  First principles density functional theory DFT+U calculations and
experimental neutron diffraction structure analyses were used to determine the
low-temperature crystallographic and magnetic structure of bixbyite Mn2O3. The
energies of various magnetic arrangements, calculated from first principles,
were fit to a cluster-expansion model using a Bayesian method that overcomes a
problem of underfitting caused by the limited number of input magnetic
configurations. The model was used to predict the lowest-energy magnetic
states. Experimental determination of magnetic structure benefited from
optimized sample synthesis, which produced crystallite sizes large enough to
yield a clear splitting of peaks in the neutron powder diffraction patterns,
thereby enabling magnetic-structure refinements under the correct orthorhombic
symmetry. The refinements employed group theory to constrain magnetic models.
Computational and experimental analyses independently converged to similar
ground states, with identical antiferromagnetic ordering along a principal
magnetic axis and secondary ordering along a single orthogonal axis, differing
only by a phase factor in the modulation patterns. The lowest-energy magnetic
states are compromise solutions to frustrated antiferromagnetic interactions
between certain corner-sharing MnO6 octahedra.
