Magnetization in molecular iron rings

The organometallic ring molecules ${\mathrm{Fe}}_6$ and ${\mathrm{Fe}}_{10}$ are leading examples of a class of nanoscopic molecular magnets which have been of intense recent interest both for their intrinsic magnetic properties and as candidates for the observation of macroscopic quantum coherent phenomena. Torque magnetometry experiments have been performed to measure the magnetization in single crystals of both systems. We provide a detailed interpretation of these results, with a view to full characterization of the material parameters. We present both the most accurate numerical simulations performed to date for ring molecules, using exact diagonalization and density-matrix renormalization-group techniques, and a semiclassical description for purposes of comparison. The results permit quantitative analysis of the variation of critical fields with angle, of the nature and height of magnetization and torque steps, and of the width and rounding of the plateau regions in both quantities.