We report here first extensive measurements of the temperature dependence of phonon density of states of BaFe2As2, the parent compound of the newly discovered FeAs-based superconductors, using inelastic neutron scattering. The experiments were carried out on the thermal time-of-flight neutron spectrometer IN4 at the ILL on a polycrystalline sample. There is no appreciable change in the spectra between T = 10 K and 200 K, although the sample undergoes a magnetic as well as a tetragonal-to-orthorhombic structural phase transition at 140 K. This indicates a rather harmonic phonon system. Shell model lattice dynamical calculations based on interatomic potentials are carried out to characterize the phonon data. The calculations predict a shift of the Ba-phonons to higher energies at 4 GPa. The average energy of the phonons of the Ba-sublattice is also predicted to increase on partial substitution of Ba by K to Ba0.6K0.4. The calculations show good agreement with the experimental phonon spectra, and also with the specific heat data from the literature.
Well defined peaks with energies of about 18 meV have been observed in a variety of inelastic neutron scattering experiments on single crystals as well as on powders of iron-based superconductors and their parent compounds using either the triple-axis or the time-of-flight technique. They can easily be mistaken for signatures of real excitations. We have found that they are due to multiple scattering events involving primarily walls of the sample environment. Hence, they are particularly troublesome in experiments using very small samples as have been used with recently developed high intensit…
Inelastic neutron scattering and susceptibility measurements have been performed on the optimally-doped Fe-based superconductor FeTe(0.5)Se(0.5), which has a critical temperature, Tc of 14 K. The magnetic scattering at the stripe antiferromagnetic wave-vector Q = (0.5,0.5) exhibits a "resonance" at ~ 6 meV, where the scattering intensity increases abruptly when cooled below Tc. In a 7-T magnetic field parallel to the a-b plane, Tc is slightly reduced to ~ 12 K, based on susceptibility measurements. The resonance in the neutron scattering measurements is also affected by the field. The resonanc…
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 …
Spin subsystem of the copper oxides within the polar Jahn-Teller centers model corresponds to a singlet-triplet magnet where the local boson movement accompanied by the induced longitudinal spin fluctuations. These fluctuations determine the features of the magnetic inelastic scattering in the high-Tc cuprates.
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.
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.
We measured two magnetic modes with finite and discrete energies in an antiferromagnetic ordered phase of a geometrically frustrated magnet MgCr2O4 by single-crystal inelastic neutron scattering, and clarified the spatial spin correlations of the two levels: one is an antiferromagnetic hexamer and the other is an antiferromagnetic heptamer. Since these correlation types are emblematic of quasielastic scattering with geometric frustration, our results indicate instantaneous suppression of lattice distortion in an ordered phase by spin-lattice coupling, probably also supported by orbital and cha…
The effects of nonmagnetic impurities on the neutron scattering intensity are studied for a model of the copper oxide layers in the normal state. The contribution to the Q=(pi,pi) neutron scattering intensity from processes involving the scattering of the spin fluctuations from an impurity with large momentum transfers are calculated within the random phase approximation. It is shown that this type of scatterings could lead to a peak in the neutron scattering intensity in the normal state.
The anisotropy of the magnetic excitations in BaFe$_2$As$_2$ was studied by polarized inelastic neutron scattering which allows one to separate the components of the magnetic response. Despite the in-plane orientation of the static ordered moment we find the in-plane polarized magnons to exhibit a larger gap than the out-of-plane polarized ones indicating very strong single-ion anisotropy within the layers. It costs more energy to rotate a spin within the orthorhombic {\it a-b} plane than rotating it perpendicular to the FeAs layers.
Tunneling and inelastic neutron scattering (INS) measurements in cuprates are discussed. There is a clear discrepancy among energy-gap values for different 90 K cuprates, inferred from tunneling measurements. By using the phase diagram of hole-doped cuprates we interpret tunneling measurements in 90 K cuprates and INS data in YBCO.
The $t-U-V-J$ model is used to describe the positions of the experimental peaks associated with commensurate and incommensurate structure of the magnetic susceptibility probed by neutron scattering in cuprate compounds. Assuming that the tight-binding form of the mean-field electron energy and the maximum gap can be obtained by fitting the angle-resolved photoemission spectroscopy (ARPES) data, we have determined the strengths of the on-site repulsive interaction $U$, the spin-independent attractive interaction $V$ and the spin-dependent antiferromagnetic interaction $J$ from the positions of …
Using a Fermi-liquid-based theory we calculate the in-plane anisotropy of the spin susceptibility for hole-doped high-T_c cuprates. Employing the two-dimensional one-band Hubbard model and a generalized RPA-type theory we consider anisotropic hopping matrix elements ($t_x \neq t_y$) and a mixing of d- and s-wave symmetry of the superconducting order parameter in order to describe orthorhombic superconductors. We compare our calculations with available inelastic neutron scattering data on untwinned YBa{2}Cu{3}O{7-δ} and find good agreement. Furthermore, we predict a strongly anisotropic in-plan…
Inelastic Neutron Scattering (INS) data in LSCO, YBCO and Bi2212 are discussed. In the literature, the INS spectra remain far from being comprehensively understood. We show that local (Q-integrated) susceptibility data and the energy dependence of the spin susceptibility at antiferromagnetic vector, Q = (p,p), can be interpreted by using the phase diagram for hole-doped cuprates. We analyze also the origin of the resonant peak which relates to the order parameter for long-range phase coherence in hole-doped cuprates. Thus, we present an interpretation of neutron data in LSCO, YBCO and Bi2212 p…
This article is a reply to the comment by Nagai and Kuroki [arXiv:1106.2376] for our unpublished paper in arXiv [arXiv:1105.6233]. Contrary to their claim, we certainly obtain a large hump structure at $q=(π,0)$ in the $s_{++}$-wave state in iron pnictides due to the ``dissipationless mechanism'', even when similar parameters used by Nagai and Kuroki are employed.
Magnetic excitations in Ba(Fe0.94Co0.06)2As2 are studied by polarized inelastic neutron scattering (INS) above and below the superconducting transition. In the superconducting state we find clear evidence for two resonance-like excitations. At a higher energy of about 8 meV there is an isotropic resonance mode with weak dispersion along the c-direction. In addition we find a lower excitation at 4 meV that appears only in the c-polarized channel and whose intensity strongly varies with the L-component of the scattering vector. These resonance excitations behave remarkably similar to the gap mod…
We investigate the neutron scattering spectrum in iron pnictides based on the random-phase approximation in the five-orbital model with a realistic superconducting (SC) gap, Delta=5meV. In the normal state, the neutron spectrum is suppressed by large inelastic quasi-particle (QP) scattering rate gamma* ~ Delta. In the fully-gapped s-wave state without sign reversal (s++), a hump-shaped enhancement appears in the neutron spectrum just above 2Delta, since the inelastic QP scattering is prohibited by the SC gap. That is, the hump structure is produced by the dissipationless QPs for Ek<3Delta. The…
We present neutron scattering spectra taken from a single crystal of Na0.75CoO2, the precursor to a novel cobalt-oxide superconductor. The data contain a prominent inelastic signal at low energies (~10 meV), which is localized in wavevector about the origin of two-dimensional reciprocal space. The signal is highly dispersive, and decreases in intensity with increasing temperature. We interpret these observations as direct evidence for the existence of ferromagnetic spin fluctuations within the cobalt-oxygen layers.
Polarized neutron scattering experiments on the slightly overdoped superconductor Ba$_{0.5}$K$_{0.5}$Fe$_2$As$_2$ reveal broad magnetic resonance scattering peaking at approximately 15 meV. In spite of doping far beyond the suppression of magnetic order, this compound exhibits dispersive and anisotropic magnetic excitations. At energies below the resonance maximum, magnetic correlations polarized parallel to the layers but perpendicular to the propagation vector are reduced by a factor two compared to those in the two orthogonal directions; in contrast correlations at the peak maximum are isot…
Inelastic neutron scattering was performed for an iron-based superconductor LaFeAsO0.9D0.1, where most of D (deuterium) replaces oxygen, while a tiny amount goes into interstitial sites. By first-principle calculation, we characterize the interstitial sites for D (and for H slightly mixed) with four equivalent potential minima. Below the superconducting transition temperature Tc = 26 K,new excitations emerge in the range 5-15 meV, while they are absent in the reference system LaFeAsO0.9F0.1. The strong excitations at 14.5 meV and 11.1 meV broaden rapidly around 15 K and 20 K, respectively, whe…
It is widely accepted that: (i) the angle-resolved photoemission spectroscopy (ARPES) data produce evidences for the opening of a d-wave pairing gap in cuprates compounds described at low energies and temperatures by a BCS theory, and (ii) the basic pairing mechanism arises from the antiferromagnetic exchange correlations, but the charge fluctuations associated with double occupancy of a site also play an essential role in doped systems. The simplest model that is consistent with the two statements is the $t$-$U$-$V$-$J$ model. We have shown that the inelastic neutron scattering data on $YBa_2…
Inelastic neutron scattering experiments were performed to investigate the crystalline electric field (CEF) excitations of Nd3+ (J = 9/2) in the iron pnictide NdFeAsO. The crystal field level structures for both the high-temperature paramagnetic phase and the low-temperature antiferromagnetic phase of NdFeAsO are constructed. The variation of CEF excitations of Nd3+ reflects not only the change of local symmetry but also the change of magnetic ordered state of the Fe sublattice. By analyzing the crystal field interaction with a crystal field Hamiltonian, the crystal field parameters are obtain…
Lattice Dynamics of LiFeAs studied by Inelastic Neutron Scattering and Density Functional Theory calculations
II. Physikalisches Institut, Universität zu Köln（科隆大学第二物理研究所）；Institut Laue Langevin（朗之万研究所）；Karlsruher Institut für Technologie (KIT)（卡尔斯鲁厄理工学院）；Université Paris-Saclay, CNRS, CEA, Laboratoire Léon Brillouin（巴黎萨克雷大学）；CNRS UMR 7198, Université de Lorraine（洛林大学）；Leibniz-Institut für Festkörper u. Werkstoffforschung (IFW) Dresden（德累斯顿莱布尼茨固体与材料研究所）；Indian Institute of Science Education and Research, Pune（浦那印度科学教育与研究学院）
The low-energy magnetic excitations of the noncentrosymmetric heavy-fermion superconductor CePt3Si have been measured with inelastic neutron scattering on a single crystal. Kondo-type spin fluctuations with an anisotropic wave vector dependence are observed in the paramagnetic state. These fluctuations do not survive in the antiferromagnetically ordered state below TN=2.2 K but are replaced by damped spin waves, whose dispersion is much stronger along the c-axis than in other directions. No change is observed in the excitation spectrum or the magnetic order as the system enters the superconduc…
We present an inelastic neutron scattering study on single-crystalline LiFeAs devoted to the characterization of the incommensurate antiferromagnetic fluctuations at $\mathbf{Q}=(0.5\pmδ, 0.5\mpδ, q_l)$. Time-of-flight measurements show the presence of these magnetic fluctuations up to an energy transfer of 60 meV, while polarized neutrons in combination with longitudinal polarization analysis on a triple-axis spectrometer prove the pure magnetic origin of this signal. The normalization of the magnetic scattering to an absolute scale yields that magnetic fluctuations in LiFeAs are by a factor …
This paper, I, presents new results from neutron inelastic scattering experiments on single crystals of UPd2Al3. The focus is on the experimental position whilst the sequel, II, advances theoretical perspectives. We present a detailed and complete characterisation of the wavevector- and energy-dependent magnetisation dynamics in UPd2Al3 as measured by neutron inelastic scattering primarily in the form of extensive surveys in energy-momentum space under a wide range of experimental conditions, and put our observations in context with data that has been previously published by two independent gr…
Magnetic excitations in \srruo ~ have been studied by inelastic neutron scattering. The magnetic fluctuations are dominated by incommensurate peaks related to the Fermi surface nesting of the quasi-one-dimensional $d_{xz}$- and $d_{yz}$-bands. The shape of the incommensurate signal agrees well with RPA calculations. At the incommensurate {\bf Q}-positions the energy spectrum considerably softens upon cooling pointing to a close magnetic instability : \srruo ~does not exhibit quantum criticality but is very close to it. $ω/ T$-scaling may be fitted to the data for temperatures above 30 K. Below…
Assuming the exchange of antiferromagnetic spin fluctuations as the Cooper pairing mechanism we calculate the doping dependence of the resonance peak seen in inelastic neutron scattering and the magnetic coherence effect. Most importantly, we find that the resonance peak in the magnetic susceptibility, ${Im}χ({\bf q},ω)$, appears {\it only} in the superconducting state, that it scales with $T_c$, and that magnetic coherence is a result of a d-wave order parameter. We further analyze the structure of ${Im}χ$ below $T_c$, the position of the peak at $ω_{res}$ and the consequences for photoemissi…
Inelastic neutron scattering measurements have been performed on a superconducting single crystal FeTe$_{0.5}$Se$_{0.5}$ to examine the ${\bf Q}$-dependent enhancement of the dynamical structure factor, $S({\bf Q},E)$, from ${\bf Q}$ = (0, 0) to ($π$, $π$), including ($π$, 0) in the superconducting state. In most of iron-based superconductors, $S({\bf Q},E)$ is enhanced at ${\bf Q}$ = ($π$, 0), where the "magnetic resonance mode" is commonly observed in the unfolded Brillouin zone. Constant-$E$ cuts of $S({\bf Q},E)$ suggest that the enhancement is not uniform in the magnetic excitation, and l…
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 use inelastic neutron scattering (INS) to investigate the effect of electron correlations on spin dynamics in the iron-based superconductor Ba$_{0.75}$K$_{0.25}$Fe$_{2}$As$_{2}$. Our INS data show a spin-wave-like dispersive feature, with a zone boundary energy of 200 meV. A first principles analysis of dynamical spin susceptibility, incorporating the mass renormalization factor of 3, as determined by angle-resolved photoemission spectroscopy, provides a reasonable description of the observed spin excitations. This analysis shows that electron correlations in the Fe-3$d$ bands yield enhance…
Metamaterial approach is capable of drastically increasing the critical temperature, Tc, of composite metal-dielectric superconductors. Tripling of Tc was observed in bulk Al-Al2O3 core-shell metamaterials. A theoretical model based on the Maxwell-Garnett approximation provides a microscopic explanation of this effect in terms of electron-electron pairing mediated by a hybrid plasmon-phonon excitation. We report the first observation of this excitation in Al-Al2O3 core-shell metamaterials using inelastic neutron scattering. This result provides support for this novel mechanism of superconducti…
An optimally doped iron-based superconductor LaFeAsO$_{0.92}$F$_{0.08}$ with $T_c = 29$ K has been studied by inelastic powder neutron scattering. The magnetic excitation at $Q=1.15$ Å$^{-1}$ is enhanced below $T_c$, leading to a peak at $E_{res}\sim13$ meV as the resonance mode, in addition to the formation of a gap at low energy below the crossover energy $Δ_{c}\sim10 meV$. The peak energy at $Q=1.15$ Å$^{-1}$ corresponds to $5.2 k_B T_c$ in good agreement with the other values of resonance mode observed in the various iron-based superconductors, even in the high-$T_c$ cuprates. Although the…
We report inelastic neutron scattering measurements of the magnetic excitations in SrFe2As2, the parent of a family of iron-based superconductors. The data extend throughout the Brillouin zone and up to energies of ~260meV. An analysis with the local-moment J_1-J2 model implies very different in-plane nearest-neighbor exchange parameters along the $a$ and $b$ directions, both in the orthorhombic and tetragonal phases. However, the spectrum calculated from the J1-J2 model deviates significantly from our data. We show that the qualitative features that cannot be described by the J1-J2 model are …
Superconductivity appears to compete against the spin-density-wave in Fe pnictides. However, optimally cobalt doped samples show a quasi-two-dimensional spin excitation centered at the (0.5, 0.5, L) wavevector, "the spin resonance peak", that is strongly tied to the onset of superconductivity. By inelastic neutron scattering on single crystals we show the similarities and differences of the spin excitations in BaFe1.84Co0.16As2, with respect to the spin excitations in the high-temperature superconducting cuprates. As in the cuprates the resonance occurs as an enhancement to a part of the spin …
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…
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…
The spin gap evolution upon Ca doping in Sr14-xCaxCu24O41 was systematically investigated using inelastic neutron scattering. We discover that the singlet-triplet spin gap excitation survives in this series with x up to 13, indicating the singlet dimer ground state in these compounds. This observation corrects the previous speculation that the spin gap collapses at x~13 by the NMR technique. The strong intensity modulation along QH in x=0 gradually evolves into a Q-independent feature in x>11. This could be attributed to the localized Cu moment magnetism developing into an itinerant magnetism …
We report an inelastic neutron scattering study of single crystals of (Li$_{0.8}$Fe$_{0.2}$)ODFeSe. Temperature-dependent low-energy spin excitations are observed near $\mathbf{Q}=$ (0.5, 0.27, 0.5) and equivalent wave vectors symmetrically surrounding $\mathbf{Q}=$ (0.5, 0.5, 0.5) in the 1-Fe Brillouin zone, consistent with a Fermi-surface-nesting description. The excitations are broadly distributed in energy, ranging from 16 to 35 meV. Upon cooling below the superconducting critical temperature ($T_\mathrm{c}$), magnetic response below twice the superconducting gap $2Δ_\mathrm{SC}$ exhibits …
