Charge-orbital ordering and phase separation in the two-orbital model for manganites: Roles of Jahn-Teller phononic and Coulombic interactions

Abstract

The main properties of realistic models for manganites are studied using analytic mean-field approximations and computational numerical methods, focusing on the two-orbital model with electrons interacting through Jahn-Teller ͑JT͒ phonons and/or Coulombic repulsions. Analyzing the model including both interactions by the combination of the mean-field approximation and the exact diagonalization method, it is argued that the spin-charge-orbital structure in the insulating phase of the purely JT-phononic model with a large Hund coupling J H is not qualitatively changed by the inclusion of the Coulomb interactions. As an important application of the present mean-field approximation, the CE-type antiferromagnetic state, the charge-stacked structure along the z axis, and (3x 2 Ϫr 2 )/(3y 2 Ϫr 2 )-type orbital ordering are successfully reproduced based on the JT-phononic model with large J H for the half-doped manganite, in agreement with recent Monte Carlo simulation results. Topological arguments and the relevance of the Heisenberg exchange among localized t 2g spins explains why the inclusion of the nearest-neighbor Coulomb interaction does not destroy the charge stacking structure. It is also verified that the phase-separation tendency is observed both in purely JT-phononic ͑large J H ) and purely Coulombic models in the vicinity of the hole undoped region, as long as realistic hopping matrices are used. This highlights the qualitative similarities of both approaches and the relevance of mixedphase tendencies in the context of manganites. In addition, the rich and complex phase diagram of the two-orbital Coulombic model in one dimension is presented. Our results provide robust evidence that Coulombic and JT-phononic approaches to manganites are not qualitatively different ways to carry out theoretical calculations, but they share a variety of common features.

Doping and Field-Induced Insulator-Metal Transitions in Half-Doped Manganites

“…This accommodates the CE state as well as several other competing commensurate states. Compared to earlier numerical approaches [12] that were limited to small clusters, our calculations are practically in the thermodynamic limit. We confirm the phase diagram that was previously obtained [12,14] and obtain detailed predictions on the strength of the JT-distortions Q, etc.…”

“…The last two terms include the vibrational energy of JT phonons (where K is the lattice stiffness of a simplified non-cooperative model) and their coupling to the e g electrons. Q ia and Θ ia represent the amplitude and the angle of the two (Q 2 , Q 3 ) JT modes, and the τ matrix the symmetry of their coupling [12]. On-site Coulomb interactions can be ignored in a first approximation when large JT distortions are present (as the JT coupling suppresses double occupancy) and for large J H .…”

Instabilities and insulator-metal transitions in half-doped manganites induced by magnetic-field and doping

“…To stabilise the (π, π, 0) order in a wider regime of parameters, JT interactions between the Mn ions and their surrounding oxygen octahedra, which are supposed to be quite large, 13 have to be included. 31 The consequent JT distortions further lower the energy of the CE phase because of the already present (3x 2 −r 2 )/(3y 2 −r 2 ) orbital order. Classical Monte Carlo simulations including static JT distortions on small clusters as well as self-consistent mean field treatments of models including JT and Coulomb interactions 31 suggest that the CE charge stacked state has the lowest energy in an intermediate range of J AF , unless the nearest neighbour coulomb interaction V becomes much too large.…”

“…This allows us to determine them self-consistently without using finite-size clusters, thereby extending and reinforcing earlier work. 31,60 In particular we obtain analytic results for the phase boundaries at strong JT coupling. Next, we show that the periodic ferromagnetic phase obtained at small J AF by the method discussed above can become unstable with respect to a phase with two types (ℓ − b) of electrons when the JT coupling is lowered.…”

Effect of strain on the electrical transport and magnetization of the epitaxialPr0.5Ca0.5MnO3∕La

“…Since the orbital ordering, and hence the magnetic structures, is closely related to different types of cooperative JT vibration modes, [14] the apically compressed MnO 6 octahedra for the sample on STO imply a 3dx 2 −r 2 /3dy 2 −r 2 polarization of the e g orbitals, while the apically elongated octahedra for the sample on LAO imply a 3dz 2 −r 2 polarization of the e g orbitals [6,15]. So in the sample on STO and LAO the possible CO state is charge exchange (CE) type and C type respectively [16,17].…”