  The organometallic ring molecules Fe_6 and 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.
