addition, decreasing the temperature causes a spin reorientation transition towards a collinear antiferromagnetic structure with spin moments along the b -axis near 418 K. Our theoretical investigations reveal that the peculiar charge ordering of Pb generates two Fe 3+ magnetic sublattices with competing anisotropic energies, giving rise to the spin reorientation at such a high critical temperature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Probing the effect of magnetic field on charge order in the quasi-two-dimensional Mott insulator κ - (ET) 2 Hg(SCN) 2 Cl

Molecular-based quasi-two-dimensional charge-ordered Mott insulators can possess both spin S = 1/2 and an electric dipole degree of freedom residing on each (BEDT - TTF) 2 lattice site. There exists a theoretical proposal for a magnetoelectric effect in such a material, which can manifest itself as a sensitivity of charge distribution on (BEDT - TTF) 2 dimers to the magnetic field. Here in this work, we used Raman scattering spectroscopy in the magnetic field up to 31 T applied perpendicular to the two-dimensional triangular lattice planes to probe a magnetoelectric effect in $\kappa$ - (ET) 2 H g (SCN) 2 Cl. This is a model compound, which shows charge order and antiferromagnetic correlations at temperatures below 30 K. We discuss possible reasons for the absence of an observable magnetoelectric effect in the probed temperature and magnetic field ranges.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Charge order driven multiferroic behavior in Sr 4 Fe 6 O 12 : An ab-initio study

Here, in this paper, we report the structural, electronic, and ferroelectric properties of the layered mixed-valent transition-metal compound Sr 4 ⁢ Fe 6 ⁢O 12 (SFO). We demonstrate how SFO undergoes a phase transition from a high-temperature (𝑇) centrosymmetric tetragonal phase (𝑃⁢4 2 /𝑚⁢𝑛⁢𝑚) to a low-𝑇 polar orthorhombic phase (𝑃⁢𝑚⁢𝑛⁢2 1 ). The transition is primarily driven by charge ordering at tetrahedral Fe-layer creating Fe 3+ and Fe 2+ cations between two edge-sharing tetrahedra. This charge ordering induces electronic polarization, which is remarkably larger (3.5 times) in magnitude than ionic polarization and oppositely directed, giving a net polarization of 0.05 C/m 2 which is comparable to the state-of-the-art rare-earth nickelets and manganite perovskites. The direction of structural distortion, governed by the polar mode irrep $Γ^−_5$, depends sensitively on the type of magnetic ordering in the Fe-octahedral layer. Consequently, both the ionic and electronic polarization directions are influenced by magnetic ordering, suggesting the potential for multiferroic behavior with strong magnetoelectric coupling in this material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Probing Charge Ordering in Fractional Mixed-Valence Charge Density Wave Systems with Oriented HERFD-XANES Spectroscopy

In this paper, we present oriented Pt L III edge high energy resolution fluorescence detected X-ray absorption near edge structure (HERFD-XANES) measurements on a series of structurally tunable quasi-one-dimensional mixed-valence platinum-halide linear chain materials, [Pt(en) 2 ][Pt(en) 2 X 2 ](ClO 4 ) 4 with X = Cl, Br, I, together with ab initio modeling of the spectral components and electronic structure. The materials exhibit a commensurate charge density wave (CDW) with an amplitude controlled by the bridging halide ion, giving rise to fractional mixed valence states. Ab initio FEFF9 modeling of the spectra and the associated angular momentum projected density of states (lDOS) are used to interpret the results, revealing systematic changes in the platinum orbital occupancy through the series of materials that reflect the fractional mixed valence states of the CDW. A significant contribution to a post-edge feature in the oriented spectra is identified as resulting from quantum interference between the final states of the X-ray absorption transition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗