Relationship between charge stripe order and structural phase transitions in La$_{1.875}$Ba$_{0.125-x}$Sr$_{x}$CuO$_{4}$

The nature of charge stripe order and its relationship with structural phase transitions were studied using synchrotron X-ray diffraction in La$_{1.875}$Ba$_{0.125-x}$Sr$_{x}$CuO$_{4}$ ($0.05\leq x\leq 0.10$). For $x=0.05$, as temperature increased, incommensurate superlattice peaks associated with the charge order disappeared just at the structural phase transition temperature, $T_{\rm d2}$. However, for $x=0.075$ and 0.09, the superlattice peaks still existed as a short range correlation even above $T_{\rm d2}$, indicating a precursor of charge ordering. Furthermore, temperature dependences of the superlattice peak intensity, correlation length, and incommensurability for $x=0.05$ are different from those for $x=0.075$ and 0.09. These results suggest that the transition process into the charge stripe order strongly correlates with the order of the structural phase transitions. A quantitative comparison of the structure factor associated with the charge order have been also made for all the samples.