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We have performed powder inelastic neutron scattering measurements on theunconventional superconductor $\beta$-FeSe ($T_{\rm c} \simeq 8\,\mathrm{K}$).The spectra reveal highly dispersive paramagnetic fluctuations emerging fromthe square-lattice wave vector $(\pi,0)$ extending beyond 80 meV in energy.Measurements as a function of temperature at an energy of $\sim13\,\mathrm{meV}$ did not show any variation from $T_{\rm c}$ to$104\,\mathrm{K}$. The results show that FeSe is close to an instabilitytowards $(\pi,0)$ antiferromagnetism characteristic of the parent phases of thehigh-$T_{\rm c}$ iron arsenide superconductors, and that the iron paramagneticmoment is neither affected by the orthorhombic-to-tetragonal structuraltransition at $T_{\rm s} \simeq 90\,\mathrm{K}$ nor does it undergo a change inspin state over the temperature range studied.

Strong $(\pi,0)$ spin fluctuations in $\beta$-FeSe observed by neutron spectroscopy