We calculate the indirect charge carrier mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities for two selected graphene nanoflakes containing four hexagonal rings in their structure, differing by their geometry. We describe the electronic structure of either charge-neutral or doped nanoflakes using the tight-binding approximation with the Hubbard term, which is treated within the molecular-field approximation. We find pronounced differences in the RKKY coupling energies, dependent on the placement of the pair of magnetic moments in the nanostructure and on the edge form. For an odd total number of electrons in the structure, we predict in some circumstances the existence of ferromagnetic coupling with leading first-order perturbational contribution, while for an even number of charge carriers the usual, second-order mechanism dominates. Therefore, doping of the nanoflake with a single charge carrier is found to be able to change the coupling from an antiferromagnetic to a ferromagnetic one for some geometries.

The electronic structure of $1T-\mathrm{Ta}{\mathrm{S}}_2$ showing a metal-insulator transition and a sequence of different charge density wave (CDW) transformations was discussed in the frame of variable temperature angle-resolved photoelectron spectroscopy (ARPES), scanning tunneling spectroscopy (STS), and density functional theory (DFT) calculations. For the commensurate charge density wave phase (CCDW) the Mott gap was estimated to be 0.4 eV and energy gaps ${\mathrm{\Delta }}_{\text{CCDW},1},{\mathrm{\Delta }}_{\text{CCDW},2},{\mathrm{\Delta }}_{B3-\mathit{HHB}},{\mathrm{\Delta }}_{B4-B3}$ were observed. For the nearly commensurate charge density wave phase (NCCDW), the reminiscent of higher and lower Hubbard bands and a very pronounced electronic state associated with the parabolic band at the $\overline{\mathrm{\Gamma }}$ point in the Brillouin zone were identified. The incommensurate charge density wave phase (ICCDW) showed a high value of local density of states at the Fermi level and a very pronounced edge of the metallic surface state located in the range of 0.15–0.20 eV above the Fermi level. The obtained STS and ARPES results were consistent with our theoretical calculations performed within DFT formalism including spin-orbit coupling.

The thermodynamics of a spin-1/2 magnetic multilayer system with antiferromagnetic interplanar couplings is studied using the pair approximation method. Special attention is paid to magnetocaloric properties, quantified by isothermal entropy change. The multilayer consists of two kinds of magnetic planes, one of which is diluted. The intraplanar couplings in both planes have arbitrary anisotropy ranging between Ising and isotropic Heisenberg interactions. The phase diagram related to the occurrence of magnetic compensation phenomenon is constructed and discussed. Then the isothermal entropy change is discussed as a function of interaction parameters, magnetic component concentration and external magnetic field amplitude. The ranges of normal and inverse magnetocaloric effect are found and related to the presence or absence of compensation.