Investigation of the charge-orbital ordering mechanism in single-layered Pr_0.5Ca_1.5MnO₄

Motivated by the experimental study of half-doped single-layered Pr_0.5Ca_1.5MnO₄ showing charge, orbital, and spin orderings [1], we propose a model to theoretically study the system to explain such ordering phenomena. The ground state electron configuration reveals that the charges form a checkerboard pattern with alternating Mn³⁺/Mn⁴⁺ sites, while the orbitals are aligned in zigzag chains [1, 2]. We calculate the ground state energy of this system to find the most preferable configuration by comparing three types of configurations (charge-unordered, charge-ordered, and charge-orbital-ordered states). The calculations are based on a tight-binding model representing effective electron hoppings among Mn ions in MnO₂-plane. We take into account the horizontally- and vertically-oriented orbital and spin degrees of freedom at Mn sites. We assume that the hopping integral values depend on the relative orientation between the corresponding orbitals of adjacent Mn ions. The interaction terms we incorporate into our effective Hamiltonian include inter-orbital, intra-orbital Hubbard repulsions, and Jahn-Teller distortion [2]. We absorb the exchange interaction between spins into local self-energy that we calculate within dynamical mean field algorithm [2]. Within our model we show a circumstance in which the charge-orbital ordered configuration has the lowest energy, consistent with the ground state ordering revealed by the experimental data.