  In most existing theories for iron-based superconductors, spin-orbit coupling
(SOC) has been assumed insignificant. Even though recent experiments have
revealed an influence of SOC on the electronic band structure, whether SOC
fundamentally affects magnetism and superconductivity remains an open question.
Here we use spin-polarised inelastic neutron scattering to show that collective
low-energy spin fluctuations in the orthorhombic (or "nematic") phase of FeSe
possess nearly no in-plane component. Such spin-space anisotropy can only be
caused by SOC. It is present over an energy range greater than the
superconducting gap 2$\Delta _\mathrm{sc}$ and gets fully inherited in the
superconducting state, resulting in a distinct $c$-axis polarised "spin
resonance". Our result demonstrates the importance of SOC in defining the
low-energy spin excitations in FeSe, which helps to elucidate the nearby
magnetic instabilities and the debated interplay between spin and orbital
degrees of freedom. The prominent role of SOC also implies a possible unusual
nature of the superconducting state.
