Spontaneous scalarization of regular Hayward black holes in Einstein-nonlinear electromagnetic-scalar gravity

In this paper, we discuss the spontaneous scalarization of Hayward black holes in Einstein-nonlinear electromagnetic-scalar gravity. Taking into account the tachyonic instability, we obtain scalarized charged black holes (SCBHs) with quadratic (1-$\alpha {\phi }^2$) and exponential ($e^{-\alpha {\phi }^2}$) couplings, respectively. Moreover, these SCBHs can be labelled by the number of $n=0,1,2,\mathrm{.}\mathrm{.}\mathrm{.}$, where $n=0$ is called the fundamental black hole and $n=1,2,\mathrm{.}\mathrm{.}\mathrm{.}$ denote the $n$-excited black holes. We recover that the $n=0$ branch for both couplings is stable against radial perturbations. This stability shows that this branch can be used for further observational implications.