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The 5d^1 ordered double perovskites present an exotic playground for studying novel multipolar physics due to large spin-orbit coupling. We present Re L₃ edge resonant inelastic x-ray scattering (RIXS) results that reveal the presence of the dynamic Jahn-Teller effect in the A₂MgReO₆ (A=Ca, Sr, Ba) family of 5d^1 double perovskites. The spin-orbit excitations in these materials show a strongly asymmetric line shape and exhibit substantial temperature dependence, indicating that they are dressed with lattice vibrations. Our experimental results are explained quantitatively through a RIXS calculation based on a spin-orbit-lattice entangled electronic ground state with the dynamic Jahn-Teller effect taken into consideration. We find that the spin-orbit-lattice entangled state is robust against magnetic and structural phase transitions as well as against significant static Jahn-Teller distortions. Our results illustrate the importance of including vibronic coupling for a complete description of the ground state physics of 5d^1 double perovskites.
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