  The iron-based high temperature superconductors exhibit a rich phase diagram
reflecting a complex interplay between spin, lattice, and orbital degrees of
freedom [1-4]. The nematic state observed in many of these compounds epitomizes
this complexity, by entangling a real-space anisotropy in the spin fluctuation
spectrum with ferro-orbital order and an orthorhombic lattice distortion [5-7].
A more subtle and much less explored facet of the interplay between these
degrees of freedom arises from the sizable spin-orbit coupling present in these
systems, which translates anisotropies in real space into anisotropies in spin
space. Here, we present a new technique enabling nuclear magnetic resonance
under precise tunable strain control, which reveals that upon application of a
tetragonal symmetry-breaking strain field, the magnetic fluctuation spectrum in
the paramagnetic phase of BaFe$_{2}$As$_{2}$ also acquires an anisotropic
response in spin-space. Our results unveil a hitherto uncharted internal spin
structure of the nematic order parameter, indicating that similar to liquid
crystals, electronic nematic materials may offer a novel route to
magneto-mechanical control.
