Spin wave spectrum and exchange interactions in the antiferromagnetic garnet Ca3Cr2Ge3O12 by inelastic neutron scattering

We have measured the spin wave spectrum for the garnet Ca₃Cr₂Ge₃O₁₂ by means of inelastic neutron scattering. The data can be well described in the framework of linear spin wave theory if we assume a Heisenberg model with two exchange parameters up to the next nearest neighbours (J ₁ andJ ₂) and a staggered anisotropy field (A). A least squares fit to the observed dispersion relations yield the following values for these parameters: J ₁=–0.582(8)K,J ₂=0.416(4)K,A=0.25(8)K. Although symmetry requires that two nearest neighbour exchange constantsJ ₁ andJ ₁ ^' must be distinguished, only the average J ₁=(J ₁+3J ₁ ^' )/4 and the condition –0.35 K <J ₁=J ₁-J ₁ ^' <0.50 K could be deduced from the experiment. The most striking result is the positive value ofJ ₂. We discuss the implications for an understanding of superexchange mediated by more than one oxygen atom. In an extension of the conventional analysis we have calculated the integrated intensities in order to check the eigenvectors directly. Good agreement between observed and calculated intensities was obtained.     

Magnetic excitations and phase transition of CsFeBr3 in an external magnetic field

In CSFeBr₃ the Fe²⁺ ion with effective spin one has locally a singlet ground state (m=0). The antiferromagnetic interactions between neighbouring Fe-ions are too weak as compared with the anisotropy constant to introduce long range order in the absence of an external field. By inelastic neutron scattering we studied the magnetic excitations in an external magnetic field up to 5 Tesla applied along thec-axis. A linear Zeeman splitting was observed with a Landé factorg=2.4. The field renormalizes the dispersion curves in such a way that the exchange interaction has decreasing influence with increasing field. Theoretical calculations according to the excitonic model of Lindgård describe the experimental results very well. At 4.1 Tesla a phase transition appears to a commensurate long range order with a 120° arrangement of the spins in the hexagonal plane. Within the limits of experimental observation this phase transition has no influence on the dynamical behaviour. No critical phenomena could be observed. The dynamical structure factor |G _j()|² of the lower Zeeman split modes decreases with increasing field.     

Magnetic excitations in the quasi one-dimensional antiferromagnetic singlet groundstate system CsFeBr3

We have measured the magnetic excitations in CsFeBr₃ along the chain direction (z-axis) and perpendicular to it by inelastic neutron scattering. The measured dispersion curves can be reproduced by the formula $$\omega ^2 (q) = A^2 - 8A[J\cos (\pi q_c ) + J'\gamma (2\pi q_ \bot )]R(T)$$ which is very different from dispersion relations for usual 1 D antiferromagnets, because of the singlet groundstate of this system. The large value of the anisotropy energyA/k=29.8±0.5 K, which is independent of temperature, causes the singlet groundstate. The intra-and inter-chain exchange parameters areJ/k=?3.2±0.15K andJ'/k=?0.32±0.02 K determined atT=1.4 K. At 1.4 K the renormalisation factor is taken to beR(T)=1. AtT=30 K the value forR(T) was found to be 0.5±0.1 keepingJ andJ' unchanged. The excitations at (1/3 1/31) show soft mode behaviour but no phase transition. The observed intensities are interpreted by a heuristic model for the eigenvectors in the excited state including antiferro-as well as ferromagnetic configurations of the fluctuations.     

Soft modes in semiconducting SrTiO3: II. The ferroelectric mode

The frequency, temperature and wavevector dependence of the ferroelectric soft mode in semiconducting SrTiO₃ was investigated by temperature derivative Raman spectroscopy and by inelastic neutron scattering. A tremendous shift in mode frequency with free electron and oxygen vacancy concentration, respectively, was observed.     

Temperature and magnetic field dependent correlations in the singlet ground state system CsFeBr3

The magnetic excitations in CsFeBr₃ have been measured with inelastic scattering of cold neutrons to high precision at 80 mK. The fact that the lowest frequency mode softens with decreasing temperature but stabilizes at 0.11 THz below 2.5 K is the indication that CsFeBr₃ remains a SGS system forT0.From dispersion curves measured earlier in a magnetic field along the chain axis experimental intensities were derived and in turn correlation lengths. Correlation lengths were also calculated using the new parameters for exchange and anisotropy. The experimental results and the calculations both show that the correlation lengths increase for increasing magnetic field, flatten off around the phase transformation at 4.1 Tesla with a maximum of about 35 Å and then decrease again for higher fields. No critical phenomena connected with this phase transformation could be detected.The Mirror Mode published earlier was found to be of spurious origin due to double scattering. It does not exist.     

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Coherent neutron inelastic scattering intensifies for two low-frequency Γ₄ internal modes in anthracene-d₁₀ have been measured at several different Brillouin zone centres. These intensifies have been used to determine the eigenvectors of the two modes involved. It is shown that the motion in both cases is a combination of a butterfly motion (B) and a twisting motion (T). The energy proportions in these two modes are 0.97B and 0.03T (±0.01) for the mode at 3.16 THz and 0.94T and 0.06B (±0.04) for the mode at 4.60 THz. This experimental result strengthens our reliance on model calculations for the assignment of phonon frequencies measured by neutron coherent inelastic scattering.     

Determination of the lattice vibrations of imidazole by neutron scattering

The external molecular vibrations of deuterated imidazole have been investigated at 12 K for wave vectors along the three principal directions of the Brillouin zone by neutron scattering and by Raman scattering at the zone center. A complete symmetry assignment is obtained. The dominant role of the N-H … N hydrogen bond within the intermolecular interactions is reflected in a relatively simple manner in the shape of the dispersion curves because of the chain-like arrangement of hydrogen bonds. The experiment yields directly a stretching force constant of 0.33 mdyn Å^?1 for this bond. This value is compatible with monopole-dipole and dipole-dipole interactions as major contributions to the attractive interactions of the hydrogen bond of this length (2.86 Å). Relatively strong static monopoles and dipoles are confirmed by a $\text{CNDO}\text{2}$ calculation and are consequently incorporated into the interaction model.     

Dynamics of a quantum phase transition

We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatment of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses Landau-Zener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.