Unusual suppression of a spin resonance mode with magnetic field in underdoped NaFe$_{1-x}$Co$_x$As: Evidence for orbital-selective pairing

We use inelastic neutron scattering to study the fate of the two spin resonance modes in underdoped superconducting NaFe$_{1-x}$Co$_x$As ($x=0.0175$) under applied magnetic fields. While an applied in-plane magnetic field of $B=12$ T only modestly suppresses superconductivity and enhances static antiferromagnetic order, the two spin resonance modes display disparate responses. The spin resonance mode at higher energy is mildly suppressed, consistent with the field effect in other unconventional superconductors. The spin resonance mode at lower energy, on the other hand, is almost completely suppressed. Such dramatically different responses to applied magnetic field indicate distinct origins of the two spin resonance modes, resulting from the strongly orbital-selective nature of spin excitations and Cooper-pairing in iron-based superconductors.

Temperature and polarization dependence of low-energy magnetic fluctuations in nearly-optimal-doped NaFe$_{0.9785}$Co$_{0.0215}$As

We use unpolarized and polarized neutron scattering to study the temperature and polarization dependence of low-energy magnetic fluctuations in nearly-optimal-doped NaFe$_{0.9785}$Co$_{0.0215}$As, with coexisting superconductivity ($T_{rm c}approx19$ K) and weak antiferromagnetic order ($T_{rm N}approx30$ K, ordered moment $approx0.02$ $mu_{rm B}$/Fe). A single spin resonance mode with intensity tracking the superconducting order parameter is observed, although energy of the mode only softens slightly on approaching $T_{rm c}$. Polarized neutron scattering reveals that the single resonance is mostly isotropic in spin space, similar to overdoped NaFe$_{0.935}$Co$_{0.045}$As but different from optimal electron-, hole-, and isovalent-doped BaFe$_2$As$_2$ compounds, all featuring an additional prominent anisotropic component. Spin anisotropy in NaFe$_{0.9785}$Co$_{0.0215}$As is instead present at energies below the resonance, which becomes partially gapped below $T_{rm c}$, similar to the situation in optimal-doped YBa$_2$Cu$_3$O$_{6.9}$. Our results indicate that anisotropic spin fluctuations in NaFe$_{1-x}$Co$_x$As appear in the form of a resonance in the underdoped regime, become partially gapped below $T_{rm c}$ near optimal doping and disappear in overdoped compounds.

Electron doping evolution of the magnetic excitations in NaFe$_{1-x}$Co$_x$As

We use time-of-flight (ToF) inelastic neutron scattering (INS) spectroscopy to investigate the doping dependence of magnetic excitations across the phase diagram of NaFe$_{1-x}$Co$_x$As with $x=0, 0.0175, 0.0215, 0.05,$ and $0.11$. The effect of electron-doping by partially substituting Fe by Co is to form resonances that couple with superconductivity, broaden and suppress low energy ($Ele 80$ meV) spin excitations compared with spin waves in undoped NaFeAs. However, high energy ($E> 80$ meV) spin excitations are weakly Co-doping dependent. Integration of the local spin dynamic susceptibility $chi^{primeprime}(omega)$ of NaFe$_{1-x}$Co$_x$As reveals a total fluctuating moment of 3.6 $mu_B^2$/Fe and a small but systematic reduction with electron doping. The presence of a large spin gap in the Co-overdoped nonsuperconducting NaFe$_{0.89}$Co$_{0.11}$As suggests that Fermi surface nesting is responsible for low-energy spin excitations. These results parallel Ni-doping evolution of spin excitations in BaFe$_{2-x}$Ni$_x$As$_2$, confirming the notion that low-energy spin excitations coupling with itinerant electrons are important for superconductivity, while weakly doping dependent high-energy spin excitations result from localized moments.

Neutron spin resonance as a probe of superconducting gap anisotropy in partially detwinned electron underdoped NaFe$_{0.985}$Co$_{0.015}$As

We use inelastic neutron scattering (INS) to study the spin excitations in partially detwinned NaFe$_{0.985}$Co$_{0.015}$As which has coexisting static antiferromagnetic (AF) order and superconductivity ($T_c=15$ K, $T_N=30$ K). In previous INS work on a twinned sample, spin excitations form a dispersive sharp resonance near $E_{r1}=3.25$ meV and a broad dispersionless mode at $E_{r1}=6$ meV at the AF ordering wave vector ${bf Q}_{rm AF}={bf Q}_1=(1,0)$ and its twinned domain ${bf Q}_2=(0,1)$. For partially detwinned NaFe$_{0.985}$Co$_{0.015}$As with the static AF order mostly occurring at ${bf Q}_{rm AF}=(1,0)$, we still find a double resonance at both wave vectors with similar intensity. Since ${bf Q}_1=(1,0)$ characterizes the explicit breaking of the spin rotational symmetry associated with the AF order, these results indicate that the double resonance cannot be due to the static and fluctuating AF orders, but originate from the superconducting gap anisotropy.

Anisotropic neutron spin resonance in underdoped superconducting NaFe1-xCoxAs

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 isotropic similar to that of C45. Since the a-axis polarized spin excitations of the anisotropic resonance appear below Tc, our data suggests that the itinerant electrons contributing to the magnetism are also coupled to the superconductivity.

Double neutron spin resonances and gap anisotropy in underdoped superconducting NaFe0.985Co0.015As

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 indicates that both the double neutron spin resonances and gap anisotropy originate from the orbital dependence of the superconducting pairing in the iron pnic- tides. Our discovery also shows the importance of the inelastic neutron scattering in detecting the multiorbital superconducting gap structures of iron pnictides.

In-plane spin excitation anisotropy in the paramagnetic phase of NaFeAs

We use unpolarized and polarized inelastic neutron scattering to study low-energy spin excitations in NaFeAs, which exhibits a tetragonal-to-orthorhombic lattice distortion at $T_sapprox 58$ K followed by a collinear antiferromagnetic (AF) order below $T_Napprox 45$ K. In the AF ordered state ($T<T_N$), spin waves are entirely c-axis polarized below $sim$10 meV, exhibiting a gap of $sim4$ meV at the AF zone center and disperse to $sim$7 meV near the c-axis AF zone boundary. On warming to the paramagnetic state with orthorhombic lattice distortion ($T_N<T<T_s$), spin excitations become anisotropic within the FeAs plane. Upon further warming to the paramagnetic tetragonal state ($T>T_s$), spin excitations become more isotropic. Since similar magnetic anisotropy is also observed in the paramagnetic tetragonal phase of superconducting BaFe$_{1.904}$Ni$_{0.096}$As$_2$, our results suggest that the spin excitation anisotropy in superconducting iron pnictides originates from similar anisotropy already present in their parent compounds.

Spin excitation anisotropy as a probe of orbital ordering in the paramagnetic tetragonal phase of superconducting BaFe1.904Ni0.096As2

We use polarized neutron scattering to demonstrate that in-plane spin excitations in electron doped superconducting BaFe1.904Ni0.096As2 (Tc=19.8 K) change from isotropic to anisotropic in the tetragonal phase well above the antiferromagnetic (AF) ordering and tetragonal-to-orthorhombic lattice distortion temperatures (Tn=Ts=33 K) without an uniaxial pressure. While the anisotropic spin excitations are not sensitive to the AF order and tetragonal-to-orthorhombic lattice distortion, superconductivity induces further anisotropy for spin excitations along the [1,1,0] and [1,-1,0] directions. These results indicate that the spin excitation anisotropy is a probe of the electronic anisotropy or orbital ordering in the tetragonal phase of iron pnictides.

Distinguishing $s^{pm}$ and $s^{++}$ electron pairing symmetries by neutron spin resonance in superconducting NaFe$_{0.935}$Co$_{0.045}$As

A determination of the superconducting (SC) electron pairing symmetry forms the basis for establishing a microscopic mechansim for superconductivity. For iron pnictide superconductors, the $s^pm$-pairing symmetry theory predicts the presence of a sharp neutron spin resonance at an energy below the sum of hole and electron SC gap energies ($Eleq 2Delta$) below $T_c$. On the other hand, the $s^{++}$-pairing symmetry expects a broad spin excitation enhancement at an energy above $2Delta$ below $T_c$. Although the resonance has been observed in iron pnictide superconductors at an energy below $2Delta$ consistent with the $s^pm$-pairing symmetry, the mode has also be interpreted as arising from the $s^{++}$-pairing symmetry with $Ege 2Delta$ due to its broad energy width and the large uncertainty in determining the SC gaps. Here we use inelastic neutron scattering to reveal a sharp resonance at E=7 meV in SC NaFe$_{0.935}$Co$_{0.045}$As ($T_c = 18$ K). On warming towards $T_c$, the mode energy hardly softens while its energy width increases rapidly. By comparing with calculated spin-excitations spectra within the $s^{pm}$ and $s^{++}$-pairing symmetries, we conclude that the ground-state resonance in NaFe$_{0.935}$Co$_{0.045}$As is only consistent with the $s^{pm}$-pairing, and is inconsistent with the $s^{++}$-pairing symmetry.

Magnetic anisotropy in hole-doped superconducting Ba 0.67K 0.33Fe 2As2 probed by polarized inelastic neutron scattering

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, $chi^{primeprime}(Q,omega)$, 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 $(0.5,0.5,1)$, respectively, with a broad neutron spin resonance at $E_r=15$ meV. Our neutron polarization analysis reveals that the large difference in spin gaps is purely due to different spin gaps in the c-axis and in-plane polarized spin excitations, resulting resonance with different energy widths for the c-axis and in-plane spin excitations. The observation of spin anisotropy in both opitmally electron and hole-doped BaFe$_2$As$_2$ is due to their proximity to the AF ordered BaFe$_2$As$_2$ where spin anisotropy exists below $T_N$.