Elastic Softness of Hybrid Lead Halide Perovskites.

Much recent attention has been devoted towards unraveling the microscopic optoelectronic properties of hybrid organic-inorganic perovskites. Here we investigate by coherent inelastic neutron scattering spectroscopy and Brillouin light scattering, low frequency acoustic phonons in four different hybrid perovskite single crystals: MAPbBr_{3}, FAPbBr_{3}, MAPbI_{3}, and α-FAPbI_{3} (MA: methylammonium, FA: formamidinium). We report a complete set of elastic constants characterized by a very soft shear modulus C_{44}. Further, a tendency towards an incipient ferroelastic transition is observed in FAPbBr_{3}. We observe a systematic lower sound group velocity in the technologically important iodide-based compounds compared to the bromide-based ones. The findings suggest that low thermal conductivity and hot phonon bottleneck phenomena are expected to be enhanced by low elastic stiffness, particularly in the case of the ultrasoft α-FAPbI_{3}.

Strong interplay between stripe spin fluctuations, nematicity and superconductivity in FeSe.

In iron-based superconductors the interactions driving the nematic order (that breaks four-fold rotational symmetry in the iron plane) may also mediate the Cooper pairing. The experimental determination of these interactions, which are believed to depend on the orbital or the spin degrees of freedom, is challenging because nematic order occurs at, or slightly above, the ordering temperature of a stripe magnetic phase. Here, we study FeSe (ref. )-which exhibits a nematic (orthorhombic) phase transition at Ts = 90 K without antiferromagnetic ordering-by neutron scattering, finding substantial stripe spin fluctuations coupled with the nematicity that are enhanced abruptly on cooling through Ts. A sharp spin resonance develops in the superconducting state, whose energy (∼4 meV) is consistent with an electron-boson coupling mode revealed by scanning tunnelling spectroscopy. The magnetic spectral weight in FeSe is found to be comparable to that of the iron arsenides. Our results support recent theoretical proposals that both nematicity and superconductivity are driven by spin fluctuations.

Hourglass Dispersion and Resonance of Magnetic Excitations in the Superconducting State of the Single-Layer Cuprate HgBa_{2}CuO_{4+δ} Near Optimal Doping.

We use neutron scattering to study magnetic excitations near the antiferromagnetic wave vector in the underdoped single-layer cuprate HgBa_{2}CuO_{4+δ} (superconducting transition temperature T_{c}≈88 K, pseudogap temperature T^{*}≈220 K). The response is distinctly enhanced below T^{*} and exhibits a Y-shaped dispersion in the pseudogap state, whereas the superconducting state features an X-shaped (hourglass) dispersion and a further resonancelike enhancement. A large spin gap of about 40 meV is observed in both states. This phenomenology is reminiscent of that exhibited by bilayer cuprates. The resonance spectral weight, irrespective of doping and compound, scales linearly with the putative binding energy of a spin exciton described by an itinerant-spin formalism.

Hidden magnetic excitation in the pseudogap phase of a high-T(c) superconductor.

The elucidation of the pseudogap phenomenon of the high-transition-temperature (high-T(c)) copper oxides-a set of anomalous physical properties below the characteristic temperature T* and above T(c)-has been a major challenge in condensed matter physics for the past two decades. Following initial indications of broken time-reversal symmetry in photoemission experiments, recent polarized neutron diffraction work demonstrated the universal existence of an unusual magnetic order below T* (refs 3, 4). These findings have the profound implication that the pseudogap regime constitutes a genuine new phase of matter rather than a mere crossover phenomenon. They are furthermore consistent with a particular type of order involving circulating orbital currents, and with the notion that the phase diagram is controlled by a quantum critical point. Here we report inelastic neutron scattering results for HgBa(2)CuO(4+δ) that reveal a fundamental collective magnetic mode associated with the unusual order, and which further support this picture. The mode's intensity rises below the same temperature T* and its dispersion is weak, as expected for an Ising-like order parameter. Its energy of 52-56 meV renders it a new candidate for the hitherto unexplained ubiquitous electron-boson coupling features observed in spectroscopic studies.

Temperature-dependent interplay of Dzyaloshinskii-Moriya interaction and single-ion anisotropy in multiferroic BiFeO3.

Low-energy magnon excitations in multiferroic BiFeO3 were measured in detail as a function of temperature around several Brillouin zone centers by inelastic neutron scattering experiments on single crystals. Unique features around 1 meV are directly associated with the interplay of the Dzyaloshinskii-Moriya interaction and a small single-ion anisotropy. The temperature dependence of these and the exchange interactions were determined by fitting the measured magnon dispersion with spin-wave calculations. The spectra best fit an easy-axis type magnetic anisotropy and the deduced exchange and anisotropy parameters enable us to determine the anharmonicity of the magnetic cycloid. We then draw a direct connection between the changes in the parameters of spin Hamiltonian with temperature and the physical properties and structural deformations of BiFeO3.

Unusual magnetic order in the pseudogap region of the superconductor HgBa2CuO4+delta.

The pseudogap region of the phase diagram is an important unsolved puzzle in the field of high-transition-temperature (high-T(c)) superconductivity, characterized by anomalous physical properties. There are open questions about the number of distinct phases and the possible presence of a quantum-critical point underneath the superconducting dome. The picture has remained unclear because there has not been conclusive evidence for a new type of order. Neutron scattering measurements for YBa(2)Cu(3)O(6+delta) (YBCO) resulted in contradictory claims of no and weak magnetic order, and the interpretation of muon spin relaxation measurements on YBCO and of circularly polarized photoemission experiments on Bi(2)Sr(2)CaCu(2)O(8+delta)(refs 12, 13) has been controversial. Here we use polarized neutron diffraction to demonstrate for the model superconductor HgBa(2)CuO(4+delta) (Hg1201) that the characteristic temperature T* marks the onset of an unusual magnetic order. Together with recent results for YBCO, this observation constitutes a demonstration of the universal existence of such a state. The findings appear to rule out theories that regard T* as a crossover temperature rather than a phase transition temperature. Instead, they are consistent with a variant of previously proposed charge-current-loop order that involves apical oxygen orbitals, and with the notion that many of the unusual properties arise from the presence of a quantum-critical point.

Mixed acoustic phonons and phase modes in an aperiodic composite crystal.

Aperiodic crystals which are long range ordered materials present original dynamics features due to the lack of translational symmetry formally implying the nonvalidity of the Brillouin zone concept. This Letter reports the observation by neutron scattering of an overdamped acousticlike mode at a Bragg peak position in a n-alkane-urea inclusion crystal. This result implies the existence of a gap in the dispersion branch. The gap and anomalous damping of these collective modes are discussed in terms of specific dynamics and interaction in aperiodic materials.

Anisotropic critical magnetic fluctuations in the ferromagnetic superconductor UCoGe.

We report neutron scattering measurements of critical magnetic excitations in the weakly ferromagnetic superconductor UCoGe. The strong non-Landau damping of the excitations we observe, although unusual, has been found in another related ferromagnet, UGe(2) at zero pressure. However, we also find that there is a significant anisotropy of the magnetic correlation length in UCoGe that contrasts with an almost isotropic length for UGe(2). The values of the magnetic correlation length and damping are found to be compatible with superconductivity on small Fermi-surface pockets. The anisotropy may be important to explain why UCoGe is a superconductor at zero pressure while UGe(2) is not.

Confined linear molecules inside an aperiodic supramolecular crystal: the sequence of superspace phases in n-hexadecane/urea.

High-resolution studies of the host-guest inclusion compound n-hexadecane/urea are reported at atmospheric pressure, using both cold neutrons and x-ray diffraction. This intergrowth crystal presents a misfit parameter, defined by the ratio c(h)/c(g) (c(host)/c(guest)), which is temperature independent and irrational (γ = 0.486 ± 0.002) from 300 to 30 K. Three different structural phases are reported for this aperiodic crystal over this temperature range. The crystallographic superspaces are of rank 4 in phases I and II, whereas phase III is associated with an increase in rank to 5, with a supplementary misfit parameter (δ = 0.058 ± 0.002) that is constant throughout this phase. The superspace group of phase I is hexagonal P6(1)22(00γ) down to T(c1) = 149.5 ± 0.5 K; phase II, which persists down to T(c2) = 127.8 ± 0.5 K is orthorhombic P2(1)2(1)2(1)(00γ), and phase III is orthorhombic P2(1)2(1)2(1)(00γ)(00δ).

Two-dimensional orbital-like magnetic order in the high-temperature La(2-x)Sr(x)CuO4 superconductor.

In high-temperature copper oxide superconductors, a novel magnetic order associated with the pseudogap phase has been identified in two different cuprate families over a wide region of temperature and doping. We report here the observation below 120 K of a similar magnetic ordering in the archetypal cuprate La(2-x)Sr(x)CuO4 (LSCO) system for x=0.085. In contrast with the previous reports, the magnetic ordering in LSCO is only short range with an in-plane correlation length of ∼10 A and is bidimensional (2D). Such a less pronounced order suggests an interaction with other electronic instabilities. In particular, LSCO also exhibits a strong tendency towards stripes ordering at the expense of the superconducting state.

Incommensurate magnetic order and dynamics induced by spinless impurities in YBa(2)Cu(3)O(6.6).

We report an inelastic-neutron-scattering and muon-spin-relaxation study of the effect of 2% spinless (Zn) impurities on the magnetic order and dynamics of YBa(2)Cu(3)O(6.6), an underdoped high-temperature superconductor that exhibits a prominent spin pseudogap in its normal state. Zn substitution induces static magnetic order at low temperatures and triggers a large-scale spectral-weight redistribution from the magnetic resonant mode at 38 meV into uniaxial, incommensurate spin excitations with energies well below the spin pseudogap. These observations indicate a competition between incommensurate magnetic order and superconductivity close to a quantum critical point. Comparison to prior data on La(2-x)Sr(x)CuO(4) suggests that this behavior is universal for the layered copper oxides and analogous to impurity-induced magnetic order in one-dimensional quantum magnets.

Two-dimensional geometry of spin excitations in the high-transition-temperature superconductor YBa2Cu3O6+x.

The fundamental building block of the copper oxide superconductors is a Cu4O4 square plaquette. The plaquettes in most of these materials are slightly distorted to form a rectangular lattice, for which an influential theory predicts that high-transition-temperature (high-T(c)) superconductivity is nucleated in 'stripes' aligned along one of the axes. This theory received strong support from experiments that indicated a one-dimensional character for the magnetic excitations in the high-T(c) material YBa2Cu3O6.6 (ref. 4). Here we report neutron scattering data on 'untwinned' YBa2Cu3O6+x crystals, in which the orientation of the rectangular lattice is maintained throughout the entire volume. Contrary to the earlier claim, we demonstrate that the geometry of the magnetic fluctuations is two-dimensional. Rigid stripe arrays therefore appear to be ruled out over a wide range of doping levels in YBa2Cu3O6+x, but the data may be consistent with liquid-crystalline stripe order. The debate about stripes has therefore been reopened.

Commensurate antiferromagnetic excitations as a signature of the pseudogap in the tetragonal high-Tc cuprate HgBa2CuO(4+δ).

Antiferromagnetic correlations have been argued to be the cause of the d-wave superconductivity and the pseudogap phenomena exhibited by the cuprates. Although the antiferromagnetic response in the pseudogap state has been reported for a number of compounds, there exists no information for structurally simple HgBa2CuO(4+δ). Here we report neutron-scattering results for HgBa2CuO(4+δ) (superconducting transition temperature Tc≈71 K, pseudogap temperature T*≈305 K) that demonstrate the absence of the two most prominent features of the magnetic excitation spectrum of the cuprates: the X-shaped 'hourglass' response and the resonance mode in the superconducting state. Instead, the response is Y-shaped, gapped and significantly enhanced below T*, and hence a prominent signature of the pseudogap state.

Intra-unit-cell magnetic correlations near optimal doping in YBa2Cu3O6.85.

The pseudo-gap phenomenon in copper oxide superconductors is central to any description of these materials as it prefigures the superconducting state itself. A magnetic intra-unit-cell order was found to occur just at the pseudo-gap temperature in four cuprate high-Tc superconducting families. Here we present polarized neutron-scattering measurements of nearly optimally doped YBa2Cu3O6.85, carried out on two different spectrometers, that reveal several features. The intra-unit-cell order consists of finite-sized planar domains that are very weakly correlated along the c axis. At high temperature, only the out-of-plane magnetic components correlate, indicating a strong Ising anisotropy. An aditional in-plane response develops at low temperature, giving rise to an apparent tilt of the magnetic moment. The discovery of these two regimes puts stringent constraints, which are tightly bound to the pseudo-gap physics, on the intrinsic nature of intra-unit-cell order.

Phonons of Fe-based superconductor Ca10Pt4As8(Fe1-x Pt x As)10.

We report the results of inelastic neutron scattering measurements on particular phonons of a superconducting (SC) Ca10Pt4As8(Fe1-x Pt x As)10 with the onset transition temperature T c ~ 33 K to investigate mainly what roles orbital fluctuation plays in Cooper pairing, where we observed a slight softening of the in-plane transverse acoustic mode corresponding to the elastic constant C 66. This softening starts at temperature T well above the SC T c, as T decreases. An anomalously strong change of the scattering intensity of in-plane optical modes was observed at the M point of the pseudo tetragonal reciprocal space in the range of 35 < ω < 40 meV with decreasing T from far above T c. Because this ω region mainly corresponds to the motion of Fe and As atoms in the FeAs planes, the finding presents information on the coupling between the orbital fluctuation of Fe 3d electrons and the lattice system, useful for studying the possible roles of orbital fluctuation in the pairing mechanism and/or the appearance of the so-called nematic phase.

The temperature dependence of the phononic band gap of NaI.

The position and size of the energy gap in the phonon density of states of NaI single crystal have been investigated by inelastic neutron scattering in a wide range of temperatures from 10 to 700 K. The results reveal a pronounced temperature effect which effectively leads to closure of the phonon gap at temperatures in the range of 700-800 K. The results are discussed in the context of studies of possible intrinsic localized modes in the phonon gap of alkali halides.

Dispersion and damping of zone-boundary magnons in the noncentrosymmetric superconductor CePt3Si.

Inelastic neutron scattering (INS) is employed to study damped spin-wave excitations in the noncentrosymmetric heavy-fermion superconductor CePt3Si along the antiferromagnetic Brillouin zone boundary in the low-temperature magnetically ordered state. Measurements along the (1/2 1/2 L) and (H H 1/2 - H) reciprocal-space directions reveal deviations in the spin-wave dispersion from the previously reported model. The broad asymmetric shape of the peaks in energy signifies strong spin-wave damping by interactions with the particle-hole continuum. Their energy width exhibits no evident anomalies as a function of momentum along the (1/2 1/2 L) direction which could be attributed to Fermi surface nesting effects, implying the absence of pronounced commensurate nesting vectors at the magnetic zone boundary. In agreement with a previous study, we find no signatures of the superconducting transition in the magnetic excitation spectrum, such as a magnetic resonant mode or a superconducting spin gap, either at the magnetic ordering wavevector (0 0 1/2) or at the zone boundary. However, the low superconducting transition temperature in this material still leaves the possibility of such features being weak and therefore hidden below the incoherent background at energies ≲ 0.1 meV, precluding their detection by INS.