  Based on high-throughput density functional theory calculations, we performed
screening for stable magnetic MAB compounds and predicted potential strong
magnets for permanent magnet and magnetocaloric applications. The
thermodynamical, mechanical, and dynamical stabilities are systematically
evaluated, resulting in 21 unreported compounds on the convex hull, and 434
materials being metastable considering convex hull tolerance to be 100
meV/atom. Analysis based on the Hume-Rothery rules revealed that the valence
electron concentration and size factor difference are of significant importance
in determining the stability, with good correspondence with the local atomic
bonding. We found 71 compounds with the absolute value of magneto-crystalline
anisotropy energy above 1.0 MJ/m$^3$ and 23 compounds with a uniaxial
anisotropy greater than 0.4 MJ/m$^3$, which are potential gap magnets. Based on
the magnetic deformation proxy, 99 compounds were identified as potential
materials with interesting magnetocaloric performance.
