Density functional approach for the magnetism of $\beta$-TeVO${}_4$

Density functional calculations have been carried out to investigate the microscopic origin of the magnetic properties of $\beta$-TeVO${}_4$. Two different approaches, based either on a perturbative treatment of the multiorbital Hubbard model in the strongly correlated limit or on the calculation of supercell total energy differences, have been employed to evaluate magnetic couplings in this compound. The picture provided by these two approaches is that of weakly coupled frustrated chains with ferromagnetic nearest-neighbor and antiferromagnetic second-nearest-neighbor couplings. These results, differing substantially from previous reports, should motivate further experimental investigations of the magnetic properties of this compound.

Figure 1

(a) Crystal structure of $\beta$-TeVO${}_4$. The coordination square pyramids of vanadium are shown in green, oxygen ions are in red, and tellurium ions are in blue. The crystal unit cell is also represented. (b) Magnetic couplings in $\beta$-TeVO${}_4$ up to the eighth nearest neighbor. Couplings occurring within the chains are represented in red ($J_1$ and $J_4$), couplings between chains in the $(b,c)$ planes are represented in blue ($J_3$ and $J_8$), and couplings between chains of distinct $(b,c)$ planes are represented in green ($J_2$, $J_5$, $J_6$, and $J_7$).

Figure 2

Nonmagnetic GGA-PBE electronic structure of $\beta$-TeVO${}_4$. (a) Total and projected densities of states and (b) DFT-GGA (black solid line) and Wannier-interpolated (in blue) band structure of $\beta$-TeVO${}_4$. The high-symmetry point coordinates in the Brillouin zone are given in units of the reciprocal lattice basis vectors of the monoclinic P2${}_1$/c unit cell.

Figure 3

MLWF of dominant V-$d_{xy}$ character calculated with wannier90 in $\beta$-TeVO${}_4$. Antibonding $2p$ tails on neighboring oxygens are also clearly visible.

Figure 4

Determination of the magnetic couplings by the method of total energy differences. For each configuration, the DFT relative energy is represented versus the optimized Ising energy. The best-fit values are given in the inset. According to the convention used in Eq. (3), positive couplings correspond to AFM interactions.