Fig. 3
From: Unique crystal field splitting and multiband RKKY interactions in Ni-doped EuRbFe4As4

Fermi surfaces, crystal field splitting, and the relative contributions to Ruderman−Kittel−Kasuya−Yosida (RKKY) interactions of Fermi surfaces. a–d Fermi surfaces of EuRbFe4As4. a Typical hole pocket due to dxy with little dispersion along kz; b typical hole pockets due to \(d_{z^2}\) with strong dispersion along kz; c typical electron pockets due to dzx/dzy; and d all pockets combined together. The zone center is Γ in all panels. e–h Crystal field splitting of Fe-3d orbitals in e BaFe2As2(paramagnetic state), f CaRbFe4As4(paramagnetic state), g EuRbFe4As4(ferromagnetic state) and h EuRbNi4As4(ferromagnetic state) respectively. i Band-decomposed contribution to RKKY interaction in the pristine EuRbFe4As4. The band indices are labeled from lowest to highest at the Γ point. There are ten bands crossing the Fermi levels, among which six are hole-like and four are electron-like. The sixth band with the largest contributions corresponds to the Γ-centered outmost hole pocket due to \(d_{z^2}\) shown in (b)