  Magnetic materials with high mobilities are intriguing subject of research
from both fundamental and application perspectives. Based on first-principle
calculations, we investigate the physical properties of the already synthesized
AMnBi(A =K, Rb, Cs)-family materials. We show that these materials are
antiferromagnetic (AFM), with Neel temperatures above 300 K. They contain AFM
ordered Mn layers, while the interlayer coupling changes from ferromagnetic
(FM) for KMnBi to AFM for RbMnBi and CsMnBi. We find that these materials are
narrow gap semiconductors. Owing to the small effective mass, the electron
carrier mobility can be very high, reaching up to 100,000 cm2/(Vs) for KMnBi.
In contrast, the hole mobility is much suppressed, typically lower by two
orders of magnitude. We further study their two-dimensional (2D) single layer
structures, which are found be AFM with fairly high mobility (1000 cm2/(Vs)).
Their Neel temperatures can still reach room temperature. Interesting, we find
that the magnetic phase transition is also accompanied by a metal-insulator
phase transition, with the paramagnetic metal phase possessing a pair of
nonsymmorphic-symmetry-protected 2D spin-orbit Dirac points. Furthermore, the
magnetism can be effectively controlled by the applied strain. When the
magnetic ordering is turned into FM, the system can become a quantum anomalous
Hall insulator with gapless chiral edge states.
