Influence of spin waves on transport through a quantum-dot spin valve

We study the influence of spin waves on transport through a single-level quantum dot weakly coupled to ferromagnetic electrodes with noncollinear magnetizations. Side peaks appear in the differential conductance due to emission and absorption of spin waves. We, furthermore, investigate the nonequilibrium magnon distributions generated in the source and drain lead. In addition, we show how magnon-assisted tunneling can generate a fully spin-polarized current without an applied transport voltage. We discuss the influence of spin waves on the current noise. Finally, we show how the magnonic contributions to the exchange field can be detected in the finite-frequency Fano factor.

Figure 1

(Color online) Sketch of a quantum-dot spin valve with spin wave excitations in the leads and coordinate system used.

Figure 2

(Color online) Exchange field as a function of the level position $\epsilon$ for $p_r=0.9$ (upper panel) and $p_r=0.1$ (lower panel). Other parameters are $U=50k_{\text{B}}T$ and ${\omega }_B=10k_{\text{B}}T$.

Figure 3

(Color online) Transport processes that arise in a quantum-dot spin valve with spin wave degrees of freedom in the leads as well as their dependence on the polarization $p$.

Figure 4

(Color online) Schematic of the differential conductance in the $\epsilon -V$ plane. The labels at the conductance lines indicate whether a magnon is emitted (E) or absorbed (A) in the source (S) or drain (D) electrode. The dotted horizontal line marks the position of the cuts shown in Fig. 5.

Figure 5

(Color online) Differential conductance as a function of the level position for $V=30k_{\text{B}}T$, $U=50k_{\text{B}}T$, ${\omega }_B=10k_{\text{B}}T$, ${\Gamma }_{\text{L}}={\Gamma }_{\text{R}}$, $\tau =2/\Gamma$, $\lambda =0.3$, and $T_B=5T$ for small and large polarizations. In the upper panel, we show the case of parallel magnetizations, while in the lower panel they are chosen to be antiparallel. As in Fig. 4, the labels of the side peaks indicate the emission (E) and absorption (A) of magnons in source (S) and drain (D) lead.

Figure 6

(Color online) Difference between the average number of magnons in the source and drain lead in the parallel (upper panel) and antiparallel (lower panel) configuration for $\tau =100/\Gamma$, $p=0.9$, and $T_B=T$. Other parameters are the same as in Fig. 5.

Figure 7

(Color online) Current at zero bias voltage vs. level position for $U=50k_{\text{B}}T$, $\omega =20k_{\text{B}}T$, ${\Gamma }_{\text{L}}={\Gamma }_{\text{R}}$, $\tau =1/\Gamma$, $\lambda =1/3$, and $T_B=10T$ at different polarizations. Inset: Increased relaxation time leads to a reduction in the magnon-driven current (shown here the peak value at $\epsilon =10k_{\text{B}}T$) since it allows a stronger cooling of the magnons.

Figure 8

(Color online) Fano factor as a function of the level position for parallel (upper panel) and antiparallel (lower panel) magnetizations. In both cases the Fano factor can be increased or decreased by the coupling to the magnons. Parameters are $V=40k_{\text{B}}T$, $U=50k_{\text{B}}T$, ${\omega }_b=10k_{\text{B}}T$, ${\Gamma }_{\text{L}}={\Gamma }_{\text{R}}$, $p=0.9$, $\tau =2/\Gamma$, and $T_B=T$.

Figure 9

(Color online) Zero-frequency Fano factor for a quantum dot symmetrically coupled to collinear magnetized leads as a function of the polarization of the right lead for different values of the polarization of the left lead. In the upper panel, transport takes place through the empty and singly occupied dot only, while in the lower panel, it takes place through the singly and doubly occupied dot only.

Figure 10

(Color online) Frequency-dependent Fano factor for perpendicular magnetizations for $V=25k_{\text{B}}T$ (upper panel) and $V=75k_{\text{B}}T$ (lower panel). Other parameters are $U=50k_{\text{B}}T$, $\epsilon =10k_{\text{B}}T$, ${\omega }_B=10k_{\text{B}}T$, ${\Gamma }_{\text{L}}=2{\Gamma }_{\text{R}}$, $\tau =1/{\Gamma }_{\text{L}}$, $p=0.8$, and $T_B=T$.