Spin waves and magnetic exchange interactions in insulating Rb0.89Fe1.58Se2

Spin fluctuations in the 112-type iron-based superconductor Ca0.82La0.18Fe0.96Ni0.04As2

We report time-of-flight inelastic neutron scattering (INS) investigations on the spin fluctuation spectrum in the 112-type iron-based superconductor (FeSC) Ca_0.82La_0.18Fe_0.96Ni_0.04As₂(CaLa-112). In comparison to the 122-type FeSCs with a centrosymmetric tetragonal lattice structure (space groupI4/mmm) at room temperature and an in-plane stripe-type antiferromagnetic (AF) order at low temperature, the 112 system has a noncentrosymmetric structure (space groupP21) with additional zigzag arsenic chains between Ca/La layers and a magnetic ground state with similar wavevectorQAFbut 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⟨m2⟩≈4.6±0.2μB2/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.

Detecting Crystallographic Lattice Chirality using Resonant Inelastic X-ray Scattering

The control and detection of crystallographic chirality is an important and challenging scientific problem. Chirality has wide ranging implications from medical physics to cosmology including an intimate but subtle connection in magnetic systems, for example Mn1-xFexSi. X-ray diffraction techniques with resonant or polarized variations of the experimental setup are currently utilized to characterize lattice chirality. We demonstrate using theoretical calculations the feasibility of indirect K -edge bimagnon resonant inelastic X-ray scattering (RIXS) spectrum as a viable experimental technique to distinguish crystallographic handedness. We apply spin wave theory to the recently discovered √5 × √5 vacancy ordered chalcogenide Rb0.89Fe1.58Se2 for realistic X-ray experimental set up parameters (incoming energy, polarization, Bragg angle, and experimental resolution) to show that the computed RIXS spectrum is sensitive to the underlying handedness (right or left) of the lattice. A Flack parameter definition that incorporates the right- and left- chiral lattice RIXS response is introduced. It is shown that the RIXS response of the multiband magnon system RbFeSe arises both from inter- and intra- band scattering processes. The extinction or survival of these RIXS peaks are sensitive to the underlying chiral lattice orientation. This in turn allows for the identification of the two chiral lattice orientations.

Novel Magnetic Block States in Low-Dimensional Iron-Based Superconductors

Inelastic neutron scattering recently confirmed the theoretical prediction of a ↑↑↓↓-magnetic state along the legs of quasi-one-dimensional iron-based ladders in the orbital-selective Mott phase (OSMP). We show here that electron doping of the OSMP induces a whole class of novel block states with a variety of periodicities beyond the previously reported π/2 pattern. We discuss the magnetic phase diagram of the OSMP regime that could be tested by neutrons once appropriate quasi-1D quantum materials with the appropriate dopings are identified.

Spin dynamics of the block orbital-selective Mott phase

Iron-based superconductors display a variety of magnetic phases originating in the competition between electronic, orbital, and spin degrees of freedom. Previous theoretical investigations of the multi-orbital Hubbard model in one-dimension revealed the existence of an orbital-selective Mott phase (OSMP) with block spin order. Recent inelastic neutron scattering (INS) experiments on the BaFe₂Se₃ ladder compound confirmed the relevance of the block-OSMP. Moreover, the powder INS spectrum revealed an unexpected structure, containing both low-energy acoustic and high-energy optical modes. Here we present the theoretical prediction for the dynamical spin structure factor within a block-OSMP regime using the density-matrix renormalization-group method. In agreement with experiments, we find two dominant features: low-energy dispersive and high-energy dispersionless modes. We argue that the former represents the spin-wave-like dynamics of the block ferromagnetic islands, while the latter is attributed to a novel type of local on-site spin excitations controlled by the Hund coupling.

Exploring the orbital-selective Mott phase (OSMP) addresses the central issue of electron correlations in the iron-based superconductors. Here the authors theoretically study the dynamical spin structure factor in the block-OSMP regime and unveil momentum dependent characteristics for different spin excitation modes.

Two-dimensional Dirac nodal loop magnons in collinear antiferromagnets

We study the nontrivial linear magnon band crossings in the collinear antiferromagnets on the two-dimensional (2D) CaVO lattice, also realized in some iron-based superconductors such as AFe_1.6+x Se₂ (A  =  K, Rb, Cs). It is shown that the combination of space-inversion and time-reversal symmetry ([Formula: see text] symmetry) leads to doubly-degenerate eight magnon branches, which cross each other linearly along a one-dimensional loop in the 2D Brillouin zone. We show that the Dirac nodal loops (DNLs) are not present in the collinear ferromagnet on this lattice. Thus, the current 2D antiferromagnetic DNLs are symmetry-protected and they provide a novel platform to search for their analogs in 2D electronic antiferromagnetic systems.

Understanding Doping, Vacancy, Lattice Stability, and Superconductivity in K x Fe2-y Se2

Metal-intercalated iron selenides are a class of superconductors that have received much attention but are less understood in comparison with their FeAs-based counterparts. Here, the controversial issues such as Fe vacancy, the real phase responsible for superconductivity, and lattice stability have been addressed based on first-principles calculations. New insights into the distinct features in terms of carrier doping have been revealed.

Pressure-induced electronic phase separation of magnetism and superconductivity in CrAs

The recent discovery of pressure (p) induced superconductivity in the binary helimagnet CrAs has raised questions on how superconductivity emerges from the magnetic state and on the mechanism of the superconducting pairing. In the present work the suppression of magnetism and the occurrence of superconductivity in CrAs were studied by means of muon spin rotation. The magnetism remains bulk up to p  3.5 kbar while its volume fraction gradually decreases with increasing pressure until it vanishes at p  7 kbar. At 3.5 kbar superconductivity abruptly appears with its maximum T_c  1.2 K which decreases upon increasing the pressure. In the intermediate pressure region (3.5  p  7 kbar) the superconducting and the magnetic volume fractions are spatially phase separated and compete for phase volume. Our results indicate that the less conductive magnetic phase provides additional carriers (doping) to the superconducting parts of the CrAs sample thus leading to an increase of the transition temperature (T_c) and of the superfluid density (ρ_s). A scaling of ρ_s with as well as the phase separation between magnetism and superconductivity point to a conventional mechanism of the Cooper-pairing in CrAs.

Orbital characters and electronic correlations in KCo2Se2

We report a comprehensive study of the tridimensional nature and orbital characters of the low-energy electronic structure in KCo2Se2, using polarization- and photon energy-dependent angle-resolved photoemission spectroscopy. We observed one electron-like Fermi surface (FS) at the Brillouin zone (BZ) center, four electron-like FSs centered at the BZ corner, and one hole-like FS at the BZ boundary. The FSs show weak dispersion along the kz direction, indicating the near-two-dimensional nature of FSs in KCo2Se2. In combination with the local-density approximation calculations, we determined the orbital characters of the low-energy electronic bands, which are mainly derived from the Co 3d orbital, mixed with part of the Se 4p states. The [Formula: see text] orbital gives a significant contribution to the band crossing the Fermi level. A band renormalization of about 1.6 is needed to capture the essential dispersive features, which suggests that electronic correlations are much weaker than that in KyFe2-xSe2.

Block Magnetic Excitations in the Orbitally Selective Mott Insulator BaFe_{2}Se_{3}

Iron pnictides and selenides display a variety of unusual magnetic phases originating from the interplay between electronic, orbital, and lattice degrees of freedom. Using powder inelastic neutron scattering on the two-leg ladder BaFe_{2}Se_{3}, we fully characterize the static and dynamic spin correlations associated with the Fe_{4} block state, an exotic magnetic ground state observed in this low-dimensional magnet and in Rb_{0.89}Fe_{1.58}Se_{2}. All the magnetic excitations of the Fe_{4} block state predicted by an effective Heisenberg model with localized spins are observed below 300 meV and quantitatively reproduced. However, the data only account for 16(3)μ_{B}^{2} per Fe^{2+}, approximatively 2/3 of the total spectral weight expected for localized S=2 moments. Our results highlight how orbital degrees of freedom in iron-based magnets can conspire to stabilize an exotic magnetic state.

Structure, magnetic order and excitations in the 245 family of Fe-based superconductors

Elastic neutron scattering simultaneously probes both the crystal structure and magnetic order in a material. Inelastic neutron scattering measures phonons and magnetic excitations. Here, we review the average composition, crystal structure and magnetic order in the 245 family of Fe-based superconductors and in related insulating compounds from neutron diffraction works. A three-dimensional phase-diagram summarizes various structural, magnetic and electronic properties as a function of the sample composition. A high pressure phase diagram for the superconductor is also provided. Magnetic excitations and the theoretic Heisenberg Hamiltonian are provided for the superconductor. Issues for future works are discussed.

Superconductivity at the border of electron localization and itinerancy

The superconducting state of iron pnictides and chalcogenides exists at the border of anti-ferromagnetic order. Consequently, these materials could provide clues about the relationship between magnetism and unconventional superconductivity. One explanation, motivated by the so-called bad metal behaviour of these materials proposes that magnetism and superconductivity develop out of quasi-localized magnetic moments that are generated by strong electron-electron correlations. Another suggests that these phenomena are the result of weakly interacting electron states that lie on nested Fermi surfaces. Here we address the issue by comparing the newly discovered alkaline iron selenide superconductors, which exhibit no Fermi-surface nesting, to their iron pnictide counterparts. We show that the strong-coupling approach leads to similar pairing amplitudes in these materials, despite their different Fermi surfaces. We also find that the pairing amplitudes are largest at the boundary between electronic localization and itinerancy, suggesting that new superconductors might be found in materials with similar characteristics.

Spin fluctuations and pairing symmetry in AxFe₂-ySe₂: dual effect of the itinerant and the localized nature of electrons

We investigate the spin fluctuations and the pairing symmetry in AxFe2-ySe2 by the fluctuation exchange approximation. Besides the on-site interactions, the next-nearest-neighbor antiferromagnetic coupling J2 is also included. We find that both the itinerant and the localized natures of electrons are important to describe recent experimental results on the spin fluctuations and the pairing symmetry. In particular, a small J2 coupling can change the pairing gap from the d-wave symmetry to the extended s-wave symmetry. We have also studied the real-space structures of the gap functions for different orbits in order to gain more insight into the nature of the pairing mechanism.

The hybrid lattice of K(x)Fe(2-y)Se2: where superconductivity and magnetism coexist

Much remains unknown of the microscopic origin of superconductivity in atomically disordered systems of amorphous alloys or in crystals riddled with defects. A manifestation of this conundrum is envisaged in the highly defective superconductor of K_xFe_2−ySe₂. How can superconductivity survive under such crude conditions that call for strong electron localization? Here, we show that the Fe sublattice is locally distorted and accommodates two kinds of Fe valence environments giving rise to a bimodal bond-distribution, with short and long Fe bonds. The bimodal bonds are present even as the system becomes superconducting in the presence of antiferromagnetism, with the weight continuously shifting from the short to the long with increasing K content. Such a hybrid state is most likely found in cuprates as well while our results point to the importance of the local atomic symmetry by which exchange interactions between local moments materialize.

Orbital-selective Mott phase in multiorbital models for alkaline iron selenides K1-xFe2-ySe2

We study a multiorbital model for the alkaline iron selenides K(1-x)Fe(2-y)Se(2) using a slave-spin method. With or without ordered vacancies, we identify a metal-to-Mott-insulator transition at the commensurate filling of six 3d electrons per iron ion. For Hund's couplings beyond a threshold value, this occurs via an intermediate orbital-selective Mott phase, in which the 3d xy orbital is Mott localized while the other 3d orbitals remain itinerant. This phase is still stabilized over a range of carrier dopings. Our results lead to an overall phase diagram for the alkaline iron selenides, which provides a unified framework to understand the interplay between the strength of the vacancy order and carrier doping. In this phase diagram, the orbital-selective Mott phase provides a natural link between the superconducting K(1-x)Fe(2-y)Se(2) and its Mott-insulating parent compound.

Quantum Monte Carlo study of a dominant s-wave pairing symmetry in iron-based superconductors

We perform a systematic quantum Monte Carlo study of the pairing correlation in the S(4) symmetric microscopic model for iron-based superconductors. It is found that the pairing with an extensive s-wave symmetry robustly dominates over other pairings at low temperature in a reasonable parameter region regardless of the change of Fermi surface topologies. The pairing susceptibility, the effective pairing interaction, and the (π, 0) antiferromagnetic correlation strongly increase as the on-site Coulomb interaction increases, indicating the importance of the effect of electron-electron correlation. Our nonbiased numerical results provide a unified understanding of the superconducting mechanism in iron pnictides and iron chalcogenides and demonstrate that the superconductivity is driven by strong electron-electron correlation effects.

Dynamic approach to finite-temperature magnetic phase transitions in the extended J1-J2 model with vacancy order

The recently discovered iron-based superconductors A(y)Fe(2-x)Se(2) (A=K, Rb, Cs, Tl) show a long-range antiferromagnetic order with an unexpectedly high transition temperature T(N)~550 K and a unique √5×√5 vacancy order. Taking the extended J(1)-J(2) model as a minimal model, we investigate the finite-temperature magnetic phase transitions in a square lattice with a √5×√5 vacancy superstructure by using large-scale Monte Carlo simulations. By the parallel tempering technique, the block spin checkerboard and stripe antiferromagnetic states are detected to be the ground states for three representative sets of model parameters. The short-time dynamic approach is applied to accurately determine the critical temperature as well as the static and dynamic exponents. Our results indicate that the dramatic enhancement of the critical temperature as observed in experiments should be mainly due to a combination of the vacancy order and the block lattice contraction.

Spin wave excitations in AFe1.5Se2 (A = K, Tl): analytical study

By generalizing the equation of motion method, we can analytically solve the spin wave excitations for the intercalated ternary iron-selenide AFe(1.5)Se(2) (A = K, Tl) in a complex 4 × 2 collinear antiferromagnetic order. It is found that there are one acoustic branch (gapless Goldstone mode) and two gapful optical branches of spin wave excitations with each in double degeneracy. By examining the non-imaginary excitation frequency condition, we can determine the corresponding phase boundary. The exchange couplings between Fe moments in AFe(1.5)Se(2) are derived based on the first-principles total energy calculations. The Fe spin is found to be S = 3/2 through computing the antiferromagnetic quantum fluctuation. It is also found that a very small spin-orientation anisotropy can remarkably suppress the antiferromagnetic quantum fluctuation. The spin dynamical structure factors are calculated and discussed in association with neutron inelastic scattering experiment.

Three dimensionality and orbital characters of the Fermi surface in (Tl,Rb)(y)Fe(2-x)Se2

We report a comprehensive angle-resolved photoemission spectroscopy study of the tridimensional electronic bands in the recently discovered Fe selenide superconductor ((Tl,Rb)(y)Fe(2-x)Se2 (T(c)=32  K). We determined the orbital characters and the k(z) dependence of the low energy electronic structure by tuning the polarization and the energy of the incident photons. We observed a small 3D electron Fermi surface pocket near the Brillouin zone center and a 2D like electron Fermi surface pocket near the zone boundary. The photon energy dependence, the polarization analysis and the local-density approximation calculations suggest a significant contribution from the Se 4p(z) and Fe 3d(xy) orbitals to the small electron pocket. We argue that the emergence of Se 4p(z) states might be the cause of the different magnetic properties between Fe chalcogenides and Fe pnictides.

Local antiferromagnetic exchange and collaborative Fermi surface as key ingredients of high temperature superconductors

Cuprates, ferropnictides and ferrochalcogenides are three classes of unconventional high temperature superconductors, who share similar phase diagrams in which superconductivity develops after a magnetic order is suppressed, suggesting a strong interplay between superconductivity and magnetism, although the exact picture of this interplay remains elusive. Here we show that there is a direct bridge connecting antiferromagnetic exchange interactions determined in the parent compounds of these materials to the superconducting gap functions observed in the corresponding superconducting materials: in all high temperature superconductors, the Fermi surface topology matches the form factor of the pairing symmetry favored by local magnetic exchange interactions. We suggest that this match offers a principle guide to search for new high temperature superconductors.

The superconducting transition temperatures of Fe(1+x)Se(1-y), Fe(1+x)Se(1-y)Te(y) and (K/Rb/Cs)(z)Fe(2-x)Se2

In a recent contribution to this journal, it was shown that the transition temperatures of optimal high-T(C) compounds obey the algebraic relation T(C0) = k(-1)(B)/ℓζ, where ℓ is related to the mean spacing between interacting charges in the layers, ζ is the distance between interacting electronic layers, β is a universal constant and k(B) is Boltzmann's constant. The equation was derived assuming pairing based on interlayer Coulomb interactions between physically separated charges. This theory was initially validated for 31 compounds from five different high-T(C) families (within an accuracy of ±1.37 K). Herein we report the addition of Fe(1+x)Se(1-y) and Fe(1+x)Se(1-y)Te(y) (both optimized under pressure) and A(z)Fe(2-x)Se(2) (for A = K, Rb or Cs) to the growing list of Coulomb-mediated superconducting compounds in which T(C0) is determined by the above equation. Doping in these materials is accomplished through the introduction of excess Fe and/or Se deficiency, or a combination of alkali metal and Fe vacancies. Consequently, a very small number of vacancies or interstitials can induce a superconducting state with a substantial transition temperature. The confirmation of the above equation for these Se-based Fe chalcogenides increases to six the number of superconducting families for which the transition temperature can be accurately predicted.