Magnetic phase transitions and time-dependent tunneling in a coupled quantum well system

In this work, we have numerically integrated in space and time the effective-mass nonlinear Schrödinger equation for an electron wave packet in a bilayer electron system. Considering both polarized and unpolarized magnetic phases, we have calculated the tunneling dynamics between the two quantum wells when an external bias is applied. In our coupled quantum well system, we have considered a magnetic phase transition from the usual spin-polarized ground state to an unpolarized one. We have found the possibility of having a shift in the position of the resonant tunneling peak when the magnetic phase transition occurs.