Relaxation-shape Function Research Articles

Spin dynamics in lightly dopedLa2−xSrxCuO4: Relaxation function within thet−Jmodel

The relaxation function theory of doped two-dimensional $S=1/2$ Heisenberg antiferromagnetic (AF) system in the paramagnetic state is presented taking into account the hole subsystem as well as both the electron and AF correlations. The expression for fourth frequency moment of relaxation shape function is derived within the $t-J$ model. The presentation obeys rotational symmetry of the spin correlation functions and is valid for all wave vectors through the Brillouin zone. The spin diffusion contribution to relaxation rates is evaluated and is shown to play a significant role in carrier free and doped antiferromagnet in agreement with exact diagonalization calculations. At low temperatures the main contribution to the nuclear spin-lattice relaxation rate, $^{63}(1/T_1)$, of plane $^{63}$Cu arises from the AF fluctuations, and $^{17}(1/T_1)$, of plane $^{17}$O, has the contributions from the wavevectors in the vicinity of $(\pi,\pi)$ and small $q \sim 0$. It is shown that the theory is able to explain the main features of experimental data on temperature and doping dependence of $^{63}(1/T_1)$ in the paramagnetic state of both carrier free La$_2$CuO$_4$ and doped La$_{2-x}$Sr$_x$CuO$_4$ compounds.

Dynamics of the classical two dimensional XY ferromagnet at low temperatures: a memory function approach

The spin dynamics of two dimensional XY ferromagnet are reexamined at low temperatures in the framework of the Mori continued fraction formalism using the Gaussian approximation. In this formalism, the terms on denominators for the Laplace transform of the relaxation function R(t) are related to the frequency moments<img src="http:/img/fbpe/bjp/v28n4/sd6.gif" alt="sd6.gif (174 bytes)" align="absmiddle"> of the relaxation shape function R(q,w). In the Gaussian approximation scheme, we truncate the continued fraction for R(t) on the second stage. Adopting this approximation, we calculated up to the sixth moment. The moments are writing in terms the static spin correlation functions. In the estimation of the fourth and sixth moment at finite temperature, the four and six-spin correlation functions may be approximated by a sum of products of appropriate pair correlation functions(mode-mode decoupling). In this work we calculated the static spin correlation functions for the expressions to the fourth and sixth moments, needed in the study of the dynamics.

Effects of the BijSxiSxj Interaction on the IMTF's Dynamics

AbstractAdditively to the Ising model in a transverse field (IMTF) an interaction BijSS is considered. For a S = 1/2 three‐dimensional cubic latticethe longitudinal relaxation shape function is calculated by means of Mori's continued‐fraction representation in a three‐pole approximation. The effects of this new term on the fluctuation spectra are studied for T &gt; Tc and the results compared with those obtained for the pure IMTF.

Dynamics of quasi-one- and two-dimensional spin systems in the high-temperature limit

Analytic expressions for the low-order frequency moments (n=0, 2, 4, 6), of the relaxation shape function F(K, omega ), are derived for a Heisenberg paramagnet at infinite temperature. Tucker's work is extended to systems with quasi-one- and two-dimensional character. Second-stage Gaussian truncation of the memory function, which preserves these moments, is employed to compute the spin correlation as a function of the wavevector and the frequency. Time dependence of the self-correlation is also examined. Results of this paper should be useful in understanding neutron scattering and NMR data on a wide variety of such magnetic systems now available to the experimentalists.

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.

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.

Spin dynamics of a diluted Heisenberg magnet at elevated temperatures

The relaxation-shape function F(k, omega ) for a diluted isotropic Heisenberg magnet at elevated temperatures is studied. A semi-phenomenological representation of the relaxation-shape function is employed in which a Gaussian choice for the memory function associated with the spin-velocity relaxation function is made which preserves all the frequency moments of F(k, omega ), up to and including the sixth. The relaxation-shape function is examined for several concentrations in the case of simple, body-centred and face-centred cubic lattices with nearest-neighbour interactions and the results are compared to those of Tahir-Kheli and Kawasaki (1975-1977); which are based on a Gaussian representation of the generalised diffusivity. In addition, the effect of extending the range of interaction to include next-nearest neighbour exchange is examined and the variation of the diffusion constant with concentration is studied.

On the second moment of the relaxation-shape function for a Heisenberg magnet

A high-temperature power series for the second moment of the relaxation-shape function including second neighbour interactions is calculated to order (J/kBT)5. The second neighbour specific heat series is inferred from this calculation. For first neighbours only it is shown how this second moment can be obtained from the specific heat series.

The sixth frequency moment of the relaxation-shape function for a Heisenberg paramagnet

A correction to the hitherto published expression for the sixth frequency moment of the relaxation-shape function of a Heisenberg paramagnet at elevated temperatures is presented. The results are in accord with a computer calculation for a face-centred cubic lattice with nearest- neighbour exchange interactions.

A three-peak structure for the critical relaxation function in the transverse Ising model

The dynamical properties of the transverse Ising model with an interaction of uniaxial dipolar nature are shown to exhibit a marked q-anisotropy in the critical region. For any wave vector q strictly non perpendicular to the z -axis the longitudinal relaxation shape function F q zz exhibits a three-peak structure and consequently a finite width of its central peak.

Temperature dependence of nuclear magnetic resonance linewidths in RbMnF 3

The temperature dependence of the 55Mn NMR linewidth in RbMnF 3 is calculated above T N using a representation for the relaxation-shape function based on the method of moments. A room temperature linewidth of 0.90 MHz is obtained in good accord with experiment.

Zero-field critical relaxation in cubic ferromagnet EuO

The zero-field critical relaxation rate in EuO closely above T c is examined. Mode-coupling theory is applied to it and corrections for the q = 0 decay of the relaxation shape function and the dipolar influence on χ q are introduced.

Use of the continued-fraction representation in the determination of the relaxation-shape function of a Heisenberg magnet

The continued-fraction expansion of Mori is employed in a study of the relaxation-shape function of a one-dimensional Heisenberg magnet. The case of spin 1 2 is examined for which the first ten frequency moments are known. It is shown that a termination of the continued-fraction at successive orders leads to quite different features in the form of the relaxation-shape function.

Spin dynamics for the one-dimensionalXYmodel at infinite temperature

The infinite-temperature space- and time-dependent spin-correlation functions ${g}_{r}^{x}(t)$ are studied for the one-dimensional $\mathrm{XY}$ model. Numerical calculations are performed to obtain the exact autocorrelation function ${g}_{0}^{x}(t)$ for chains containing 5, 7, and 9 spins ($S=\frac{1}{2}$). This yields exact results for the first 16 moments of the frequency autocorrelation function of the infinite chain, and estimates for a few of the higher moments as well. The analysis suggests that ${g}_{0}^{x}(t)$ for the infinite chain is identical to $\frac{\mathrm{exp}(\ensuremath{-}{J}^{2}{t}^{2})}{4}$. We show that ${g}_{r}^{x}(t)$ for $r\ensuremath{\ne}0$ vanishes identically for all values of time, implying a wave-vector-independent relaxation shape function. Our result for ${g}_{0}^{x}(t)$ is compared with that obtained by Huber for the classical ($S=\ensuremath{\infty}$) chain.

Spin dynamics in one-dimensional systems: Proton soin-lattice relaxation in TMMC

The recently proposed representations of the relaxation-shape function for a classical one-dimensional spin system are applied in a calculation of the temperature dependence of the spin-lattice relaxation rate in TMMC. Comparison with experiment is made.

Dynamics of the Iongitudinal spin for the three-dimensional, spin-½ Ising model in a transverse field

The dynamics of the Iongitudinal (i.e., parrallel to the $z$ axis) spin fluctuations of the three-dimensional Ising model in a transverse field, $H=\ensuremath{-}\ensuremath{\Gamma}\ensuremath{\Sigma}{i}^{}{S}_{i}^{x}\ensuremath{-}(\frac{1}{2})\ensuremath{\Sigma}{\mathrm{ij}}^{}{J}_{\mathrm{ij}}{S}_{i}^{z}{S}_{j}^{z}$, is studied. An approximate expression for the relaxation shape function is given which gives a simple but realistic view of the dynamics for the entire temperature range ${T}_{c}&lt;T&lt;\ensuremath{\infty}$. Plots of the shape function are obtained and analyzed.

Temperature dependence of nuclear magnetic relaxation above the magnetic transition temperature: application to19F in RbMnF3

A theory of the temperature dependence of the nuclear magnetic relaxation in the paramagnetic phase is presented. The relaxation rate is expressed as a product of the wavevector-dependent susceptibility and the wavevector-frequency-dependent relaxation-shape function for which a semi-phenomenological representation, based on the method of moments, is used. The temperature dependence, which is contained in the susceptibility and the moments of the relaxation-shape function, is estimated on the basis of a spherical model. The theory is applied to the 19F resonance in RbMnF3 and comparison with the experimental measurements of Hess and Hunt (see abstr. A48113 of 1972) is made.

Relaxation-shape function of a Heisenberg paramagnet based on the method of moments

The sixth frequency moment of the frequency-wavevector dependent relaxation-shape function F(k, omega ), at elevated temperatures is presented for a model applicable to RbMnF3. The exact value of this moment is compared to the approximate values predicted by the semi-phenomenological representations of the relaxation-shape function based on a knowledge of only the second and fourth moments. Finally, a Gaussian choice for the memory function associated with the spin-velocity relaxation function is made which preserves all the frequency moments of F(k, omega ), up to and including the sixth. The form of F(k, omega ) obtained with this memory function is compared to the first principle calculations of Blume and Hubbard and of Reiter. The value of the diffusion constant is found to be very close to that given by Mori and Kawasaki and by Bennett and Martin.

The memory function in the mode-mode coupling theory for the Heisenberg paramagnet

The equation for the relaxation shape function given by the mode-mode theory is studied in the critical region. The emphasis is put on the long-time behaviour of the memory function. A selfconsistent solution of the approximate equation for the generalized wave-vector-dependent diffusion constant is found in the limits q<<K and K<<q. This solution is used to obtain the explicit time dependence of the memory function. In the hydrodynamic region, q<<K, it has the asymptotic form t-5/2 exp(-Dq2t/2) with an inverse fractional power dependence on t. This leads to the conclusion that the equation of motion in the mode-mode theory does not have a characteristic spin diffusion solution with pure exponential decay for asymptotically large times.

Magnetic field dependence of the 31P longitudinal nuclear-spin relaxation time in GdP at high temperatures

The magnetic field dependence of the longitudinal nuclear-spin relaxation time for 31P nuclei in paramagnetic GdP is expressed in terms of a wavevector frequency-dependent relaxation-shape function. A Gaussian representation of the memory function associated with the spin-velocity relaxation function is chosen that satisfies the first six frequency moments. The results are compared with the experimental data of Myers and Narath.