  Topological antiferromagnetic (AFM) spintronics is an emerging field of
research, which involves the topological electronic states coupled to the AFM
order parameter known as the N$\acute{\rm e}$el vector. The control of these
states is envisioned through manipulation of the N$\acute{\rm e}$el vector by
spin-orbit torques driven by electric currents. Here we propose a different
approach favorable for low-power AFM spintronics, where the control of the
topological states in a two-dimensional material, such as graphene, is
performed via the proximity effect by the voltage induced switching of the
N$\acute{\rm e}$el vector in an adjacent magnetoelectric AFM insulator, such as
chromia. Mediated by the symmetry protected boundary magnetization and the
induced Rashba-type spin-orbit coupling at the interface between graphene and
chromia, the emergent topological phases in graphene can be controlled by the
N$\acute{\rm e}$el vector. Using density functional theory and tight-binding
Hamiltonian approaches, we model a graphene/Cr2O3 (0001) interface and
demonstrate non-trivial band gap openings in the graphene Dirac bands
asymmetric between the K and K' valleys. This gives rise to an unconventional
quantum anomalous Hall effect (QAHE) with a quantized value of $2e^2/h$ and an
additional step-like feature at a value close to $e^2/2h$, and the emergence of
the spin-polarized valley Hall effect (VHE). Furthermore, depending on the
N$\acute{\rm e}$el vector orientation, we predict the appearance and
transformation of different topological phases in graphene across the
$180^{\circ}$ AFM domain wall, involving the QAHE, the valley-polarized QAHE
and the quantum VHE (QVHE), and the emergence of the chiral edge state along
the domain wall. These topological properties are controlled by voltage through
magnetoelectric switching of the AFM insulator with no need for spin-orbit
torques.
