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

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