Thermodynamics of magnetic chains withS≤52

Abstract

The specific heat (C) and entropy (q) in zero field are calculated for infinite chains of spins, coupled by a nearest-neighbor Heisenberg exchange. The data presented include all spin values S & 5/2 and cover ferromagnetic and antiferromagnetic exchange. Several techniques are used to obtain reliable estimates for the infinite chains, and much attention is given to the theory underlying these techniques. For high temperatures the series expansion of C is used for the estimates. Coefficients in the series are obtained from the energy spectra of different finite chains. This method is fully described, and attention is given to the estimation of further coefficients. For intermediate temperatures, around the region where C displays the characteristic broad maximum, the series expansions fail and here the estimates of the infinite chain are obtained from a suitable extrapolation of the data for finite chains. This method is shown to be correct for sufFiciently high temperatures. It is applicable to a wide temperature range. For temperatures near T = 0, C is described by a polynomial based on the spin-wave theory. The coefficients in this polynomial are equated such that a smooth fit in with the intermediate temperature specific heat is obtained and that at the same time the over-all entropy gain is correct. The results are, as far as possible, tabulated.

Magnetically linear and quadratic hexanitrocuprates

“…It should be noted that these theoretical results are not in good agreement with those of de Neef [16] at low temperatures. However, since the latter predictions are in serious disagreement with the analytical result of Takahashi [17] that lim JC =!…”

Magnetic Properties of Ferromagnetic Quasi-1D Copper-Peptide Compounds: Exchange Interactions and Very Low Temperature Phase Transitions

“…Considering basic concepts in ferromagnetism, Bonner and Fisher, Blöte, and de Neef et al proposed that ∝ T 1/2 in the very low temperature range, where calculations with finite chains are not valid. De Neef 23 also used a polynomial in x with three half integer terms ( x 1/2 , x 3/2 , and x 5/2 ) to extrapolate intermediate temperature results to lower temperatures where approaches the spin wave limit.…”

A Prerequisite for Purely Organic Molecule-Based Ferrimagnetics: Breakdown of Simple Classical Pictures

“…The following Heisenberg−Dirac Hamiltonian with lowered symmetry of J AF is exploited: where J AF1 , J AF2 , J AF3 , and J AF4 are allowed to differ from each other and the periodic boundary condition is retained. To obtain both the S value and the degeneracy, including accidental ones, simultaneously for low-lying eigenstates, the canonical orthogonalization procedure , has been taken first. Then, with respect to the eigenvectors of S 2 thus obtained, diagonalization by Householder method has been carried out.…”