Berry-Phase Blockade in Single-Molecule Magnets

We formulate the problem of electron transport through a single-molecule magnet (SMM) in the Coulomb blockade regime taking into account topological interference effects for the tunneling of the large spin of a SMM. The interference originates from spin Berry phases associated with different tunneling paths. We show that, in the case of incoherent spin states, it is essential to place the SMM between oppositely spin-polarized source and drain leads in order to detect the spin tunneling in the stationary current, which exhibits topological zeros as a function of the transverse magnetic field.

Figure 1

The diagrams show the SMM ${\mathrm{Ni}}_4$ between (a) unpolarized leads and (b) fully oppositely polarized leads. The discrete lines represent available electronic states of the SMM, and $E_c$ is the charging energy.

Figure 2

(a) The transitions of the spin of the SMM in the case of unpolarized leads. The transitions arise from the sequential tunneling of unpolarized electrons in and out of the SMM. (b) The transitions in the case of fully polarized leads in opposite directions ${\nu }_{\uparrow }^{(L)}={\nu }_{\downarrow }^{(R)}=1$.

Figure 3

The graph shows ${log}_{10}{I}_p$ versus $H_{\perp }$ for ${\nu }_{\uparrow }^{(R)}={\nu }_{\downarrow }^{(L)}=1$, ${\nu }_{\downarrow }^{(R)}={\nu }_{\uparrow }^{(L)}=0$, $w_{\downarrow }^{(L)}=1\times {10}^9{\mathrm{s}}^{-1}$, and $w_{\downarrow }^{(R)}=10w_{\downarrow }^{(L)}$. The polarizations of the left and right leads are given by $P^R=-P^L={\nu }_{\uparrow }^R-{\nu }_{\downarrow }^R=100\%$. At the zeros of the tunnel splitting $\Delta E_{s,-s}$ or $\Delta E_{s^{\prime },-s^{\prime }}$, the current is completely suppressed. The scale varies from $I_p=0.1\mathrm{nA}$ to 1 fA.

Figure 4

The graphs show (a) ${log}_{10}(\Delta E_{4,-4})$ and (b) ${log}_{10}(\Delta E_{7/2,-7/2})$ versus transverse magnetic field $H_{\perp }$. These zeros correspond to those displayed in Fig. 3.