  Effects of electron correlations on Anderson insulators have been one of the
central themes for recent two decades, suggesting that the Anderson insulating
phase turns into a novel insulating state referred to as many body localization
(MBL). However, the role of spin degrees of freedom in this dynamical phase
transition still remains unclarified as a function of the interaction strength.
In this study, we perform real-space spin-resolved Hartree-Fock-Anderson
simulations to investigate metal-insulator transitions above a critical
disorder strength in three spatial dimensions, where all single-particle states
are Anderson-localized without interactions. Here, relatively weak correlations
below the Mott regime are taken into account in the mean-field fashion but
disorder effects are introduced essentially exactly. We find two types of
single-particle mobility edges, where the multifractal spectrum of the
interaction-driven low-energy mobility edge deviates from that of the
high-energy one smoothly connected with the multifractal spectrum of the
metal-insulator transition without interactions. We show that the weakly
interacting insulating phase remains to be a paramagnetic Anderson insulating
state up to the temperature of the order of the band width. On the other hand,
we uncover that the relatively strongly interacting insulating phase still
below the Mott regime is ferromagnetic, which turns into a ferromagnetic
metallic state at a critical temperature much lower than the order of the
bandwidth. Based on all these results, we propose a quantum phase transition
from a paramagnetic Anderson insulating state to a ferromagnetic MBL insulating
phase via an intermediate ferromagnetic metallic state, which intervenes
between these two insulators at the Fermi energy.
