  Novel static black hole solutions with electric and magnetic charges are
derived for the class of modified gravities: $f({\cal R})={\cal
R}+2\beta\sqrt{{\cal R}}$, with or without a cosmological constant. The new
black holes behave asymptotically as flat or (A)dS space-times with a dynamical
value of the Ricci scalar given by $R=\frac{1}{r^2}$ and
$R=\frac{8r^2\Lambda+1}{r^2}$, respectively. They are characterized by three
parameters, namely their mass and electric and magnetic charges, and constitute
black hole solutions different from those in Einstein's general relativity.
Their singularities are studied by obtaining the Kretschmann scalar and Ricci
tensor, which shows a dependence on the parameter $\beta$ that is not permitted
to be zero. A conformal transformation is used to display the black holes in
Einstein's frame and check if its physical behavior is changed w.r.t. the
Jordan one. The thermal stability of the solutions is discussed by using
thermodynamical quantities, in particular the entropy, the Hawking temperature,
the quasi-local energy, and the Gibbs free energy. Also, the casual structure
of the new black holes is studied, and a stability analysis is performed in
both frames using the odd perturbations technique and the study of the geodesic
deviation. It is concluded that, generically, there is coincidence of the
physical properties of the novel black holes in both frames, although this
turns not to be the case for the Hawking temperature.
