We identify the possible ground states for a mixture of two superfluid condensates (one neutral, the other electrically charged) using a phenomenological Ginzburg-Landau model. While this framework is applicable to any interacting condensed-matter mixture of a charged and a neutral component, we focus on nuclear matter in neutron star cores, where proton and neutron condensates are coupled via non-dissipative entrainment. We employ the Skyrme interaction to determine the neutron star's equilibrium composition, and hence obtain realistic coefficients for our Ginzburg-Landau model at each depth within the star's core. We then use the Ginzburg-Landau model to determine the ground state in the presence of a magnetic field. In this way, we obtain superconducting phase diagrams for six representative Skyrme models, revealing the microphysical magnetic flux distribution throughout the neutron star core. The phase diagrams are rather complex and the locations of most of the phase transitions can only be determined through numerical calculations. Nonetheless, we find that for all equations of state considered in this work, much of the outer core exhibits type-1.5 superconductivity, rather than type-II superconductivity as is generally assumed. For local magnetic field strengths $\lesssim 10^{14} \, {\rm G}$, the magnetic flux is distributed inhomogeneously, with bundles of magnetic fluxtubes separated by flux-free Meissner regions. We provide an approximate criterion to determine the transition between this type-1.5 phase and the type-I region in the inner core.
The interior of a neutron star is likely to be predominantly a mixture of superfluid neutrons and superconducting protons. This results in the quantisation of the star's magnetic field into an array of thin fluxtubes, producing a macroscopic force very different from the Lorentz force of normal matter. We show that in an axisymmetric superconducting equilibrium the behaviour of a magnetic field is governed by a single differential equation. Solving this, we present the first self-consistent superconducting neutron star equilibria with poloidal and mixed poloidal-toroidal fields, also giving th…
Buoyancy of proton vortices is considered as one of the important mechanisms of magnetic field expulsion from the superconducting interiors of neutron stars. Here we show that the generally accepted expression for the buoyancy force is not correct and should be modified. The correct expression is derived for both neutron and proton vortices. It is argued that this force is already contained in the coarse-grained hydrodynamics of Bekarevich & Khalatnikov and its various multifluid extensions, but is absent in the hydrodynamics of Hall. Some potentially interesting buoyancy-related effects are b…
We have developed a superconducting phase gradiometer consisting of two parallel DNA-templated nanowires connecting two thin-film leads. We have ramped the cross current flowing perpendicular to the nanowires, and observed oscillations in the lead-to-lead resistance due to cross-current-induced phase differences. By using this gradiometer we have measured the temperature and magnetic field dependence of the superfluid density and observed an amplification of phase gradients caused by elastic vortex displacements. We examine our data in light of Miller-Bardeen theory of dirty superconductors an…
The differential cross section for the inelastic magnetic scattering of neutrons by superconducting rings is derived theoretically taking account of the interaction of the neutron magnetic moment with magnetic field created by the superconducting current. In this scattering process the neutron kinetic energy increases discretely and, respectively, the number of the magnetic flux quanta trapped in the ring, reduces. Quantitative calculations of the scattering cross section for cold neutrons is carried out for thin film rings from type-II superconductors with the film thickness $d<λ$($λ$ is the …
Inelastic neutron scattering provides a probe for studying the spin and momentum structure of the superconducting gap. Here, using a two-orbital model for the Fe-pnicitide superconductors and an RPA-BCS approximation for the dynamic spin susceptibility, we explore the scattering response for various gaps that have been proposed.
We use inelastic neutron scattering to show that superconductivity in electron-underdoped NaFe0.985Co0.015As induces a dispersive sharp resonance near Er1 = 3:25 meV and a broad dis- persionless mode at Er2 = 6 meV. However, similar measurements on overdoped superconducting NaFe0:955Co0:045As find only a single sharp resonance at Er = 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 indi…
Measurements of the superconducting transition temperatures for Al-doped, C-doped and neutron-damaged-annealed MgB2 samples under pressure up to ~8 kbar are presented. The dT_c/dP values change systematically with the decrease of the ambient pressure T_c in a regular fashion. The evolution of the pressure derivatives can be understood assuming that the change in phonon spectrum is a dominant contribution to dT_c/dP.
Starting from the generalized t-J-G model Hamiltonian, we analyze the spin response in the superconducting cuprates taking into account both local and itinerant spin components which are coupled to each other self-consistently. Derived expression reproduces the basic observations of neutron scattering data in YBa2Cu3O6+y compounds near the optimal doping level.
The inelastic magnetic scattering of neutrons from thin superconducting films irradiated with microwave radiations, is analyzed. This process is due to the interaction of the magnetic field generated by the neutron, with the oscillating current induced by the electromagnetic field penetrated into the film. In the Born approximation, the neutron energy can both increase and decrease by the energy quantum of the field. The scattering cross section, which increases with decreasing the field frequency, is derived, and its numerical calculations are carried out. Measurements of this cross section g…
Neutron spin-flip scattering observations of a resonance in the superconducting state is often taken as evidence of an unconventional superconducting state in which the gap changes sign $Δ(k+Q)=-Δ(k)$ for momentum transfers $Q$ which play an important role in the pairing. Recently questions regarding this identification for the Fe-pnictide superconductors have been raised and it has been suggested that $Δ(k+Q)=Δ(k)$. Here we propose that inelastic neutron or x-ray scattering measurements of the spectral weight of a phonon of momentum $Q$ can distinguish between these two pairing scenarios.
Effect of atomic disordering induced by irradiation with fast neutrons on the properties of the normal and superconducting states of polycrystalline samples FeSe has been studied. The irradiation with fast neutrons of fluencies up to 1.25\cdot10^20 cm^-2 at the irradiation temperature Tirr ~ 50 \degree C results in relatively small changes in the temperature of the superconducting transition T_c and electrical resistivity Rho_25. Such a behavior is considered to be traceable to rather low, with respect to that possible at a given irradiation temperature, concentration of radiation defects, whi…
In this letter we present the effect of neutron irradiation up to fluences of 3.9 1019 n/cm2 on the superconducting properties of MgB2. In order to obtain a disorder structure homogeneously distributed, the experiment was carried out on bulk samples prepared with the 11B isotope. Up to fluences of 1018 n/cm2 the critical temperature is slightly diminished (36 K) and the superconducting properties are significantly improved; the upper critical field is increased from 13.5 T to 20.3 T at 12 K and the irreversibility field is doubled at 5 K. For larger neutron fluences the critical temperature is…
Force on proton vortices in superfluid and superconducting matter of neutron stars is calculated at vanishing stellar temperature. Both longitudinal (dissipative) and transverse (Lorentz-type) components of the force are derived in a coherent way and compared in detail with the corresponding expressions available in the literature. This allows us to resolve a controversy about the form of the Lorentz-type force component acting on proton vortices. The calculated force is a key ingredient in magnetohydrodynamics of superconducting neutron stars and is important for modeling the evolution of ste…
Motivated by neutron scattering data, we develop a model of electrons interacting with a magnetic resonance and use it to analyze angle resolved photoemission (ARPES) and tunneling data in the superconducting state of Bi_2Sr_2CaCu_2O_{8+d}. We not only can explain the peak-dip-hump structure observed near the (pi,0) point, and its particle-hole asymmetry as seen in SIN tunneling spectra, but also its evolution throughout the Brillouin zone, including a velocity `kink' near the d-wave node.
We use polarized inelastic neutron scattering to show that the neutron spin resonance below $T_c$ in superconducting BaFe$_{1.9}$Ni$_{0.1}$As$_2$ ($T_c=20$ K) is purely magnetic in origin. Our analysis further reveals that the resonance peak near 7~meV only occurs for the planar response. This challenges the common perception that the spin resonance in the pnictides is an isotropic triplet excited state of the singlet Cooper pairs, as our results imply that only the $S_{001}=\pm1$ components of the triplet are involved.
The relativistic dynamic equations are derived for a superfluid-superconducting mixture coupled to the electromagnetic field. For definiteness, and bearing in mind possible applications of our results to neutron stars, it is assumed that the mixture is composed of superfluid neutrons, superconducting protons, and normal electrons. Proton superconductivity of both I and II types is analysed, and possible presence of neutron and proton vortices (or magnetic domains in the case of type-I proton superconductivity) is allowed for. The derived equations neglect all dissipative effects except for the…
We use polarized inelastic neutron scattering to study low-energy spin excitations and their spatial anisotropy in electron-overdoped superconducting BaFe$_{1.85}$Ni$_{0.15}$As$_{2}$ ($T_c=14$ K). In the normal state, the imaginary part of the dynamic susceptibility, $χ^{\prime\prime}(Q,ω)$, at the antiferromagnetic (AF) wave vector $Q=(0.5,0.5,1)$ increases linearly with energy for $E\le 13$ meV. Upon entering the superconducting state, a spin gap opens below $E\approx 3$ meV and a broad neutron spin resonance appears at $E\approx 7$ meV. Our careful neutron polarization analysis reveals that…
Recent neutron-scattering experiments on La(2-x)Sr(x)CuO4 single crystals by Wakimoto et al. have revealed that elastic magnetic peaks appear at low temperatures in both insulating (x=0.02-0.05) and superconducting (x=0.06) samples. We have carried out further investigations particularly on the elastic incommensurate peaks for x=0.06, and found that the integrated intensity drastically changes across the low temperature insulator- superconductor boundary; the intensity of x=0.06 is 4 times smaller than that of x=0.05, while the intensity in the insulating region stays constant.
Correlation in temperature behavior of the optical, neutron, and muon experimental data is established for YBa2Cu3O6+x in both the pseudogap state at Tc<T<T* and the superconducting state at T<Tc. We have showed that our absorption spectra measured in the vicinity of the optical gap are very sensitive to the development of antiferromagnetic fluctuations and to the formation of a stripe structure. The inelastic neutron scattering and zero-field muon spin relaxation data analyzed in this paper were taken from the measurements made by Dai et al. and Sonier et al., respectively. Comparative analys…
We have investigated the intermediate mixed state of a superconducting niobium sample by Very Small Angle Neutron Scattering.We show that this state is stabilized through a sequence where a regular vortex lattice appears, which then coexists with vortex clusters before vanishing at low temperature. Vortices in clusters have a constant periodicity regardless of the applied field, exhibit a temperature dependence close to the one of the penetration depth. The clusters disappear in the high temperature limit. All the results agree with an explanation in terms of vortex attraction due non local ef…
We use polarized inelastic neutron scattering (INS) to study spin excitations in superconducting NaFe0.985Co0.015As (C15) with static antiferromagnetic (AF) order along the a-axis of the orthorhombic structure and NaFe0.935Co0.045As (C45) without AF order. In previous unpolarized INS work, spin excitations in C15 were found to have a dispersive sharp resonance near Er1=3.25 meV and a broad dispersionless mode at Er2=6 meV. Our neutron polarization analysis reveals that the dispersive resonance in C15 is highly anisotropic and polarized along the a- and c-axis, while the dispersionless mode is …
The heavy fermion superconductor UPt$_3$ is thought to have odd-parity, a state for which the temperature dependence of the spin susceptibility is an important signature. In order to address conflicting reports from two different experiments, the NMR Knight shift and measurements of the anisotropy of the upper critical field, we have measured the bulk susceptibility in a high quality single crystal using polarized-neutron diffraction. A temperature independent susceptibility was observed for $H||a$ through the transitions between the normal state and the superconducting A-, B- and C-phases, co…
We develop an analytical tool to extract bulk electronic properties of unconventional superconductors through inelastic neutron scattering (INS) spectra. Since the spin excitation spectrum in the superconducting (SC) state originates from Bogoliubov quasiparticle scattering associated with Fermi surface nesting, its energy-momentum relation--the so called `hour-glass' feature--can be inverted to reveal the Fermi momentum dispersion of the single-particle spectrum as well as the corresponding SC gap function. The inversion procedure is analogous to the quasiparticle interference (QPI) effect in…
We observed in superconducting (Tl,Rb)2Fe4Se5 spin-wave branches that span an energy range from 6.5 to 209 meV. Spin dynamics are successfully described by a Heisenberg localized spin model whose dominant in-plane interactions include only the nearest (J1 and J1') and next nearest neighbor (J2 and J2') exchange terms within and between the tetramer spin blocks, respectively. These experimentally determined exchange constants would crucially constrain the theoretical viewpoints on magnetism and superconductivity in the Fe-based materials.
We have performed a systematic study of the evolution of the superconducting and normal state properties of neutron irradiated MgB$_2$ wire segments as a function of fluence and post exposure annealing temperature and time. All fluences used suppressed the transition temperature, Tc, below 5 K and expanded the unit cell. For each annealing temperature Tc recovers with annealing time and the upper critical field, Hc2(T=0), approximately scales with Tc. By judicious choice of fluence, annealing temperature and time, the Tc of damaged MgB2 can be tuned to virtually any value between 5 and 39 K. F…
The role of antiferromagnetic spin correlations in high-temperature superconductors remains a matter of debate. We present inelastic neutron scattering evidence that gapless spin fluctuations coexist with superconductivity in La$_{1.905}$Ba$_{0.095}$CuO$_4$. Furthermore, we observe that both the low-energy magnetic spectral weight and the spin incommensurability are enhanced by the onset of superconducting correlations. We propose that the coexistence occurs through intertwining of spatial modulations of the pair wave function and the antiferromagnetic correlations. This proposal is also direc…
Resistivity Rho(T), Hall coefficient RH(T), superconducting transition temperature Tc and slopes of the upper critical field dHc2/dT were studied in (Ba1-xKx)Fe2As2 (x = 0.218, 0.356, 0.531) single crystals irradiated with fast neutrons. It is found that dTc/dRhoSC - the rate of decreasing Tc as a function of the RhoSC (RHoSC is the resistivity at T = Tc) - linearly increases with concentration x. Slow changes in the Hall coefficient RH, as well as the quadratic electronic contribution to the resistivity, show that there are no substantial changes in the topology of the Fermi surface caused by…
Based on the slave-boson theory of the two-dimensional $t-t'-J$ model, we calculate the superconducting condensation energy for optimally doped and overdoped high $T_{c}$ cuprates at finite temperatures using a renormalized random phase approximation. The contributions come from the mean-field part and the antiferromagnetic spin fluctuations. In the presence of neutron resonance peak at $(π,π)$, the latter is shown to have similar temperature and doping dependences as the difference in antiferromagnetic (AF) exchange energy between the normal and the superconducting state. This difference has …
The spin dynamics of high temperature superconductors measured by inelastic neutron scattering is reviewed. The spin susceptibility evolves a lot with increasing doping from the undoped insulating state to the overdoped metallic state. In the superconducting state, a strong magnetic resonance peak occurs in the spin excitation spectrum whose energy is proportional to the superconducting temperature. In underdoped and optimally doped regimes, normal state antiferromagnetic fluctuations are observed, proving the existence of strong electronic correlations in cuprates. They are characterized by a…
We use transport and neutron scattering to study the electronic phase diagram and spin excitations of NaFe$_{1-x}$Cu$_x$As single crystals. Similar to Co- and Ni-doped NaFeAs, a bulk superconducting phase appears near $x\approx2\%$ with the suppression of stripe-type magnetic order in NaFeAs. Upon further increasing Cu concentration the system becomes insulating, culminating in an antiferromagnetically ordered insulating phase near $x\approx 50\%$. Using transport measurements, we demonstrate that the resistivity in NaFe$_{1-x}$Cu$_x$As exhibits non-Fermi-liquid behavior near $x\approx1.8\%$. …
We use inelastic neutron scattering with spin polarization analysis to study the magnetic excitations in the normal and superconducting states of YBa2Cu3O6.9. Polarization analysis allows us to determine the spin polarization of the magnetic excitations and to separate them from phonon scattering. In the normal state, we find unambiguous evidence of magnetic excitations over the 10-60meV range of the experiment with little polarization dependence to the excitations. In the superconducting state, the magnetic response is enhanced near the "resonance energy" and above. At lower energies, 10<E<30…
We use neutron powder diffraction to study on the non-superconducting phases of ThFeAsN$_{1-x}$O$_x$ with $x=0.15, 0.6$. In our previous results on the superconducting phase ThFeAsN with $T_c=$ 30 K, no magnetic transition is observed by cooling down to 6 K, and possible oxygen occupancy at the nitrogen site is shown in the refinement(H. C. Mao \emph{et al.}, EPL, 117, 57005 (2017)). Here, in the oxygen doped system ThFeAsN$_{1-x}$O$_x$, two superconducting region ($0\leqslant x \leqslant 0.1$ and $0.25\leqslant x \leqslant 0.55$) have been identified by transport experiments (B. Z. Li \emph{e…
We present a quantitative comparison of the magnetization measured by spin-polarized neutron reflectivity (SPNR) and DC magnetometry on a 1370 Å -thick Nb superconducting film. As a function of magnetic field applied in the film plane, SPNR exhibits reversible behavior whereas the DC magnetization shows substantial hysteresis. The difference between these measurements is attributed to a rotation of vortex magnetic field out of the film plane as the applied field is reduced. Since SPNR measures only the magnetization parallel to the film plane whereas DC magnetization is strongly influenced by …
Samples were examined using a superconducting (Nb) neutron imaging system employing a delay-line technique which in previous studies was shown to have high spatial resolution. We found excellent correspondence between neutron transmission and scanning electron microscope (SEM) images of Gd islands with sizes between 15 and 130 micrometer which were thermally-sprayed onto a Si substrate. Neutron transmission images could be used to identify tiny voids in a thermally-sprayed continuous Gd2O3 film on a Si substrate which could not be seen in SEM images. We also found that neutron transmission ima…
The existence of a neutron scattering resonance at a wavevector q* implies a sign change of the gap between two Fermi surface regions separated by wavevector q* . For the Fe pnictides, a resonance has been observed for a wavevector q* which connects a hole Fermi surface around the $Γ$ point with an electron Fermi surface around the X or Y points of the 1 Fe/unit cell Brillouin zone. Here we study the neutron scattering resonance for a five orbital model within an RPA-BCS approximation. Our results show that both sign-switched and extended s-wave gaps are consistent with the present data for q*…
Superconducting vortex lattices, glasses and liquids attract great interest as model systems of crystallization and as a source of microscopic information of the nature of superconductivity. We report for the first time direct microscopic measurements of the vortex lattice tilt modulus c44 in ultra-pure niobium using time-resolved small angle neutron scattering. Besides a general trend to faster vortex lattice dynamics for increasing temperatures we observe a dramatic changeover of the relaxation process associated with the non-trivial vortex lattice morphology in the intermediate mixed state.…
We have investigated the influence of Ca ions substitution on the structural and superconducting properties of (Nd1-xCax)(Ba1.6La0.4)Cu3Oz system. Magnetization, X-ray diffraction and neutron diffraction studies have been carried out on a series of compounds with x = 0.0 to 0.6. The superconducting transition temperature Tc, determined from magnetization measurements increases with increasing Ca2+ substitution. Neutron diffraction studies reveal that these compounds crystallize in a tetragonal structure (space group P4/mmm). A detailed analysis of the neutron diffraction data reveals that Ca a…
Neutron powder diffraction has been used to investigate the structural and magnetic behavior of the isoelectronically doped Fe pnictide material PrFe1-xRuxAsO. Substitution of Ru for Fe suppresses the structural and magnetic phase transitions that occur in the undoped compound PrFeAsO. Contrary to the behavior usually observed in 1111 pnictide materials, the suppression of both the structural and magnetic transitions does not result in the emergence of superconductivity or any other new ground state. Interestingly, PrFeAsO itself shows an unusual negative thermal expansion (NTE) along the c-ax…
Recent observations [A.~Pustogow et al. Nature 574, 72 (2019)] of a drop of the $^{17}$O nuclear magnetic resonance (NMR) Knight shift in the superconducting state of Sr$_2$RuO$_4$ challenged the popular picture of a chiral odd-parity paired state in this compound. Here we use polarized neutron scattering to show that there is a $34 \pm 6$ % drop in the magnetic susceptibility at the ruthenium site below the superconducting transition temperature. Measurements are made at lower fields $H \sim \tfrac{1}{3} H_{c2}$ than a previous study allowing the suppression to be observed. Our results are co…
The magnetic structure of superconducting Eu(Fe0.82Co0.18)2As2 is unambiguously determined by single-crystal neutron diffraction. A long-range ferromagnetic order of the Eu2+ moments along the c-direction is revealed below the magnetic phase transition temperature Tc = 17 K. In addition, the antiferromagnetism of the Fe2+ moments still survives and the tetragonal-to-orthorhombic structural phase transition is also observed, although the transition temperatures of the Fe-spin density wave (SDW) order and the structural phase transition are significantly suppressed to Tn = 70 K and Ts = 90 K, re…
We calculate the spin susceptibility in the s_{+-} and s_{++} superconducting states of the iron pnictides using the effective five orbital model and considering the quasiparticle damping. For the experimentally evaluated magnitude of the quasiparticle damping and the superconducting gap, the results at the wave vector ~ (pi,0) show that the s_{+-} state is more consistent with the neutron scattering experiments, while for larger quasiparticle damping and the superconducting gap, the s_{++} state can be more consistent. To distinguish between two cases that reproduce the experiments at the wav…
We use neutron scattering to study the electron-doped superconducting NaFe$_{0.985}$Co$_{0.015}$As ($T_c=14$ K), which has co-existing static antiferromagnetic (AF) order ($T_N=31$ K) and exhibits two neutron spin resonances ($E_{r1}\approx 3.5$ meV and $E_{r2}\approx 6$ meV) at the in-plane AF ordering wave vector ${\bf Q}_{\rm AF}={\bf Q}_{1}=(1,0)$ in reciprocal space. In the twinned state below the tetragonal-to-orthorhombic structural transition $T_s$, both resonance modes appear at ${\bf Q}_{1}$ but cannot be distinguished from ${\bf Q}_{2}=(0,1)$. By detwinning the single crystal with u…
We use polarized inelastic neutron scattering (INS) to study spin excitations of optimally hole-doped superconductor Ba$_{0.67}$K$_{0.33}$Fe$_2$As$_{2}$ ($T_c=38$ K). In the normal state, the imaginary part of the dynamic susceptibility, $χ^{\prime\prime}(Q,ω)$, shows magnetic anisotropy for energies below $\sim$7 meV with c-axis polarized spin excitations larger than that of the in-plane component. Upon entering into the superconducting state, previous unpolarized INS experiments have shown that spin gaps at $\sim$5 and 0.75 meV open at wave vectors $Q=(0.5,0.5,0)$ and $(0.5,0.5,1)$, respecti…
We report neutron scattering measurements of spin density wave order within the superconducting state of a single crystal of predominately stage-4 La2CuO4+y with a Tc(onset) of 42 K. The low temperature elastic magnetic scattering is incommensurate with the lattice and is characterized by long-range order in the copper-oxide plane with the spin direction identical to that in the insulator. Between neighboring planes, the spins exhibit short-range correlations with a stacking arrangement reminiscent of that in the undoped antiferromagnetic insulator. The elastic magnetic peak intensity appears …
Motivated by predictions of a substantial contribution of the "buckling" vibration of the CuO2 layers to d-wave superconductivity in the cuprates, we have performed an inelastic neutron scattering study of this phonon in an array of untwinned crystals of YBa2Cu3O7. The data reveal a pronounced softening of the phonon at the in-plane wave vector q = (0, 0.3) upon cooling below ~ 105 K, but no corresponding anomaly at q = (0.3, 0). Based on the observed in-plane anisotropy, we argue that the electron-phonon interaction responsible for this anomaly supports an electronic instability associated wi…
We present studies of the magnetic field distribution around the vortices in LuNi2B2C. Small-angle neutron scattering measurements of the vortex lattice (VL) in this material were extended to unprecedentedly large values of the scattering vector q, obtained both by using high magnetic fields to decrease the VL spacing and by using higher order reflections. A square VL, oriented with the nearest neighbor direction along the crystalline [110] direction, was observed up to the highest measured field. The first-order VL form factor, |F(q10)|, was found to decrease exponentially with increasing mag…
Using the transport and magnetization measurements the influence of neutron irradiation at a fluence of 5x10$^{17}$ n cm$^{-2}$ on (B0.65C0.35)Ba1.4Sr0.6Ca2Cu3Oz has been investigated. The neutron irradiation was found to decrease critical temperature and transport critical current density, increase the residual and normal state resistivity, and improve the intragranular critical current density with 1.6x10$^{57}$ A/cm$^{2}$ (at 77.3K and in the applied field up to 160 kA m) and ΔMirr/ΔMnonirr ratio (up to factor of 3) at highest field used for investigation. The field dependence of this ratio…
The so-called neutron spin resonance consists of a prominent enhancement of the magnetic response at a particular energy and momentum transfer upon entering the superconducting state of unconventional superconductors. In the case of iron-based superconductors, the neutron resonance has been extensively studied experimentally, and a peculiar spin-space anisotropy has been identified by polarized inelastic neutron scattering experiments. Here we perform a theoretical study of the energy- and spin-resolved magnetic susceptibility in the superconducting state with $ s_{+-} $-wave order parameter, …
We have performed inelastic neutron scattering measurements on a powder sample of the superconductor lithium iron selenide hydroxide Li$_{1-x}$Fe$_{x}$ODFe$_{1-y}$Se ($x \simeq 0.16, y \simeq 0.02$, $T_{\rm c} = 41$\,K). The spectrum shows an enhanced intensity below $T_{\rm c}$ over an energy range $0.64\times2Δ< E < 2Δ$, where $Δ$ is the superconducting gap, with maxima at the wave vectors $Q_1 \simeq 1.46$\,Å$^{-1}$ and $Q_2 \simeq 1.97$\,Å$^{-1}$. The behavior of this feature is consistent with the spin resonance mode found in other unconventional superconductors, and strongly resembles th…
We have performed Raman-scattering measurements on high-quality single crystals of A$_{0.8}$Fe$_{1.6}$Se$_2$ superconductors of several compositions. We find a broad, asymmetric peak around 1600 cm$^{-1}$ (200 meV), which we identify as a two-magnon process involving optical magnons. The intensity of the two-magnon peak falls sharply on entering the superconducting phase. This effect, which is entirely absent in the non-superconducting system KFe$_{1.5}$Se$_2$, requires a strong mutual exclusion between antiferromagnetism and superconductivity arising from proximity effects within regions of m…
We use inelastic neutron scattering to study energy and wave vector dependence of the superconductivity-induced resonance in hole-doped Ba$_{0.67}$K$_{0.33}$(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ ($x=0,0.08$ with $T_c\approx 37, 28$ K, respectively). In previous work on electron-doped Ba(Fe$_{0.963}$Ni$_{0.037}$)$_2$As$_2$ ($T_N=26$ K and $T_c=17$ K), the resonance is found to peak sharply at the antiferromagnetic (AF) ordering wave vector ${\bf Q}_{\rm AF}$ along the longitudinal direction, but disperses upwards away from ${\bf Q}_{\rm AF}$ along the transverse direction. For hole doped $x=0, 0.0…
Recently, Onari and Kontani submitted a paper [arXiv:1105.6233] which criticizes our recent theoretical study [arXiv:1103.0586] on the neutron scattering experiment as a probe for determining the superconducting gap in the iron pnictides. In their paper, Onari and Kontani have developed a formalism in which the imaginary part of the dynamical spin susceptibility (Im$χ_s(\Vec{q},ω)$) in the superconducting state can be more accurately calculated especially in the $ω<2Δ$ regime, where $Δ$ is the superconducting gap. In section IIIC of their paper, they mention that the conclusions of our paper a…
We review the explanation for resonant neutron scattering experiments in $YBa_2Cu_3O_{6+δ}$ and $Bi_2 Sr_2 Ca_2 O_{8+δ}$ materials from the point of view of triplet excitation in the particle-particle channel, the pi excitation. Relation of these resonances to the superconducting condensation energy and their role in stabilizing the superconducting state is discussed. Due to the superconducting fluctuations, the pi resonance may appear as a broad peak above Tc. Analogue problem to the pi excitation for the case of s-wave pairing, the eta excitation, is considered in the strong coupling limit w…
We present local structural evidence supporting the presence of charge inhomogeneities in the CuO2 planes of underdoped La2-xSrxCuO4. High-resolution atomic pair distribution functions have been obtained from neutron powder diffraction data over the range of doping 0 < x < 0.30 at 10 K. Despite the average structure getting less orthorhombic we see a broadening of the in-plane Cu-O bond distribution as a function of doping up to optimal doping. Thereafter the peak abruptly sharpens. Complementary evidence is also evident from the observation of octahedral tilt disorder in the PDF at higher ato…
We present a phenomenological calculation of the quasiparticle-interference (QPI) pattern and inelastic Neutron scattering (INS) spectra in iron-pnictide and layered iron-selenide compounds by using materials specific band-structure and superconducting (SC) gap properties. As both the QPI and the INS spectra arise due to scattering of the Bogolyubov quasiaprticles, they exibit an one-to-one correspondence of the scattering vectors and the energy scales. We show that these two spectroscopies complement each other in such a way that a comparative study allows one to extract the quantitative and …
