We report neutron scattering measurements of the structural correlations associated with the apparent relaxor transition in K$_{1-x}$Li$_x$TaO$_3$ for $x=0.02$ (KLT(0.02)). This compound displays a broad and frequency-dependent peak in the dielectric
permittivity, which is the accepted hallmark of all relaxors. However, no evidence of elastic diffuse scattering or any soft mode anomaly is observed in KLT(0.02) [J. Wen et al., Phys. Rev. B 78, 144202 (2008)], a situation that diverges from that in other relaxors such as PbMg$_{1/3}$Nb$_{2/3}$O$_3$. We resolve this dichotomy by showing that the structural correlations associated with the transition in KLT(0.02) are purely dynamic at all temperatures, having a timescale on the order of $sim$THz. These fluctuations are overdamped, non-propagating, and spatially uncorrelated. Identical measurements made on pure KTaO$_3$ show that they are absent (within experimental error) in the undoped parent material. They exhibit a temperature dependence that correlates well with the dielectric response, which suggests that they are associated with local ferroelectric regions induced by the Li$^+$ doping. The ferroelectric transition that is induced by the introduction of Li$^+$ cations is therefore characterized by quasistatic fluctuations, which represents a stark contrast to the soft harmonic-mode-driven transition observed in conventional perovskite ferroelectrics like PbTiO$_3$. The dynamic, glass-like, structural correlations in KLT(0.02) are much faster than those measured in random-field-based lead-based relaxors, which exhibit a frequency scale of order of $sim$GHz and are comparatively better correlated spatially. Our results support the view that random fields give rise to the relaxor phenomena, and that the glass-like dynamics observed here characterize a nascent response.
PbZr_{1-x}Ti_xO_3 (PZT) and Pb(Mg_{1/3}Nb_{2/3})_{1-x}Ti_xO_3 (PMN-$x$PT) are complex lead-oxide perovskites that display exceptional piezoelectric properties for pseudorhombohedral compositions near a tetragonal phase boundary. In PZT these composit
ions are ferroelectrics, but in PMN-xPT they are relaxors because the dielectric permittivity is frequency dependent and exhibits non-Arrhenius behavior. We show that the nanoscale structure unique to PMN-xPT and other lead-oxide perovskite relaxors is absent in PZT and correlates with a greater than 100% enhancement of the longitudinal piezoelectric coefficient in PMN-xPT relative to that in PZT. By comparing dielectric, structural, lattice dynamical, and piezoelectric measurements on PZT and PMN-xPT, two nearly identical compounds that represent weak and strong random electric field limits, we show that quenched (static) random fields establish the relaxor phase and identify the order parameter.
Neutron scattering is used to investigate the single-ion spin and orbital excitations below the Mott-Hubbard gap in CoO. Three excitations are reported at 0.870 $pm$ 0.009 eV, 1.84 $pm$ 0.03, and 2.30 $pm$ 0.15 eV. These were parameterized within a w
eak crystal field scheme with an intra-orbital exchange of $J(dd)$=1.3 $pm$ 0.2 eV and a crystal field splitting 10Dq=0.94 $pm$ 0.10 eV. A reduced spin-orbit coupling of lambda=-0.016 $pm$ 0.003 eV is derived from dilute samples of Mg$_{0.97}$Co$_{0.03}$O, measured to remove complications due to spin exchange and structural distortion parameters which split the cubic phase degeneracy of the orbital excitations complicating the inelastic spectrum. The 1.84 eV, while reported using resonant x-ray and optical techniques, was absent or weak for non resonant x-ray experiments and overlaps with the expected position of a $^{4}A_{2}$ level. This transition is absent in the dipolar approximation but expected to have a finite quadrupolar matrix element that can be observed with neutron scattering techniques at larger momentum transfers. Our results agree with a crystal field analysis (in terms of Racah parameters and Tanabe-Sugano diagrams) and with previous calculations performed using local-density band theory for Mott insulating transition metal oxides. The results also demonstrate the use of neutron scattering for measuring dipole forbidden transitions in transition metal oxide systems.
A neutron scattering investigation of the magnetoelectric coupling in PbFe_{1/2}Nb_{1/2}O_{3} (PFN) has been undertaken. Ferroelectric order occurs below 400 K, as evidenced by the softening with temperature and subsequent recovery of the zone center
transverse optic phonon mode energy (hbar Omega_{0}). Over the same temperature range, magnetic correlations become resolution limited on a terahertz energy scale. In contrast to the behavior of nonmagnetic disordered ferroelectrics (namely Pb(Mg,Zn)_{1/3}Nb_{2/3}O_{3}), we report the observation of a strong deviation from linearity in the temperature dependence of (hbar Omega_{0})^{2}. This deviation is compensated by a corresponding change in the energy scale of the magnetic excitations, as probed through the first moment of the inelastic response. The coupling between the short-range ferroelectric and antiferromagnetic correlations is consistent with calculations showing that the ferroelectricity is driven by the displacement of the body centered iron site, illustrating the multiferroic nature of magnetic lead based relaxors in the dynamical regime.
In this reply, we point out several criticisms of the analysis in arXiv:0909.2633 and show that the comment does not change the underlying conclusion presented by ourselves that there is no measurable deficit in the scattering cross section of hydrog
en. We therefore consider that our original conclusions are correct namely that the previous anomalies in the cross section are due to experimental effects related to the use of indirect geometry spectrometers.
We have measured the spin fluctuations in the YBa2Cu3O6.5 (YBCO6.5, Tc=59 K) superconductor at high-energy transfers above ~ 100 meV. Within experimental error, the momentum dependence is isotropic at high-energies, similar to that measured in the in
sulator for two dimensional spin waves, and the dispersion extrapolates back to the incommensurate wave vector at the elastic position. This result contrasts with previous expectations based on measurements around 50 meV which were suggestive of a softening of the spin-wave velocity with increased hole doping. Unlike the insulator, we observe a significant reduction in the intensity of the spin excitations for energy transfers above ~ 100 meV similar to that observed above ~ 200 meV in the YBCO6.35 (Tc=18 K) superconductor as the spin waves approach the zone boundary. We attribute this high energy scale with a second gap and find agreement with measurements of the pseudogap in the cuprates associated with electronic anomalies along the antinodal positions. In addition, we observe a sharp peak at around 400 meV whose energy softens with increased hole doping. We discuss possible origins of this excitation including a hydrogen related molecular excitation and a transition of electronic states between d levels.
We have investigated the spin fluctuations in the langasite compound Ba3NbFe3Si2O14 in both the ordered state and as a function of temperature. The low temperature magnetic structure is defined by a spiral phase characterized by magnetic Bragg peaks
at q=(0,0,tau ~ 1/7) onset at TN=27 K as previously reported by Marty et al. The nature of the fluctuations and temperature dependence of the order parameter is consistent with a classical second order phase transition for a two dimensional triangular antiferromagnet. We will show that the physical properties and energy scales including the ordering wavevector, Curie-Weiss temperature, and the spin-waves can be explained through the use of only symmetric exchange constants without the need for the Dzyaloshinskii-Moriya interaction. This is accomplished through a set of ``helical exchange pathways along the c direction imposed by the chiral crystal structure and naturally explains the magnetic diffuse scattering which displays a strong vector chirality up to high temperatures well above the ordering temperature. This illustrates a strong coupling between magnetic and crystalline chirality in this compound.
We have characterized the dynamics of the polar nanoregions in Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) through high-resolution neutron backscattering and spin-echo measurements of the diffuse scattering cross section. We find that the diffuse scatterin
g intensity consists of emph{both} static and dynamic components. The static component first appears at the Curie temperature $Theta sim 400$ K, while the dynamic component freezes completely at the temperature T$_{f} sim 200$ K; together, these components account for all of the observed spectral weight contributing to the diffuse scattering cross section. The integrated intensity of the dynamic component peaks near the temperature at which the frequency-dependent dielectric constant reaches a maximum (T$_{max}$) when measured at 1 GHz, i. e. on a timescale of $sim 1$ ns. Our neutron scattering results can thus be directly related to dielectric and infra-red measurements of the polar nanoregions. Finally, the global temperature dependence of the diffuse scattering can be understood in terms of just two temperature scales, which is consistent with random field models.
Deep inelastic neutron scattering experiments using indirect time-of-flight spectrometers have reported a smaller cross section for the hydrogen atom than expected from conventional scattering theory. Typically, at large momentum transfers, a deficit
of 20-40% in the neutron scattering intensity has been measured and several theories have been developed to explain these results. We present a different approach to this problem by investigating the hydrogen cross section in polyethylene using the direct geometry time-of-flight spectrometer MARI with the incident energy fixed at a series of values ranging from Ei=0.5 eV to 100 eV. These measurements span a much broader range in momentum than previous studies and with varying energy resolutions. We observe no momentum dependence to the cross section with an error of 4% and through a comparison with the scattering from metal foil standards measure the absolute bound cross section of the hydrogen atom to be sigma(H)= 80 +/- 4 barns. These results are in agreement with conventional scattering theory but contrast with theories invoking quantum entanglement and neutron experiments supporting them. Our results also illustrate a unique use of direct geometry chopper instruments at high incident energies and demonstrate their capability for conducting high-energy spectroscopy.
The S=2 anisotropic triangular lattice alpha-NaMnO2 is studied by neutron inelastic scattering. Antiferromagnetic order occurs at T ~ 45 K with opening of a spin gap. The spectral weight of the magnetic dynamics above the gap (Delta ~ 7.5 meV) has be
en analysed by the single-mode approximation. Excellent agreement with the experiment is achieved when a dominant exchange interaction (|J|/k_B ~ 73 K), along the monoclinic b-axis and a sizeable easy-axis magnetic anisotropy (|D|/k_B ~ 3 K) are considered. Despite earlier suggestions for two-dimensional spin interactions, the dynamics illustrate strongly coupled antiferromagnetic S=2 chains and cancellation of the interchain exchange due to the lattice topology. alpha-NaMnO2 therefore represents a model system where the geometric frustration is resolved through the lowering of the dimensionality of the spin interactions.
