Oxygen Isotope Effect on the Spin State Transition in (Pr$_{0.7}$Sm$_{0.3}$)$_{0.7}$Ca$_{0.3}$CoO${_3}$

Oxygen isotope substitution is performed in the perovskite cobalt oxide (Pr$_{0.7}$Sm$_{0.3}$)$_{0.7}$Ca$_{0.3}$CoO${_3}$ which shows a sharp spin state transition from the intermediate spin (IS) state to the low spin (LS) state at a certain temperature. The transition temperature of the spin state up-shifts with the substitution of $^{16}O$ by $^{18}$O from the resistivity and magnetic susceptibility measurements. The up-shift value is 6.8 K and an oxygen isotope exponent ($\alpha_S$) is about -0.8. The large oxygen isotope effect indicates strong electron-phonon coupling in this material. The substitution of $^{16}$O by $^{18}$O leads to a decrease in the frequency of phonon and an increase in the effective mass of electron ($m$$^\ast$), so that the bandwidth W is decreased and the energy difference between the different spin states is increased. This is the reason why the $T_s$ is shifted to high temperature with oxygen isotopic exchange.