  A computational search for stable structures among both $\alpha$ and $\beta$
phases of ternary ATB4 borides (A= Mg, Ca, Sr, Ba, Al, Ga, and Zn, T is 3d or
4d transition elements) has been performed. We found that $\alpha$-ATB4
compounds with A=Mg, Ca, Al, and T=V, Cr, Mn, Fe, Ni, and Co form a family of
structurally stable or almost stable materials. These systems are metallic in
non-magnetic states and characterized by the formation of the localized
molecular-like state of 3d transition metal atom dimers, which leads to the
appearance of numerous Van Hove singularities (VHS) in the electronic spectrum.
The closeness of these VHS to the Fermi level can be easily tuned by electron
doping. For the atoms in the middle of the 3d row (Cr, Mn, and Fe), these VHS
led to magnetic instabilities and new magnetic ground states with a weakly
metallic or semiconducting nature. The magnetic ground states in these systems
appear as an analog of the spin glass state. Experimental attempts to produce
MgFeB4 and associated challenges are discussed, and promising directions for
further synthetic studies are formulated.
