Sr$_2$FeOsO$_6$ is an insulating double perovskite compound which undergoes antiferromagnetic transitions at 140 K ($T_{N1}$) and 67 K ($T_{N2}$). To study the underlying electronic and magnetic interactions giving rise to this behavior we have performed inelastic neutron scattering (INS) and resonant inelastic x-ray scattering (RIXS) experiments on polycrystalline samples of Sr$_2$FeOsO$_6$. The INS data reveal that the spectrum of spin excitations remains ungapped below T$_{N1}$, however below T$_{N2}$ a gap of 6.8 meV develops. The RIXS data reveals splitting of the T$_{2g}$ multiplet consistent with that seen in other 5d$^3$ osmium based double perovskites. Together these results suggest that spin-orbit coupling is important for ground state selection in 3d-5d$^3$ double perovskite materials.
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