  A recently proposed model for nonlinear electrodynamics has been minimally
coupled to dimensionally continued gravity and the topological black holes in
the presence of conformal scalar field were studied. In this setup, the new
magnetized hairy black hole solution has been found and its thermodynamic
properties have also been analyzed. The exact expressions for mass, entropy,
Hawking temperature and heat capacity are derived and local thermodynamic
stability for the resulting black holes has been checked. In addition to this,
the modified Smarr's formula is constructed and the generalized first law has
also been verified. Finally, the hairy magnetized black holes in general
Lovelock-scalar gravity have also been studied.
