Effects of $^{18}$O/$^{16}$O Isotopic substitution on the specific heat of Single Crystalline Nd$_{0.5}$Sr$_{0.5}$MnO$_{3}$

Substantial studies of magnetic susceptibility and specific heat on Nd$_{0.5}$Sr$_{0.5}$MnO$_{3}$ have demonstrated the existence of ferromagnetic (FM), antiferromagnetic (AFM) and charge ordering transitions (CO). In this work, effects of oxygen isotopic substitution on the specific heat of single crystalline Nd$_{0.5}$Sr$_{0.5}$MnO$_{3}$ were studied on two samples, each containing $^{16}$O or high concentration of $^{18}$O. Specific heat was measured for each sample from 3K to 350 K in zero and 50 kOe applied magnetic fields using a Quantum Design Physical Property Measurement System (PPMS) with Specific Heat option. Below 30 K, a Schottky-like anomaly was found for both samples, which seemed to be unaffected by isotope substitution. The FM, AFM and CO transitions were present in both samples, and the CO temperature (T$_{\mathrm{co}}$) seems to depend strongly on the oxygen isotope mass in both zero and 50 kOe fields, which seems to agree with previous magnetization measurement in powder samples.