We use inelastic neutron scattering to study acoustic phonons and spin excitations in single crystals of NaFeAs, a parent compound of iron pnictide superconductors. NaFeAs exhibits a tetragonal-to-orthorhombic structural transition at $T_sapprox 58$
K and a collinear antiferromagnetic (AF) order at $T_Napprox 45$ K. While longitudinal and out-of-plane transverse acoustic phonons behave as expected, the in-plane transverse acoustic phonons reveal considerable softening on cooling to $T_s$, and then harden on approaching $T_N$ before saturating below $T_N$. In addition, we find that spin-spin correlation lengths of low-energy magnetic excitations within the FeAs layer and along the $c$-axis increase dramatically below $T_s$, and show weak anomaly across $T_N$. These results suggest that the electronic nematic phase present in the paramagnetic tetragonal phase is closely associated with dynamic spin-lattice coupling, possibly arising from the one-phonon-two-magnon mechanism.
Neutron scattering from high-quality YBa2Cu3O6.33 (YBCO6.33) single crystals with a Tc of 8.4 K shows no evidence of a coexistence of superconductivity with long-range antiferromagnetic order at this very low, near-critical doping of p~0.055. However
, we find short-range three dimensional spin correlations that develop at temperatures much higher than Tc. Their intensity increases smoothly on cooling and shows no anomaly that might signify a Neel transition. The system remains subcritical with spins correlated over only one and a half unit cells normal to the planes. At low energies the short-range spin response is static on the microvolt scale. The excitations out of this ground state give rise to an overdamped spectrum with a relaxation rate of 3 meV. The transition to the superconducting state below Tc has no effect on the spin correlations. The elastic interplanar spin response extends over a length that grows weakly but fails to diverge as doping is moved towards the superconducting critical point. Any antiferromagnetic critical point likely lies outside the superconducting dome. The observations suggest that conversion from Neel long-range order to a spin glass texture is a prerequisite to formation of paired superconducting charges. We show that while pc =0.052 is a critical doping for superconducting pairing, it is not for spin order.
Iron-based superconductivity develops near an antiferromagnetic order and out of a bad metal normal state, which has been interpreted as originating from a proximate Mott transition. Whether an actual Mott insulator can be realized in the phase diagr
am of the iron pnictides remains an open question. Here we use transport, transmission electron microscopy, X-ray absorption spectroscopy, and neutron scattering to demonstrate that NaFe$_{1-x}$Cu$_x$As near $xapprox 0.5$ exhibits real space Fe and Cu ordering, and are antiferromagnetic insulators with the insulating behavior persisting above the Neel temperature, indicative of a Mott insulator. Upon decreasing $x$ from $0.5$, the antiferromagnetic ordered moment continuously decreases, yielding to superconductivity around $x=0.05$. Our discovery of a Mott insulating state in NaFe$_{1-x}$Cu$_x$As thus makes it the only known Fe-based material in which superconductivity can be smoothly connected to the Mott insulating state, highlighting the important role of electron correlations in the high-$T_{rm c}$ superconductivity.
We use inelastic neutron scattering to systematically investigate the Ni-doping evolution of the low-energy spin excitations in BaFe2-xNixAs2 spanning from underdoped antiferromagnet to overdoped superconductor (0.03< x < 0.18). In the undoped state,
the low-energy (<80 meV) spin waves of BaFe2As2 form transversely elongated ellipses in the [H, K] plane of the reciprocal space. Upon Ni-doping, the c-axis magnetic exchange coupling is rapidly suppressed and the momentum distribution of spin excitations in the [H, K] plane is enlarged in both the transverse and longitudinal directions with respect to the in-plane AF ordering wave vector of the parent compound. As a function of increasing Ni-doping x, the spin excitation widths increase linearly but with a larger rate along the transverse direction. These results are in general agreement with calculations of dynamic susceptibility based on the random phase approximation (RPA) in an itinerant electron picture. For samples near optimal superconductivity at x= 0.1, a neutron spin resonance appears in the superconducting state. Upon further increasing the electron-doping to decrease the superconducting transition temperature Tc, the intensity of the low-energy magnetic scattering decreases and vanishes concurrently with vanishing superconductivity in the overdoped side of the superconducting dome. Comparing with the low-energy spin excitations centered at commensurate AF positions for underdoped and optimally doped materials (x<0.1), spin excitations in the over-doped side (x=0.15) form transversely incommensurate spin excitations, consistent with the RPA calculation. Therefore, the itinerant electron approach provides a reasonable description to the low-energy AF spin excitations in BaFe2-xNixAs2.
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 promine
nt 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.
