constant-Q Scans Research Articles

Soft modes and phonon interactions in studied by means of neutron scattering

This paper presents an inelastic neutron scattering study of the proper ferroelectric and elastic neutron scattering results on the satellite diffraction pattern which characterizes the modulated phase. The temperature dependences of the satellite intensities and modulation wavevector are in fair agreement with results from previous x-ray experiments. Close to the incommensurate-to-ferroelectric transition temperature , an unexpected intensity overshoot is observed, similar to that seen in birefringence and dilatation experiments. The relationship between the lattice dynamics and the observed phase transition sequence is examined. The dispersion of the ferroelectric soft optic phonon (-polarization) and of the acoustic phonons is followed along the and -directions. In the ferroelectric phase, the TO mode shows a considerable softening as the incommensurate phase is approached from below. In the paraelectric and incommensurate phases, the response from the TO (-polarization) and TA ( strain) branches has been investigated via a series of constant-q scans in the -direction (approximately the modulation wavevector direction). The combined inelastic line-shapes, as observed in a number of non-equivalent Brillouin zones, could all be analysed in terms of a coupled-mode damped harmonic oscillator model. In addition, a diverging, resolution-limited, central peak is observed close to . It is suggested that the TO-TA coupling lies at the origin of the incommensurate instability. A phenomenological free energy is developed, in the continuum approximation, in which the TO-TA interaction is included via a pseudo-Lifshitz term of the type .

Central peaks in (NH 4I) x(KI) 1− x

Quasielastic measurements are reported on (NH 4I) x (KI) 1− x . This mixed molecular system reveals a variety of structural phases and different glass states. Close to the structural phase transition, in constant Q-scans through the reciprocal lattice points at which superstructure reflections appear in the orientationally ordered phase, two central peaks were detected.

The plastically crystalline phase of NaOH, NaOD, KOH and KOD

The high-temperature cubic phases of sodium hydroxide and potassium hydroxide have been investigated using X-ray, elastic and inelastic neutron scattering from single crystals. As a special feature of these experiments the crystals had to be kept at temperatures of around 550 K as grown from melt, since they are destroyed when passing through the structural phase transition. In these compounds the OH or OD groups are known to undergo rapid reorientational motions. The X-ray diffraction results are characterized by a rapid decrease in the Bragg intensities with increasing diffraction angle and diffuse rods passing through the Bragg reflections. By neutron diffraction, about 20 symmetrically non-equivalent reflections have been observed. Different means of analysis will be presented; one obtains the probability distribution of H+ or D+ around oxygen, and the OH distance. This is of interest in the context of possible H bonding and proton conductivity. The disorder of H or D gives rise to diffuse scattering of neutrons as an approximately spherical halo around the origin in Q-space. The orientations of OH groups at different sites being correlated cannot be excluded from the experimental findings; a 2D correlation model, however, does not predict a dramatic narrowing of this halo. Inelastic scattering yielded rather ill-defined phonon groups in constant-Q scans. In particular, the shear modes showed strong overdamping. The observed features can be explained by treating the OH groups as elastic dipoles coupled to the lattice distortions, with the dynamics of a relaxator, and by extending conventional soft-mode theory to allow for the mixing of several softened modes. The softened modes also explain the diffuse rods in X-ray photographs.

Magnetic field and temperature dependent correlations in the singlet ground state system CsFeBr 3

In the singlet ground state system CsFeBr 3 the temperature and magnetic field dependence of the magnetic dispersion curves have been measured by inelastic neutron scattering. At a field of 4.1 T magnetic Bragg peaks appear at (⅓ ⅓ 1) and (⅔ ⅔ 1). The correlation lengths were derived from the experimental data by integrating the constant Q-scans over the energy transfer. The Q-dependence was fitted to Lorentzians and correlations lengths were extracted for different directions in the lattice. These correlation lengths decrease with increasing temperature and increase with increasing field. Above the phase transition the correlation lengths decrease again.

Spin fluctuations in Ni above T C

Numerical computations of the temperature dependence of the cross section for the magnetic scattering of unpolarized neutrons in nickel above TC are reported. The calculations are based on semiempirical bands assuming no exchange splitting above TC . The thermal fluctuations are taken into account through the introduction of an effective temperature-dependent interaction, which is evaluated in the mode-mode coupling approximation. Cross sections are shown for constant-q scans for three different values of q and for several different temperatures from 650 to 946 K. There is some small structure in the calculated cross section due to band-structure effects, but we do not predict propagating spin waves above TC.

Polarized neutron studies of forbidden magnons in the two-dimensional ferromagnet K2CuF4.

Polarized inelastic neutron scattering has been used to study the spin dynamics of the quasi-two-dimensional nonmetallic Heisenberg ferromagnet ${\mathrm{K}}_{2}$${\mathrm{CuF}}_{4}$ in weak magnetic fields at temperature in the vicinity of ${T}_{c}$. We have observed underdamped allowed and ``forbidden'' excitations in constant-Q scans for two different applied magnetic fields over the temperature range from 0.9${T}_{C}$ to 2.9${T}_{C}$. A frequency difference between the allowed magnon and its forbidden counterpart (with the allowed magnon being slightly higher) was also observed. The difference between the allowed and forbidden magnon integrated intensities was found to be directly proportional to the overall magnetization for the two different fields applied. The observations are in agreement with the slowly fluctuating spin-density theory of itinerant ferromagnetism. Surprisingly, the reduction in magnon frequency with increasing temperature follows a ${T}^{5/2}$ over a wide temperature range. Such dependence is much like that which occurs at low temperatures.

High temperature behaviour of spin waves in Fe 3-xMn xSi

Neutron scattering measurements of spin waves in the substitutionally ordered alloy Fe 2.68Mn 0.32Si have been performed by the constant-E and constant-Q methods in the temperature range 293–720 K. In the ferromagnetic region the spin wave dispersion relation is quadratic, E=Dq 2, with stiffness constant equal to 160 meV. Å 2 at room temperature. Magnon-like peaks observed above T c in constant-E scans were not detected in constant-Q scans leading us to the conclusion that they originated from paramagnetic scattering.

Neutron scattering investigation of incommensurate ThBr4

The structural and lattice dynamical aspects of the incommensurate phase transition in ThBr4(Tc=95K) are studied by means of elastic and inelastic neutron scattering. Above Tc the temperature-dependent softening of a low-lying optic mode of wavevector qs approximately=0.3 c* is observed. The combined analysis of the room-temperature optical spectra and of the satellite extinction rules (T<Tc) allows one to determine the irreducible representation of the soft optic branch. The corresponding eigenvector consists of a simple linear combination of B1u-type and B2g-type bromine displacements. The resulting site symmetry for the thorium ions is discussed. Below Tc, constant-Q scans, near the strong (2, 3, 0.69) satellite reflection reveal the existence of two soft excitations: a low-frequency branch with a linear-like dispersion which the authors identify as the (propagating) phase mode, and an upper branch whose temperature dependence is consistent with that expected for the amplitude mode. The predictions of elementary theory concerning the dispersion, damping and oscillator strength for each of the two soft excitations are compared with the experimental data. Effects related to possible interactions with the long-wavelength acoustic models are considered.

Structure and collective excitations in amorphous selenium

The structure factor and the dynamical scattering function of Se in the amorphous state are determined by means of neutron scattering. The structure factor is used to obtain, by means of suitable theoretical approximations, firstly a two-body potential and secondly, from this potential, the dispersion on relations of transverse and longitudinal collective excitations. The dynamical structure factors, obtained by constant-Q scans in triple-axis spectrometry, are found to be consistent with the presence of side peaks arising from the existence of such collective excitations, whose positions are independently obtained by the theoretical calculations.