Magnetic-Field-Modulated Resonant Tunneling in Ferromagnetic-Insulator-Nonmagnetic Junctions

We present a theory for resonance-tunneling magnetoresistance (MR) in ferromagnetic-insulator-nonmagnetic junctions. The theory sheds light on many of the recent electrical spin injection experiments, suggesting that this MR effect rather than spin accumulation in the nonmagnetic channel corresponds to the electrically detected signal. We quantify the dependence of the tunnel current on the magnetic field by quantum rate equations derived from the Anderson impurity model, with the important addition of impurity spin interactions. Considering the on-site Coulomb correlation, the MR effect is caused by competition between the field, spin interactions, and coupling to the magnetic lead. By extending the theory, we present a basis for operation of novel nanometer-size memories.

Figure 1

(a) Nonlocal and local electrical setups for detecting spin accumulation. (b) The measured signal $\delta R(B)=[V(B)-V(0)]/I_T$ is a change in junction resistance when applying in-plane or out-of-plane magnetic fields. The Lorentzian due to the in-plane field is typically observed only in the local setup. Resonant tunneling via (c) type $A$ or (d) type $B$ impurities for spin injection (electrons flow from $F$ to $N$).

Figure 2

Calculated MR via an impurity with $\alpha =0.1$ embedded in the $F\text{−}I\text{−}N$ junction with $p=1/3$. MR due to resonant tunneling via an (a) $E^{\prime }$ and (b) $P_d$ defect in silicon-oxide interfaces. (c) MR in the presence of molecular fields due to exchange between nearest-neighbor impurities.

Figure 3

Nano-size tunnel memory relying on the MR effect. (a) The basic cell is a 1D conducting nanowire in an insulator (e.g., DXP molecules in zeolites [61]), or adjacent insulating and conducting wires as shown in (b). In either configuration, the writing voltage ($V_W$) sets the position of an unpaired electron in one of two impurities embedded in the insulator (labeled ‘1’ and ‘0’). The conducting wire includes a critical $A\text{−}B\text{−}A$ impurity chain which becomes Pauli blocked when applying a magnetic field [56]. (c) The MR effect facilitates the information readout due to its strong dependence on the exchange field of the unpaired electron (see text).