Dynamic Spin Correlation Function Research Articles

Dynamics of a system of randomly distributed spins with multipolar interactions: Application to dipolar systems

A general first-principles method for the calculation of dynamical spin correlation functions in a system of randomly distributed, strongly interacting spins with multipolar interactions is presented. The method is valid in the high-temperature limit and is applicable at all spin concentrations $c$. As a numerical example, the case of dipolar forces is treated and the magnetic-resonance frequency line shape is calculated for a variety of values of $c$. The general trend of the change in line shape with $c$ obtained agrees with phenomenological theories and with experiment. The theoretical linewidth has the correct $c$ dependence in both the $c\ensuremath{\rightarrow}1$ and $c\ensuremath{\rightarrow}0$ limits.

Higher-order approximations for dynamical spin correlation functions in high-temperature paramagnets

A method of generating equations for dynamical two-point spin correlation functions for systems interacting via spin-spin interactions in the high-temperature limit is presented. The method is exact in the sense that all moments of the correlation functions are exact to order $\frac{1}{Z}$ where $Z$ is the effective number of nearest spin neighbors. Thus the equations are formally exact in the limit of large dimensionality with nearest-neighbor interactions. As an example the method is applied to the isotropic Heisenberg paramagnet.

On the dynamics of Heisenberg magnets with lattice anisotropy near the phase transition

The kinetic theory (mode-mode coupling theory) is applied to lattice anisotropic Heisenberg ferromagnets and anti-ferromagnets in the paramagnetic region near the phase transition. The distinction of a hydrodynamic and a critical region is refined by introducing regimes of essentially lower-dimensional (1-d or 2-d) behavior and three-dimensional behavior of the magnet. In the regime of 3-d behavior the scaling function of the line-width of the dynamic spin correlation function is discussed extensively.

Dynamical Spin Correlations in Many-Spin Systems. I. The Ferromagnetic Case

The quantum-statistical mechanics of an anisotropic Heisenberg spin system is studied by a temperature-time-dependent Green's-function formalism. A consistent scheme of higher-order random-phase approximations (RPA) is developed and the second-order (2nd) RPA is examined in detail. It turns out that the 2nd RPA can be defined in two alternative versions, I and II, with equal a priori justification. These two versions of the 2nd RPA have then to be supplemented with either a dynamical or a kinematical sum rule, thus leading to four possible alternative descriptions of the problem. Each of these descriptions can in principle be used to determine the spectral functions of both the longitudinal and the transverse dynamical spin-correlation functions. However, upon detailed examination of the 2nd RPA, it is found that only one of these four possible descriptions satisfies all the various consistency requirements. At low temperatures, this description reproduces the spin-wave results. To facilitate analytical solutions, an approximate version of the 2nd RPA, called the modified (mod) RPA, is introduced which leads to a satisfactory expression for the longitudinal correlation function over the entire range of temperatures. Upon examination it is found that the mod RPA determines the longitudinal correlation to the same accuracy, for the case of the isotropic exchange, as the first RPA determines the transverse correlation function. In addition to this mod RPA version of the consistent 2nd RPA, there also appears to be another relatively satisfactory solution for the longitudinal correlation function which follows from one of the less consistent versions of the 2nd RPA. This is treated as a phenomenological result. The system thermodynamics is analyzed in the region of the transition temperature in terms of both the consistent version of the mod RPA, i.e., the I mod RPA, as well as the phenomenological representation, i.e., the II mod RPA, with results which in addition to being an improvement on those following from the first RPA are also free from the inherent inconsistencies of the first RPA. In conclusion, the related work of other authors is discussed and it is shown that all these works suffer from serious internal inconsistencies which render their results for the longitudinal correlation function completely unacceptable and erroneous.