Spin and orbital ordering in La_2−2xSr_1+2xMn₂O₇ compounds

In this Brief Report, the electronic and magnetic structures of the bilayer Ruddlesden-Popper compounds, La_2−2xSr_1+2xMn₂O₇ (0.0⩽x⩽1.0), have been investigated using the unrestricted Hartree-Fock approximation and the real-space recursion method. Various ground states are found as a function of Sr doping which reveal an interesting interplay between spin and orbital degrees of freedom. The undoped La₂Sr₁Mn₂O₇ takes the A-type antiferromagnetic ground state with d_3x²−r²∕d_3y²−r² orbital ordering. As doping increases, the ground state of system takes consecutively the ferromagnetic state with d_3x²−r²∕d_3y²−r² orbital ordering (0.01⩽x⩽0.23), the ferromagnetic state with d_x²−y² orbital ordering (0.23<x⩽0.34), the A-type antiferromagnetic state with d_x²−y² orbital ordering (0.34<x⩽0.86), the C-type antiferromagnetic state with d_x²−y² orbital ordering (0.86<x⩽0.92), and finally the G-type antiferromagnetic state with d_3z²−r² orbital ordering (0.92<x⩽1).