  In strongly correlated electronic systems, several novel physical properties
are induced by the orbital degree of freedom. In particular, orbital degeneracy
near the Fermi level leads to spontaneous symmetry breaking, such as the
nematic state in FeSe and the orbital ordering in several perovskite systems.
Here, the novel layered perovskite material CsVF$_4$, with a $3d^2$ electronic
configuration, was systematically studied using density functional theory and a
multiorbital Hubbard model within the Hatree-Fock approximation. Our results
show that CsVF$_4$ should be magnetic, with a G-type antiferromagnetic
arrangement in the $ab$ plane and weak antiferromagnetic exchange along the
$c$-axis, in agreement with experimental results. Driven by the Jahn-Teller
distortion in the VF$_6$ octahedra that shorten the $c$-axis, the system
displays an interesting electron occupancy $d_{xy}^1(d_{xz}d_{yz})^1$
corresponding to the lower nondegenerate $d_{xy}$ orbital being half-filled and
the other two degenerate $d_{yz}$ and $d_{xz}$ orbitals sharing one electron
per site. We show that this degeneracy is broken and a novel $d_{yz}$/$d_{xz}$
staggered orbital pattern is here predicted by both the first-principles and
Hubbard model calculations. This orbital ordering is driven by the electronic
instability associated with degeneracy removal to lower the energy.
