Nematic phase with colossal magnetoresistance and orbital polarons in manganite La$_{1-x}$Sr$_x$MnO$_3$

The origin of colossal magnetoresistance (CMR) is still controversial. The spin dynamics of La$_{1-x}$Sr$_x$MnO$_3$ is revisited along the Mn-O-Mn direction at $xleq 0.5$, $Tleq T_C$ with a new study at $x$=0.4. A new lattice dynamics study is also reported at $x_0$=0.2,representative of the optimal doping for CMR. In large-$q$ wavevector range, typical of the scale of polarons, spin dynamics exhibits a discrete spectrum, $E^n_{rm mag}$ with $n$ equal to the degeneracy of orbital-pseudospin transitions and energy values in coincidence with the phonon ones. It corresponds to the spin-orbital excitation spectrum of short life-time polarons, in which the pseudospin degeneracy is lift by phonons. For $xneq x_0$, its q-range reveals a $ell approx 1.7a$ size of with a dimension $2d$ at $x=1/8$ partly increasing to $approx$ $3d$ at $x=0.3$. At $x_0=0.2$ ($T T_C$). Both characterize a nematic-phase defined by chains of orbital polarons of $2a$ size, distant from $3a$, typical of $x_0=1/6$. It could explain CMR.