Here, we study intrinsic Hall effects in 4d,5d transition metal compounds and f-electron compounds based on the realistic multiorbital tight-binding models. We calculate various transport coefficients using Nakano-Kubo linear response theory. Effect of strong spin-orbit interaction (SOI) is taken into account correctly. First, we analyze the intrinsic spin Hall conductivity (SHC) in transition metals and f-electron compounds, and found that the SHC is negative when the number of d, f electrons is less than half-filling (e.g., Ta, Nb, Ce), whereas it is positive in case of more than half-filling (e.g., Pt, Pd, Yb). In f-electron systems, various multipole degrees of freedom (such as quadrupole, octupole, hexadecapole) are active due to strong SOI. We find that such multipole degrees of freedom exhibit interesting Hall effects, by analyzing the multiorbital periodic Anderson model. For example, we predict that huge qudrupole Hall effect appears in some Ce-based compounds. In addition, we discuss the generation of spin current driven by surface induced superconductivity.
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