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The interaction energy for the indirect-exchange or Ruderman-Kittel-Kasuva-Yosida (RKKY) interaction between magnetic spins localized on lattice sites of the $alpha$-${cal T}_3$ model is calculated using linear response theory. In this model, the $texttt{AB}$-honeycomb lattice structure is supplemented with $texttt{C}$ 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 $alpha$-${cal T}_3$, 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 $texttt{A,B}$ and $texttt{C}$ sublattice sites. Additionally, comparison of the behavior of the susceptibility of $alpha$-${cal T}_3$ with graphene shows that there is a phase transition at $alpha=0$.
We predict the occurrence of Bose-Einstein condensation and superfluidity of dipolar magnetoexcitons for a pair of quasi-two-dimensional spatially separated $alpha$-${cal T}_3$ layers. We have solved a two-body problem for an electron and a hole for
The spin chemical potential characterizes the tendency of spins to diffuse. Probing the spin chemical potential could provide insight into materials such as magnetic insulators and spin liquids and aid optimization of spintronic devices. Here, we int
At the LaAlO$_3$-SrTiO$_3$ interface, electronic phase transitions can be triggered by modulation of the charge carrier density, making this system an excellent prospect for the realization of versatile electronic devices. Here, we report repeatable
We address the issue of inter-particle dipolar interactions in the context of magnetic hyperthermia. More precisely, the main question dealt with here is concerned with the conditions under which the specific absorption rate is enhanced or reduced by
We probe the local inhomogeneities of the electronic properties of graphene at the nanoscale using scanning probe microscopy techniques. First, we focus on the study of the electronic inhomogeneities caused by the graphene-substrate interaction in gr