J W Tucker

Transverse current correlations in simple liquids

An approximate expression for the memory function associated with transverse current correlations have been evaluated for models both of liquid rubidium and liquid argon. Results for the frequency spectrum of the current correlation function are also presented for a range of wavenumbers and compared, where possible, with those obtained from computer simulation studies. From the memory function an expression for the shear viscosity coefficient may be derived, but the values obtained for the latter near the melting points of the liquids are of the order of 40% smaller than the experimentally determined values.

Theory of the acoustic Faraday and Cotton-Mouton effects in Ni2+-doped KMgF3

The theory of the acoustic Faraday and Cotton-Mouton effects in Ni2+-doped KMgF3 is presented. These effects occur when degenerate transverse acoustic phonons are propagating respectively parallel and perpendicular to an applied magnetic field. At a frequency of 9.4 GHz and a magnetic field of 4.4 kG the Faraday rotation and the Cotton-Mouton phase shift are calculated to be 1.99 and 1.12 rad cm-1 at 4.2K for a nickel ion concentration of 1%. It is suggested that this material might be a suitable candidate for the first known observation of these effects in a 3d transition ion paramagnet involving only single ion effects. The importance of using the full spin-phonon Hamiltonian as dictated by symmetry is stressed. At low frequencies the Cotton-Mouton phase shift is found to be proportional to omega 3 in contrast to the rare-earth ion situation recently discussed in the literature.

Spin dynamics of site- and bond-diluted anisotropic paramagnets at high temperatures

The relaxation-shape function F(k, omega ) for a diluted anisotropic paramagnet at elevated temperatures is studied. A semi-phenomenological representation of the relaxation-shape function is used. In this representation, a Gaussian choice for the memory function associated with the spin-velocity relaxation function is made that preserves all the frequency moments of F(k, omega ) up to and including the sixth. The sixth moment is evaluated with the aid of a computer for both site and bond disorder. For bond disorder two models previously studied by Kawasaki and Tahir-Kheli (1978) are adopted, one in which the existence of transverse and longitudinal bonds depends only on a single random variable, and a second in which these bonds can fluctuate independently. Both the longitudinal and transverse dynamics are studied and the results are compared with those obtained using a Gaussian representation of the generalised diffusivity.

The frequency moments of the spin-correlation function for a dilute isotropic Heisenberg paramagnet

Analytic expressions for the low-order frequency moments omega n (n=0,2,4,6) of the spin correlation function for a dilute isotropic Heisenberg paramagnet at infinite temperature are obtained for arbitrary spin and arbitrary range of the magnetic interactions. A check on the accuracy of the expressions is provided by computer results for a number of simple lattices restricted to nearest-neighbour magnetic interactions.

Phonon scattering by paramagnetic ions. II. Ions having S=1 in a crystal field of uniaxial symmetry

For pt.I see ibid., vol.9, p.4237, 1976. The phonon scattering by paramagnetic ions having an effective spin of unity in a crystal field of uniaxial symmetry is calculated for arbitrary concentrations of ions. The calculation employs a Green function technique based on the use of semi-invariants. To evaluate the semi-invariants a Wicks theorem is introduced that allows for the presence of crystal-field terms in the static spin Hamiltonian. The lifetime of the coupled spin-phonon excitations is calculated in the phonon regime and the frequency, temperature and concentration dependence is examined in detail. Comparison with the Born approximation in the dilute limit is also made as it provides a valuable check on the accuracy of the expressions and gives additional physical insight into the origin of the scattering processes.

Phonon scattering by paramagnetic ions with S>1/2. I. Zeeman levels in the absence of a zero-field splitting

In an interacting spin-phonon system, coherences in the phonon scattering from different ions lead to coupled spin-phonon modes. The lifetime of these excitations in the phonon regime is calculated for a crystal containing ions with S>1/2. The poles of the phonon Green function are related directly to those of a generalized cumulant spin Green function for which a diagrammatic expansion in terms of a polarization matrix is presented. Averages of time-ordered products of spin operators occur and these are expressed in terms of semi-invariants. To evaluate the latter, a generalized Wicks theorem is developed that deals directly with operators that are of higher order than linear in the spin components. A detailed analysis of the attenuation is made in the case when paramagnetic ions are in sites of octahedral symmetry in a cubic crystal. An explicit expression is given in a situation of experimental interest, namely, for transverse wave propagation along a cubic axis with the propagation and polarization vectors respectively perpendicular and parallel to the axis of quantization.

Phonon scattering by paramagnetic ions in a concentrated paramagnetic crystal

In an interacting spin-phonon system, coherences in the phonon scattering from different ions lead to coupled spin-phonon modes. The lifetime of the excitations is calculated for a fully concentrated crystal containing ions with S=1/2. The poles of the phonon Green function are related directly to those of the generalized spin susceptibility for which a diagrammatic expansion in terms of a polarization matrix M is presented. Averages of time-ordered products of spin operators that occur are expressed in terms of semi-invariants and evaluated using the Vaks diagrammatic technique. Inclusion of the diagrams in the expansion of M to second order lead away from resonance, to a phonon lifetime consistent with that obtained in previous treatments using the drone-fermion representation. A new feature of the present method however is that a partial summation of M to all orders, at least at low temperatures, is possible that enables the lifetime of the coupled excitations to be found over the entire frequency range. Results for the lifetime of the excitations close to the spin resonance frequency are presented.

The longitudinal sixth moment for an anisotropic paramagnet having site or exchange-bond dilution

Analytic expressions are derived for the longitudinal sixth frequency moment of the spin correlation function for a dilute anisotropic Heisenberg paramagnet in the high-temperature limit. The results are valid for arbitrary spin and arbitrary range of the exchange interactions. Both site and exchange-bond dilution are treated. The latter is treated using two models introduced by Kawasaki and Tahir-Kheli (1978). In one the existence of longitudinal and transverse bonds depends only on a single random variable, whilst in the other they can fluctuate independently. As an application of the use of the moments, the extent to which pseudo-dipolar interactions can affect the high-temperature spin dynamics of a Heisenberg magnet is examined.

The effects of exchange-bond dilution on the dynamics of an anisotropic paramagnet at elevated temperatures

The spin dynamics of an anisotropic paramagnet having exchange-bond dilution is studied at elevated temperatures using a semi-phenomenological representation of the relaxation-shape function and a knowledge of the low-order frequency moments. The calculations are made for a model in which the three cartesian components of the exchange-bond between each pair of atoms can fluctuate independently. Results are presented for an anisotropic paramagnet having, on average, cylindrical symmetry. For the longitudinal correlations a substantial difference is found between the results of this model and those of the model adopted by Kawasaki and Tahir-Kheli (1978) having only two degrees of randomness in the bond dilution.

The frequency moments for an anisotropic paramagnet with exchange-bond dilution in the high-temperature limit

The low-order frequency moments omega n (n=0, 2, 4, 6) of the spin correlation function for a Heisenberg paramagnet with bond dilution are calculated at infinite temperature. The calculations are for a model in which the three cartesian components of the exchange between each pair of atoms can fluctuate independently. The results are for general spin but are restricted to nearest-neighbour exchange interactions.