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We present a method to determine the model Hamiltonians to treat rare-earth multiplets in solids from the results of the quasiparticle self-consistent \textit{GW} (QSGW) method. We apply the method to trivalent Eu compounds EuCl$_3$, EuN, and Eu-doped GaN after examining free rare-earth ions. We solve the model Hamiltonian by the exact diagonalization. Our results justify applying the Dieke diagram to ions in solid, while its limitation is clarified. In particular, we show that the crystal fields cause sizable breaking of the Russell-Saunders coupling., Comment: 7 pages, 3 figures, 2 tables

It is well known that the temperature dependence of the effective magnetocrystalline anisotropy energy obeys the $l(l+1)/2$ power law of magnetization in the Callen-Callen theory. Therefore, according to the Callen-Callen theory, the magnetocrystalline anisotropy energy is assumed to be zero at the critical temperature where the magnetization is approximately zero. This study estimates the temperature dependence of the magnetocrystalline anisotropy energy by integrating the magnetization versus magnetic field ($M$--$H$) curves, and found that the magnetocrystalline anisotropy is still finite even above the Curie temperature in the uniaxial anisotropy, whereas this does not appear in the cubic anisotropy case. The origin is the fast reduction of the anisotropy field, which is the magnetic field required to saturate the magnetization along the hard axis, in the case of cubic anisotropy. Therefore, the magnetization anisotropy and anisotropic magnetic susceptibility, those are the key factors of magnetic anisotropy, could not be established in the case of cubic anisotropy. In addition, the effect of magnetocrystalline anisotropy on magnetocaloric properties, as the difference between the entropy change curves of AlFe$_{2}$B$_{2}$ appears above the Curie temperature, which is in good agreement with a previous experimental study. This is proof of magnetic anisotropy at slightly above Curie temperature.

The mobility and disorder in the lattice of Cu atoms as liquid-like behavior is an important characteristic affecting the thermoelectric properties of Cu$_{2}$S. In this study, using a theoretical model called acanthite-like structure for Cu$_{2}$S at a low-temperature range, we systematically investigate the electronic structure, intrinsic defect formation, and transport properties by first-principles calculations. Thereby, previous experimental reports on the indirect bandgap nature of Cu$_{2}$S were confirmed in this work with an energy gap of about 0.9-0.95 eV. As a result, the optical absorption coefficient estimated from this model also gives a potential value of $\alpha > 10^{4}$ cm$^{-1}$ in the visible spectrum range. According to the bonding analysis and formation energy aspect, Cu vacancy is the most preferred defect to form in Cu$_{2}$S, which primarily affects the conductive behavior as a $p$-type, as experimentally observed. Finally, the transport properties of Cu$_{2}$S system were successfully reproduced using an electron-phonon scattering method, highlighting the important role of relaxation time prediction in conductivity estimation instead of regarding it as a constant., Comment: 10 pages

We introduce a new extended Heisenberg model. The model contains the orbital-dependent spins together with the retarded effects of spin torque. The model is directly derived from the dynamical linear response functions on the transversal spin fluctuation. Our model allows us to address effects which are not accessible via the usual Heisenberg model. With the model, we can describe not only the relaxation effects due to the Landau damping caused by the Stoner excitations, but also the nesting effects of the Fermi surface. We discuss possibilities of the extended Heisenberg model based on the high-resolution plots of the spin susceptibility for Fe.

High $ZT$ value and large Seebeck coefficient have been reported in the nanostructured Fe-doped Si-Ge alloys. In this work, the large Seebeck coefficient in Fe-doped Si-Ge systems is qualitatively reproduced from the computed electronic density of states, where a hybrid functional, HSE06, is used for an exchange-correlation functional, as well as a special quasi-random structure (SQS) for a disordered atomic configuration. Furthermore, by replacing Fe with other transition metals, such as Mn, Co, Ni, Cu, Zn, and Au, a better dopant that produces a larger Seebeck coefficient in Si-Ge alloy systems is explored., Comment: 6 pages

We calculate transverse spin susceptibility in the linear response method based on the ground states determined in the quasi-particle self-consistent $GW$ (QSGW) method. Then we extract spin wave (SW) dispersions from the susceptibility. We treat bcc Fe, hcp Co, fcc Ni, and B2-type FeCo. Because of the better description of the independent-particle picture in QSGW, calculated spin stiffness constants for Fe, Co, and Ni give much better agreement with experiments in QSGW than that in the local density approximation (LDA), where the stiffness for Ni in LDA is two times bigger than the experiment. For Co, both acoustic and optical branches of SWs agree with the experiment. As for FeCo, we have some discrrepancy between the spin stiffness in QSGW and that in the experiment. We may need further theoretical and experimental investigations on the discrepancy., Comment: 10 pages, 9 figures

We have recently implemented a new version of the quasiparticle self-consistent GW (QSGW) method in the ecalj package released at http://github.com/tkotani/ecalj. Since the new version of the ecalj is numerically stable and accurate compared to the previous versions, we can perform calculations easily without being bothered with setting input parameters. Here we examine its ability to describe energy band properties, e.g., band-gap energy, eigenvalues at special points and effective mass, for variety of semiconductors and insulators. We treat C, Si, Ge, Sn, SiC (in 2H, 3C, and 4H structures), (Al, Ga, N)x(N, P, As, Pb), (Zn, Cd, Mg)x(O, S, Se, Te), SiO2, HfO2, ZrO2, SrTiO3, PbS, PbTe, MnO, NiO, and HgO. We propose that a hybrid QSGW method, where we mix 80 percent of QSGW and 20 percent of LDA, gives universally good agreement with experiments for these materials., Comment: 8 pages, 3 figures, 4 tables