Spin Density Wave Gap Research Articles

Superconducting gap and critical behavior in the Iron-Pnictides

In the phase diagram of iron pnictides, superconductivity arises at the border of antiferromagnetism, which raises the question of the role of symmetry of the gap and quantum criticality. Although more than 15-years of extensive research, the microscopic origin of the pairing symmetry inside the superconducting (SC) dome and its link to quantum criticality still remains elusive. Here, we report two new findings on BaFe2−xNixAs2: (1) A sharp peak in the x-dependence of the lower and upper critical fields, the SC critical current density Jc, the size of the jump in the specific heat ΔCel/T and the Sommerfeld coefficient (γ) at the optimum composition x = 0.10, where the SC transition temperature Tc reaches a maximum. Our obtained reliable values as a function of doping of the normal-state Sommerfeld coefficient increase with doping, illustrating the strong competition between magnetism and superconductivity and attributed to closing of spin density wave gap with Ni doping. (2) We show that doping induced a sudden change of the gap structure from nodeless to nodal. Our results imply that the superconductivity in BaFe2−xNixAs2 is closely linked to the quantum criticality and is characterized by a complex order parameter.

Theoretical Model Study of Low-Energy Spin Excitations in Iron Chalcogenide AxFe2−xSe2: One Band Approach

In this paper, we propose a one band tight binding model Hamiltonian for the newly discovered 122-type Selenide family of the iron-based system incorporated with the nearest-neighbor (NN) and the next-nearest-neighbor (NNN) hopping integrals [Formula: see text] and [Formula: see text], respectively. The spin–spin interactions of the electrons leading to the antiferromagnetic spin density wave (SDW) order have been studied at wave vector [Formula: see text]. The electron Green’s functions are calculated from the Hamiltonian model using Green’s function technique and finally the SDW gap equation is derived and studied using their NN and NNN spin coupling [Formula: see text] and [Formula: see text], respectively.

Isostructural Spin-Density-Wave and Superconducting Gap Anisotropies in Iron-Arsenide Superconductors.

When passing through a phase transition, electronic system saves energy by opening energy gaps at the Fermi level. Delineating the energy gap anisotropy provides insights into the origin of the interactions that drive the phase transition. Here, we report the angle-resolved photoemission spectroscopy (ARPES) study on the detailed gap anisotropies in both the tetragonal magnetic and superconducting phases in Sr_{1-x}Na_{x}Fe_{2}As_{2}. First, we found that the spin-density-wave (SDW) gap is strongly anisotropic in the tetragonal magnetic phase. The gap magnitude correlates with the orbital character of Fermi surface closely. Second, we found that the SDW gap anisotropy is isostructural to the superconducting gap anisotropy regarding to the angular dependence, gap minima locations, and relative gap magnitudes. Our results indicate that the superconducting pairing interaction and magnetic interaction share the same origin. The intraorbital scattering plays an important role in constructing these interactions resulting in the orbital-selective magnetism and superconductivity in iron-based superconductors.

Switching dynamics of the spin density wave in superconducting CeCoIn5

The ordering wave vector $\mathbf{Q}$ of a spin density wave (SDW), stabilized within the superconducting state of $\mathrm{CeCoIn_5}$ in a high magnetic field, has been shown to be hypersensitive to the direction of the field. $\mathbf{Q}$ can be switched from a nodal direction of the $d$-wave superconducting order parameter to a perpendicular node by rotating the in-plane magnetic field through the antinodal direction within a fraction of a degree. Here, we address the dynamics of the switching of $\mathbf{Q}$. We use a free energy functional based on the magnetization density, which describes the condensation of magnetic fluctuations of nodal quasiparticles, and show that the switching process includes closing of the SDW gap at one $\mathbf{Q}$ and then reopening the SDW gap at another $\mathbf{Q}$ perpendicular to the first one. The magnetic field couples to $\mathbf{Q}$ through the spin-orbit interaction. Our calculations show that the width of the hysteretic region of switching depends linearly on the deviation of magnetic field from the critical field associated with the SDW transition, consistent with our thermal conductivity measurements. The agreement between theory and experiment supports our scenario of the hypersensitivity of the $Q$ phase on the direction of magnetic field, as well as the magnon condensation as the origin of the SDW phase in $\mathrm{CeCoIn_5}$.

Quasiparticle scattering interference in iron pnictides: A probe of the origin of nematicity

In this paper, we investigate the quasiparticle scattering interference(QPI) in the nematic phase of iron pnictides, based on the magnetic and orbital scenarios of nematicity, respectively. In the spin density wave(SDW) state, the QPI pattern exhibits a dimer structure in the energy region of the SDW gap, with its orientation along the ferromagnetic direction of the SDW order. When the energy is increased to be near the Fermi level, it exhibits two sets of dimers along the same direction. The dimer structure of the QPI patterns persists with the decrease of the SDW correlation length in the magnetic driven nematic phase, although it tends to merge together for the scattering patterns with energies close to the Fermi level. While in the orbital scenario, the QPI patterns exhibit a dimer structure in a wide energy region. It undergoes a {\pi}/2 rotation with the increasing of energy, which is associated with the inequivalent energies of the two Dirac nodes induced by the orbital order. These distinct features may be used to probe or distinguish two kinds of scenarios of the nemeticity.

Weakening of the spin density wave gap at low temperatures in single crystals

AbstractWe report on temperature dependent scanning tunneling microscopy and spectroscopy studies of undoped SrFeAs single crystals from 6 to 292 K. Resistivity data show spin density wave (SDW) transition at 205 K and the superconducting transition at 21 K while magnetic susceptibility does not show any superconductivity. Tunnel spectra correlate well with the SDW transition with a depression in the density of states near the Fermi energy below . On further lowering the temperature, the width of this partial energy gap associated with the SDW decreases. Using the anti‐correlation of superconducting phase with SDW, we interpret this gap weakening as a precursor to superconductivity. This may give rise to a facile nucleation of superconductivity near defects.

Thermodynamic Properties of Superconductor with Competing Spin-Density Wave and Charge-Density Wave

The mean field Hamiltonian describing the coexistence of the spin-density wave (SDW) and charge-density wave (CDW) for high- Tc superconductor in the underdoped region before the onset of the superconductivity was studied. From self-consistent equations for SDW and CDW gaps derived from Green’s function method, the theromodynamic properties of the superconductor were derived. Our results show the competition between the SDW and CDW state on thermodynamic properties of superconductor that deviate gap-to- Tc ratio, critical temperature, and the specific heat jump from the BCS universal value.

Electronic inhomogeneities in the superconducting phase of CaFe1.96Ni0.04As2 single crystals

Superconductivity in CaFe2−xNixAs2 emerges in close proximity to an antiferromagnetic (AFM) ordered parent state and the AFM phase overlaps with superconducting (SC) phase for a small range of x-values. We present scanning tunneling microscopy and spectroscopy study of an underdoped CaFe2−xNixAs2 single crystal in the vicinity of the boundary of the two phases. Both resistivity and magnetic susceptibility measurements show a superconducting TC of 15K and from later we deduce a superconducting fraction of 1.2%. Topographic images show reasonably flat surface with signatures of atomic resolution. Spectra between 120K and 20K are spatially homogeneous and show signatures of spin density wave (SDW) gap. Below TC, spectra show significant spatial inhomogeneity with a depression in density of states in±5meV energy range. Inhomogeneity reduces significantly as the temperature goes above TC and disappears completely far above TC. These observations are discussed in terms of an inhomogeneous electronic phase that may exist due to the vicinity of this composition to the SC dome boundary on the underdoped side of the phase diagram.

Crossover from spin waves to diffusive spin excitations in underdoped Ba(Fe1−xCox)2As2

Using inelastic neutron scattering, we show that the onset of superconductivity in underdoped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ coincides with a crossover from well-defined spin waves to overdamped and diffusive spin excitations. This crossover occurs despite the presence of long-range stripe antiferromagnetic order for samples in a compositional range from x=0.04-0.055, and is a consequence of the shrinking spin-density wave gap and a corresponding increase in the particle-hole (Landau) damping. The latter effect is captured by a simple itinerant model relating Co doping to changes in the hot spots of the Fermi surface. We argue that the overdamped spin fluctuations provide a pairing mechanism for superconductivity in these materials.

Dynamic competition between spin-density wave order and superconductivity in underdoped Ba(1-x)K(x)Fe2As2.

An intriguing aspect of unconventional superconductivity is that it always appears in the vicinity of other competing phases, whose suppression brings the full emergence of superconductivity. In the iron pnictides, these competing phases are marked by a tetragonal-to-orthorhombic structural transition and a collinear spin-density wave (SDW) transition. There has been macroscopic evidence for competition between these phases and superconductivity as the magnitude of both the orthorhombicity and magnetic moment are suppressed in the superconducting state. Here, using angle-resolved photoemission spectroscopy on detwinned underdoped Ba(1-x)K(x)Fe2As2, we observe a coexistence of both the SDW gap and superconducting gap in the same electronic structure. Furthermore, our data reveal that following the onset of superconductivity, the SDW gap decreases in magnitude and shifts in a direction consistent with a reduction of the orbital anisotropy. This observation provides direct spectroscopic evidence for the dynamic competition between superconductivity and both SDW and electronic nematic orders in these materials.

Temperature-induced change in the Fermi surface topology in the spin density wave phase of Sr(Fe1−xCox)2As2

We report electronic Raman scattering measurements of Sr(Fe$_{1-x}$Co$_x$)$_2$As$_2$ single crystals in their magnetic - Spin Density Wave (SDW) phase. The spectra display multiple, polarization-resolved SDW gaps as expected in a band-folding itinerant picture for a multiband system. The temperature dependence of the SDW gaps reveals an unusual evolution of the reconstructed electronic structure with at least one gap being activated only well below the magnetic SDW transition $T_N$. A comparison with temperature dependent Hall measurements allows us to assign this activated behavior to a change in the Fermi surface topology deep in the SDW phase, which we attribute to the disappearance of a hole-like Fermi pocket. Our results highlight the strong sensitivity of the low energy electronic structure to temperature in iron-arsenide superconductors.

Unification of the pressure and composition dependence of superconductivity in Ru substituted BaFe2As2

Temperature dependent high pressure electrical resistivity studies have been carried out on Ba(Fe1−x Rux)2As2 single crystals with x=0.12, 0.26 and 0.35, which correspond to under-doped, optimally doped and over-doped composition regimes, respectively. The evolution of structural/magnetic (TS–M) and superconducting transition (Tc) temperatures, with pressure for various compositions has been obtained. The normal state resistivity has been analyzed in terms of a model that incorporates both spin fluctuations and the opening of the gap in the spin density wave (SDW) phase. It is shown that Tc scales with the strength of the spin fluctuation, B, and TS–M scales with the SDW gap parameter, Δ. This provides a prescription for the unification of the composition and pressure induced superconductivity in BaFe2As2.

Ultrafast quasiparticle dynamics in spin-density-wave LaOFeAs single crystal

Ultrafast quasiparticle dynamics of single. crystalline LaOFeAs were investigated by pump-probe measurement. The compound experiences structural and spin-density-wave (SDW) phase transitions at 150 K (T-S1) and 130 K (T-S2), respectively. The relaxation time of quasiparticles was somewhat temperature independent at high temperature but exhibited a sharp upturn at T-S1 and reached the maximum at approximately T-S2. The remarkable slowing down of quasiparticle relaxation time is caused by the formation of energy gap. By employing the Rothwarf-Taylor model analysis, we found that there should be already energy gaps opening just below the structural transition. The magnitude of SDW gap was identified to be 72 meV.

A temperature dependent tunneling study of the spin density wave gap in EuFe2As2 single crystals

We report temperature dependent scanning tunneling microscopy and spectroscopy measurements on single crystals of EuFe2As2 in the 15–292 K temperature range. The in situ cleaved crystals show atomic terraces with homogeneous tunnel spectra that correlate well with the spin density wave (SDW) transition at a temperature, TSDW ≈ 186 K. Above TSDW the local tunnel spectra show a small depression in the density of states (DOS) near the Fermi energy (EF). The gap becomes more pronounced upon entering the SDW state with a gap value ∼90 meV at 15 K. However, the zero bias conductance remains finite down to 15 K indicating a finite DOS at the EF in the SDW phase. Furthermore, no noticeable change is observed in the DOS at the antiferromagnetic ordering transition of Eu2+ moments at 19 K.

Pressure Suppression of Spin-Density-Wave Gap in the Optical Conductivity of SrFe2As2

Optical reflectance R(w) of a pressure-induced superconductor SrFe2As2 has been measured under external pressure to 6 GPa and at temperatures to 8 K. Optical conductivity s(w) has been derived from the measured R(w). At ambient pressure, in the antiferromagnetic state below T_N=198 K, a pronounced feature develops in s(w) due to the opening of a spin density wave (SDW) gap, as already reported in the literature. With increasing pressure, the SDW gap feature in s(w) is progressively suppressed. At 4 GPa, where the sample is superconducting, the SDW gap feature in s(w) is strongly reduced than that at ambient pressure, but is still clearly observed. At 6 GPa, the SDW gap is completely suppressed. The pressure evolutions of the SDW gap magnitude and the spectral weight closely follow the pressure evolution of T_N.

Visualizing the microscopic coexistence of spin density wave and superconductivity in underdoped NaFe1−xCoxAs

Although the origin of high temperature superconductivity in the iron pnictides is still under debate, it is widely believed that magnetic interactions or fluctuations have a crucial role in triggering Cooper pairing. A key issue regarding the iron pnictide phase diagram is whether long-range magnetic order can coexist with superconductivity microscopically. Here we use scanning tunnelling microscopy to investigate the local electronic structure of underdoped NaFe1-xCoxAs near the spin density wave and superconducting phase boundary. Spatially resolved spectroscopy directly reveals both the spin density wave and superconducting gaps at the same atomic location, providing compelling evidence for the microscopic coexistence of the two phases. The strengths of the two orders are shown to anti-correlate with each other, indicating the competition between them. This work implies that Cooper pairing in the iron pnictides can occur when portions of the Fermi surface are already gapped by the spin density wave order.

Band filling and correlation controlling electronic properties and magnetism in KxFe2−ySe2: a slave boson study

We investigate the electronic and magnetic properties of KxFe2−ySe2 materials at different band fillings utilizing the multi-orbital Kotliar–Ruckenstein slave boson mean-field approach. We find that the ground state of KFe2Se2 is a paramagnetic (PM) bad metal with intermediate correlation, in contrast with the previous antiferromagnetic (AFM) results obtained by the local density approximation. Our PM metallic ground state suggests that KFe2Se2 is the parent phase of superconducting KxFe2−ySe2, supporting a recent scanning tunneling spectroscopy experiment. For pure Fe2+-based systems, the ground state is a striped AFM (SAFM) metal with a spin density wave gap partially opened near the Fermi level. In comparison, for Fe3+-based compounds, besides SAFM, a Néel AFM metal without orbital ordering is observed, and an orbital selective Mott phase (OSMP) accompanied by an intermediate-spin to high-spin transition is also found, giving a possible scenario of an OSMP in KxFe2−ySe2. These results demonstrate that the band filling and correlation control the Fermi surface topology, electronic state and magnetism in KxFe2−ySe2.

Selective Raman Scattering Detection of the Dirac Node and the Anti-node of the Spin Density Wave Gap and Magnetic Excitations in BaFe2As2

The electronic and magnetic excitations at the spin density wave (SDW) transition are investigated by Raman scattering. The multi-orbital electronic states induce the Dirac nodes in the SDW gap. The excitations near the nodes and anti-nodes are separately detected in accordance with the two-orbital tight-binding model. The exchange interactions are found to be given by the second derivative of the total energy with respect to the angle of the moment from two-magnon scattering. The two-magnon peak has the large spectral weight above twice the maximum energy of magnon. It is interpreted by the magnetic self-energy of the electron spectral function in the localized spin model or particle-hole excitations in the itinerant spin model.

Transient Spin Density Wave Order Induced in the Normal State of BaFe2As2by Coherent Lattice Oscillations

We trace the ultrafast dynamics of the spin density wave gap of the pnictide system BaFe2As2 probing resonantly with broadband multi-terahertz pulses. The photoexcitation in the low-temperature ground state leads to a fast suppression of the spin order followed by a slower recovery process. Surprisingly, in the normal state, we observe periodic oscillations of the spin density wave feature at a frequency as high as 5.5 THz. Our results indicate a transient development of a macroscopic order driven by a coherent lattice oscillation and attest to a pronounced spin–phonon coupling in pnictides.

Evolution from Unconventional Spin Density Wave to Superconductivity and a Pseudogaplike Phase inNaFe1−xCoxAs

We report the doping, temperature, and spatial evolutions of the electronic structure of NaFe(1-x)Co(x)As studied by scanning tunneling microscopy. In the parent state we directly observe the spin density wave gap, which exhibits unconventional features that are incompatible with simple Fermi surface nesting. The optimally doped sample has a single superconducting gap, but in the overdoped regime a novel pseudogaplike feature emerges. The pseudogaplike phase coexists with superconductivity in the ground state, persists well into the normal state, and shows strong spatial variations. The characteristics of the three distinct electronic states revealed here shed important new lights on the microscopic models for the iron-based superconductors.