Iron
oxide nanorings have great promise for biomedical applications
because of their magnetic vortex state, which endows them with a low
remanent magnetization while retaining a large saturation magnetization.
Here we use micromagnetic simulations to predict the exact shapes
that can sustain magnetic vortices, using a toroidal model geometry
with variable diameter, ring thickness, and ring eccentricity. Our
model phase diagram is then compared with simulations of experimental
geometries obtained by electron tomography. High axial eccentricity
and low ring thickness are found to be key factors for forming vortex
states and avoiding net-magnetized metastable states. We also find
that while defects from a perfect toroidal geometry increase the stray
field associated with the vortex state, they can also make the vortex
state more energetically accessible. These results constitute an important
step toward optimizing the magnetic behavior of toroidal iron oxide
nanoparticles.