  The origin of the electronic nematicity in FeSe is one of the most important
unresolved puzzles in the study of iron-based superconductors. In both spin-
and orbital-nematic models, the intrinsic magnetic excitations at
$\mathbf{Q}_1=(1, 0)$ and $\mathbf{Q}_2=(0, 1)$ of twin-free FeSe are expected
to provide decisive criteria for clarifying this issue. Although a
spin-fluctuation anisotropy below 10 meV between $\mathbf{Q}_1$ and
$\mathbf{Q}_2$ has been observed by inelastic neutron scattering around
$T_c\sim 9$ K ($<<T_s\sim 90$ K), it remains unclear whether such an anisotropy
also persists at higher energies and associates with the nematic transition
$T_{\rm s}$. Here we use resonant inelastic x-ray scattering (RIXS) to probe
the high-energy magnetic excitations of uniaxial-strain detwinned FeSe and
{\BFA}. A prominent anisotropy between the magnetic excitations along the $H$
and $K$ directions is found to persist to $\sim200$ meV in FeSe, which is even
more pronounced than the anisotropy of spin waves in {\BFA}. This anisotropy
decreases gradually with increasing temperature and finally vanishes at a
temperature around the nematic transition temperature $T_{\rm s}$. Our results
reveal an unprecedented strong spin-excitation anisotropy with a large energy
scale well above the $d_{xz}/d_{yz}$ orbital splitting, suggesting that the
nematic phase transition is primarily spin-driven. Moreover, the measured
high-energy spin excitations are dispersive and underdamped, which can be
understood from a local-moment perspective. Our findings provide the
much-needed understanding of the mechanism for the nematicity of FeSe and
points to a unified description of the correlation physics across seemingly
distinct classes of Fe-based superconductors.
