Scalarized dyonic black holes in vector-tensor Horndeski gravity

The vector-tensor Horndeski theory is supplemented by a real, massless scalar field nonminimally coupled to the interaction term. generic dyonic Reissner-Nordstrom solutions characterized electric and magnetic charges, acquire an instability bifurcate into electromagnetically charged presenting horizon cloud of hairs at specific values nonminimal coupling constant. These hairy black holes are studied in terms physical parameters model critical phenomena limiting their domain existence discussed.