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First-principles theory of intrinsic spin and orbital Hall and Nernst effects in metallic monoatomic crystals

The generation of spin and orbital currents is of crucial importance in the field of spin-orbitronics. In this work, using relativistic density functional theory and the Kubo linear-response formalism, we systematically investigate the spin Hall and orbital Hall effects for 40 monoatomic metals. The spin Hall conductivity (SHC) and orbital Hall conductivity (OHC) are computed as a function of the electrochemical potential and the influence of the spin-orbit interaction strength is also investigated. Our calculations predict a rather small OHC in $sp$ metals, but a much larger OHC in $d$-band metals, with maximum values [$\sim 8000\,(\hbar/e)Ω^{-1}{\rm cm}^{-1}$] near the middle of the $d$ series. Using the Mott formula, we evaluate the thermal counterparts of the spin and orbital Hall effects, the spin Nernst effect (SNE) and the orbital Nernst effect (ONE). We find that the as-yet unobserved ONE is significantly larger ($\sim 10 \times$) than the SNE and has maximum values for group 10 elements (Ni, Pd, and Pt). Our work provides a broad overview of electrically- and thermally-induced spin and orbital transport in monoatomic metals.