Anisotropic epitaxial strain effect on the charge-order phase of Nd$_{0.5}$Sr$_{0.5}$MnO$_{3}$

Strain effect in charge and orbital ordered state has been investigated for Nd$_{0.5}$Sr$_{0.5}$MnO$_{3}$ thin films deposited on (100), (110), and (111)-oriented SrTiO$_{3}$ (STO) substrates. Films on STO (001) and (111) substrates have monotonous temperature dependence for magnetic and transport properties showing no first-order phase transition. On the other hand, films on STO (110) show a clear ferromagnetic-antiferromagnetic and metal-insulator transition due to the onset of the charge and orbital order. Optical transmission spectra for the films on STO (110) show anisotry between the in-plane two axes. From the result, the orbital order plane of the film on STO (110) is deduced to be (100) or (010) plane, which lies out of the film surface. The reason for the difference in the magnetic and transport properties among the films on different substrate orientations, and why the clear metal-insulator transition occurs only on (110) substrates will be discussed.