2005/12/01 by Larry Engelhardt, Marshall Luban · 38 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Energy (signal processing) #Excitation #Excited state #Ground state #Heisenberg model #Magnetic field #Magnetism in coordination complexes #Magnetization #Mathematics #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Quantum Monte Carlo #Quantum mechanics #Spin (aerodynamics) #Spins #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.73.054430
published in Physical Review B 73(5) (American Physical Society) · Submitted to Physical Review B, 10 pages, 10 figures
arxiv created 2005/12/01 · openalex publication_date 2006/02/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 EN(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\ensuremath\leqslant5∕2, data are presented for all even N\ensuremath\leqslant20, which are particularly relevant for experiments on finite magnetic rings. Furthermore, we find that for s\ensuremath\geqslant3∕2, the dependence of EN(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\ensuremath\leqslants\ensuremath\leqslant7∕2. Considering ring sizes in the interval 8\ensuremath\leqslantN\ensuremath\leqslant50, we find that the energy gap between the ground state and the first excited state approaches zero proportional to 1∕N^\ensuremathα, where \ensuremathα\ensuremath≈0.76 for s=3∕2 and \ensuremathα\ensuremath≈0.84 for s=5∕2. Finally, we demonstrate the usefulness of our present results for EN(S,s) by examining the Fe12 ring-type magnetic molecule, leading to a more accurate estimate of the exchange constant for this system than has been obtained heretofore.