To obtain an effective many-body model of graphene and related materials from first principles we calculate the partially screened frequency dependent Coulomb interaction. In graphene, the effective on-site (Hubbard) interaction is $U_{00}=9.3\mathrm{eV}$ in close vicinity to the critical value separating conducting graphene from an insulating phase emphasizing the importance of nonlocal Coulomb terms. The nearest-neighbor Coulomb interaction strength is computed to $U_{01}=5.5\mathrm{eV}$. In the long-wavelength limit, we find the effective background dielectric constant of graphite to be $ϵ=2.5$ in very good agreement with experiment.

The effective on-site Coulomb interaction (Hubbard U) between localized d electrons in 3d, 4d, and 5d transition metals is calculated employing a parameter-free realization of the constrained random-phase approximation using Wannier functions within the full-potential linearized augmented-plane-wave method. The U values lie between 1.5 and 5.7 eV and depend on the crystal structure, spin polarization, d electron number, and d orbital filling. On the basis of the calculated U parameters, we discuss the strength of the electronic correlations and the instability of the paramagnetic state toward the ferromagnetic one for 3d metals.

We present extensive first-principles calculations on the inverse full-Heusler compounds having the chemical formula ${X}_{2}YZ$, where $X=\text{Sc}$, Ti, V, Cr, or Mn; $Z=\text{Al}$, Si, or As; and the $Y$ ranges from Ti to Zn. Several of these compounds are identified to be half-metallic magnets. We show that the appearance of half-metallicity is associated in all cases with a Slater-Pauling behavior of the total spin-magnetic moment. There are three different variants of this rule for the inverse Heusler compounds depending on the chemical type of the constituent transition-metal atoms. Simple arguments regarding the hybridization of the $d$ orbitals of neighboring atoms can explain these rules. We expect our results to trigger further experimental interest in these types of half-metallic Heusler compounds.

We employ ab-initio electronic structure calculations to study 60 LiMgPdSn-type (also known as LiMgPdSb-type) quaternary Heusler compounds. All compounds obey the Slater-Pauling rule with diverse electronic and magnetic properties. 41 compounds are found to be half-metals, 8 spin-gapless semiconductors, and 9 semiconductors. CoVTiAl and CrVTiAl compounds are identified as ferromagnetic and antiferromagnetic semiconductors, respectively, with large energy gaps in both spin directions. All magnetic compounds are expected to have high Curie temperatures making them suitable for spintronics/magnetoelectronics applications.

The interatomic exchange interactions and Curie temperatures in $\mathrm{Ni}$-based full Heusler alloys ${\mathrm{Ni}}_2\mathrm{Mn}X$ with $X=\mathrm{Ga},\mathrm{In},\mathrm{Sn}$, and $\mathrm{Sb}$ are studied within the framework of the density-functional theory. The calculation of the exchange parameters is based on the frozen-magnon approach. Despite closeness of the experimental Curie temperatures for all four systems, their magnetism appeared to differ strongly. This difference involves both the $\mathrm{Mn}\text{−}\mathrm{Mn}$ and $\mathrm{Mn}\text{−}\mathrm{Ni}$ exchange interactions. The Curie temperatures, $T_C$, are calculated within the mean-field approximation by solving a matrix equation for a multisublattice system. Good agreement with experiment for all four systems is obtained. The role of different exchange interactions in the formation of $T_C$ of the systems is discussed.

We study the exchange interactions in half-metallic Heusler alloys using first-principles calculations in conjunction with the frozen-magnon approximation. The Curie temperature is estimated within both mean-field (MF) and random-phase-approximation (RPA) approaches. For the half-Heusler alloys NiMnSb and CoMnSb, the dominant interaction is between the nearest Mn atoms. In this case, the MF and RPA estimations differ strongly. The RPA approach provides better agreement with the experiment. The exchange interactions are more complex in the case of full-Heusler alloys ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Si}$ and ${\mathrm{Co}}_2\mathrm{Cr}\mathrm{Al}$ where the dominant effects are the intersublattice interactions between the Mn(Cr) and Co atoms and between Co atoms at different sublattices. For these compounds, we find that both MF and RPA give very close values of the Curie temperature slightly underestimating experimental quantities. We study the influence of the lattice compression on the magnetic properties. The temperature dependence of the magnetization is calculated using the RPA method within both quantum mechanical and classical approaches.