Magnetic correlations and neutron scattering

TLDR

Recent statistical thermodynamics studies of Heisenberg‑coupled spin‑only magnets reveal that magnetic moment correlation functions, relaxation functions, generalized susceptibilities, and power spectra are deeply interrelated with neutron‑scattering theory, and that spin‑diffusion approximations and dynamical slowing‑down near phase transitions highlight the limits of these connections. The authors employ approximate theories—including the method of moments for power‑spectrum analysis, Green‑function techniques, and spin‑diffusion approximations—to model the magnetic dynamics and examine the slowing‑down of fluctuations near critical points. They calculate molecular‑field and other simple approximations to obtain susceptibility frequency‑spectrum expressions that, across temperature ranges, reduce to delta functions, pseudo‑Gaussian, or pseudo‑Lorentzian forms and illustrate the transitions among these cases.

Abstract

An introduction is given to the methods and results of some recent researches into statistical thermodynamics bearing upon the correlation functions of magnetic moments in Heisenberg-coupled spin-only magnets, and their intimate connection with neutron-scattering theory and practice is brought out. The interrelationships between the correlation function, the relaxation function, the generalized susceptibility, the power spectrum of the fluctuations and the neutron scattering are explained, and it is shown that insights into any one of these aspects can serve to illuminate the others. Different forms of approximate theory are seen to be suitable in approaching the topic through these different avenues; the method of moments for analysing the power spectrum and the connection with Green function theory are described in particular. Some examples are calculated in molecular-field theory and with various other simple approximations; expressions for the frequency spectrum of the susceptibility are obtained in various temperature ranges. The extreme forms of the frequency spectrum in appropriate conditions as a set of delta functions, as a pseudo-Gaussian and as a pseudo-Lorentzian are derived, and the transitions between these cases are considered. The approximation of spin diffusion and its limitations are analysed; the problem of the dynamical slowing-down of magnetic fluctuations near the phase-transition point is examined and the current position in this enquiry is set out.