  We provide evidence that spin ferroquadrupolar (FQ) order is the likely
ground state in the nonmagnetic nematic phase of stoichiometric FeSe. By
studying the variational mean-field phase diagram of a bilinear-biquadratic
Heisenberg model up to the 2nd nearest neighbor, we find the FQ phase in close
proximity to the columnar antiferromagnet commonly realized in iron-based
superconductors; the stability of FQ phase is further verified by the density
matrix renormalization group. The dynamical spin structure factor in the FQ
state is calculated with flavor-wave theory, which yields a qualitatively
consistent result with inelastic neutron scattering experiments on FeSe at both
low and high energies. We verify that FQ can coexist with $C_4$ breaking
environments in the mean-field calculation, and further discuss the possibility
that quantum fluctuations in FQ act as a source of nematicity.
