We report an Fe $L$-edge resonant inelastic x-ray scattering (RIXS) study of the unusual superconductor $beta$-FeSe. The high energy resolution of this RIXS experiment ($approx,$55$,$meV FWHM) made it possible to resolve low-energy excitations of the Fe $3d$ manifold. These include a broad peak which shows dispersive trends between 100-200$,$meV along the $(pi,0)$ and $(pi,pi)$ directions of the one-Fe square reciprocal lattice, and which can be attributed to paramagnon excitations. The multi-band valence state of FeSe is among the most metallic in which such excitations have been discerned by soft x-ray RIXS.
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