Nature of phase transitions in the parent and lightly electron doped BaFe$_{2}$As$_{2}$ compounds*

We present a combined high-resolution x-ray diffraction and x-ray resonant magnetic scattering study of as-grown BaFe$_{2}$As$_{2}$. The structural and magnetic transitions must be described as a two-step process. The undoped BaFe$_{2}$As$_{2}$ parent compound manifests a second-order structural transition from the high-temperature paramagnetic tetragonal structure to a paramagnetic orthorhombic phase and a first-order antiferromagnetic transition from the paramagnetic orthorhombic phase to an antiferromagnetic orthorhombic phase at slightly lower temperature. As electrons are introduced by Co or Rh, the phase transitions evolve toward second-order transitions. Using these results, we provide an estimate of the position of a tricritical point in the phase diagram of Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$.