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 int
erest both for their intrinsic magnetic properties and as candidates for th
e observation of macroscopic quantum coherent phenomena. Torque magnetometr
y experiments have been performed to measure the magnetization in single cr
ystals of both systems. We provide a detailed interpretation of these resul
ts, with a view to full characterization of the material parameters. We pre
sent both the most accurate numerical simulations performed to date for rin
g molecules, using exact diagonalization and density-matrix renormalization
-group techniques, and a semiclassical description for purposes of comparis
on. The results permit quantitative analysis of the variation of critical f
ields with angle, of the nature and height of magnetization and torque step
s, and of the width and rounding of the plateau regions in both quantities.