Transient charging and discharging of spin-polarized electrons in a quantum dot

We study spin-polarized transient transport in a quantum dot coupled to two ferromagnetic leads subjected to a rectangular bias voltage pulse. Time-dependent spin-resolved currents, occupations, spin accumulation, and tunneling magnetoresistance (TMR) are calculated using both nonequilibrium Green function and master equation techniques. Both parallel- and antiparallel-lead magnetization alignments are analyzed. Our main findings are a dynamical spin accumulation that changes sign in time, a short-lived pulse of spin polarized current in the emitter lead (but not in the collector lead), and a dynamical TMR that develops negative values in the transient regime. We also observe that the intradot Coulomb interaction can enhance even further the negative values of the TMR.

Figure 1

Sketch of the system: a quantum dot coupled to two ferromagnetic leads via tunnel barriers. The left FM lead has its magnetization fixed while the right-hand side can be either in parallel or antiparallel alignment. A pulsed bias voltage of duration $s$ is applied across the system in order to generate transient spin-polarized currents. When the bias voltage is turned on $(0<t<s)$ the dot’s level ${ϵ}_d$ moves into resonance with the emitter states and the dot becomes populated (a charging process) with a current passing through it. When the bias is turned off $(t>s)$, ${ϵ}_d$ moves above ${\mu }_L$ and ${\mu }_R$ and the dot’s occupation decays into the leads (a discharging process). Due to the ferromagnetism of the leads, these transient charging and discharging processes become spin dependent.

Figure 2

Occupations $n_{\uparrow }$ (solid line) and $n_{\downarrow }$ (dashed line) and the spin accumulation $m=n_{\uparrow }-n_{\downarrow }$ (dotted line) as a function of time for both (a) parallel and (b) antiparallel configurations. When the bias is turned on (off) the dot is charged (discharged) in a spin-dependent manner. This results in a time-dependent spin accumulation, with a sign reversal in the parallel case.

Figure 3

(Color online) Spin-resolved currents against time for both left and right leads and both alignments. In both configurations the currents in the left (right) lead are suppressed (enhanced) just after the voltage is turned on, and then they attain stationary plateaus. When the bias voltage is turned off $(t>3\mathrm{ns})$ the left and right currents become the same for each spin component in the P configuration, while in the AP case the $\uparrow$ current becomes larger than the $\downarrow$ current in the left lead.

Figure 4

Total current in the left ferromagnetic lead, $I_{\uparrow }^L+I_{\downarrow }^L$, for both parallel (solid line) and antiparallel (dotted line) configurations. After the bias voltage is turned off $(t>3\mathrm{ns})$ the total antiparallel current becomes greater than the parallel one, lifted by the spike of $\uparrow$ current seen in Fig. 3b. This results in the time-dependent negative TMR seen in the inset.

Figure 5

(Color online) Spin-resolved occupations (a), (b) and currents (c), (d) in both parallel (P) and antiparallel (AP) configurations. We take $U=1\mathrm{meV}$ and $U=3\mathrm{meV}$, labeling the traces by (1) and (3), respectively. For $U=1\mathrm{meV}$ the results are indistinguishable from the $U=0$ case. For $U=3\mathrm{meV}$, though, we find a suppression of the spin-resolved occupations and currents. In the AP alignment this suppression results in an enhancement of the spin accumulation and in a spin-polarized current in the stationary plateaus $(\mid I_{\uparrow }^{L,R}\mid >\mid I_{\downarrow }^{L,R}\mid )$. To clarify the range $t>3\mathrm{ns}$, in panel (c) the currents $I_{\sigma }^L$ are on top of $I_{\sigma }^R$ while in panel (d) they are apart from each other. In addition in the AP case, $\mid I_{\uparrow }^L\mid$ and $\mid I_{\uparrow }^R\mid$ for $U=1\mathrm{meV}$ are slightly greater than their corresponding values for $U=3\mathrm{meV}$, and $I_{\downarrow }^R$ is almost on top of $I_{\uparrow }^R$.

Figure 6

Tunnel magnetoresistance (TMR) as a function of time for $U=1$ and $U=3\mathrm{meV}$. For $U=3\mathrm{meV}$ the TMR is enhanced in the stationary regime $(2<t<3\mathrm{ns})$ and becomes even more negative after the bias voltage is turned off $(t>3\mathrm{ns})$.