Title: Nematic phase with colossal magnetoresistance and orbital polarons in manganite La$_{1-x}$Sr$_x$MnO$_3$,
Abstract: 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 $x\leq 0.5$, $T\leq T_C$ 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 orbital pseudospin
degeneracy is lift by phonons. For $x\neq x_0$, its q-range reveals a $\ell
\approx 1.7a$ size of polarons with a dimension $2d$ at $x=1/8$ partly
increasing to $\approx$ $3d$ at $x=0.3$. At $x_0=0.2$ ($T<T_C$) two distinct
$q$ and energy ranges appear separated by $\Delta E(q_0\approx 0.35)=3meV$. The
same $\Delta E(q_0)$ value separates two unusual transverse acoustic branches
($T>T_C$). 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.