Spin and charge order in the CE phase of La_1−xCa_xMnO₃

The CE phase of La_1−xCa_xMnO₃ is stable for x≳0.5 and displays long-range magnetic, charge, and orbital orders. The magnetic order of the Mn spins arises from the competition of the superexchange and double-exchange interactions and the checkerboard charge and the orbital order is the consequence of the Jahn-Teller coupling of the e_g orbitals to the lattice. Using a mean-field slave-boson approach for the e_g electrons in two orbitals per site with excluded multiple occupancy and Hund’s rule coupling between the e_g and t_2g states, we obtain the tight-binding band structure of the CE phase. The unit cell of the CE phase consists of 16 sites. The 32 e_g bands in the Brillouin zone are grouped into two sets of 16 bands separated by a charge order gap. The phase diagram including the A, B, C, CE, and G phases reproduces the phase sequence observed in La_1−xCa_xMnO₃.