Reissner-Nordstr\"om black holes with non-Abelian hair

We consider $d\geqslant 4$ Einstein--(extended-)Yang-Mills theory, where the gauge sector is augmented by higher order terms. Linearizing the (extended) Yang-Mills equations on the background of the electric Reissner-Nordstr\"om (RN) black hole, we show the existence of normalizable zero modes, dubbed non-Abelian magnetic stationary clouds. The non-linear realization of these clouds bifurcates the RN family into a branch of static, spherically symmetric, electrically charged and asymptotically flat black holes with non-Abelian hair. Generically, the hairy black holes are thermodynamically preferred over the RN solution, which, in this model, becomes unstable against the formation of non-Abelian hair, for sufficiently large values of the electric charge.