Negative differential conductance and magnetoresistance oscillations due to spin accumulation in ferromagnetic double-island devices

Spin-dependent electronic transport in magnetic double-island devices is considered, theoretically, in the sequential tunneling regime. Electric current and tunnel magnetoresistance are analyzed as a function of the bias voltage and spin-relaxation time in the islands. It is shown that the interplay of spin accumulation on the islands and charging effects leads to periodic modification of the differential conductance and tunnel magnetoresistance. For a sufficiently long spin-relaxation time, the modulations are associated with periodic oscillations of the sign of both the tunnel magnetoresistance and differential conductance.

Figure 1

Shifts of the Fermi levels for spin-majority electrons (a) and currents (b) in the P and AP configurations; differential conductance in the AP configuration (c); and TMR (d) as a function of the bias voltage for ${\tau }_{\mathrm{sf},1}={\tau }_{\mathrm{sf},2}\to \infty$. The other parameters are: $T=140\mathrm{K}$, $C_{\mathrm{L}}=0.45\mathrm{aF}$, $C_{\mathrm{M}}=0.2\mathrm{aF}$, $C_{\mathrm{R}}=0.35\mathrm{aF}$, ${\beta }_1={\beta }_2={\beta }_{\mathrm{R}}=0.2$, and ${\beta }_{\mathrm{L}}=1$. The total barrier resistances in the P configuration are: $R_{\mathrm{L}}∕3500=R_{\mathrm{M}}=R_{\mathrm{R}}=1\mathrm{M}\Omega$. In the AP configuration, $R_{r,\uparrow }^{\mathrm{AP}}=R_{r,\downarrow }^{\mathrm{AP}}={\left(R_{r,\uparrow }^{\mathrm{P}}{R}_{r,\downarrow }^{\mathrm{P}}\right)}^{1∕2}$, for $r=\mathrm{M},\mathrm{R}$. The parameters correspond to the experimental ones taken from Ref. 9.

Figure 2

(Color online) Differential conductance in the antiparallel configuration as a function of the bias voltage calculated for different values of the spin relaxation time ${\tau }_{\mathrm{sf},1}={\tau }_{\mathrm{sf},2}={\tau }_{\mathrm{sf}}$ and for $D_{\mathrm{I}1}^{+}{\Omega }_{\mathrm{I}1}=D_{\mathrm{I}2}^{+}{\Omega }_{\mathrm{I}2}=1000∕\mathrm{eV}$. The other parameters are the same as in Fig. 1.

Figure 3

(Color online) The TMR effect as a function of the bias voltage calculated for different values of spin relaxation time ${\tau }_{\mathrm{sf},1}={\tau }_{\mathrm{sf},2}={\tau }_{\mathrm{sf}}$ and for $D_{\mathrm{I}1}^{+}{\Omega }_{\mathrm{I}1}=D_{\mathrm{I}2}^{+}{\Omega }_{\mathrm{I}2}=1000∕\mathrm{eV}$. The other parameters are the same as in Fig. 1.