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Scalarized black holes (BH) have been shown to form dynamically inextended-scalar-tensor theories, either through spontaneous scalarization --when the BH is unstable against linear perturbations -- or through a non-linearscalarization. In the latter, linearly stable BHs can ignite scalarization whensufficiently perturbed. These phenomena are, however, not incompatible andmixed scalarization is also possible. The objective of this work is twofold:first, study mixed scalarization on a family of Einstein-Maxwell-scalar models;and second, study the effect of the counter scalarization that occurs when oneof the coupling parameters has a sign opposite to the one that generatesscalarization. Both objectives are addressed by constructing and examining themixed scalarization's domain of existence. An overall dominance of thespontaneous scalarization over the non-linear scalarization is observed.Thermodynamically, an entropical preference for mixed over the standardscalarization (spontaneous or non-linear) exists. In the presence of counterscalarization, a quench of the scalarization occurs, mimicking the effect of ascalar particle's mass/positive self-interaction term.

Mixed scalarization of charged black holes: from spontaneous to non-linear scalarization