Theory of digital magnetoresistance in ferromagnetic resonant-tunneling diodes

We propose a ferromagnetic spintronic system, which consists of two serial connected resonant-tunneling diodes. One diode is nonmagnetic whereas the other comprises a ferromagnetic emitter and quantum well. Using a self-consistent coherent transport model we show that the current-voltage characteristic of the ferromagnetic diode can be strongly modulated by changing the relative orientation of the magnetizations in the emitter and quantum well, respectively. By a continuous change of the relative magnetization angle the total resistance exhibits a discrete jump realizing digital magnetoresistance. The interplay between the emitter’s Fermi energy level and the relative magnetization orientations allows to tailor the current voltage characteristics of the ferromagnetic diode from ohmic to negative differential resistance regime at low voltages.

Figure 1

(Color online) Left: The circuit configuration of the proposed ferromagnetic MOBILE. The load is a conventional RTD, whose peak current can be modified by an external gate voltage $V_G$. The driver device consists of a ferromagnetic RTD. The peak current of the driver is controlled by twisting the QW magnetization. Right: The schematic conduction band profile of the ferromagnetic RTD [here made of a $\mathrm{Ga}(\mathrm{Al},\mathrm{Mn})\mathrm{N}$ material system] used in the numerical simulations discussed in the text.

Figure 2

Contour plots of the local density of states versus energy and growth direction $z$ for parallel magnetization alignment in the case of (a) equilibrium $V_a=0$ and (b) at the peak voltage of $V_a=0.12\mathrm{V}$. The exchange splitting of spin up and down level is clearly visible for the quasibound ground state in the well. The solid lines indicate the self-consistent conduction band profile.

Figure 3

(Color online) Self-consistent current-voltage characteristics of the magnetic driver-RTD for several relative orientations of the quantum well magnetization (indicated by the angle $\phi$) at the temperature of $T=100\mathrm{K}$. The solid black lines show the mirrored $IV$ curve of the load-RTD for low and high input voltages, respectively; working points are indicated by circles. For these fixed low and high input voltages the output voltages are restricted to the intervals $\mathrm{\Delta }{V}_i^{\mathrm{out}}$, $i=1,2,3$.

Figure 4

(Color online) Current-voltage characteristics of the magnetic driver-RTD in the non-self-consistent case for different relative orientations $\phi$ of the quantum well magnetization at the lattice temperature $T=100\mathrm{K}$. The peak voltage and currents are smaller when compared to the self-consistent case of Fig. 3 and there exists a common crossing points for all $IV$ curves.

Figure 5

(Color online) Voltage-dependent magnetocurrent (MC) in the case of different relative orientations $\phi$ of the magnetization in the quantum well at the temperature of $T=100\mathrm{K}$.

Figure 6

(Color online) Current spin polarization as a function of the applied voltage for different orientations of the quantum well magnetization (indicated by angle $\phi$) at the lattice temperature of $T=100\mathrm{K}$.

Figure 7

(Color online) Illustration of the analytic model discussed in the text for the case of parallel (P) and antiparallel (AP) magnetization alignment. In the model the magnetization of the emitter is “soft,” whereas the QW magnetization is assumed to be fixed. Part (a) shows the spin resolved conduction band profile in the emitter with the spin splitting $\Delta$, the first quasibound states $E_{\uparrow }$ and $E_{\downarrow }$ in the quantum well energetically separated by $\delta$, and the emitter Fermi energy level $E_f$. Part (b) illustrates graphically the relative positions of the emitter Fermi and well energies (top axis) and of the so-called “on” and “off” switching voltages introduced in the model (middle and bottom axis) on a $1∕\alpha$ voltage scale with the parameter $\alpha$ defined in Eq. (12). The on-switching voltages (light-colored circles) $V_{\uparrow ,\downarrow }^{\mathrm{on}}=(E_{\uparrow ,\downarrow }-E_f)∕\alpha$ are defined as voltages at which the well states start to become resonant and the off-switching voltages (blacked filled circles) denote the voltages at which the well states are pushed below the emitters spin up and down conduction band, respectively, for both the P and AP cases. The relative position between the on- and off-switching voltages can be changed by moving the Fermi energy level.

Figure 8

(Color online) Blow up of the self-consistent current-voltage characteristics displayed in Fig. 3 for low voltages. By replacing the load-RTD by a linear load resistance (indicated by the black solid line) allows us to perform the monostable-to-bistable transition by flipping the QW magnetization from P to AP. The working points are indicated by circles. The inset schematically shows the arrangement of the quasibound levels at the peak voltage in the AP case.