  Two-dimensional Ferrovalley materials with intrinsic valley polarization are
rare but highly promising for valley-based nonvolatile random access memory and
valley filter. Using Kinetically Limited Minimization (KLM), an unconstrained
crystal structure prediction algorithm, and prototype sampling based on
first-principles calculations, we have discovered 17 new Ferrovalley materials
(rare-earth iodides RI$_2$, where R is a rare-earth element belonging to Sc, Y,
or La-Lu, and I is Iodine). The rare-earth iodides are layered and demonstrate
2H, 1T, or 1T$_d$ phase as the ground-state in bulk, analogous to transition
metal dichalcogenides (TMDCs). The calculated exfoliation energy of monolayers
is comparable to that of graphene and TMDCs, suggesting possible experimental
synthesis. The monolayers in the 2H phase exhibit two-dimensional
ferromagnetism due to unpaired electrons in $d$ and $f$ orbitals. Throughout
the rare-earth series, $d$ bands show valley polarization at $K$ and $\bar{K}$
points in the Brillouin zone near the Fermi level. Due to strong magnetic
exchange interaction and spin-orbit coupling, large intrinsic valley
polarization in the range of 15-143 meV without external stimuli is observed,
which can be tuned and enhanced by applying a biaxial strain. These valleys can
selectively be probed and manipulated for information storage and processing,
potentially offering superior performance beyond conventional electronics and
spintronics. We further show that the 2H ferromagnetic phase of RI$_2$
monolayers possesses non-zero Berry curvature and exhibits the valley Hall
effect with considerable anomalous Hall conductivity. Our work will incite
exploratory synthesis of the predicted Ferrovalley materials and their
application in valleytronics and beyond.
