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

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-alpha, where alpha approximate to 0.76 for s=3/2 and alpha approximate to 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.