  We present and discuss a new family of topological hairy dyonic black hole
solutions in asymptotically anti-de Sitter (AdS) space. The coupled
Einstein-Maxwell-Scalar gravity system, that carries both the electric and
magnetic charges is solved, and exact hairy dyonic black hole solutions are
obtained analytically. The scalar field profiles that give rise to such black
hole solutions are regular everywhere. The hairy solutions are obtained for
planar, spherical, and hyperbolic horizon topologies. In addition, analytic
expressions of regularized action, stress tensor, conserved charges, and free
energies are obtained. We further comment on different prescriptions for
computing the black hole mass with hairy backgrounds. We analyze the
thermodynamics of these hairy dyonic black holes in canonical and grand
canonical ensembles, and we find that both electric and magnetic charges have a
constructive effect on the stability of the hairy solution. For the case of
planar and hyperbolic horizons, we find thermodynamically stable hairy black
holes which are favoured at low temperatures compared to the non-hairy
counterparts. We further find that, for a spherical hairy dyonic black hole,
the thermodynamic phase diagram resembles to that of a Van der Waals fluid not
only in canonical but also in the grand canonical ensemble.
