Spin excitation anisotropy as a probe of orbital ordering in the paramagnetic tetragonal phase of superconducting BaFe1.904Ni0.09As2

Eliminating Orbital Selectivity from the Metal-Insulator Transition by Strong Magnetic Fluctuations

The orbital-selective electronic behavior is one of the most remarkable manifestations of strong electronic correlations in multiorbital systems. A prominent example is the orbital-selective Mott transition (OSMT), which is characterized by the coexistence of localized electrons in some orbitals, and itinerant electrons in other orbitals. The state-of-the-art theoretical description of the OSMT in two- and three-dimensional systems is based on local nonperturbative approximations to electronic correlations provided by dynamical mean-field theory or slave spin method. In this work we go beyond this local picture and focus on the effect of spatial collective electronic fluctuations on the OSMT. To this aim, we consider a half-filled Hubbard-Kanamori model on a cubic lattice with two orbitals that have different bandwidths. We show that strong magnetic fluctuations that are inherent in this system prevent the OSMT and favor the Néel transition that occurs at the same critical temperature for both orbitals.

Multicommodity routing optimization for engineering networks

Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this formalism has empirical validity on engineering networks. We address this issue by considering different response functions—quantities determining the interaction between passengers—in the dynamics implementing the optimal transport formulation. Particularly, we couple passengers’ fluxes by taking their sum or the sum of their squares. The first choice naturally reflects edges occupancy in transportation networks, however the second guarantees convergence to an optimal configuration of flows. Both modeling choices are applied to the Paris metro. We measure the extent of traffic bottlenecks and infrastructure resilience to node removal, showing that the two settings are equivalent in the congested transport regime, but different in the branched one. In the latter, the two formulations differ on how fluxes are distributed, with one function favoring routes consolidation, thus potentially being prone to generate traffic overload. Additionally, we compare our method to Dijkstra’s algorithm to show its capacity to efficiently recover shortest-path-like graphs. Finally, we observe that optimal transport networks lie in the Pareto front drawn by the energy dissipated by passengers, and the cost to build the infrastructure.

Preferred Spin Excitations in the Bilayer Iron-Based Superconductor CaK(Fe_{0.96}Ni_{0.04})_{4}As_{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. 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.

Anisotropic effect of a magnetic field on the neutron spin resonance in FeSe

We use inelastic neutron scattering to study the effect of a magnetic field on the neutron spin resonance (E r = 3.6 meV) of superconducting FeSe (T c = 9 K). While a field aligned along the in-plane direction broadens and suppresses the resonance, a c-axis aligned field does so much more efficiently, consistent with the anisotropic field-induced suppression of the superfluid density from the heat capacity measurements. These results suggest that the resonance in FeSe is associated with the superconducting electrons arising from orbital selective quasiparticle excitations between the hole and electron Fermi surfaces.

Coexistence of Ferromagnetic and Stripe Antiferromagnetic Spin Fluctuations in SrCo_{2}As_{2}

We use inelastic neutron scattering to study energy and wave vector dependence of spin fluctuations in SrCo_{2}As_{2}, derived from SrFe_{2-x}Co_{x}As_{2} iron pnictide superconductors. Our data reveal the coexistence of antiferromagnetic (AF) and ferromagnetic (FM) spin fluctuations at wave vectors Q_{AF}=(1,0) and Q_{FM}=(0,0)/(2,0), respectively. By comparing neutron scattering results with those of dynamic mean field theory calculation and angle-resolved photoemission spectroscopy experiments, we conclude that both AF and FM spin fluctuations in SrCo_{2}As_{2} are closely associated with a flatband of the e_{g} orbitals near the Fermi level, different from the t_{2g} orbitals in superconducting SrFe_{2-x}Co_{x}As_{2}. Therefore, Co substitution in SrFe_{2-x}Co_{x}As_{2} induces a t_{2g} to e_{g} orbital switching, and is responsible for FM spin fluctuations detrimental to the singlet pairing superconductivity.

Preferred Magnetic Excitations in the Iron-Based Sr_{1-x}Na_{x}Fe_{2}As_{2} Superconductor

With spin-orbit coupling, both local-moment magnetism and itinerant electrons are expected to behave anisotropically in spin space, but such effects' influence on the formation of unconventional superconductivity has been hitherto unexplored. Here, in an iron-based superconductor, Sr_{1-x}Na_{x}Fe_{2}As_{2}, we report spectroscopic evidence that itinerant electrons "prefer" to be assisted by c-axis polarized magnetic excitations in their formation of superconducting Cooper pairs, against the polarization of the local-moment excitations. Our result naturally explains why the superconductivity competes strongly with the tetragonal magnetic phase in this material, and provides a fresh view on how to make a good superconductor out of a magnetic "Hund's metal."

Spin-Orbit Coupling and Magnetic Anisotropy in Iron-Based Superconductors

We determine theoretically the effect of spin-orbit coupling on the magnetic excitation spectrum of itinerant multiorbital systems, with specific application to iron-based superconductors. Our microscopic model includes a realistic ten-band kinetic Hamiltonian, atomic spin-orbit coupling, and multiorbital Hubbard interactions. Our results highlight the remarkable variability of the resulting magnetic anisotropy despite constant spin-orbit coupling. At the same time, the magnetic anisotropy exhibits robust universal behavior upon changes in the band structure corresponding to different materials of iron-based superconductors. A natural explanation of the observed universality emerges when considering optimal nesting as a resonance phenomenon. Our theory is also of relevance to other itinerant systems with spin-orbit coupling and nesting tendencies in the band structure.

Odd and Even Modes of Neutron Spin Resonance in the Bilayer Iron-Based Superconductor CaKFe_{4}As_{4}

We report an inelastic neutron scattering study on the spin resonance in the bilayer iron-based superconductor CaKFe_{4}As_{4}. In contrast to its quasi-two-dimensional electron structure, three strongly L-dependent modes of spin resonance are found below T_{c}=35  K. The mode energies are below and linearly scale with the total superconducting gaps summed on the nesting hole and electron pockets, essentially in agreement with the results in cuprate and heavy fermion superconductors. This observation supports the sign-reversed Cooper pairing mechanism under multiple pairing channels and resolves the long-standing puzzles concerning the broadening and dispersive spin resonance peak in iron pnictides. More importantly, the triple resonant modes can be classified into odd and even symmetries with respect to the distance of Fe-Fe planes within the Fe-As bilayer unit. Thus, our results closely resemble those in the bilayer cuprates with nondegenerate spin excitations, suggesting that these two high-T_{c} superconducting families share a common nature.

Neutron Spin Resonance in the 112-Type Iron-Based Superconductor

We use inelastic neutron scattering to study the low-energy spin excitations of the 112-type iron pnictide Ca_{0.82}La_{0.18}Fe_{0.96}Ni_{0.04}As_{2} with bulk superconductivity below T_{c}=22  K. A two-dimensional spin resonance mode is found around E=11  meV, where the resonance energy is almost temperature independent and linearly scales with T_{c} along with other iron-based superconductors. Polarized neutron analysis reveals the resonance is nearly isotropic in spin space without any L modulations. Because of the unique monoclinic structure with additional zigzag arsenic chains, the As 4p orbitals contribute to a three-dimensional hole pocket around the Γ point and an extra electron pocket at the X point. Our results suggest that the energy and momentum distribution of the spin resonance does not directly respond to the k_{z} dependence of the fermiology, and the spin resonance intrinsically is a spin-1 mode from singlet-triplet excitations of the Cooper pairs in the case of weak spin-orbital coupling.

Uniaxial strain control of spin-polarization in multicomponent nematic order of BaFe2As2

The iron-based high temperature superconductors exhibit a rich phase diagram reflecting a complex interplay between spin, lattice, and orbital degrees of freedom. The nematic state observed in these compounds epitomizes this complexity, by entangling a real-space anisotropy in the spin fluctuation spectrum with ferro-orbital order and an orthorhombic lattice distortion. A subtle and less-explored facet of the interplay between these degrees of freedom arises from the sizable spin-orbit coupling present in these systems, which translates anisotropies in real space into anisotropies in spin space. We present nuclear magnetic resonance studies, which reveal that the magnetic fluctuation spectrum in the paramagnetic phase of BaFe₂As₂ acquires an anisotropic response in spin-space upon application of a tetragonal symmetry-breaking strain field. Our results unveil an internal spin structure of the nematic order parameter, indicating that electronic nematic materials may offer a route to magneto-mechanical control.

A fundamental understanding of nematic order is one of the most important issues to explore in the high temperature superconductors. Here, the authors unveil an internal spin structure of the nematic order in BaFe₂As₂ by using nuclear magnetic resonance under precisely controlled tunable strain.

Anisotropic resonance modes emerging in an antiferromagnetic superconducting state

Two strong arguments in favor of magnetically driven unconventional superconductivity arise from the coexistence and closeness of superconducting and magnetically ordered phases on the one hand, and from the emergence of magnetic spin-resonance modes at the superconducting transition on the other hand. Combining these two arguments one may ask about the nature of superconducting spin-resonance modes occurring in an antiferromagnetic state. This problem can be studied in underdoped BaFe₂ As₂, for which the local coexistence of large moment antiferromagnetism and superconductivity is well established by local probes. However, polarized neutron scattering experiments are required to identify the nature of the resonance modes. In the normal state of Co underdoped BaFe₂ As₂ the antiferromagnetic order results in broad magnetic gaps opening in all three spin directions that are reminiscent of the magnetic response in the parent compound. In the superconducting state two distinct anisotropic resonance excitations emerge, but in contrast to numerous studies on optimum and over-doped BaFe₂ As₂ there is no isotropic resonance excitation. The two anisotropic resonance modes appearing within the antiferromagnetic phase are attributed to a band selective superconducting state, in which longitudinal magnetic excitations are gapped by antiferromagnetic order with sizable moment.

Magnetic excitations in the normal and nematic phases of iron pnictides

In this paper, we theoretically study the behaviors of the magnetic excitations (MEs) in the normal and nematic phases of iron pnictides. The normal state MEs exhibit commensurability to diamond and square-like structure transition with the increase of energy. This structure transition persists in the spin and orbital scenarios of nematic phases, although the MEs show anisotropic behaviors due to the C ₄ symmetry breaking induced by the nematic orders. The MEs exhibit distinct energy evolution behaviors between the spin and orbital scenarios of nematicity. For the spin-nematic scenario, the anisotropy of the MEs persists up to the high energy region. In contrast, for the orbital-nematic scenario, it reduces dramatically in the low energy region and is negligible in the high energy region. These distinct behaviors of the MEs are attributed to the different origins between the spin and orbital scenarios of nematic orders.

Robust upward dispersion of the neutron spin resonance in the heavy fermion superconductor Ce1-xYbxCoIn5

The neutron spin resonance is a collective magnetic excitation that appears in the unconventional copper oxide, iron pnictide and heavy fermion superconductors. Although the resonance is commonly associated with a spin-exciton due to the d(s±)-wave symmetry of the superconducting order parameter, it has also been proposed to be a magnon-like excitation appearing in the superconducting state. Here we use inelastic neutron scattering to demonstrate that the resonance in the heavy fermion superconductor Ce1-xYbxCoIn5 with x=0, 0.05 and 0.3 has a ring-like upward dispersion that is robust against Yb-doping. By comparing our experimental data with a random phase approximation calculation using the electronic structure and the momentum dependence of the -wave superconducting gap determined from scanning tunnelling microscopy (STM) for CeCoIn5, we conclude that the robust upward-dispersing resonance mode in Ce1-xYbxCoIn5 is inconsistent with the downward dispersion predicted within the spin-exciton scenario.

Orbital nematic order and interplay with magnetism in the two-orbital Hubbard model

Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) on FeSe and iron pnictide families of iron-based superconductors, we have studied the orbital nematic order and its interplay with antiferromagnetism within the two-orbital Hubbard model. We used random phase approximation (RPA) to calculate the dependence of the orbital and magnetic susceptibilities on the strength of interactions and electron density (doping). To account for strong electron correlations not captured by RPA, we further employed non-perturbative variational cluster approximation (VCA) capable of capturing symmetry broken magnetic and orbitally ordered phases. Both approaches show that the electron and hole doping affect the two orders differently. While hole doping tends to suppress both magnetism and orbital ordering, the electron doping suppresses magnetism faster. Crucially, we find a realistic parameter regime for moderate electron doping that stabilizes orbital nematicity in the absence of long-range antiferromagnetic order. This is reminiscent of the non-magnetic orbital nematic phase observed recently in FeSe and a number of iron pnictide materials and raises the possibility that at least in some cases, the observed electronic nematicity may be primarily due to orbital rather than magnetic fluctuations.

Neutron-scattering measurements of spin excitations in LaFeAsO and Ba(Fe(0.953)Co(0.047))(2)As(2): evidence for a sharp enhancement of spin fluctuations by nematic order

Inelastic neutron scattering is employed to investigate the impact of electronic nematic order on the magnetic spectra of LaFeAsO and Ba(Fe(0.953)Co(0.047))(2)As(2). These materials are ideal to study the paramagnetic-nematic state, since the nematic order, signaled by the tetragonal-to-orthorhombic transition at T(S), sets in well above the stripe antiferromagnetic ordering at T(N). We find that the temperature-dependent dynamic susceptibility displays an anomaly at T(S) followed by a sharp enhancement in the spin-spin correlation length, revealing a strong feedback effect of nematic order on the low-energy magnetic spectrum. Our findings can be consistently described by a model that attributes the structural or nematic transition to magnetic fluctuations, and unveils the key role played by nematic order in promoting the long-range stripe antiferromagnetic order in iron pnictides.