Transport through quantum-dot spin valves containing magnetic impurities

We investigate transport through a single-level quantum dot coupled to noncollinearly magnetized ferromagnets in the presence of localized spins in either the tunnel barrier or on the quantum dot. For a large, anisotropic spin embedded in the tunnel barrier, our main focus is on the impurity excitations and the current-induced switching of the impurity that lead to characteristic features in the current. In particular, we show how the Coulomb interaction on the quantum dot can provide more information from tunnel spectroscopy of the impurity spin. In the case of a small spin on the quantum dot, we find that the frequency-dependent Fano factor can be used to study the nontrivial, coherent dynamics of the spins on the dot due to the interplay between exchange interaction and coupling to external and exchange magnetic fields.

Figure 1

(Color online) Schematic of model A, a quantum-dot spin valve with a magnetic impurity localized in the right tunnel barrier.

Figure 2

(Color online) Schematic of model B which consists of a quantum-dot spin valve with a magnetic impurity on the quantum dot.

Figure 3

(Color online) Exchange field due to virtual tunneling through the right barrier as a function of bias voltage $V$ for $p=0.3$ (upper panel) and $p=0.9$ (lower panel). Other parameters are $\epsilon =-300k_{\text{B}}T$, $U=250k_{\text{B}}T$, $D=17.5k_{\text{B}}T$, $B=10k_{\text{B}}T$, ${\Gamma }_{\text{R}}=10J_{\text{R}}$, $\eta =+1$, $W=500k_{\text{B}}T$, and $S=3$.

Figure 4

(Color online) Schematic of the differential conductance as a function of level position and applied bias voltage. Thick black lines mark the onset of transport through the dot. Dark (blue) dashed lines indicate the onset of impurity excitations. Dashed lines mark the gaining of energy from the impurity to allow all three charge states of the dot.

Figure 5

(Color online) Current as a function of bias voltage for parallel magnetizations, $p=0.3$ and ${\Gamma }_{\text{L}}={\Gamma }_{\text{R}}=J_{\text{R}}$. Other parameters are the same as in Fig. 3.

Figure 6

(Color online) Average $z$ component of dot and impurity spin as a function of bias voltage for $\eta =+1$. Other parameters are the same as in Fig. 5.

Figure 7

Fano factor as function of bias voltage. Parameters are the same as in Fig. 6. The sharp peak at $V=295k_{\text{B}}T$ arises at the onset of spin excitations (dashed, blue line in Fig. 4).

Figure 8

(Color online) Probabilities to find the impurity in spin state $|S_z⟩$ as a function of bias voltage (upper panel). The middle (lower) panel shows the probability to find the system in the state $|\uparrow ⟩\otimes |S_z⟩\left(|\downarrow ⟩\otimes |S_z⟩\right)$. Parameters are the same as in Fig. 6.

Figure 9

(Color online) Current as a function of bias voltage for perpendicular magnetizations for $p=0.9$ and ${\Gamma }_{\text{L}}={\Gamma }_{\text{R}}=10J_{\text{R}}$. Black curves are for $\eta =+1$ while gray (red) curves are for $\eta =-1$. For the upper panel, $\epsilon =-300k_{\text{B}}T$ while for the lower panel $\epsilon =50k_{\text{B}}T$. Other parameters as in Fig. 3. While the solid lines represent the full result, for the dashed curves the exchange field was set to zero by hand.

Figure 10

(Color online) $x$, $y$, and $z$ component of the average dot spin and $z$ component of the average impurity spin for perpendicular magnetizations as function of bias voltage for positive (upper panel) and negative (lower panel) sign of the interference term. Parameters as in Fig. 9a.

Figure 11

(Color online) Frequency-dependent Fano factor for moderate ($p=0.3$, upper panel) and large ($p=0.9$, lower panel) polarizations. For $p=0.3$, an external magnetic field perpendicular $B_{\text{ext}}=1.5\Gamma$ is applied to the quantum dot alongs its quantization axis. Other parameters are the same as in Fig. 9, except that now $D=0$ and $\eta =+1$.

Figure 12

(Color online) Schematic of the conductance for the situation, where $B⪢\Gamma$, $J\lesssim \Gamma$. The lines indicate peaks in the differential conductance.

Figure 13

(Color online) Finite-frequency Fano factor for different values of the exchange coupling $J$. The Fano factor shows a peak at the Larmor frequency associated with the exchange field. Parameters are ${\Gamma }_{\text{L}}=2{\Gamma }_{\text{R}}$, $k_{\text{B}}T=10{\Gamma }_{\text{L}}$, $B=50k_{\text{B}}T$, $U=5B$, $\epsilon =B/2$, and $V=11B$.

Figure 14

(Color online) Frequency-dependent Fano factor as a function of frequency and external magnetic field (upper panel) or exchange coupling (lower panel). The level splittings calculated for a system of two exchange coupled spins in a magnetic field which is the sum of the exchange fields and the external fields are indicated by dotted lines. Parameters are $J=2\Gamma$ (upper panel), $B=2\Gamma$ (lower panel), ${\Gamma }_{\text{L}}=10{\Gamma }_{\text{R}}=0.05k_{\text{B}}T$, $\epsilon =50k_{\text{B}}T$, $V=105k_{\text{B}}T$, $U=150k_{\text{B}}T$, $p=0.9$, and $\varphi =\pi /2$.