Iron-based Superconductor BaFe Research Articles

Anomalous sharp peak in the London penetration depth induced by the nodeless-to-nodal superconducting transition in BaFe2(As1−xPx)2

The issue of whether the quantum critical point (QCP) is hidden inside unconventional superconductors is a matter of hot debate. Although a prominent experiment on London penetration depth has demonstrated the existence of the QCP in the isovalent-doped iron-based superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$, with the observation of a sharp peak in the penetration depth in the vicinity of the disappearance of magnetic order at zero temperature, the nature of such an emerging QCP remains unclear. Here, we provide a unique picture to understand well the phenomena of the QCP based on the framework of linear response theory. Evidence from the density of states and superfluid density calculations suggests the nodeless-to-nodal pairing transition accompanied the appearance of a sharp peak in the penetration depth in BaFe$_2$(As$_{1-x}$P$_x$)$_2$. Such a pairing transition originates from the three-dimensional electronic properties with a strong interlayer superconducting pairing. This finding provides a significant insight into the understanding of the QCP observed in experiment in BaFe$_2$(As$_{1-x}$P$_x$)$_2$.

Theoretical investigation of the coexistence of superconductivity and spin density wave (SDW) in two-band model for the iron-based superconductor BaFe2(As1−xPx)2

This study focuses on the theoretical investigation of the coexistence of superconductivity and spin density wave (SDW) in a two-band model for the iron-based superconductor BaFe2(As1−xPx)2. By employing a system Hamiltonian in a two-band model for a given system and by using the double time temperature dependent Green’s function formalism at the Bardeen-Cooper-Schrieffer (BCS) mean field approximation (MFA) level, we obtained mathematical expressions for the dependence of superconducting transition temperature (TC) on SDW order parameter (ΔSDW) in the electron and hole intra-band interactions, and in the inter-band interactions for superconductor BaFe2(As1−xPx)2. Similarly, we have obtained an expression for the dependence of SDW transition temperature (TSDW) on the SDW order parameter (ΔSDW) for BaFe2(As1−xPx)2. By using experimental values and considering some plausible approximations of the parameters in the obtained expressions, phase diagrams of TC versus ΔSDW in the electron and hole intra-band interactions, and in the inter-band interactions are plotted for the BaFe2(As1−xPx)2 superconductor. Similarly, a phase diagram of TSDW versus ΔSDW is plotted for the same superconductor. By merging the two phase diagrams, we have demonstrated the possible coexistence of superconductivity and SDW in the electron and hole intra-band interactions, and in the inter-band interactions for BaFe2(As1−xPx)2. Furthermore, we have investigated the dependence of ΔSDW on temperature in pure SDW region and the phase diagram is plotted for the variation of ΔSDW with temperature for superconductor BaFe2(As1−xPx)2. Our findings are in agreement with previous experimental results.

Spin glass in the bond-diluted J1−J2 Ising model on the square lattice

We use Monte Carlo (MC) methods to simulate a two-dimensional (2D) bond-diluted Ising model on the square lattice which has frustration between the nearest-neighbor interaction J1 and the next-nearest-neighbor interaction J2. In this paper, we use the parallel tempering algorithm to study the thermodynamics for different diluted ratio x and give the phase diagram. The presence of both frustration and disorder results in a spin-glass phase, which exists between the stripe antiferromagnetic phase and the Neel phase. We present the ground-state energy of T -> 0 and the size-dependence of Edwards-Anderson (EA) order parameter for the spin glass phase. By scaling the mean energy and the EA order parameter from the simulated annealing with the Kibble-Zurek (KZ) mechanism, we obtain two different dynamic exponents z_E and z_q for the spin glass phase. Experimentally, this model has close implication with the FeAs plane of the iron-based superconductor BaFe2(As(1-x)P(x))2, where a spin-glass like phase was found.

Neutron scattering studies on the magnetic interaction in iron-based superconductor BaFe<sub>2</sub><sub>−</sub><sub><italic>x</italic></sub>Ni<sub><italic>x</italic></sub>As<sub>2</sub>

Iron-based superconductivity emerges from the suppression of the long-ranged antiferromagnetic order in the parent compounds. To solve the microscopic mechanism of the superconductivity, the key issue is fully understanding about the evolution of magnetic interaction and its relationship between superconductivity. Here, we take the electron-doped iron-based superconductor BaFe2- x Ni x As2 as atypical example, and summarize the neutron scattering results on the electronic phase diagram, magnetic ordered state, low-energy spin excitations and high-energy spin fluctuations, particularly for their systematic evolution versus electron dopings and the recent progress on the spin nematicity. Firstly, we will introduce about the crystal structure and magnetic structure, detailed procedure of the single crystal growth is also presented. By focusing on the structural transition temperature ( T s) and magnetic transition temperature ( T N) near the optimal doping level, we have found both T s and T N vanish above the superconducting transition temperature ( T c) as a first order manner, due to the lattice distortion and magnetically ordered moment decrease beyond the lower limit of the instrument resolution, giving an avoid quantum critical point at the optimal doping. In addition, the magnetic order becomes incommensurate and short-ranged magnetic cluster and competes with superconducting order, suggesting strong interplay between magnetism and superconductivity. Secondly, we will discuss about the itinerant magnetism and spin resonance mode at low energy for spin dynamics. The spin resonance mode in iron pnictides is explained as the collective quasiparticle excitations from the Fermi surface nesting between the hole pocket at the Γ point and electron pocket at the M point. This requires itinerant magnetism from the electrons near Fermi surfaces, which is further confirmed by neutron scattering by discovering the longitudinal mode and line shape change of low-energy spin excitations upon doping. Thirdly, we will present the doping evolution of spin fluctuations throughout the whole phase diagram. Although the spin waves in the parent compound can be described by an effective Heisenberg mode with anisotropic exchange coupling in FeAs plane, the damping features and unexpected low total fluctuation moments reveal both local moments and itinerant electrons contribute to the magnetism. Upon Ni doping, the high energy spin fluctuations is very robust, but the low energy spin excitations are suppressed quickly to zero when cross the boundary of the overdoped superconducting regime. The analysis on the change of the magnetic coupling energy associated with the superconducting transition gives evidence that the magnetic fluctuations are strong enough to drive the condensation of the Cooper pairs. Fourthly, we will further introduce the recent progress on the spin anisotropy by polarized neutron scattering experiments, and spin nematicity measured on detwinned samples. Anisotropic spin excitations at low energy are discovered by polarized neutron scattering, which is caused by the in-plane orbital ordering and persists away up to the tetragonal paramagnetic state. Further experiments on the detwinned sample under uniaxial pressure give direct evidence of the spin nematicity shown as breaking C4 rotation symmetry spin excitations in the tetragonal phase, similar to the anisotropic resistivity and electronic nematic phase discovered in other probes. Such novel electron state in these materials suggests the iron pnictides are unconventional. Finally, we summarize the results about the magnetic phase transition and spin dynamics and discuss its physical origin. Then a possible picture about the spin driven unconventional superconductivity in these materials is proposed. Further perspectives on the research of magnetism in iron-based superconductivity are also given.

Impact of Disorder on the Superconducting Phase Diagram in BaFe2(As1−xPx)2

In many classes of unconventional superconductors, the question of whether the superconductivity is enhanced by the quantum-critical fluctuations on the verge of an ordered phase remains elusive. One of the most direct ways of addressing this issue is to investigate how the superconducting dome traces a shift of the ordered phase. Here, we study how the phase diagram of the iron-based superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$ changes with disorder via electron irradiation, which keeps the carrier concentrations intact. With increasing disorder, we find that the magneto-structural transition is suppressed, indicating that the critical concentration is shifted to the lower side. Although the superconducting transition temperature $T_c$ is depressed at high concentrations ($x\gtrsim$0.28), it shows an initial increase at lower $x$. This implies that the superconducting dome tracks the shift of the antiferromagnetic phase, supporting the view of the crucial role played by quantum-critical fluctuations in enhancing superconductivity in this iron-based high-$T_c$ family.

Theoretical Study of Superconducting Gap Parameters, Density of States, and Condensation Energy of Two-Band Iron-Based Superconductor BaFe2(As1−x P x )2

This research work focuses on the theoretical study of superconducting gap parameters, density of states, and condensation energy of two-band iron-based superconductor BaFe2(As1−x P x )2. By developing a model Hamiltonian for the given system and by using the double time temperature-dependent Green’s function formalism, we obtained mathematical expressions for superconducting order parameters for the electron intra-band (Δe), hole intra-band (Δh), inter-band between the two bands (Δeh) and superconducting transition temperature (T C). Furthermore, we obtained the density of states for each intra-band, N(e) and condensation energy (E c) for BaFe2(As1−x P x )2. By using the experimental values and by considering some plausible approximations of the parameters in the obtained expressions, phase diagrams of superconducting order parameters for Δe, Δh, and Δeh versus temperature and superconducting transition temperature (T C) versus the inter-band pairing potential (V eh) are plotted. We also plotted the density of states for the electron intra-band, N e(e) and hole intra-band, N h(e) versus excitation energy (e) at T = 0K, and the variation of density of states with temperature. Similarly, phase diagrams of condensation energy (E c) versus temperature, inter-band pairing potential, and superconducting transition temperature are plotted for the material. Our results are in agreement with previous findings.

Enhanced critical-current in P-doped BaFe2As2 thin films on metal substrates arising from poorly aligned grain boundaries.

Thin films of the iron-based superconductor BaFe2(As1−xPx)2 (Ba122:P) were fabricated on polycrystalline metal-tape substrates with two kinds of in-plane grain boundary alignments (well aligned (4°) and poorly aligned (8°)) by pulsed laser deposition. The poorly aligned substrate is not applicable to cuprate-coated conductors because the in-plane alignment >4° results in exponential decay of the critical current density (Jc). The Ba122:P film exhibited higher Jc at 4 K when grown on the poorly aligned substrate than on the well-aligned substrate even though the crystallinity was poorer. It was revealed that the misorientation angles of the poorly aligned samples were less than 6°, which are less than the critical angle of an iron-based superconductor, cobalt-doped BaFe2As2 (~9°), and the observed strong pinning in the Ba122:P is attributed to the high-density grain boundaries with the misorientation angles smaller than the critical angle. This result reveals a distinct advantage over cuprate-coated conductors because well-aligned metal-tape substrates are not necessary for practical applications of the iron-based superconductors.

Nematic Quantum Critical Fluctuations in BaFe_{2-x}Ni_{x}As_{2}.

We have systematically studied the nematic fluctuations in the electron-doped iron-based superconductor BaFe_{2-x}Ni_{x}As_{2} by measuring the in-plane resistance change under uniaxial pressure. While the nematic quantum critical point can be identified through the measurements along the (110) direction, as studied previously, quantum and thermal critical fluctuations cannot be distinguished due to similar Curie-Weiss-like behaviors. Here we find that a sizable pressure-dependent resistivity along the (100) direction is present in all doping levels, which is against the simple picture of an Ising-type nematic model. The signal along the (100) direction becomes maximum at optimal doping, suggesting that it is associated with nematic quantum critical fluctuations. Our results indicate that thermal fluctuations from striped antiferromagnetic order dominate the underdoped regime along the (110) direction. We argue that either there is a strong coupling between the quantum critical fluctuations and the fermions, or more exotically, a higher symmetry may be present around optimal doping.

Anisotropy of the superconducting gap in the iron-based superconductor BaFe2(As(1-x)P(x))2.

We report peculiar momentum-dependent anisotropy in the superconducting gap observed by angle-resolved photoemission spectroscopy in BaFe2(As1-xPx)2 (x = 0.30, Tc = 30 K). Strongly anisotropic gap has been found only in the electron Fermi surface while the gap on the entire hole Fermi surfaces are nearly isotropic. These results are inconsistent with horizontal nodes but are consistent with modified s± gap with nodal loops. We have shown that the complicated gap modulation can be theoretically reproduced by considering both spin and orbital fluctuations.

Disorder, critical currents, and vortex pinning energies in isovalently substituted BaFe2(As1−xPx)2

We present a comprehensive overview of vortex pinning in single crystals of the isovalently substituted iron-based superconductor BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$, a material that qualifies as an archetypical clean superconductor, containing only sparse strong point-like pins [in the sense of C.J. van der Beek {\em et al.}, Phys. Rev. B {\bf 66}, 024523 (2002)]. Widely varying critical current values for nominally similar compositions show that flux pinning is of extrinsic origin. Vortex configurations, imaged using the Bitter decoration method, show less density fluctuations than those previously observed in charge-doped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ single crystals. Analysis reveals that the pinning force and -energy distributions depend on the P-content $x$. However, they are always much narrower than in Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$, a result that is attributed to the weaker temperature dependence of the superfluid density on approaching $T_{c}$ in BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$. Critical current density measurements and pinning force distributions independently yield a mean distance between effective pinning centers $\bar{\mathcal L} \sim 90$ nm, increasing with increasing P-content $x$. This evolution can be understood as being the consequence of the P-dependence of the London penetration depth. Further salient features are a wide vortex free "Meissner belt", observed at the edge of overdoped crystals, and characteristic chain-like vortex arrangements, observed at all levels of P-substitution.

Interplane resistivity of isovalent doped BaFe2(As1−xPx)2

Temperature-dependent interplane resistivity ${\ensuremath{\rho}}_{c}(T)$ was measured for the iron-based superconductor BaFe${}_{2}$(As${}_{1\ensuremath{-}x}$P${}_{x}$)${}_{2}$ over a broad isoelectron phosphorus substitution range from $x=0$ to $x=0.60$, from nonsuperconducting parent compound to heavily overdoped superconducting composition with ${T}_{c}\ensuremath{\approx}10\phantom{\rule{4.pt}{0ex}}\text{K}$. The features due to structural and magnetic transitions are clearly resolved in ${\ensuremath{\rho}}_{c}(T)$ of the underdoped crystals. A characteristic maximum in ${\ensuremath{\rho}}_{c}(T)$, found in the parent BaFe${}_{2}$As${}_{2}$ at around 200 K, moves rapidly with phosphorus substitution to high temperatures. At the optimal doping, the interplane resistivity shows $T$-linear temperature dependence without any crossover anomalies, similar to the previously reported in-plane resistivity. This observation is in stark contrast with dissimilar temperature dependencies found at optimal doping in electron-doped Ba(Fe${}_{1\ensuremath{-}x}$Co${}_{x}$)${}_{2}$As${}_{2}$. Our finding suggests that despite similar values of the resistivity and its anisotropy, the temperature-dependent transport in the normal state is very different in electron and isoelectron-doped compounds. Similar temperature dependence of both in-plane and interplane resistivities, in which the dominant contributions are coming from different parts of the Fermi surface, suggests that scattering is the same on the whole Fermi surface. Since magnetic fluctuations are expected to be much stronger on the quasinested sheets, this observation may point to the importance of the interorbital scattering between different sheets.

Nodal superconducting-gap structure in ferropnictide superconductor BaFe2(As0.7P0.3)2

The Cooper pairs of conventional superconductors exhibit a nodeless s-wave symmetry, and most unconventional superconductors, including cuprates and heavy-fermion materials, exhibit nodal d-wave pairing. In contrast to both, angle-resolved photoemission spectroscopy measurements indicate that the iron-based superconductor BaFe2(As0.7P0.3)2 exhibits an unusual nodal s-wave pairing. The superconducting-gap distribution is a pivotal characteristic for a superconductor. Whereas the cuprates and conventional phonon-mediated superconductors are characterized by distinct d-wave and s-wave pairing symmetries with nodal and nodeless gap distributions respectively, the superconducting-gap distributions in iron-based superconductors are rather diversified. Whereas nodeless gap distributions have been directly observed in Ba1−xKxFe2As2, BaFe2−xCoxAs2, KxFe2−ySe2 and FeTe1−xSex (refs 1, 2, 3, 4), the signatures of nodal superconducting gaps have been reported in LaOFeP, LiFeP, KFe2As2, BaFe2(As1−xPx)2, BaFe2−xRuxAs2 and FeSe (refs 5, 6, 7, 8, 9, 10, 11, 12). We here report the angle-resolved photoemission spectroscopy measurements on the superconducting-gap structure of BaFe2(As0.7P0.3)2, and in particular the direct observation of a circular line node on the largest hole Fermi surface around the Z point at the Brillouin zone boundary. Our findings rule out a d-wave-pairing origin for the nodal gap, and establish the existence of nodes in iron pnictides under the s-wave pairing symmetry.

S±-like spin resonance in the iron-based nodal superconductor BaFe2(As0.65P0.35)2observed using inelastic neutron scattering

We performed inelastic neutron scattering on a powder sample of iron-based superconductor BaFe${}_{2}$(As${}_{0.65}$P${}_{0.35}$)${}_{2}$ with ${T}_{c}=30$ K. Although this system is expected to have line nodes in its superconducting order parameter, we have observed spin resonance at the same scattering vector as that appearing in the ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave iron-based superconductors without line nodes. Moreover, the resonance enhancement, which can be a measure of the area of sign reversal between the hole and electron Fermi surfaces (FSs), is comparable to those without line nodes. These facts indicate that the sign reversal between the FSs is still dominant in this system, and the line nodes should create only a limited area of sign reversal on a single FS. Hence the system can hold higher ${T}_{c}$ than the other iron-based superconductors with nodal symmetry, such as LaFePO${}_{1\ensuremath{-}y}$ and KFe${}_{2}$As${}_{2}$ (${T}_{c}<10$ K). Comparison with theoretical calculation indicates horizontal line nodes may be a candidate for reproducing the observation.

Inelastic neutron scattering on iron-based superconductor BaFe2(As,P)2

Inelastic neutron scattering has been performed on powder sample of an iron-based superconductor BaFe2(As0.65P0.35)2 with superconducting transition temperature (Tc)=30K, whose superconducting (SC) order parameter is expected to have line node. In the normal state, constant-E scan of dynamical structure factor, S(Q,E), exhibits a peak structure centered at momentum transfer Q∼1.20Å−1, corresponding to antiferromagnetic wave vector. Below Tc, the redistribution of the magnetic spectral weight takes place, resulting in the formation of a peak at E∼12meV and a gap below 6meV. The enhanced magnetic peak structure is ascribed to the spin resonance mode, evidencing sign change in the SC order parameter similar to other iron-based high-Tc superconductors. It suggests that fully-gapped s± symmetry dominates in this superconductor, which gives rise to high-Tc (=30K) despite the nodal symmetry.

Theoretical Analysis for Inelastic Neutron Scattering on BaFe2(As1-xPx)2Using Realistic Three-Dimensional 10-Orbital Tight-Binding Model

We calculate spin susceptibility on the basis of the multi-orbital random-phase approximation with use of the realistic three-dimensional 10-orbital tight-binding model for an iron-based superconductor BaFe 2 (As 1- x P x ) 2 which seems to have gap-nodes. We show that the shape of nodes on the Fermi surface for BaFe 2 (As 1- x P x ) 2 is distinguishable by examining measurement data of inelastic neutron scattering experiments. Moreover, we propose that comparative study on the middle energy excitation can reveal whether nodes are located on the hole or electron Fermi surfaces.