  Inelastic neutron scattering recently confirmed the theoretical prediction of
a $\uparrow\uparrow\downarrow\downarrow$-magnetic state along the legs of
quasi-one-dimensional (quasi-1D) iron-based ladders in the orbital-selective
Mott phase (OSMP). We show here that electron-doping of the OSMP induces a
whole class of novel block-states with a variety of periodicities beyond the
previously reported $\pi/2$ pattern. We discuss the magnetic phase diagram of
the OSMP regime that could be tested by neutrons once appropriate quasi-1D
quantum materials with the appropriate dopings are identified.

Strongly Correlated Electrons