  Here we demonstrate the occurrence of robust itinerant ferromagnetism in
Mott-Hubbard systems at both low and high doping concentrations. Specifically,
we study the effect of hole doping on the experimentally synthesized LaCrAsO
via first-principles calculations and observe that the parent G-type
antiferromagnetism vanishes quickly at low doping concentration ($x$ $\sim$
0.20) and the system becomes ferromagnetic metal due to the canonical double
exchange (CDE) mechanism. As $x$ continues to increase, the onsite energy
difference between Cr 3$d$ and As 4$p$ orbitals decreases and the system
transitions to a ferromagnetic negative charge-transfer energy metal.
Therefore, the itinerant ferromagnetism doesn't terminate at intermediate $x$
as CDE mechanism usually predicts. Furthermore, our calculations reveal that
both nearest and next-nearest ferromagnetic exchange coupling strengths keep
growing with $x$, showing that ferromagnetism caused by negative
charge-transfer energy state is "stronger" than that of CDE picture. Our work
not only unveils an alternative mechanism of itinerant ferromagnetism, but also
has the potential to attract immediate interest among experimentalists.
