We consider a two-dimensional magnetic tunnel junction of the FM/I/QW(FM+SO)/I/N structure, where FM, I and QW(FM+SO) stand for a ferromagnet, an insulator and a quantum wire (QW) with both magnetic ordering and Rashba spin-orbit (SOC), respectively.
The tunneling magneto-resistance (TMR) exhibits strong anisotropy and switches sign as the polarization direction varies relative to the QW axis, due to interplay among the one-dimensionality, the magnetic ordering, and the strong SOC of the QW. The results may provide a possible explanation for the sign-switching anisotropic TMR recently observed in the LaAlO$_3$/SrTiO$_3$ interface.
The Kibble-Zurek mechanism (KZM) is generalized to a class of multi-level systems and applied to study the quenching dynamics of one-dimensional (1D) topological superconductors (TS) with open ends. Unlike the periodic boundary condition, the open bo
undary condition, that is crucial for the zero-mode Majorana states localized at the boundaries, requires to consider many coupled levels. which is ultimately related to the zero-mode Majorana modes. Our generalized KZM predictions agree well with the numerically exact results for the 1D TS.
