Nontrivial magnetoresistive behavior of a single-wall carbon nanotube with an attached molecular magnet

The spin-resolved transport properties of a single-wall carbon nanotube quantum dot, with an attached single molecular magnet, are studied theoretically. With the aid of the real-time diagrammatic technique in the lowest-order perturbation expansion with respect to the tunnel coupling, the current, differential conductance, and the tunnel magnetoresistance (TMR) are determined in both the linear and nonlinear response regimes. It is shown that transport properties depend greatly on both the shell filling sequence of the carbon nanotube and the type of exchange interaction between the molecular magnet and nanotube. This results in highly nontrivial behavior of the TMR, which is especially visible in the low bias voltage regime. Depending on the gate voltage and parameters of the system, we find transport regimes where either a greatly enhanced or negative TMR develops. The mechanism leading to such behavior is associated with nonequilibrium spin accumulation, which builds up in the antiparallel magnetic configuration of the device. We show that it is crucial whether the spin accumulation occurs in the highest-weight spin states or in states with lower spin values. While in the former case it leads to enhanced TMR, in the latter case it may result in negative tunnel magnetoresistance. In addition, we analyze how the above effects depend on the magnitude of the molecular magnet's spin, and show that this dependence is generally nonmonotonic.

Figure 1

Schematic of the considered system. It consists of a single-wall carbon nanotube quantum dot, with an attached single molecular magnet (with coupling $J_S$) characterized by the spin operator $\mathbf{S}$, coupled to external ferromagnetic leads with coupling strengths ${\mathrm{\Gamma }}_L^{\sigma }$ and ${\mathrm{\Gamma }}_R^{\sigma }$. The easy axis of the molecule coincides with the magnetization of the left lead, while the magnetization of the right lead can change direction, resulting in two magnetic configurations: the parallel and antiparallel one. The two subbands of the nanotube are sketched with dashed lines, $\delta$ denotes the energy mismatch between the subbands, while $\mathrm{\Delta }$ is the nanotube level spacing. A voltage drop $V$ is applied symmetrically between the leads.

Figure 2

The bias voltage and energy level dependence of the differential conductance in (a) the parallel and (b) antiparallel magnetic configuration and (c) the resulting TMR calculated in the case of ferromagnetic exchange coupling ($J_S>0$) between the CNT and SMM. The parameters are: $J/E_C=0.4, \delta /E_C=0.8, J_S/E_C=0.15, D/E_C=0.1, T/E_C=0.05, \mathrm{\Gamma }/E_C=0.01$, with $E_C\equiv 1$ the energy unit and $p=0.5$.

Figure 3

The bias voltage dependence of (a) and (d) the current, (b) and (e) differential conductance in both magnetic configurations, and (c) and (f) the TMR for (left column) $\varepsilon /E_C=-2.8$ and (right column) $\varepsilon /E_C=-1.2$. The other parameters are the same as in Fig. 2.

Figure 4

The bias voltage dependence of the TMR in the case of (a) $\varepsilon /E_C=-2.8$ and (b) $\varepsilon /E_C=-1.2$ for different magnitude of the molecular magnet's spin $S$. The other parameters are the same as in Fig. 2.

Figure 5

The same as in Fig. 2 calculated in the case of antiferromagnetic exchange coupling ($J_S<0$) between the molecular magnet and the nanotube, $J_S/E_C=-0.15$.

Figure 6

The bias voltage dependence of (a) and (d) the current, and (b) and (e) differential conductance in both magnetic configurations, as well as (c) and (f) the TMR for (left column) $\varepsilon /E_C=-2.8$ and (right column) $\varepsilon /E_C=-1.2$. The other parameters are the same as in Fig. 2 with $J_S/E_C=-0.15$.

Figure 7

The bias voltage dependence of the TMR in the case of (a) $\varepsilon /E_C=-2.8$ and (b) $\varepsilon /E_C=-1.2$ for different magnitude of the SMM's spin $S$. The other parameters are the same as in Fig. 2 with $J_S/E_C=-0.15$.

Figure 8

The bias and gate voltage dependence of the differential conductance in (a) the parallel and (b) antiparallel magnetic configuration and (c) the resulting TMR calculated in the case of ferromagnetic exchange coupling ($J_S>0$) between the nanotube and molecular magnet. The parameters are the same as in Fig. 2 with $\delta /E_C=0$.

Figure 9

The same as in Fig. 8 calculated in the case of antiferromagnetic exchange coupling ($J_S<0$) between CNT and SMM, $J_S/E_C=-0.15$.

Figure 10

The bias voltage dependence of (a) and (d) the current, (b) and (e) differential conductance in both magnetic configurations, and (c) and (f) the TMR in the case of ferromagnetic ($J_S>0$, left column) and antiferromagnetic ($J_S<0$, right column) exchange interaction. The other parameters are the same as in Fig. 8 with $|J_S|/E_C=0.15$ and $\varepsilon /E_C=-2.4$.

Figure 11

The tunnel magnetoresistance as a function of the bias voltage in the case of (a) ferromagnetic and (b) antiferromagnetic exchange interaction calculated for $\varepsilon /E_C=-2.4$ and for different values of SMM's spin, as indicated. The other parameters are the same as in Fig. 8 with $|J_S|/E_C=0.15$.