Electronic structure of the two-dimensional Heisenberg antiferromagnet VOCl: A multiorbital Mott insulator

We have studied the electronic structure of the two-dimensional Heisenberg antiferromagnet VOCl using photoemission spectroscopy and density-functional theory including local Coulomb repulsion. From calculated exchange integrals and the observed energy dispersions we argue that the degree of one dimensionality regarding both the magnetic and electronic properties is noticeably reduced compared to the isostructural compounds TiOCl and TiOBr. Also, our analysis provides conclusive justification to classify VOCl as a multiorbital Mott insulator. In contrast to the titanium-based compounds density-functional theory here gives a better description of the electronic structure. However, a quantitative account of the low-energy features and detailed line shapes calls for further investigations including dynamical and spatial correlations.

Figure 1

(Color online) Left: three-dimensional view of the VOCl crystal structure along the $b$ axis. Two bilayers separated by a van der Waals gap are shown. Top right: local octahedron around a V ion with the corresponding crystal axes. Lower right: triangular V sublattice projected onto the $ab$ plane and viewed along $c$. Also shown are the occupied $d_{x^2-y^2}$ (left) and $d_{xz}$ (right) orbitals to illustrate the hopping paths provided through overlapping electron clouds. In reality, neighboring V ions along $a$ are shifted along $c$ (see left structure).

Figure 2

(Color online) Magnetic susceptibility of VOCl measured with an external field of 0.1 T applied along the different crystallographic axes over an extended temperature range. At $T_{N\acute{e}el}=79\text{K}$ a transition into an antiferromagnetic phase occurs, accompanied by an anisotropic behavior, evidenced by the sharp drop if the external field is applied along $a$. The inset shows specific-heat measurements which display a peak anomaly at the same temperature.

Figure 3

(Color online) Comparison of calculated pDOS for $U_{eff}=1.3\text{eV}$ with angle-integrated PE spectra (no background subtraction). The former have been weighted with the respective photoionization cross sections at the corresponding excitation energies (top: UPS, $\text{He}{\text{I}}_{\alpha }$; bottom: XPS, $\text{Al}K\alpha$). Also shown are the sums of the weighted pDOS (solid red curves) and their convolutions with a Gaussian in order to mimic the experimental energy resolution (gray-shaded areas).

Figure 4

(Color online) (a) Comparison of the calculated DOS (gray-shaded areas) using $\text{GGA}+U$ with ferromagnetic spin alignment for different values of $U_{eff}$. While the gap between occupied and unoccupied states decreases from top to bottom, the separation between the high- and low-binding-energy regions increases. The widths of these bands, however, remain constant. (b) Orbital-resolved $\text{V}3d$ pDOS calculated using GGA. Three partially filled bands cross the Fermi energy leading to a metallic state. (c) Same as in (b) but calculated with $\text{GGA}+U$. Only $d_{x^2-y^2}$ and $d_{xz}$ are occupied with one electron each, all other bands are empty.

Figure 5

(Color online) Upper panel: ARPES intensity plots $I\left(k,E\right)$ of the valence region along $\Gamma \text{Y}$ ($b$ axis; left) and $\Gamma \text{X}$ ($a$ axis; right) together with band dispersions from $\text{GGA}+U\left(U_{eff}=1.3\text{eV}\right)$. The latter have been shifted in energy to account for the effects described in Sec. 3. The similarities especially in the high-energy parts (O/Cl bands) are remarkable. Lower panel: EDCs along $\text{Y}\Gamma \text{Y}$ (left) and $\text{X}\Gamma \text{X}$ (right).

Figure 6

(Color online) $\text{V}3d$ part of the valence band. Upper panel: ARPES intensity plots $I\left(k,E\right)$ along $\Gamma \text{Y}$ ($b$ axis; left) and $\Gamma \text{X}$ ($a$ axis; right) together with band dispersions from $\text{GGA}+U\left(U_{eff}=1.3\text{eV}\right)$. The latter have been shifted in energy to account for the effects described in Sec. 3. Lower panel: EDCs along $\text{Y}\Gamma \text{Y}$ (left) and $\text{X}\Gamma \text{X}$ (right).