lattice

The interaction energy for the indirect-exchange or Ruderman-Kittel-Kasuva-Yosida (RKKY) interaction between magnetic spins localized on lattice sites of the α-T₃ model is calculated using linear response theory. In this model, the AB-honeycomb lattice structure is supplemented with C atoms at the centers of the hexagonal lattice. This introduces a parameter alpha for the ratio of the hopping integral from hub-to-rim and that around the rim of the hexagonal lattice. A valley and alpha-dependent retarded Green’s function matrix in momentum-energy space is generated using the (A,B,C) lattice basis forming the low-energy Hamiltonian. The corresponding coordinate space Green’s functions not only depend on which sublattice (A,B or C) the interacting spins are located but the cut-off wave vector used in the Fourier transform integral restricted to lie within the first Brillouin zone (B.Z.).