Clear Experimental Signature of Charge-Orbital density wave in   Nd$_{1-x}$Ca$_{1+x}$MnO$_{4}$:Heat Capacity and Magnetization study
  Single Crystals of Nd$_{1-x}$Ca$_{1+x}$MnO$_{4}$ have been prepared by the traveling floating-zone method, and possible evidence of a charge -orbital density wave in this material presented earlier [PRB68,092405 (2003)] using High Resolution Electron Microscopy [HRTEM] and Electron Diffraction [ED]. In the current note we present direct evidence of charge-orbital ordering in this material using heat capacity measurements. Our heat capacity measurements indicate a clear transition consistent with prior observation. We find two main transitions, one at temperature $T_{_H}^{HC}=310-314$ K, and other in the vicinity of $T_{_A}^{HC}=143$ K. In addition, we may also conclude that there is a strong electron-phonon coupling in this material. In order to further study and confirm theseanomalies we have performed dc magnetization measurements. The dc magnetic measurements confirm these two transitions. Again,we find two main transitions, one at temperature $T_{_H}^{M}=318-323$ K, and other at around $T_{_A}^{M}=164$ K. 
Sher Alam, A.T.M.N. Islam, T.Nagai, M. Xu, Javed Ahmad, Y.Matsui, and   I.Tanaka