Field-induced Orbital Patterns in Ferromagnetic Layered Ruthenates

We study the evolution of orbital patterns in ferromagnetic layered ruthenates due to the competition of Coulomb interactions, compressive c axis and orthorhombic distortions in the presence of a polarizing orbital field coupled to the angular momentum. By means of the exact diagonalization on a 2x2 cluster and a cluster embedded analysis where inter-plaquette interaction is treated on mean field level, we determine the ground-state phase diagram. Specifically, we demonstrate that, via the activation of two or three of t_2g local orbital configurations, an external field applied along different symmetry directions can lead to inequivalent orbital correlated states. Starting from an antiferro-orbital pattern, for the easy axis case an orbital ordered phase is induced, having strong next nearest neighbors ferro-orbital correlations. Otherwise, a field applied along the hard axis leads a reduction of local orbital moment in a way to suppress the orbital order.