Effect of magnetic field and chemical potential on the RKKY interaction in the $\alpha$-${\mathcal{T}}_3$ lattice

Abstract

The interaction energy for the indirect-exchange or Ruderman-Kittel-Kasuva-Yosida (RKKY) interaction between magnetic spins localized on lattice sites of the $\alpha$-${\mathcal{T}}_3$ model is calculated using linear response theory. In this model, the $\text{AB}$-honeycomb lattice structure is supplemented with $\text{C}$ 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 Greens function matrix is used to form the susceptibility. Analytic and numerical results are obtained for undoped $\alpha$-${\mathcal{T}}_3$, when the chemical potential is finite and also in the presence of an applied magnetic field. We demonstrate the anisotropy of these results when the magnetic impurities are placed on the $\text{A,B}$ and $\text{C}$ sublattice sites. Additionally, comparison of the behavior of the susceptibility of $\alpha$-${\mathcal{T}}_3$ with graphene shows that there is a phase transition at $\alpha =0$.

References in corpus (17)

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• RKKY interaction in a doped pseudospin-1 fermion system at finite temperature
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• Interplay of Lorentz-Berry forces in position-momentum spaces for valley-dependent impurity scattering in alpha-T3 lattices
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Cited by in corpus (8)

• Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system
• Probing Topological signatures in an optically driven $\alpha$-$T_3$ Lattice
• Green's functions and DOS for some 2D lattices
• Effect of magnetic field on the electronic properties of an $\alpha$-$T_3$ ring
• Thermal Transport Properties of Magnons on the $\alpha$-T${}_3$ Lattice
• Orbital magnetization senses the topological phase transition in a spin-orbit coupled $\alpha$-$T_3$ system
• Generation of isolated flat bands with tunable numbers through Moiré engineering
• Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian