Signatures of electronic polarons in La$_{1-x}$Sr$_{1+x}$MnO$_4$ observed by electron energy-loss spectroscopy

The dielectric properties of La$_{1-x}$Sr$_{1+x}$MnO$_4$ single crystals with x = 0, 0.125, 0.25, and 0.5 were studied by means of electron energy-loss spectroscopy as a function of temperature and momentum transfer. A clear signature of the doped holes is observed around 1.65 eV energy loss, where spectral weight emerges with increasing x. For all $x \neq 0$, this doping-induced excitation can propagate within the ab-plane, as revealed by a clear upward dispersion of the corresponding loss peak with increasing momentum transfer. The hole-induced excitation also shifts to higher energies with the onset of magnetic correlations for x = 0.5, implying a strong coupling of charge and spin dynamics. We conclude that (i) the loss feature at 1.65 eV is a signature of electronic polarons, which are created around doped holes, and that (ii) this low-energy excitation involves the charge transfer between manganese and oxygen. The finite dispersion of these excitations further indicates significant polaron-polaron interactions.