  We report neutron scattering experiments probing the influence of uniaxial
strain on both the magnetic and structural order parameters in the parent iron
pnictide compound, BaFe$_2$As$_2$. Our data show that modest strain fields
along the in-plane orthorhombic b-axis can affect significant changes in phase
behavior simultaneous to the removal of structural twinning effects. As a
result, we demonstrate in BaFe$_2$As$_2$ samples detwinned via uniaxial strain
that the in-plane C$_4$ symmetry is broken by \textit{both} the structural
lattice distortion \textit{and} long-range spin ordering at temperatures far
above the nominal (strain-free), phase transition temperatures. Surprising
changes in the magnetic order parameter of this system under relatively small
strain fields also suggest the inherent presence of magnetic domains
fluctuating above the strain-free ordering temperature in this material.
