NbP is one member of a new class of nodal loop semimetals characterized by the cooperative effects of spin-orbit coupling (SOC) and a lack of inversion center. Here transport and spectroscopic properties of NbP are evaluated using density functional
theory methods. SOC together with the lack of inversion symmetry splits degeneracies, giving rise to Russian doll nested Fermi surfaces containing 4*10$^{-4}$ electron (hole) carriers/f.u. Due to the modest SOC strength in Nb, the Fermi surfaces map out the Weyl nodal loops. Calculated structure around T$^*$~100 K in transport properties reproduces well the observed transport behavior only when SOC is included, attesting to the precision of the (delicate) calculations and the stoichiometry of the samples. Low energy collective electron-hole excitations (plasmons) in the 20-60 meV range result from the nodal loop splitting.
We investigate the electronic structure of (Sr$_{1-x}$La$_x$)$_2$RhO$_4$ using a combination of the density functional and dynamical mean-field theories. Unlike the earlier local density approximation plus Hubbard $U$ (LDA+U) studies, we find no siza
ble enhancement of the spin-orbit splitting due to electronic correlations and show that such an enhancement is a spurious effect of the static mean-field approximation of the LDA+U method. The electron doping suppresses the importance of electronic correlations, which is reflected in quasi-particle bandwidth increasing with $x$. (Sr$_{1-x}$La$_x$)$_2$RhO$_4$ can be classified as weakly correlated metal, which becomes an itinerant in-plane ferromagnet (but possibly A-type antiferromagnet) due to Stoner instability around $x=0.2$.
Applying the correlated electronic structure method based on density functional theory plus the Hubbard $U$ interaction, we have investigated the tetragonal scheelite structure Mott insulator KOsO$_4$, whose $e_g^1$ configuration should be affected o
nly slightly by spin-orbit couping (SOC). The method reproduces the observed antiferromagnetic Mott insulating state, populating the Os $d_{z^2}$ majority orbital. The quarter-filled $e_g$ manifold is characterized by a symmetry breaking due to the tetragonal structure, and the Os ion shows a crystal field splitting $Delta_{cf}$ = 1.7 eV from the $t_{2g}$ complex, which is relatively small considering the high formal oxidation state Os$^{7+}$. The small magnetocrystalline anisotropy before including correlation (i.e., in the metallic state) is increased by more than an order of magnitude in the Mott-insulating state, a result of a strong interplay between large SOC and a strong correlation. In contrast to conventional wisdom that the $e_g$ complex will not support orbital magnetism, we find that for the easy axis [100] direction the substantial Os orbital moment $M_Lapprox-0.2 mu_B$ compensates half of the Os spin moment $M_S$ = 0.4$mu_B$. The origin of the orbital moment is analyzed and understood in terms of additional spin-orbital lowering of symmetry, and beyond that due to structural distortion, for magnetization along [100]. Further interpretation is assisted by analysis of the spin density and the Wannier function with SOC included.
Using ab initio calculations, we have investigated an insulating tetragonally distorted perovskite BaCrO$_3$ with a formal $3d^2$ configuration, the volume of which is apparently substantially enhanced by a strain due to SrTiO$_3$ substrate. Inclusio
n of both correlation and spin-orbit coupling (SOC) effects leads to a metal-insulator transition and in-plane zigzag orbital-ordering (OO) of alternating singly filled $d_{xz}+id_{yz}$ and $d_{xz}-id_{yz}$ orbitals, which results in a large orbital moment $M_L$ ~ -0.78 $mu_B$ antialigned to the spin moment $M_S$ ~ $2|M_L|$ in Cr ions. Remarkably, this ordering also induces a considerable $M_L$ for apical oxygens. Our findings show metal-insulator and OO transitions, driven by an interplay among strain, correlation, and SOC, which is uncommon in 3d systems.
