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The alloy Ca$_{2-x}$Sr$_x$RuO$_4$ exhibits a complex phase diagram with peculiar magnetic metallic phases. In this paper some aspects of this alloy are discussed based on a mean field theory for an effective Kugel-Khomskii model of localized orbital and spin degrees of freedom. This model results from an orbital selective Mott transition which in the three-band system localized two orbitals while leaving the third one itinerant. Special attention is given to the region around a structure quantum phase transition at $ x approx 0.5 $ where the crystal lattice changes from tetragonal to orthorhombic symmetry while leaving the system metallic. This transition yields, a change from ferromagnetic to antiferromagnetic spin correlations. The complete mean field phase diagram for this transition is given including orbital and spin order. The anisotropy of spin susceptibility, a consequence of spin-orbit coupling and orbital correlation, is a tell-tale sign of one of these phases. In the predominantly antiferromagnetic phase we describe a metamagnetic transition in a magnetic field and show that coupling of the itinerant band to the localized degrees of freedom yields an anomalous longitudinal magnetoresistance transition. Both phenomena are connected with the evolution of the ferromagnetic and antiferromagnetic domains in the external magnetic field and agree qualitatively with the experimental findings.
The magnetoelastic coupling in Ca$_{1.8}$Sr$_{0.2}$RuO$_4$ and in Ca$_{1.5}$Sr$_{0.5}$RuO$_4$ has been studied combining high-resolution dilatometer and diffraction techniques. Both compounds exhibit strong anomalies in the thermal-expansion coeffici
The strongly correlated insulator Ca$_{2}$RuO$_4$ is considered as a paradigmatic realization of both spin-orbital physics and a band-Mott insulating phase, characterized by orbitally selective coexistence of a band and a Mott gap. We present a high-
We report an electrical transport study in Ca$_{2-x}$Sr$_{x}$RuO$_4$ single crystals at high magnetic fields ($B$). For $x =0.2$, the Hall constant $R_{xy}$ decreases sharply at an anisotropic metamagnetic (MM) transition reaching its value for Sr$_2
Electrons in a simple correlated system behave either as itinerant charge carriers or as localized moments. However, there is growing evidence for the coexistence of itinerant electrons and local moments in transition metals with nearly degenerate $d
We review the magnetic and orbital ordered states in cro{} by performing Resonant Elastic X-ray Scattering (REXS) at the Ru L$_{2,3}$-edges. In principle, the point symmetry at Ru sites does not constrain the direction of the magnetic moment below $T