Electronic structure and exchange interactions in ${\mathrm{BaVS}}_3$

The electronic structure and spin exchange interactions of a quasi-one-dimensional sulfide ${\mathrm{BaVS}}_3$ have been studied within the density functional theory $\left(\mathrm{DFT}\right)$ with the generalized gradient approximation $\left(\mathrm{GGA}\right)$ using the projected augmented wave $\left(\mathrm{PAW}\right)$ method. The on-site Coulomb repulsion has also been taken into account in the $\mathrm{GGA}+U$ approach to unravel the correlation effects on the electronic structure. We found that in the high-temperature hexagonal structure the partially filled $t_{2g}$ conduction bands including the broad $d(3z^2-r^2)$ and two narrow $e\left(t_{2g}\right)$ orbitals contribute to the conductivity of ${\mathrm{BaVS}}_3$, suggesting a weak anisotropy in the electronic transport. Furthermore, our $\mathrm{GGA}+U$ band structure calculations predict an insulating ground state with a narrow gap of $0.15\mathrm{eV}$ for ${\mathrm{BaVS}}_3$ in the low-temperature $\left(60\mathrm{K}\right)$ orthorhombic structure, thereby indicating the Mott-Hubbard mechanism for the low-temperature insulating behavior. Our total energy analyses of the ground-state spin configuration in the low-temperature phases show that the magnetic structure with an intrachain ferromagnetic spin arrangement and an interchain antiferromagnetic spin arrangement that is consistent with a superexchange mechanism through sulfur $3p$ orbitals is preferred. We have also estimated the values of exchange integrals by mapping the calculated total energies onto the Heisenberg spin model. It is found that the stronger exchange interaction is ferromagnetic intrachain coupling, while the weaker antiferromagnetic interchain coupling occurs along the $a$ axis. A substantial magnetic anisotropy is found and results in the observed quasi-1D magnetic character in ${\mathrm{BaVS}}_3$. This suggests the separation of the spin and charge degrees of freedom as a possible cause of the anomalous properties, e.g., the 3D electronic transport and the quasi-1D magnetism of ${\mathrm{BaVS}}_3$.

Figure 1

An example of the spin configurations for the supercell of $8\left({\mathrm{BaVS}}_3\right)$ in the low-temperature phase. Only vanadium atoms and their spin orientations are shown in this picture. The influence of triagonal frustration is neglected. An abbreviation such as $FAA$ means the ferromagnetic $\left(F\right)$ spin ordering along the chain direction ($c$ axis) and the antiferromagnetic $\left(A\right)$ spin ordering along the interchain directions ($a$ and $a+b$ crystallagraphic directions), respectively.

Figure 2

Band structure of ${\mathrm{BaVS}}_3$ in the high-temperature hexagonal structure from $\mathrm{GGA}$ calculations. The Fermi level is set to zero. (a) Band dispersion relations. $\Gamma KM\Gamma$ and $AHLA$ directions are perpendicular, and $\Gamma A$ is parallel to the linear chain axis. (b) Total DOS per formula unit and partical DOS per atom in the energy interval of $-6–4\mathrm{eV}$ relative to the Fermi level.

Figure 3

Band structure of ${\mathrm{BaVS}}_3$ in the normal metallic state at room temperature from $\mathrm{GGA}+U$ calculations. (a) Band dispersion relations and (b) Total DOS per formula unit and partial DOS per atom.

Figure 4

Up-spin band structure of orthorhombic ${\mathrm{BaVS}}_3$ using the crystal structure parameters at $60\mathrm{K}$ (Ref. 14) for the FAA spin configuration (see Fig. 1) by $\mathrm{GGA}+U$ calculations with $U=4.1\mathrm{eV}$ and $J=1.1\mathrm{eV}$. The zero energy denotes the top of valence bands. (a) Dispersion relation, where the symmetry lines are selected the same as those in the hexagonal directions in order to compare with the calculations for hexagonal ${\mathrm{BaVS}}_3$ at room temperature. (b) Total DOS per formula and partial DOS per atom plots.

Figure 5

(a). Local Cartesian coordinate of a ${\mathrm{VS}}_6$ octahedron. Three symmetry-adapted $t_{2g}$ orbitals of a ${\mathrm{VS}}_6$ octahedron are labeled as $\alpha$, $\beta$, and $\gamma$, respectively. (b) The partial DOS of three $t_{2g}$ orbitals of a V atom from the $\mathrm{GGA}+U$ calculations at a low temperature of $60\mathrm{K}$.