  Magneto-structural phase transitions in Ba1-xAxFe2As2 (A = K, Na) materials
are discussed for both magnetically and orbitally driven mechanisms, using a
symmetry analysis formulated within the Landau theory of phase transitions.
Both mechanisms predict identical orthorhombic space-group symmetries for the
nematic and magnetic phases observed over much of the phase diagram, but they
predict different tetragonal space-group symmetries for the newly discovered
re-entrant tetragonal phase in Ba1-xNaxFe2As2 (x ~ 0.24-0.28). In a magnetic
scenario, magnetic order with moments along the c-axis, as found
experimentally, does not allow any type of orbital order, but in an orbital
scenario, we have determined two possible orbital patterns, specified by
P4/mnc1' and I4221' space groups, which do not require atomic displacements
relative to the parent I4/mmm1' symmetry and, in consequence, are
indistinguishable in conventional diffraction experiments. We demonstrate that
the three possible space groups are however, distinct in resonant X-ray Bragg
diffraction patterns created by Templeton & Templeton scattering. This provides
an experimental method of distinguishing between magnetic and orbital models.
