  In the search for rare-earth free permanent magnets, various ideas related to
shape anisotropy are being pursued. In this work we assess the limits of shape
contributions to the reversal stability using micromagnetic simulations. In a
first series of tests we altered the aspect ratio of single phase prolate
spheroids from 1 to 16. Starting with a sphere of radius $4.3$ times the
exchange length $ L_{\mathrm{ex}}$ we kept the total magnetic volume constant
as the aspect ratio was modified. For a ferromagnet with zero
magnetocrystalline anisotropy the maximum coercive field reached up to $0.5$
times the magnetization $M_{\mathrm{s}}$. Therefore, in materials with moderate
uniaxial magnetocrystalline anisotropy, the addition of shape anisotropy could
even double the coercive field. Interestingly due to non-uniform magnetization
reversal there is no significant increase of the coercive field for an aspect
ratio greater than 5. A similar limit of the maximum aspect ratio was observed
in cylinders. The coercive field depends on the wire diameter. By decreasing
the wire diameter from $8.7 L_{\mathrm{ex}}$ to $2.2 L_{\mathrm{ex}}$ the
coercive field increased by 40%. In the cylinders nucleation of a reversed
domain starts at the corners at the end. Smoothing the edges can improve the
coercive field by about 10%.
  In further simulations we compacted soft magnetic cylinders into a bulk-like
arrangement. Misalignment and magnetostatic interactions cause a spread of $0.1
M_{\mathrm{s}}$ in the switching fields of the rods. Comparing the volume
averaged hysteresis loops computed for isolated rods and the hysteresis loop
computed for interacting rods, we conclude that magnetostatic interactions
reduce the coercive field by up to 20%.
