Charge Ordering in Half-Doped Manganites: Small Charge Disproportion and Leading Mechanisms

The apparent contradiction between the recently observed weak charge disproportion and the traditional Mn$^{3+}$/Mn$^{4+}$ picture of the charge-orbital orders in half-doped manganites is resolved by a novel Wannier states analysis of the LDA$+U$ electronic structure. Strong electron itinerancy in this charge-transfer system significantly delocalizes the occupied low-energy ``Mn$^{3+}$'' Wannier states such that charge leaks into the Mn$^{4+}$-sites. Moreover, this feature is found to be generic in doped manganites. Based on a realistic effective Hamiltonian derived from first-principles calculations, we further quantify the leading mechanisms of the charge-orbital orders and find that both electron-lattice and electron-electron interactions are essential. \hspace{0.2 cm} {\it Preprint} arXiv:0704.1834.