Strong-Coupling Superconductivity in NaFe$_{1-x}$Co$_x$As: the Eliashberg Theory and Beyond

We study the normal-state and superconducting properties of NaFe$_{1-x}$Co$_x$As system by specific heat measurements. Both the normal-state Sommerfeld coefficient and superconducting condensation energy are strongly suppressed in the underdoped and heavily overdoped samples. The low-temperature electronic specific heat can be well fitted by either an one-gap or a two-gap BCS-type function for all the superconducting samples. The ratio $gamma_NT_c^2/H_c^2(0)$ can nicely associate the neutron spin resonance as the bosons in the standard Eliashberg model. However, the value of $Delta C/T_cgamma_N$ near optimal doping is larger than the maximum value the model can obtain. Our results suggest that the high-$T_c$ superconductivity in the Fe-based superconductors may be understood within the framework of boson-exchange mechanism but significant modification may be needed to account for the finite-temperature properties.

In-plane magnetic field effect on the neutron spin resonance in optimally doped FeSe$_{0.4}$Te$_{0.6}$ and BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ superconductors

We use inelastic neutron scattering to study the effect of an in-plane magnetic field on the magnetic resonance in optimally doped superconductors FeSe$_{0.4}$Te$_{0.6}$ ($T_c=14$ K) and BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ ($T_c=20$ K). While the magnetic field up to 14.5 Tesla does not change the energy of the resonance, it particially suppresses $T_c$ and the corresponding superconductivity-induced intensity gain of the mode. However, we find no direct evidence for the field-induced spin-1 Zeeman splitting of the resonance. Therefore, it is still unclear if the resonance is the long-sought singlet-triplet excitation directly coupled to the superconducting electron Cooper pairs.

Normal-State Hourglass Dispersion of the Spin Excitations in FeSe$_{x}$Te$_{1-x}$

We use cold neutron spectroscopy to study the low-energy spin excitations of superconducting (SC) FeSe$_{0.4}$Te$_{0.6}$ and essentially non-superconducting (NSC) FeSe$_{0.45}$Te$_{0.55}$. In contrast to BaFe$_{2-x}$(Co,Ni)$_{x}$As$_2$, where the low-energy spin excitations are commensurate both in the SC and normal state, the normal-state spin excitations in SC FeSe$_{0.4}$Te$_{0.6}$ are incommensurate and show an hourglass dispersion near the resonance energy. Since similar hourglass dispersion is also found in the NSC FeSe$_{0.45}$Te$_{0.55}$, we argue that the observed incommensurate spin excitations in FeSe$_{1-x}$Te$_{x}$ are not directly associated with superconductivity. Instead, the results can be understood within a picture of Fermi surface nesting assuming extremely low Fermi velocities and spin-orbital coupling.

Spin gap and magnetic resonance in superconducting BaFe$_{1.9}$Ni$%_{0.1}$As$_{2}$

We use neutron spectroscopy to determine the nature of the magnetic excitations in superconducting BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ ($T_{c}=20$ K). Above $T_{c}$ the excitations are gapless and centered at the commensurate antiferromagnetic wave vector of the parent compound, while the intensity exhibits a sinusoidal modulation along the c-axis. As the superconducting state is entered a spin gap gradually opens, whose magnitude tracks the $T$-dependence of the superconducting gap observed by angle resolved photoemission. Both the spin gap and magnetic resonance energies are temperature textit{and} wave vector dependent, but their ratio is the same within uncertainties. These results suggest that the spin resonance is a singlet-triplet excitation related to electron pairing and superconductivity.

First-order magnetic and structural phase transitions in Fe$_{1+y}$Se$_x$Te$_{1-x}$

We use bulk magnetic susceptibility, electronic specific heat, and neutron scattering to study structural and magnetic phase transitions in Fe$_{1+y}$Se% $_x$Te$_{1-x}$. Fe$_{1.068}$Te exhibits a first order phase transition near 67 K with a tetragonal to monoclinic structural transition and simultaneously develops a collinear antiferromagnetic (AF) order responsible for the entropy change across the transition. Systematic studies of FeSe$%_{1-x}$Te$_x$ system reveal that the AF structure and lattice distortion in these materials are different from those of FeAs-based pnictides. These results call into question the conclusions of present density functional calculations, where FeSe$_{1-x}$Te$_x$ and FeAs-based pnictides are expected to have similar Fermi surfaces and therefore the same spin-density-wave AF order.

Low energy spin waves and magnetic interactions in SrFe$_2$As$_2$

We report inelastic neutron scattering studies of magnetic excitations in antiferromagnetically ordered SrFe$_{2}$As$_{2}$ ($T_{N}=220$ K), the parent compound of the FeAs-based superconductors. At low temperatures (T=7 K), the spectrum of magnetic excitations $S(Q,hbar omega)$ consists of a Bragg peak at the elastic position ($hbar omega =0$ meV), a spin gap ($ Delta leq 6.5$ meV), and sharp spin wave excitations at higher energies. Based on the observed dispersion relation, we estimate the effective magnetic exchange coupling using a Heisenberg model. On warming across $T_{N} $, the low temperature spin gap rapidly closes, with weak critical scattering and spin-spin correlations in the paramagnetic state. The antiferromagnetic order in SrFe$_{2}$As$_{2}$ is therefore consistent with a first order phase transition, similar to the structural lattice distortion.

Destruction of Neel order and appearance of superconductivity in electron-doped cuprates by oxygen annealing process

We use thermodynamic and neutron scattering measurements to study the effect of oxygen annealing on the superconductivity and magnetism in Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-delta}$. Although the transition temperature $T_c$ measured by susceptibility and superconducting coherence length increase smoothly with gradual oxygen removal from the annealing process, bulk superconductivity, marked by a specific heat anomaly at $T_c$ and the presence of a neutron magnetic resonance, only appears abruptly when $T_c$ is close to the largest value. These results suggest that the effect of oxygen annealing must be first determined in order to establish a Ce-doping dependence of antiferromagnetism and superconductivity phase diagram for electron-doped copper oxides.

Quantum Spin Excitations through the metal-to-insulator crossover in $Y Ba_2 Cu_3 O_{6+y}$

We use inelastic neutron scattering to study the temperature dependence of the spin excitations of a detwinned superconducting YBa$_2$Cu$_3$O$_{6.45}$ ($T_c=48$ K). In contrast to earlier work on YBa$_2$Cu$_3$O$_{6.5}$ ($T_c=58$ K), where the prominent features in the magnetic spectra consist of a sharp collective magnetic excitation termed ``resonance and a large ($hbaromegaapprox 15$ meV) superconducting spin gap, we find that the spin excitations in YBa$_2$Cu$_3$O$_{6.45}$ are gapless and have a much broader resonance. Our detailed mapping of magnetic scattering along the $a^ast$/$b^ast$-axis directions at different energies reveals that spin excitations are unisotropic and consistent with the ``hourglass-like dispersion along the $a^ast$-axis direction near the resonance, but they are isotropic at lower energies. Since a fundamental change in the low-temperature normal state of YBa$_2$Cu$_3$O$_{6+y}$ when superconductivity is suppressed takes place at $ysim0.5$ with a metal-to-insulator crossover (MIC), where the ground state transforms from a metallic to an insulating-like phase, our results suggest a clear connection between the large change in spin excitations and the MIC. The resonance therefore is a fundamental feature of metallic ground state superconductors and a consequence of high-$T_c$ superconductivity.