The compound \(\hbox {La}_{1-x}\hbox {Sr}_x\hbox {MnO}_3\) exhibits a charge order (CO) state at \(x\approx 1/8\) and \(T<T_{co}\) , which recalls the CO state with a decrease in the temperature of the superconducting transition, \(T_c\) , observed in all cuprates at this doping value. Local excitations of lattice and magnetic origins measured in the two-dimensional metallic state of \(\hbox {La}_{7/8}\hbox {Sr}_{1/8}\hbox {MnO}_3\) reveal the existence of bipolarons of size 4a resulting from structural and antiferromagnetic pairings of hole-rich orbital polarons of size 2a. They are intertwined with hole-poor domains in a disordered state at \(T>T_{co}\) which become ordered on a chessboard organized in a 3D-order state of ferromagnetically paired polarons at \(T<T_{co}\) . Applied to the \(\hbox {CuO}_2\) planes of the cuprates of the “214” family, this model produces stripes of bipolarons intertwined with stripes of antiferromagnetically arranged spins, hole-poor, both of size 4a, leading to a spin density wave with a wave vector \(\delta =1/8\) , a charge density wave with \(q=1/4\) , the Yamada laws \(\delta (x)=x\) and \(T_c\propto \delta\) and a decrease of \(T_c\) at x=1/8. This work invokes relevance of a bipolaronic origin of high \(T_c\) superconductivity, in which bipolarons of size 4a can play a major role.
