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Second-order structural transition in (Ca$$_{0.5}$$Sr$$_{0.5}$$)$$_3$$Rh$$_4$$Sn$$_{13}$$

Cheung, Y. W.*; Hu, Y. J.*; Goh, S. K.*; Kaneko, Koji; Tsutsui, Satoshi; Logg, P. W.*; Grosche, F. M.*; Kanagawa, Hibiki*; Tanioku, Yasuaki*; Imai, Masaki*; Matsumoto, Takuya*; Yoshimura, Kazuyoshi*

(Ca$$_{0.5}$$Sr$$_{0.5}$$)$$_3$$Rh$$_4$$Sn$$_{13}$$ is a member of the substitution series (Ca$$_{x}$$Sr$$_{1-x}$$)$$_3$$Rh$$_4$$Sn$$_{13}$$ which has recently been argued to feature a structural quantum critical point at $$x_c$$ = 0.9. In the stoichiometric compound Sr$$_{3}$$Rh$$_{4}$$Sn$$_{13}$$, the structural transition at $$T^*$$ $$approx$$ 138 K has been shown to be a second-order phase transition. Moving towards xc, we examine the character of the structural transition in (Ca$$_{0.5}$$Sr$$_{0.5}$$)$$_3$$Rh$$_4$$Sn$$_{13}$$ (i.e. $$x$$ = 0.5, $$T^*$$ $$approx$$ 55 K) using electrical resistivity, heat capacity and X-ray scattering. The absence of the thermal hysteresis in specific heat around $$T^*$$, and the continuous evolution of the superlattice reflection detected by X-ray diffraction are consistent with the scenario that the structural transition associated with a modulation vector $$q$$ = (0.5, 0.5, 0) in (Ca$$_{0.5}$$Sr$$_{0.5}$$)$$_3$$Rh$$_4$$Sn$$_{13}$$ remains second-order on approaching the quantum critical point.



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