Spin Quantum Tunneling in Single Molecular Magnets: Fingerprints in Transport Spectroscopy of Current and Noise

We demonstrate that transport spectroscopy of single molecular magnets shows signatures of quantum tunneling at low temperatures. We find current and noise oscillations as a function of bias voltage due to a weak violation of spin-selection rules by quantum tunneling processes. The interplay with Boltzmann suppression factors leads to fake resonances with temperature-dependent position which do not correspond to any charge excitation energy. Furthermore, we find that quantum tunneling can completely suppress transport if the transverse anisotropy has a high symmetry.

Figure 1

(a) Magnetic excitation spectra for two charge states with spins $S^{(0)}=2>S^{(1)}=3/2$ and $D^{(0)}>D^{(1)}$. Since typically $B_{2n}\ll D^{(N)}$, we label the eigenstates by the approximately good quantum number $M$. The dot-dashed line is a spin-forbidden transition, all others are spin allowed. (b) Energy levels and spin-allowed transitions for $S^{(0)}=S>S^{(1)}=S-\frac{1}{2}$. (c) Electron-addition excitations in ($V_{\mathrm{gate}},V_{\mathrm{bias}}$) stability diagram. Arrows indicate how to construct the diagram going along the zigzag path in (b). Thick (thin) lines indicate visible (hidden) transitions. A transition is hidden when the initial state is not yet occupied (by other processes) at the transition energy.

Figure 2

$dI/d{V}_{\mathrm{bias}}$ in gray scale ($\mathrm{\text{gray}}=\mathrm{\text{zero}}$, $\mathrm{\text{white}}=\mathrm{\text{positive}}$, and $\mathrm{\text{black}}=\mathrm{\text{negative}}$) as function of $V_{\mathrm{gate}}$ and $V_{\mathrm{bias}}$. Parameters: $S^{(0)}=2$, $S^{(1)}=3/2$, $D^{(0)}=0.1$, $D^{(1)}=0.01$, and $T=0.01$. (a) No QTM: $B_2=0$. (b) QTM: $B_2=2\times {10}^{-5}$. (c) Same as (b) except for higher $T=0.015$.

Figure 3

Transport oscillations induced by QTM. Parameters: $S^{(0)}=10$, $S^{(1)}=9\frac{1}{2}$, $D^{(0)}=0.1$, $D^{(1)}=0.01$, $B_2=2\times {10}^{-3}$, and $T=0.015$. (a) $dI/d{V}_{\mathrm{bias}}$ for small bias: the $N=1$ “flat” parabola is mapped out by NDC excitations. (b) $dI/d{V}_{\mathrm{bias}}$ for large bias: the $N=0$ excitations give rise to positive and negative differential conductance. (c) $d\ln F/d{V}_{\mathrm{bias}}$: fake resonance lines correspond to noise suppression (black) lines and terminate at the Coulomb diamond edge. (d) Occupations of the $N=1$ states $p_M^{(1)}$ together with $\ln F$ and $I$ as function of $V_{\mathrm{bias}}$ for $V_{\mathrm{gate}}=0$. (e) Current suppression due to high-symmetry QTM: $B_4=2\times {10}^{-4}$, $B_2=0$. (f) Spin excitation spectrum for the charged state $N=1$: the value $B_4{S}^2/D^{(1)}$ used in (e) lies beyond the level crossing at approximately 1. Only the second excited state has a non-negligible admixture of the maximal $M^{\prime }=\pm S^{(1)}$ state which is required for transport.