Static and dynamic magnetism in underdoped superconductor BaFe1.92Co0.08As2

Bulk Superconductivity and Role of Fluctuations in the Iron-Based Superconductor FeSe at High Pressures

The iron-based superconductor FeSe offers a unique possibility to study the interplay of superconductivity with purely nematic as well magnetic-nematic order by pressure (p) tuning. By measuring specific heat under p up to 2.36 GPa, we study the multiple phases in FeSe using a thermodynamic probe. We conclude that superconductivity is bulk across the entire p range and competes with magnetism. In addition, whenever magnetism is present, fluctuations exist over a wide temperature range above both the bulk superconducting and the magnetic transitions. Whereas the magnetic fluctuations are likely temporal, the superconducting fluctuations may be either temporal or spatial. These observations highlight similarities between FeSe and underdoped cuprate superconductors.

Local orthorhombic lattice distortions in the paramagnetic tetragonal phase of superconducting NaFe1-xNixAs

Understanding the interplay between nematicity, magnetism and superconductivity is pivotal for elucidating the physics of iron-based superconductors. Here we use neutron scattering to probe magnetic and nematic orders throughout the phase diagram of NaFe1-xNixAs, finding that while both static antiferromagnetic and nematic orders compete with superconductivity, the onset temperatures for these two orders remain well separated approaching the putative quantum critical points. We uncover local orthorhombic distortions that persist well above the tetragonal-to-orthorhombic structural transition temperature Ts in underdoped samples and extend well into the overdoped regime that exhibits neither magnetic nor structural phase transitions. These unexpected local orthorhombic distortions display Curie-Weiss temperature dependence and become suppressed below the superconducting transition temperature Tc, suggesting that they result from the large nematic susceptibility near optimal superconductivity. Our results account for observations of rotational symmetry breaking above Ts, and attest to the presence of significant nematic fluctuations near optimal superconductivity.

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.

Antiferroic electronic structure in the nonmagnetic superconducting state of the iron-based superconductors

A major problem in the field of high-transition temperature (T_c) superconductivity is the identification of the electronic instabilities near superconductivity. It is known that the iron-based superconductors exhibit antiferromagnetic order, which competes with the superconductivity. However, in the nonmagnetic state, there are many aspects of the electronic instabilities that remain unclarified, as represented by the orbital instability and several in-plane anisotropic physical properties. We report a new aspect of the electronic state of the optimally doped iron-based superconductors by using high-energy resolution angle-resolved photoemission spectroscopy. We find spectral evidence for the folded electronic structure suggestive of an antiferroic electronic instability, coexisting with the superconductivity in the nonmagnetic state of Ba_1-x K _x Fe₂As₂. We further establish a phase diagram showing that the antiferroic electronic structure persists in a large portion of the nonmagnetic phase covering the superconducting dome. These results motivate consideration of a key unknown electronic instability, which is necessary for the achievement of high-T_c superconductivity in the iron-based superconductors.

Superconducting properties of thes±-wave state: Fe-based superconductors

Although the pairing mechanism of Fe-based superconductors (FeSCs) has not yet been settled with consensus with regard to the pairing symmetry and the superconducting (SC) gap function, the vast majority of experiments support the existence of spin-singlet sign-changings-wave SC gaps on multi-bands (s±-wave state). This multi-bands±-wave state is a very unique gap stateper seand displays numerous unexpected novel SC properties, such as a strong reduction of the coherence peak, non-trivial impurity effects, nodal-gap-like nuclear magnetic resonance signals, various Volovik effects in the specific heat (SH) and thermal conductivity, and anomalous scaling behaviors with a SH jump and condensation energy versusTc, etc. In particular, many of these non-trivial SC properties can easily be mistaken as evidence for a nodal-gap state such as ad-wave gap. In this review, we provide detailed explanations of the theoretical principles for the various non-trivial SC properties of thes±-wave pairing state, and then critically compare the theoretical predictions with experiments on FeSCs. This will provide a pedagogical overview of to what extent we can coherently understand the wide range of different experiments on FeSCs within thes±-wave gap model.

The magnetic and electronic properties of oxyselenides-influence of transition metal ions and lanthanides

Magnetic oxyselenides have been a topic of research for several decades, firstly in the context of photoconductivity and thermoelectricity owing to their intrinsic semiconducting properties and ability to tune the energy gap through metal ion substitution. More recently, interest in the oxyselenides has experienced a resurgence owing to the possible relation to strongly correlated phenomena given the fact that many oxyselenides share a similar structure to unconventional superconducting pnictides and chalcogenides. The two dimensional nature of many oxyselenide systems also draws an analogy to cuprate physics where a strong interplay between unconventional electronic phases and localised magnetism has been studied for several decades. It is therefore timely to review the physics of the oxyselenides in the context of the broader field of strongly correlated magnetism and electronic phenomena. Here we review the current status and progress in this area of research with the focus on the influence of lanthanides and transition metal ions on the intertwined magnetic and electronic properties of oxyselenides. The emphasis of the review is on the magnetic properties and comparisons are made with iron based pnictide and chalcogenide systems.

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.

Measurement of a double neutron-spin resonance and an anisotropic energy gap for underdoped superconducting NaFe0.985Co0.015As using inelastic neutron scattering

We use inelastic neutron scattering to show that superconductivity in electron-underdoped NaFe0.985Co0.015As induces a dispersive sharp resonance near E(r1)=3.25  meV and a broad dispersionless mode at E(r2)=6  meV. However, similar measurements on overdoped superconducting NaFe0.935Co0.045As find only a single sharp resonance at E(r)=7  meV. We connect these results with the observations of angle-resolved photoemission spectroscopy that the superconducting gaps in the electron Fermi pockets are anisotropic in the underdoped material but become isotropic in the overdoped case. Our analysis indicates that both the double neutron spin resonances and gap anisotropy originate from the orbital dependence of the superconducting pairing in the iron pnictides. Our discovery also shows the importance of the inelastic neutron scattering in detecting the multiorbital superconducting gap structures of iron pnictides.

Universality of the dispersive spin-resonance mode in superconducting BaFe2As2

Spin fluctuations in superconducting BaFe2(As(1-x)P(x))2 (x=0.34, T(c)=29.5 K) are studied using inelastic neutron scattering. Well-defined commensurate magnetic signals are observed at (π, 0), which is consistent with the nesting vector of the Fermi surface. Antiferromagnetic (AFM) spin fluctuations in the normal state exhibit a three-dimensional character reminiscent of the AFM order in nondoped BaFe2As2. A clear spin gap is observed in the superconducting phase forming a peak whose energy is significantly dispersed along the c axis. The bandwidth of dispersion becomes larger with approaching the AFM ordered phase universally in all superconducting BaFe2As2, indicating that the dispersive feature is attributed to three-dimensional AFM correlations. The results suggest a strong relationship between the magnetism and superconductivity.

Local structure and hyperfine interactions of 57Fe in NaFeAs studied by Mössbauer spectroscopy

Detailed 57Fe Mössbauer spectroscopy measurements on superconducting NaFeAs powder samples have been performed in the temperature range 13 K ≤ T < 300 K. The 57Fe spectra recorded in the paramagnetic range (T > TN ≈ 46 K) are discussed supposing that most of the Fe2+ ions are located in distorted (FeAs4) tetrahedra of NaFeAs phase, while an additional minor (<10%) component of the spectra corresponds to impurity or intergrowth NaFe2As2 phase with a nominal composition near NaFe2As2. Our results reveal that the structural transition (TS ≈ 55 K) has a weak effect on the electronic structure of iron ions, while at T ≤ TN the spectra show a continuous distribution of hyperfine fields HFe. The shape of these spectra is analyzed in terms of two models: (i) an incommensurate spin density wave modulation of iron magnetic structure, (ii) formation of a microdomain structure or phase separation. It is shown that the hyperfine parameters obtained using these two methods have very similar values over the whole temperature range. Analysis of the temperature dependence HFe(T) with the Bean–Rodbell model leads to ζ = 1.16 ± 0.05, suggesting that the magnetic phase transition is first order in nature. A sharp evolution of the VZZ(T) and η(T) parameters of the full Hamiltonian of hyperfine interactions near T ≈ (TN,TS) is interpreted as a manifestation of the anisotropic electron redistribution between the dxz-, dyz- and dxy-orbitals of the iron ions.

Avoided quantum criticality and magnetoelastic coupling in BaFe(2-x)Ni(x)As2

We study the structural and magnetic orders in electron-doped BaFe(2-x)Ni(x)As2 by high-resolution synchrotron x-ray and neutron scatterings. Upon Ni doping x, the nearly simultaneous tetragonal-to-orthorhombic structural (T(s)) and antiferromagnetic (T(N)) phase transitions in BaFe2As2 are gradually suppressed and separated, resulting in T(s)>T(N) with increasing x, as was previously observed. However, the temperature separation between T(s) and T(N) decreases with increasing x for x≥0.065, tending toward a quantum bicritical point near optimal superconductivity at x≈0.1. The zero-temperature transition is preempted by the formation of a secondary incommensurate magnetic phase in the region 0.088≲x≲0.104, resulting in a finite value of T(N)≈T(c) + 10  K above the superconducting dome around x≈0.1. Our results imply an avoided quantum critical point, which is expected to strongly influence the properties of both the normal and superconducting states.

Magnonlike dispersion of spin resonance in Ni-doped BaFe2As2

Inelastic neutron scattering measurements on Ba(Fe0.963Ni0.037)2As2 manifest a neutron spin resonance in the superconducting state with anisotropic dispersion within the Fe layer. Whereas the resonance is sharply peaked at the antiferromagnetic (AFM) wave vector Q(AFM) along the orthorhombic a axis, the resonance disperses upwards away from Q(AFM) along the b axis. In contrast to the downward dispersing resonance and hourglass shape of the spin excitations in superconducting cuprates, the resonance in electron-doped BaFe2As2 compounds possesses a magnonlike upwards dispersion.

Effect of electron correlations on magnetic excitations in the isovalently doped iron-based superconductor Ba(Fe(1-x)Ru(x))(2)As(2)

Magnetic correlations in isovalently doped Ba(Fe(1-x)Ru(x))(2)As(2) (x = 0.25, T(c) = 14.5 K; x = 0.35, T(c) = 20 K) are studied by elastic and inelastic neutron scattering techniques. A relatively large superconducting spin gap accompanied by a weak resonance mode is observed in the superconducting state in both samples. In the normal state, the magnetic excitation intensity is dramatically reduced with increasing Ru doping toward the optimally doped regime. Our results favor that the weakening of the electron-electron correlations by Ru doping is responsible for the dampening of the resonance mode, as well as the suppression of the normal state antiferromagnetic correlations near the optimally doped regime in this system.

Splitting of resonance excitations in nearly optimally doped Ba(Fe0.94Co0.06)2As2: an inelastic neutron scattering study with polarization analysis

Magnetic excitations in Ba(Fe0.94Co0.06)2As2: are studied by polarized inelastic neutron scattering above and below the superconducting transition. In the superconducting state, we find clear evidence for two resonancelike excitations. At a higher energy of about 8 meV, there is an isotropic resonance mode with weak dispersion along the c direction. In addition, we find a lower excitation at 4 meV that appears only in the c-polarized channel and whose intensity strongly varies with the l component of the scattering vector. These resonance excitations behave remarkably similar to the gap modes in the antiferromagnetic phase of the parent compound BaFe2As2.

Effects of transition metal substitutions on the incommensurability and spin fluctuations in BaFe2As2 by elastic and inelastic neutron scattering

The spin fluctuation spectra from nonsuperconducting Cu-substituted, and superconducting Co-substituted, BaFe(2)As(2) are compared quantitatively by inelastic neutron scattering measurements and are found to be indistinguishable. Whereas diffraction studies show the appearance of incommensurate spin-density wave order in Co and Ni substituted samples, the magnetic phase diagram for Cu substitution does not display incommensurate order, demonstrating that simple electron counting based on rigid-band concepts is invalid. These results, supported by theoretical calculations, suggest that substitutional impurity effects in the Fe plane play a significant role in controlling magnetism and the appearance of superconductivity, with Cu distinguished by enhanced impurity scattering and split-band behavior.

Crystallographic and magnetic phase transitions in the layered ruthenium oxyarsenides TbRuAsO and DyRuAsO

The crystallographic and physical properties of TbRuAsO and DyRuAsO at and below room temperature are reported, including full structure refinements from powder X-ray diffraction data and measured electrical and thermal transport properties, magnetic susceptibility, and heat capacity. Both compounds are isostructural to LaFeAsO (ZrCuSiAs-type, P4/nmm) at room temperature. However, DyRuAsO undergoes a symmetry-lowering crystallographic phase transition near 25 K, and adopts an orthorhombic structure (Pmmn) below this temperature. This structural distortion is unlike those observed in the analogous Fe compounds. Magnetic phase transitions are observed in both compounds which suggest antiferromagnetic ordering of lanthanide moments occurs near 7.0 K in TbRuAsO and 10.5 K in DyRuAsO. The nature of the structural distortion as well as thermal conductivity and heat capacity behaviors indicate strong coupling between the magnetism and the lattice. The behaviors of both materials show magnetic ordering of small moments on Ru may occur at low temperatures.

Coexistence and competition of the short-range incommensurate antiferromagnetic order with the superconducting state of BaFe(2-x)Ni(x)As2

Superconductivity in the iron pnictides develops near antiferromagnetism, and the antiferromagnetic (AF) phase appears to overlap with the superconducting phase in some materials such as BaFe(2-x)T(x)As2 (where T=Co or Ni). Here we use neutron scattering to demonstrate that genuine long-range AF order and superconductivity do not coexist in BaFe(2-x)Ni(x)As2 near optimal superconductivity. In addition, we find a first-order-like AF-to-superconductivity phase transition with no evidence for a magnetic quantum critical point. Instead, the data reveal that incommensurate short-range AF order coexists and competes with superconductivity, where the AF spin correlation length is comparable to the superconducting coherence length.

Incommensurate spin-density wave order in electron-doped BaFe2 As2 superconductors

Neutron diffraction studies of Ba(Fe(1-x)Co(x))(2)As)(2) reveal that commensurate antiferromagnetic order gives way to incommensurate magnetic order for Co compositions between 0.056 < x < 0.06. The incommensurability has the form of a small transverse splitting (0, ± ε, 0) from the commensurate antiferromagnetic propagation vector Q(AFM) = (1,0,1) (in orthorhombic notation) where ε ≈ 0.02-0.03 and is composition dependent. The results are consistent with the formation of a spin-density wave driven by Fermi surface nesting of electron and hole pockets and confirm the itinerant nature of magnetism in the iron arsenide superconductors.

Coexistence of magnetism and superconductivity in the iron-based compound Cs0.8(FeSe0.98)2

We report on muon-spin rotation and relaxation (μSR), electrical resistivity, magnetization and differential scanning calorimetry measurements performed on a high-quality single crystal of Cs(0.8)(FeSe(0.98))(2). Whereas our transport and magnetization data confirm the bulk character of the superconducting state below T(c)=29.6(2)  K, the μSR data indicate that the system is magnetic below T(N)=478.5(3)  K, where a first-order transition occurs. The first-order character of the magnetic transition is confirmed by differential scanning calorimetry data. Taken all together, these data indicate in Cs(0.8)(FeSe(0.98))(2) a microscopic coexistence between the superconducting phase and a strong magnetic phase. The observed T(N) is the highest reported to date for a magnetic superconductor.

Magnon-mediated pairing and isotope effect in iron-based superconductors

Within a minimal model for the iron-based superconductors in which itinerant electrons interact with a band of local moments, we derive a general conclusion for multiband superconductivity. In a multiband superconductor, due to the Adler theorem, the interband scattering dominates the intraband scattering at the long wavelength limit as long as both interactions are induced by the Goldstone boson (which is the magnon in our case) and the transferred momentum is non-zero. Such an interaction leads to a well known sign-reversing superconductivity even if the interband and intraband interaction are repulsive. This effect can be modeled as arising from an internal Josephson link between the Fermi surface sheets. Our model is also consistent with the recently discovered coexistence of superconductivity and magnetic order in iron-pnictides. Although the experimentally observed isotope effect is large, α = 0.4, we show that it is consistent with a non-phononic mechanism in which it is the isotope effects which result in a change in the lattice constant and, as a consequence, the zero-point motion of the Fe atoms.

Effects of nematic fluctuations on the elastic properties of iron arsenide superconductors

We demonstrate that the changes in the elastic properties of the FeAs systems, as seen in our resonant ultrasound spectroscopy data, can be naturally understood in terms of fluctuations of emerging nematic degrees of freedom. Both the softening of the lattice in the normal, tetragonal phase as well as its hardening in the superconducting phase are consistently described by our model. Our results confirm the view that structural order is induced by magnetic fluctuations.

Distinct high-T transitions in underdoped Ba(1-x)KxFe2As2

In contrast with the simultaneous structural and magnetic first order phase transition T0 previously reported, our detailed investigation on an underdoped Ba(0.84)K(0.16)Fe2As2 single crystal unambiguously revealed that the transitions are not concomitant. The tetragonal (τ: I4/mmm)-orthorhombic (ϑ: Fmmm) structural transition occurs at T(S)≃110 K, followed by an adjacent long-range antiferromagnetic (AFM) transition at T(N)≃102 K. Hysteresis and coexistence of the τ and ϑ phases over a finite temperature range observed by NMR experiments confirm the first order character of the τ-ϑ transition and provide evidence that both T(S) and T(N) are strongly correlated. Our data also show that superconductivity develops in the ϑ phase below T(c)=20 K and coexists with AFM. This new observation, T(S)≠T(N), firmly establishes another similarity between the hole-doped BaFe2As2 and the electron-doped iron-arsenide superconductors.

Coexistence and competition of magnetism and superconductivity on the nanometer scale in underdoped BaFe1.89Co0.11As2

We report muon spin rotation (μSR) and infrared spectroscopy experiments on underdoped BaFe1.89Co0.11As2 which show that bulk magnetism and superconductivity (SC) coexist and compete on the nanometer length scale. Our combined data reveal a bulk magnetic order, likely due to an incommensurate spin density wave (SDW), which develops below T(mag)≈32  K and becomes reduced in magnitude (but not in volume) below Tc=21.7  K. A slowly fluctuating precursor of the SDW seems to develop already below the structural transition at T(s)≈50  K. The bulk nature of SC is established by the μSR data which show a bulk SC vortex lattice and the IR data which reveal that the majority of low-energy states is gapped and participates in the condensate at T≪T(c).

Magnetism in Fe-based superconductors

In this review, we present a summary of experimental studies of magnetism in Fe-based superconductors. The doping dependent phase diagram shows strong similarities to the generic phase diagram of the cuprates. Parent compounds exhibit magnetic order together with a structural phase transition, both of which are progressively suppressed with doping, allowing superconductivity to emerge. The stripe-like spin arrangement of Fe moments in the magnetically ordered state shows identical in-plane structure for the RFeAsO (R = rare earth) and AFe(2)As(2) (A = Sr, Ca, Ba, Eu and K) parent compounds, notably different than the spin configuration of the cuprates. Interestingly, Fe(1 + y)Te orders with a different spin order despite having very similar Fermi surface topology. Studies of the spin dynamics of the parent compounds show that the interactions are best characterized as anisotropic three-dimensional interactions. Despite the room temperature tetragonal structure, analysis of the low temperature spin waves under the assumption of a Heisenberg Hamiltonian indicates strong in-plane anisotropy with a significant next-nearest-neighbor interaction. For the superconducting state, a resonance, localized in both wavevector and energy, is observed in the spin excitation spectrum as for the cuprates. This resonance is observed at a wavevector compatible with a Fermi surface nesting instability independent of the magnetic ordering of the relevant parent compound. The resonance energy (E(r)) scales with the superconducting transition temperature (T(C)) as E(r) ∼ 4.9k(B)T(C), which is consistent with the canonical value of ∼ 5k(B)T(C) observed for the cuprates. Moreover, the relationship between the resonance energy and the superconducting gap, Δ, is similar to that observed for many unconventional superconductors (E(r)/2Δ ∼ 0.64).

Anomalous suppression of the orthorhombic lattice distortion in superconducting Ba(Fe1-xCox)2As2 single crystals

High-resolution x-ray diffraction measurements reveal an unusually strong response of the lattice to superconductivity in Ba(Fe1-xCox)2As2. The orthorhombic distortion of the lattice is suppressed and, for Co doping near x=0.063, the orthorhombic structure evolves smoothly back to a tetragonal structure. We propose that the coupling between orthorhombicity and superconductivity is indirect and arises due to the magnetoelastic coupling, in the form of emergent nematic order, and the strong competition between magnetism and superconductivity.

Coexistence of competing antiferromagnetic and superconducting phases in the underdoped Ba(Fe0.953Co0.047)2As2 compound using x-ray and neutron scattering techniques

Neutron and x-ray diffraction studies show that the simultaneous first-order transition to an orthorhombic and antiferromagnetic (AFM) ordered state in BaFe2As2 splits into two transitions with Co doping. For Ba(Fe0.953Co0.047)2As2, a tetragonal-orthorhombic transition occurs at TS=60 K, followed by a second-order transition to AFM order at TN=47 K. Superconductivity occurs in the orthorhombic state below TC=17 K and coexists with AFM. Below TC, the static Fe moment is reduced along with a redistribution of low energy magnetic excitations indicating competition between coexisting superconductivity and AFM order.