We have performed detailed $^{57}$Fe Mössbauer spectroscopy measurements on Ba$_{0.78}$K$_{0.22}$Fe$_2$As$_2$ and BaFe$_{2-x}$Ni$_x$As$_2$ single crystal mosaics showing antiferromagnetic ordering below $T_N$ with superconductivity below $T_C$. Analysis of the Mössbauer spectra shows a decrease in the magnetic hyperfine (hf) field but no change in the magnetic volume fraction below $T_C$. This clearly indicates the coexistence of magnetism and superconductivity in these compounds. The decrease in the magnetic hf field below $T_C$ depends on the difference between $T_N$ and $T_C$, being the largest for $T_N$ close to $T_C$. Two different explanations for this observation are given. We also find that the non-magnetic volume fraction below $T_N$ correlates with the Ni doping $x$, being large for high $T_C$ and small for high $T_N$.
To investigate correlation effects on antiferromagnetic order in Fe pnictides, we apply a variational Monte Carlo method to a two-orbital model. We obtain a small ordered moment consistent with experimental observations even for a Coulomb interaction comparable to the band width. Studies of estimation of the Coulomb interaction for Fe pnictides suggest values comparable to or slightly smaller than the band width, and much larger ordered moments have been obtained by the Hartree-Fock approximation for such a large Coulomb interaction. Thus, the correlation effect is important for Fe pnictides a…
In several members of the pnictide materials, spin density wave order coexists with superconductivity over a range of dopings and temperature. In this paper we show that odd-frequency superconductivity emerges on the edges of pnictides in such a coexistence phase. In particular, the breaking of spin-rotation symmetry by SDW and translation symmetry by the edge can lead to the development of odd-frequency spin-triplet Cooper pairing on edges of superconducting pnictide samples. In this case, the odd-frequency pairing has even parity components, which are immune to disorder. Our results show tha…
We apply a Hartree-Fock approximation to a two-orbital model proposed for Fe pnictide superconductors. It is found that the antiferromagnetic (AFM) order with the ordering vector Q=(pi,0) is realized. The AFM order appears simultaneously with ferro-orbital order, the latter leads to a secondary lattice distortion. We also investigate the influence of doping on the AFM order. The size of the AFM moment changes continuously for lightly doped cases, but when the amount of doped carriers exceeds a certain value the AFM state is suddenly destroyed. We also show that Fermi surfaces remain and change…
We report electronic structure calculations for BaTi$_2$Sb$_2$O and discuss the results in relation to the observed superconductivity of this material when hole doped with Na. The Fermi surface shows several sheets. These include a nested nearly 2D cylinder. There are also two sheets, which are three dimensional, in spite of the layered crystal structure. A magnetic instability associated with Fermi surface nesting is found. A sign-changing s-wave state, different from the one in the Fe-based superconductors, is predicted within a scenario of spin-fluctuation mediated superconductivity.
We study the doping dependence of the spin-density-wave (SDW) state in four models of the 1111 pnictides. The random-phase approximation is used to determine the ordering temperature and the ordering vector as functions of doping, and to evaluate the contribution of the various orbitals to the SDW instability. In addition to the usual assumption of orbitally rotation-invariant interactions, we consider the effect of reduced interactions involving the xy orbital, which are anticipated by crystal-structure considerations. We find that changing the relative strength of the interaction in the xy o…
Electron correlations produce a rich phase diagram in the iron pnictides. Earlier theoretical studies on the correlation effect demonstrated how quantum fluctuations weaken and concurrently suppress a $C_2$-symmetric single-Q antiferromagnetic order and a nematic order. Here we examine the emergent phases near the quantum phase transition. For a $C_4$-symmetric collinear double-Q antiferromagnetic order, we show that it is accompanied by both a charge order and an enhanced nematic susceptibility. Our results provide understanding for several intriguing recent experiments in hole-doped iron ars…
The present article reviews recent experimental investigations of spin dynamics in iron-based superconductors and their parent compounds by means of inelastic neutron scattering. It mainly focuses on the most contemporary developments in this field, pertaining to the observations of magnetic resonant modes in new superconductors, spin anisotropy of low-energy magnetic fluctuations that has now been observed in a wide range of chemical compositions and doping levels, as well as their momentum-space anisotropy incurred by the spin-nematic order. The implications of these new findings for our und…
The heterogeneous coexistence of antiferromagnetism (SDW) and superconductivity on a mesoscopic scale was observed in iron-pnictides in many recent experiments. We suggest and discuss the scenario in which the heterogeneity is caused by formation of domain walls inherent to the SDW state of pnictides at a proper doping or under applied pressure. Superconductivity would emerge from the modulated SDW structure. The phenomenon is akin to the FFLO-phase in superconductors.
The recent discovery of superconductivity in the iron-based layered pnictides with T_c ranging between 26 and 56K generated enormous interest in the physics of these materials. Here, we review some of the peculiarities of the antiferromagnetic order in the iron pnictides, including the selection of the stripe magnetic order and the formation of the Ising-nematic state in the unfolded BZ within an itinerant description. In addition we analyze the properties of the quasiparticle interference spectrum in the parent antiferromagnetic phase.
We study the condition for optimizing superconductivity in the iron pnictides from the lattice structure point of view. Studying the band structure of the hypothetical lattice structure of LaFeAsO, the hole Fermi surface multiplicity is found to be maximized around the Fe-As-Fe bond angle regime where the arsenic atoms form a regular tetrahedron. Superconductivity is optimized within this three hole Fermi surface regime, while the stoner factor of the antiferromagnetism has an overall tendency of increasing upon decreasing the bond angle. Combining also the effect of the varying the Fe-As bond…
Recently, a very rich phase diagram has been obtained for an iron-based superconductor Ca4Al2O6Fe2(As1-xPx)2. It has been revealed that nodeless (x=0) and nodal (x = 1) superconductivity are separated by an antiferromagnetic phase. Here we study the origin of this peculiar phase diagram using a five orbital model constructed from first principles band calculation, and applying the fluctuation exchange approximation assuming spin fluctuation mediated pairing. Based on the calculation results, we propose a scenario where the frustration in momentum space degrades superconductivity in the interme…
High-temperature superconductivity in both the copper-oxide and the iron-pnictide/chalcogenide systems occurs in close proximity to antiferromagnetically ordered states. Neutron scattering has been an essential technique for characterizing the spin correlations in the antiferromagnetic phases and for demonstrating how the spin fluctuations persist in the superconductors. While the nature of the spin correlations in the superconductors remains controversial, the neutron scattering measurements of magnetic excitations over broad ranges of energy and momentum transfer provide important constraint…
We examine the competition of the observed stripe spin density wave (SDW) with other commensurate and incommensurate SDW phases in a two-band model of the pnictides. Starting from this microscopic model, we rigorously derive an expansion of the free energy in terms of the different order parameters at the mean-field level. We show that three distinct commensurate SDW states are possible and study their appearance as a function of the doping and the electronic structure. We show that the stripe phase is generally present, but its extent in the phase diagram depends strongly upon the number of h…
We have carried out density-functional theory (DFT) calculations for the chromium pnictide BaCr2P2, which is structurally analogous to BaFe2As2, a parent compound for iron-pnictide superconductors. Evolutionary methods combined with DFT predict that the chromium analog has the same crystal structure as the latter. DFT also predicts Neel antiferromagnetic order on the chromium sites. Comparison with a simple electron-hopping model over a square lattice of chromium atoms suggests that it is due to residual nesting of the Fermi surfaces. We have confirmed the DFT predictions directly after the su…
The magnetic excitations of the iron pnictides are explained within a degenerate double-exchange model. The local-moment spins are coupled by superexchanges $J_1$ and $J_2$ between nearest and next-nearest neighbors, respectively, and interact with the itinerant electrons of the degenerate $d_{xz}$ and $d_{yz}$ orbitals via a ferromagnetic Hund exchange. The latter stabilizes $(π,0)$ stripe antiferromagnetism due to emergent ferro-orbital order and the resulting kinetic energy gain by hopping preferably along the ferromagnetic spin direction. Taking the quantum nature of the spins into account…
Superconductivity in the iron pnictides and chalcogenides arises at the border of antiferromagnetism, which raises the question of the role of quantum criticality. In this topical review, we describe the theoretical work that led to the prediction for a magnetic quantum critical point arising out of a competition between electronic localization and itinerancy, and the proposal for accessing it by using isoelectronic P substitution for As in the undoped iron pnictides. We go on to compile the emerging experimental evidence in support of the existence of such a quantum critical point in isoelect…
By performing high-pressure single-crystal neutron diffraction measurements, the evolution of structure and magnetic ordering in EuFe2As2 under hydrostatic pressure were investigated. Both the tetragonal-toorthorhombic structural transition and the Fe spin-density-wave (SDW) transition are gradually suppressed and become decoupled with increasing pressure. The antiferromagnetic order of the Eu sublattice is, however, robust against the applied pressure up to 24.7 kbar, without showing any change of the ordering temperature. Under the pressure of 24.7 kbar, the lattice parameters of EuFe2As2 di…
To perform a local orbital analysis of electronic and magnetic interactions, we construct the Wannier functions (WFs) of the Fe $3d$ orbitals in the parent compound of the recently discovered iron pnictide superconductors, LaFeAsO, and a comparison material LaFePO. Comparing the WFs for the stripe antiferromagnetic order with those for no magnetic order, the difference is a significant spreading (``{\it de}localization'') of specifically the $d_{xy}$ and $d_{xz}$ (but not $d_{yz}$) WFs, where parallel Fe spins lie along the $x$ direction. The WF basis gives a tight-binding representation of th…
We report the effect of applied pressures on magnetic and superconducting order in single crystals of the aliovalent La-doped iron pnictide material Ca$_{1-x}$La$_{x}$Fe$_{2}$As$_{2}$. Using electrical transport, elastic neutron scattering and resonant tunnel diode oscillator measurements on samples under both quasi-hydrostatic and hydrostatic pressure conditions, we report a series of phase diagrams spanning the range of substitution concentrations for both antiferromagnetic and superconducting ground states that include pressure-tuning through the antiferromagnetic (AFM) quantum critical poi…
It is shown that a generic form of an antiferromagnetic wave function opens strong electron-phonon coupling channels in the iron-based superconductors. In the nonmagnetic state these channels exist locally on a single iron atom, but are canceled out between the two iron atoms in the primitive unit cell. Our findings are based on symmetry and the presence of an xz/yz Fermi surface near the M point and thus should be relevant for the known iron-based pnictide or chalcogenide superconductors.
We obtain and analyze the phase diagram of doped iron-pnictides under the assumption that doping adds non-magnetic impurities to the system but does not change the densities of carriers. We show that the phase diagram is quite similar to the one obtained under the opposite rigid band assumption. In both cases, there is a phase where extended s+- superconductivity and antiferromagnetism co-exist. We evaluate the jump of the specific heat at the superconducting transition across the phase diagram and show that the jump is non-monotonic, with the maximum at the onset of the co-existence phase. Ou…
In iron pnictides, high temperature superconductivity emerges after suppressing antiferromagnetism by doping. Here we show that antiferromagnetism in Ca$_{1-x}$La$_x$FeAs$_2$ is robust against and even enhanced by doping. Using $^{75}$As-nuclear magnetic resonance and nuclear quadrupole resonance techniques, we find that an antiferromagnetic order occurs below the Néel temperature $T_{\rm N}$ = 62 K at a high doping concentration ($x$ = 0.15) where superconductivity sets in at the transition temperature $T_{\rm c}$ = 35 K. Unexpectedly, $T_{\rm N}$ is enhanced with increasing doping, rising up…
The Ru doping effect on the Dirac cone states is investigated in iron pnictide superconductors Ba(Fe$_{1-x}$Ru$_x$As)$_2$ using the transverse magnetoresistance (MR) measurements as a function of temperature. The linear development of MR against magnetic field $B$ is observed for $x$ = 0 - 0.244 at low temperatures below the antiferromagnetic transition. The $B$-linear MR is interpreted in terms of the quantum limit of the Dirac cone states by using the model proposed by Abrikosov. An intriguing evidence is shown that the Dirac cone state persists on the electronic phase diagram where the anti…
We investigate the pairing in iron pnictides in the coexistence phase, which displays both superconducting and antiferromagnetic orders. By solving the pairing problem on the Fermi surface reconstructed by long-range magnetic order, we find that the pairing interaction necessarily becomes angle-dependent, even if it was isotropic in the paramagnetic phase, which results in an angular variation of the superconducting gap along the Fermi surfaces. We find that the gap has no nodes for a small antiferromagnetic order parameter M, but may develop accidental nodes for intermediate values of M, when…
We have performed an angle-resolved photoemission spectroscopy (ARPES) study of the undoped and electron-doped iron pnictides BaFe2\_{-x}CoxAs2 (Ba122) (x=0, 0.14) and studied the Fermi surfaces (FSs) and band dispersions near the Fermi level. The FS sheets we observed are consistent with the shrinkage of the hole-like pockets around the Brillouin Zone (BZ) center and the expansion of the electron pockets around the BZ corner in the electron-doped compound as compared to the undoped parent compound. Band dispersions and FSs around the BZ center strongly depend on the photon energy, indicating …
We analyze the effect of weak disorder on the competition between antiferromagnetic order and superconductivity in a model for iron-based superconductors. Under the assumption of an approximate particle-hole symmetry we show that conventional $s^{++}$ superconductivity cannot be realized in the case of coexisting magnetic and superconductive orders, observed experimentally at intermediate doping levels. This result holds for arbitrary impurity concentrations, and, in particular, in the clean limit. The inclusion of disorder further amplifies the phase competition between itinerant antiferromag…
We study a two-orbital spin model to describe (pi,0) stripe antiferromagnetism in the iron pnictides. The "double-spin" model has an on-site Hunds's coupling and inter-site interactions extending to second neighbors (inter- and intra-orbital) on the square lattice. Using a variational method based on a cluster decomposition, we optimize wave functions with up to 8 cluster sites (up to 2^16 variational parameters). We focus on the anomalously small ordered moments in the stripe state of the pnictides. To account for it, and large variations among different compounds, we show that the second-nei…
Undoped iron superconductors accommodate $n=6$ electrons in five d-orbitals. Experimental and theoretical evidence shows that the strength of correlations increases with hole-doping, as the electronic filling approaches half-filling with $n=5$ electrons. This evidence delineates a scenario in which the parent compound of iron superconductors is the half-filled system, in analogy to cuprate superconductors. In cuprates the superconductivity can be induced upon electron or hole doping. In this work we propose to search for high-Tc superconductivity and strong correlations in chromium pnictides a…
The close interplay between superconductivity and antiferromagnetism in several quantum materials can lead to the appearance of an unusual thermodynamic state in which both orders coexist microscopically, despite their competing nature. A hallmark of this coexistence state is the emergence of a spin-triplet superconducting gap component, called $π$-triplet, which is spatially modulated by the antiferromagnetic wave-vector, reminiscent of a pair-density wave. In this paper, we investigate the impact of these $π$-triplet degrees of freedom on the phase diagram of a system with competing antiferr…
We constructed an effective tight-binding model with five Cr $3d$ orbitals for LaOCrAs according to first-principles calculations. Basing on this model, we investigated possible superconductivity induced by correlations in doped LaOCrAs using the functional renormalization group (FRG). We find that there are two domes of superconductivity in electron-doped LaOCrAs. With increasing electron doping, the ground state of the system evolves from G-type antiferromagnetism in the parent compound to an incipient $s_\pm$-wave superconducting phase dominated by electron bands derived from the $d_{3z^2-r…
Like high Tc cuprates, the newly discovered iron based superconductors lie in close proximity to a magnetically ordered parent phase. However, while the magnetic order in parent cuprates is known to derive from a spin-spin local superexchange interaction, a plethora of experiments including neutron scattering have so far been unable to conclusively resolve whether a local moment Heisenberg description applies in parent iron based compounds, or whether magnetism arises from a collective SDW order instability. These two alternatives can in principle be distinguished by measuring the low energy m…
We studied the electric and magnetic behavior near the phase boundary between antiferromagnetic (AF) and superconducting (SC) phases for a prototype of high-T_c pnictides LaFeAsO_{1-x}F_{x} by using nuclear magnetic resonance, and found that paramagnetic-metal (PM) domains segregate from AF domains. PM domains grow in size with increasing electron doping level and are accompanied by the onset of superconductivity, and thus application of pressure or increasing the doping level causes superconductivity. The existence of PM domains cannot be explained by the existing paradigm that focuses only o…
The main driven force of the electronic nematic phase in iron-based superconductors is still under debate. Here, we report a comprehensive study on the nematic fluctuations in a non-superconducting iron pnictide system BaFe$_{1.9-x}$Ni$_{0.1}$Cr$_{x}$As$_{2}$ by electronic transport, angle-resolved photoemission spectroscopy (ARPES) and inelastic neutron scattering (INS) measurements. Previous neutron diffraction and transport measurements suggested that the collinear antiferromagnetism persists to $x=0.8$, with similar Néel temperature $T_N$ and structural transition temperature $T_s$ around …
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 capturin…
The ground-state properties of CuFeAs were investigated by applying density functional theory calculations within generalized gradient approximation (GGA) and GGA+U. We find that the bicollinear antiferromagnetic state with antiparallel orbital magnetic moments on each iron which violates the Hund's rule is favored by the on-site Coulomb interaction, which is further stabilized by Cu vacancy. The magnetic ground state can be used to understand weak antiferromagnetism in CuFeAs observed experimentally. We argue that breakdown of the Hund's rule may be the possible origin for reduced magnetism i…
We present a systematic study on the heavily Cr doped iron pnictides BaFe$_{1.9-x}$Ni$_{0.1}$Cr$_{x}$As$_{2}$ by using elastic neutron scattering, high-resolution synchrotron X-ray diffraction (XRD), resistivity and Hall transport measurements. When the Cr concentration increases from $x=$ 0 to 0.8, neutron diffraction experiments suggest that the collinear antiferromagnetism persists in the whole doping range, where the Néel temperature $T_N$ coincides with the tetragonal-to-orthorhombic structural transition temperature $T_s$, and both of them keeps around 35 K. The magnetic ordered moment, …
Resonant magnetic excitations are widely recognized as hallmarks of unconventional superconductivity in copper oxides, iron pnictides, and heavy-fermion compounds. Numerous model calculations have related these modes to the microscopic properties of the pair wave function, but the mechanisms underlying their formation are still debated. Here we report the discovery of a similar resonant mode in the non-superconducting, antiferromagnetically ordered heavy-fermion metal CeB6. Unlike conventional magnons, the mode is non-dispersive, and its intensity is sharply concentrated around a wave vector s…
The correlation and competition between antiferromagnetism and superconductivity are one of the most fundamental issues in all of high temperature superconductors. The superconductivity in high temperature cuprate superconductors arises from suppressing an antiferromagnetic (AFM) Mott insulator phase by doping1 while that in iron-pnictide high temperature superconductors arises from AFM semimetals and can coexist with AFM orders2-9. This key difference marked in their phase diagrams has raised many intriguing debates about whether the two materials can be placed in the same category to underst…
The discovery of superconductivity in alkali-ammonia co-intercalated FeSe has generated intensive interest because of their highest Tc (~ 45 K) among iron-chalcogenide superconductors with bulk form. Here, we report the phase diagrams of two series of Li/Na-ammonia co-intercalated FeSe1-zTez. When superconductivity is suppressed by Te doping, the magnetic ordering states are emergent. Moreover, a novel phase Lix(NH3)yFe2-δTe2 with possible antiferromagnetism is discovered. This strongly indicates the intimate relation between superconductivity and magnetism in these materials, like in other ir…
Fluctuations around an antiferromagnetic quantum critical point (QCP) are believed to lead to unconventional superconductivity and in some cases to high-temperature superconductivity. However, the exact mechanism by which this occurs remains poorly understood. The iron-pnictide superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$ is perhaps the clearest example to date of a high temperature quantum critical superconductor, and so it is a particularly suitable system in which to study how the quantum critical fluctuations affect the superconducting state. Here we show that the proximity of the QCP yiel…
The effect of selenium substitution by sulfur or tellurium in the Tl1-yFe2-zSe2 antiferromagnet was studied by x-ray and electron diffraction, magnetization and transport measurements. Tl0.8Fe1.5(Se1-xXx)2 (nominal composition) solid solutions were synthesized in the full x range (0<x<1) for X=S and up to x=0.5 for X=Te, using the sealed tube technique. No superconductivity was found down to 4.2K in the case of sulfur despite the fact that the optimal crystallographic parameters, determined by Rietveld refinements, are reached in the series (i.e. the Fe-(Se,S) interplane height and (Se,S)-Fe-(…
Muon spin rotation and relaxation studies have been performed on a "111" family of iron-based superconductors NaFe_1-xNi_xAs. Static magnetic order was characterized by obtaining the temperature and doping dependences of the local ordered magnetic moment size and the volume fraction of the magnetically ordered regions. For x = 0 and 0.4 %, a transition to a nearly-homogeneous long range magnetically ordered state is observed, while for higher x than 0.4 % magnetic order becomes more disordered and is completely suppressed for x = 1.5 %. The magnetic volume fraction continuously decreases with …
