Low-temperature magnetization and the excitation spectrum of antiferromagnetic Heisenberg spin rings

摘要

Accurate results are obtained for the low-temperature magnetization vs magnetic field of Heisenberg spin rings consisting of an even number N of intrinsic spins s = 1/2, 1, 3/2, 2, 5/2, 3, 7/2 with nearest-neighbor antiferromagnetic exchange by employing a numerically exact quantum Monte Carlo method. A straightforward analysis of this data, in particular, the values of the level-crossing fields, provides accurate results for the lowest-energy eigenvalue E_N(S,s) for each value of the total spin quantum number S. In particular, the results are substantially more accurate than those provided by the rotational band approximation. For s ≤ 5/2, data are presented for all even N ≤ 20, which are particularly relevant for experiments on finite magnetic rings. Furthermore, we find that for s ≥ 3/2, the dependence of E_N(S,s) on s can be described by a scaling relation, and this relation is shown to hold well for ring sizes up to N = 80 for all intrinsic spins in the range 3/2 ≤ s ≤ 7/2. Considering ring sizes in the interval 8 ≤ N ≤ 50, we find that the energy gap between the ground state and the first excited state approaches zero proportional to 1/N~α, where α ≈ 0.76 for s = 3/2 and α ≈ 0.84 for s = 5/2. Finally, we demonstrate the usefulness of our present results for E_N(S,s) by examining the Fe_(12) ring-type magnetic molecule, leading to a more accurate estimate of the exchange constant for this system than has been obtained heretofore.