Doping dependence of spin and orbital correlations in layered manganites

We investigate the interplay between spin and orbital correlations in monolayer and bilayer manganites using an effective spin-orbital t-J model which treats explicitly the e(g) orbital degrees of freedom coupled to classical t(2g) spins. Using finite clusters with periodic boundary conditions, the orbital many-body problem is solved by exact diagonalization, either by optimizing spin configuration at zero temperature or by using classical Monte Carlo simulations for the spin subsystem at finite temperature. In undoped two-dimensional clusters, a complementary behavior of orbital and spin correlations is found-the ferromagnetic spin order coexists with alternating orbital order, while the antiferromagnetic spin order, triggered by t(2g) spin superexchange, coexists with ferro orbital order. With a finite crystal-field term, we introduce a realistic model for La1-xSr1+xMnO4, describing a gradual change from predominantly out-of-plane 3z(2)-r(2) to in-plane x(2)-y(2) orbital occupation under increasing doping. The present electronic model is sufficient to explain the stability of the CE phase in monolayer manganites at doping x=0.5 and also yields the C-type antiferromagnetic phase found in Nd1-xSr1+xMnO4 at high doping. Also in bilayer manganites magnetic phases and the accompanying orbital order change with increasing doping. Here the model predicts C-AF and G-AF phases at high doping x > 0.75, as found experimentally in La2-2xSr1+2xMn2O7.