Charge ordered ferromagnetic phase in manganites

checkerboard charge order in three directions.² Another pos-sible mechanism for the CO phase stabilization is the cou-pling of itinerant electrons to the Jahn-Teller distortions. However, the electron Jahn-Teller phonon coupling can only stabilize a CO-FM state where the CO phase transition oc-curs before the FM transition.⁸ At half filling experiments have only observed a charge order below the FM transition temperature.^7,2 Therefore the Jahn-Teller coupling is unlikely responsible for the appearance of the CO-FM state at least at half filling. In this paper we present a possible alternative explanation for the CO-FM state in the manganites. The key idea is an interplay of the DE and randomness of the A-sitestabilizes the homogeneous FM state and may produce aThere has been much recent interest in the properties of doped manganese oxides R _{1 2 x}A_xMnO₃ (R 5 rare earth, A 5 Ca,Sr) . ^1,2 These materials present a very rich phase dia-gram involving phases with spin, charge and orbital order. The physically relevant electrons in manganites are those from the Mn 3 d levels, which are split by the cubic crystal field into triply degenerate t _{2 g} levels and higher-energy dou-bly degenerate e_g levels. Electrons from the e_g levels are able to hop between Mn sites and form a conduction band. Electrons from the t _{2 g} levels are localized. The itinerant elec-trons and local spins are correlated by the double-exchange (DE) mechanism.^3,4 The main feature of the DE is a coop-erative effect where the motion of an itinerant electron favors the ferromagnetic (FM) ordering of local spins and, vice versa, the presence of the FM order facilitates the motion of the itinerant electron. The DE model qualitatively describes some of the magnetic properties of manganites,^2,5 and pro-vides a well-established starting point toward comprehensive understanding of the phase diagram of manganites.

Recently experiments have shown that in addition to the FM order a charge order can exist in the manganites.^7,6 The charge order exists in regions with no net magnetization and, surprisingly, can also occur in FM regions.⁷ Doping of A ^{2 1} ions creates Mn^{4 1} holes in a Mn^{3 1} background. The pres-ence of two valence states Mn^{3 1} and Mn^{4 1} may lead the compounds to a charge-ordered (CO) state for appropriate doping. However, the DE model alone cannot explain the CO state which coexists in the FM phase. In principle, the nearest-neighbor Coulomb repulsion may stabilize a CO state. However, a large nearest-neighbor repulsion likely de-substitution. The randomness is inevitably introduced by experiments. The importance of the randomness has been discussed both experimentally and theoretically.^1,2 The random-ness can substantially decrease the critical temperature of the FM transition.^{9 - 11} Here we will incorporate the randomness of A-site substitution into the DE model. For simplicity, we adopt the randomness by A-site substitution as a random lo-cal potential of the itinerant electrons, although the random-ness may cause other effects, for instance, randomness of the hoping or exchange integral.¹² It is well known that the di-agonal disorder with binary distribution can be modeled by the Falicov-Kimball (FK) model.¹³ Although the FK model is simple, it contains a rich variety of phases. In particular, it illustrates the disorder-order phase transition driven by elec-tron interaction.^14,15 Incorporating the diagonal disorder of the FK type into the DE model, one may expect that a disorder-order phase transition could present. When the phase transition occurs, a CO-FM phase may be stabilized at low temperature. In order to detect the phase transition we study the charge and spin response of system by using the dynamical mean-field theory (DMFT).¹⁶ The DMFT has ex-tensively been used for investigating strongly correlated electron systems.¹⁶ Within the DMFT we explicitely calcu-late the charge and spin correlation function. We find that the system stabilizes a CO-FM state at low temperature.

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