Orbital-cooperative spin fluctuation and orbital-dependent transport in ruthenates

Unusual transport properties deviating from the Fermi liquid are observed in ruthenates near a magnetic quantum-critical point (QCP). To understand the electronic properties of the ruthenates near and away from an antiferromagnetic (AF) QCP, I study the electronic structure and magnetic and transport properties for the $t_{2g}$-orbital Hubbard model on a square lattice in fluctuation-exchange approximation including Maki-Thompson (MT) current vertex correction (CVC). The results away from the AF QCP reproduce several experimental results of Sr$_{2}$RuO$_{4}$ qualitatively and provide new mechanisms about the enhancement of spin fluctuation at $Q_{\textrm{IC-AF}}\approx (0.66\pi,0.66\pi)$, larger mass enhancement of the $d_{xy}$ orbital than that of the $d_{xz/yz}$ orbital, and nonmonotonic temperature dependence of the Hall coefficient. Also, the results near the AF QCP explain the $T$-linear inplane resistivity in Sr$_{2}$Ru$_{0.075}$Ti$_{0.025}$O$_{4}$ and give an experimental test on the obtained temperature dependence of the Hall coefficient. I reveal spatial correlation including the self-energy of electrons beyond mean-field approximations is essential to determine the electronic properties of the ruthenates. I also show several ubiquitous transport properties near an AF QCP and characteristic transport properties of a multiorbital system by comparison with results of a single-orbital system near an AF QCP.