  A small in-plane external uniaxial pressure has been widely used as an
effective method to acquire single domain iron pnictide BaFe$_2$As$_2$, which
exhibits twin-domains without uniaxial strain below the
tetragonal-to-orthorhombic structural (nematic) transition temperature $T_s$.
Although it is generally assumed that such a pressure will not affect the
intrinsic electronic/magnetic properties of the system, it is known to enhance
the antiferromagnetic (AF) ordering temperature $T_N$ ($<T_s$) and create
in-plane resistivity anisotropy above $T_s$. Here we use neutron polarization
analysis to show that such a strain on BaFe$_2$As$_2$ also induces a static or
quasi-static out-of-plane ($c$-axis) AF order and its associated critical spin
fluctuations near $T_N/T_s$. Therefore, uniaxial pressure necessary to detwin
single crystals of BaFe$_2$As$_2$ actually rotates the easy axis of the
collinear AF order near $T_N/T_s$, and such effect due to spin-orbit coupling
must be taken into account to unveil the intrinsic electronic/magnetic
properties of the system.
