Probing spin-orbital-lattice correlations in 4d(4) systems

By means of an exact diagonalization technique, we analyze the ground state configurations that emerge out of the competition between the octahedral distortions, the Coulomb interactions, and the spin-orbit coupling in the case of two effective t(2g) sites in 4d(4) configuration. We show that the crystalline field is a suitable quantum control of the magnetic and orbital correlations, leading to predominant antiferromagnetic (ferromagnetic) exchange with ferro- (antiferro-) like orbital correlations in the flat (elongated) octahedral configuration. Moreover, the role of the spin-orbit coupling is investigated with respect to the character of the octahedral deformations. One of the main findings is the occurrence of anisotropic spin patterns with partially filled orbital occupation and coexisting ferro- and antiferrolike correlations in the spin/orbital channel. Finally, the possibility of competing states with partial orbital occupation is amplified when a spin polarizing field is added to the system. Its role in controlling magnetic/orbital correlations is also presented.