We address the degeneracy of the ground state multiplet on the 5 Re ion in double perovskite BaMgReO using a combination of specific heat measurements and density functional calculations. For BaMgReO, two different ground state multiplets have previously been proposed - a quartet (with degeneracy =4) [1] and a doublet (=2) [2]. Here we employ two independent methods for the estimation of phonon contribution in heat capacity data to obtain the magnetic entropy , which reflects the degeneracy of the ground state multiplet through ln. In both cases, we obtain a better fit to ln2 indicating evidence of =2 degeneracy in the range from 2 to 120~K. The detailed nature of the ground state multiplet in BaMgReO remains an open question.

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