Study on the oxygen isotope effect in A-site ordered manganite $R$BaMn$_{2}$O$_{6}$ ($R$ = La, Pr, Nd, Sm)

A-site ordered manganites $R$BaMn$_{2}$O$_{6}$ ($R$ = La, Pr, Nd, Sm) were synthesized and the oxygen isotope effect in them was studied. It was found that the substitution of $^{16}$O by $^{18}$O has caused increases in both the Neel temperature ($T$$_{N}$) and the charge ordering temperature ($T$$_{CO}$) and an decrease in the Curie temperature ($T$$_{C}$). The isotope exponent is small on $T$$_{C}$ and $T$$_{CO}$ compared with that in A-site disordered manganites such as La$_{1-x}$Ca$_{x}$MnO$_{3}$, which may be caused by weaker electron-phonon coupling in A-site ordered ones. But the isotope exponent of $T$$_{N}$ is large for $R$ = La. We didn't observe the large oxygen-isotope shift that occurs in NdBaMn$_{2}$O$_{6}$, where a multicritical point is believed to appear near $R$ = Nd, and strong fluctuation due to the competition between ferromagnetic metal and charge ordering phase should be present.