Anomalous Nernst and Hall effects in magnetized platinum and palladium

Abstract

We study the anomalous Nernst effect (ANE) and anomalous Hall effect (AHE) in proximity-induced ferromagnetic palladium and platinum which is widely used in spintronics, within the Berry phase formalism based on the relativistic band structure calculations. We find that both the anomalous Hall ($σ_{xy}^A$) and Nernst ($α_{xy}^A$) conductivities can be related to the spin Hall conductivity ($σ_{xy}^S$) and band exchange-splitting ($Δ_{ex}$) by relations $σ_{xy}^A =Δ_{ex}\frac{e}{\hbar}σ_{xy}^S(E_F)'$ and $α_{xy}^A = -\frac{π^2}{3}\frac{k_B^2TΔ_{ex}}{\hbar}σ_{xy}^s(μ)"$, respectively. In particular, these relations would predict that the $σ_{xy}^A$ in the magnetized Pt (Pd) would be positive (negative) since the $σ_{xy}^S(E_F)'$ is positive (negative). Furthermore, both $σ_{xy}^A$ and $α_{xy}^A$ are approximately proportional to the induced spin magnetic moment ($m_s$) because the $Δ_{ex}$ is a linear function of $m_s$. Using the reported $m_s$ in the magnetized Pt and Pd, we predict that the intrinsic anomalous Nernst conductivity (ANC) in the magnetic platinum and palladium would be gigantic, being up to ten times larger than, e.g., iron, while the intrinsic anomalous Hall conductivity (AHC) would also be significant.