Recent theoretical studies [Chen et al., Phys. Rev. B 82, 174440 (2010), Ishizuka et al., Phys. Rev. B 90, 184422 (2014)] for the magnetic Mott insulator Ba2NaOsO6 have proposed a low-temperature order parameter that breaks lattice rotational symmetry without breaking time reversal symmetry leading to a nematic phase just above magnetic ordering temperature. We present high-resolution calorimetric and magnetization data of the same Ba2NaOsO6 single crystal and show evidence for a weakly field-dependent phase transition occurring at a temperature of Ts ~ 9.5K, above the magnetic ordering temperature of Tc ~ 7.5K. This transition appears as a broadened step in the low-field temperature dependence of the specific heat. The evolution of the phase boundary with applied magnetic field suggests that this phase coincides with the phase of broken local point symmetry seen in high field NMR experiments [Lu et al., Nat. Comm. 8 14407 (2017)]. Furthermore, the magnetic field dependence of the specific heat provides clear indications for magnetic correlations persisting at temperatures between Tc and Ts where long-range magnetic order is absent giving support for the existence of the proposed nematic phase.
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