Tetragonal-orthorhombic phase coexistence under magnetic fields in the nematic phase of BaFe$_2$As$_2$ and Sr(Fe$_{0.80}$Co$_{0.20}$)$_2$As$_2$
Synchrotron x-ray diffraction experiments were performed on BaFe$_2$As$_2$ and Sr(Fe$_{0.80}$Co$_{0.20}$)$_2$As$_2$ single crystals as a function of temperature and applied magnetic field along the tetragonal $[1 \bar{1} 0]$ direction, complemented by electrical resistivity and specific heat experiments. For a BaFe$_2$As$_2$ crystal with spin-density-wave antiferromagnetic ordering temperature $T_{AF}=132.5$ K and onset of the orthorhombic nematic phase at $T_{o}=137$ K, the magnetic field favors the growth of tetragonal domains that compete with orthorhombic ones at the vicinity of $T_{AF}$, indicating a slight ($\sim 1$ K) decrease of $T_{AF}$ with application of $B=5.9$ T, with no sign of field-dependence for $T_{o}$. For Sr(Fe$_{0.80}$Co$_{0.20}$)$_2$As$_2$ with more separated transitions ($T_{AF} = 132$ K and $T_{o} = 152$ K), the crystal structure also shows significant field-dependence in a narrow temperature interval close to $T_{AF}$. These results are discussed under both orbital and magnetic scenarios for the nematic transition of these materials.