Pauli spin blockade in double molecular magnets

The Pauli spin blockade effect in transport through two, coupled in series, single molecular magnets weakly attached to external leads is considered theoretically. By using the real-time diagrammatic technique in the lowest-order perturbation theory with respect to the coupling strength, the behavior of the current and the shot noise is studied in the nonlinear response regime. It is shown that the current suppression occurs due to the occupation of highest-weight spin states of the system. Moreover, transport properties are found to strongly depend on parameters of the double molecular magnet, such as the magnitude of spin, internal exchange interaction and the hopping between the molecules. It is also demonstrated that the current suppression may be accompanied by negative differential conductance and a large super-Poissonian shot noise. The mechanisms leading to those effects are discussed.

Figure 1

Schematic of the considered system. It consists of two molecular magnets with spin $S_r$ $\left(r=L,R\right)$, coupled to each other via hopping matrix elements $t$ and to the left and right metallic leads with coupling strengths ${\mathrm{\Gamma }}_L$ and ${\mathrm{\Gamma }}_R$, respectively. The energy of orbital level of left (right) molecule is denoted by ${\varepsilon }_{L\left(R\right)}$ and $J_{L\left(R\right)}$ describes the exchange interaction between the electrons occupying given orbital level and the internal spin of given molecule. The bias voltage is applied symmetrically to the system, ${\mu }_L-{\mu }_R=eV$.

Figure 2

The bias voltage dependence of (a) the current $I$ and (b) the Fano factor $F$ calculated for different values of hopping between the LUMO levels, as indicated, in the case of $J=0$. The parameters are: $U^{\prime }=-{\varepsilon }_L=0.5,{\varepsilon }_R=-1$ and $T=3\mathrm{\Gamma }=0.03$ in units of $U\equiv 1$. The current is plotted in units of $I_0=e\mathrm{\Gamma }/\hslash$.

Figure 3

The bias voltage dependence of (a) the current and (b) the Fano factor for different values of the ferromagnetic $\left(J>0\right)$ exchange coupling between the LUMO level and core spin of each molecule, as indicated. The parameters are the same as in Fig. 2 with $D/U=0.05,t/U=0.05$, and $S=3/2$.

Figure 4

The same as in Fig. 3 calculated in the case of antiferromagnetic exchange interaction $\left(J<0\right)$.

Figure 5

The bias voltage dependence of (a) the expectations values of the left and right SMM's occupation, $\langle n_L\rangle$ and $\langle n_R\rangle$, and (b) the corresponding spin expectation values calculated in the case of ferromagnetic exchange interaction, $J/U=0.3$. The other parameters are the same as in Fig. 3.

Figure 6

The same as in Fig. 5 calculated for $J/U=-0.3$.

Figure 7

The bias voltage dependence of (a) the current and (b) the Fano factor for different values of the hopping parameter $t$, as indicated, in the case of ferromagnetic exchange interaction. The parameters are the same as in Fig. 3 with $J/U=0.3$.

Figure 8

The same dependence as in Fig. 7 calculated in the case of antiferromagnetic exchange interaction $J/U=-0.3$.

Figure 9

The dependence of (a) the current and (b) the Fano factor on the applied bias voltage calculated in the case of ferromagnetic exchange interaction for different values of SMM spin $S$. The parameters are the same as in Fig. 3 with $J/U=0.3$.

Figure 10

The same dependence as in Fig. 9 calculated for antiferromagnetic exchange interaction $J/U=-0.3$ between the LUMO level and molecule's core spin.