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We have carried out inelastic neutron scattering experiments to studymagnetic excitations in ordered double perovskite Ca$_2$FeReO$_6$. We found awell-defined magnon mode with a bandwidth of $\sim$50meV below theferri-magnetic ordering temperature ($T_c\sim$520K), similar to previouslystudied Ba$_2$FeReO$_6$. The spin excitation is gapless for most temperatureswithin the magnetically ordered phase. However, a spin gap of $\sim$10meV opensup below $\sim$150K, which is well below the magnetic ordering temperature butcoincides with a previously reported metal-insulator transition and onset ofstructural distortion. The observed temperature dependence of spin gap providesstrong evidence for ordering of Re orbitals at $\sim$150~K, in accordance withearlier proposal put forward by Oikawa $\it{et.\,al}$ based on neutrondiffraction [J. Phys. Soc. Jpn., $\bf{72}$, 1411 (2003)] as well as recenttheoretical work by Lee and Marianetti [Phys. Rev. B, $\bf{97}$, 045102(2018)]. The presence of separate orbital and magnetic ordering inCa$_2$FeReO$_6$ suggests weak coupling between spin and orbital degrees offreedom and hints towards a sub-dominant role played by spin orbit coupling indescribing its magnetism. In addition, we observed only one well-defined magnonband near magnetic zone boundary, which is incompatible with simpleferrimagnetic spin waves arising from Fe and Re local moments, but suggests astrong damping of Re magnon mode.

Neutron Scattering Investigation of Rhenium Orbital Ordering in $3d-5d$ Double Perovskite Ca$_2$FeReO$_6$