  We propose and demonstrate through first-principles calculation a new
spin-dependent negative differential resistance (NDR) mechanism in magnetic
tunnel junctions (MTJ) with cubic cation disordered crystals (CCDC) AlO$_x$ or
Mg$_{1-x}$Al$_x$O as barrier materials. The CCDC is a class of insulators whose
band gap can be changed by cation doping. The gap becomes arched in an
ultrathin layer due to the space charge formed from metal-induced gap states.
With an appropriate combination of an arched gap and a bias voltage, NDR can be
produced in either spin channel. This mechanism is applicable to 2D and 3D
ultrathin junctions with a sufficiently small band gap that forms a large space
charge. It provides a new way of controlling the spin-dependent transport in
spintronic devices by an electric field. A generalized Simmons formula for
tunneling current through junction with an arched gap is derived to show the
general conditions under which ultrathin junctions may exhibit NDR.
