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 22 cluster and a cluster embedded analysis where interplaquette interaction is treated on mean-field level, we determine the groundstate phase diagram. Specifically, we demonstrate that, via the activation of two or three of t2g 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 in local orbital moment in a way to suppress the orbital order.