Magnetism and nematic order are the two non-superconducting orders observed
in iron-based superconductors. To elucidate the interplay between them and
ultimately unveil the pairing mechanism, several models have been investigated.
In models with quenched orbital degrees of freedom, magnetic fluctuations
promote stripe magnetism which induces orbital order. In models with quenched
spin degrees of freedom, charge fluctuations promote spontaneous orbital order
which induces stripe magnetism. Here we develop an unbiased approach, in which
we treat magnetic and orbital fluctuations on equal footing. Key to our
approach is the inclusion of the orbital character of the low-energy electronic
states into renormalization group analysis. Our results show that in systems
with large Fermi energies, such as BaFe2As2, LaFeAsO, and NaFeAs, orbital order
is induced by stripe magnetism. However, in systems with small Fermi energies,
such as FeSe, the system develops a spontaneous orbital order, while magnetic
order does not develop. Our results provide a unifying description of different
iron-based materials.Comment: 61 pages, 19 figure