Nontrivial effect of spin-orbit coupling on the intrinsic resistivity of ferromagnetic gadolinium

As a metallic material of a heavy atom, elemental gadolinium (Gd) has many extraordinary electronic properties associated with the strong correlation and spin-orbital coupling (SOC). Previous studies have shown that the resistivity of ferromagnetic (FM) Gd due to the spin fluctuation scattering is comparable to the intrinsic resistivity limited by electron-phonon (e-ph) scattering even near the room temperature. However, such theoretical explanations cannot account for the experimental observation quantitatively. In the present work, by performing the first-principles calculations, we find that the intrinsic resistivity is insensitive to Hubbard $U$, i.e., the electronic correlation. On the contrary, when the effect of SOC is taken into account, the band structure near the Fermi level is modified greatly. As a result, the calculated intrinsic resistivity increases by nearly 3 times over that without SOC. By further counting in the additional resistivity contributed from spin fluctuation scattering, our theoretical result of resistivity agrees very well with the experimental observation of resistivity of FM Gd as a function of temperature.