Gate-controlled Kondo effect in a single-molecule transistor with elliptical ferromagnetic leads

We present low-temperature transport measurements of ${\mathrm{C}}_{60}$-based single-molecule transistors fabricated using ferromagnetic break junction devices with planar elliptical leads, revealing a gate-modulated single-channel spin-$\frac{1}{2}$ Kondo effect. The shape anisotropy and dipole interaction of the source and drain electrodes allows for the relative alignment of their respective magnetic moments to be switched between a parallel and an antiparallel configuration. Both the ferromagnetism of the electrodes and the manipulation of their magnetization are shown to impact the magnetotransport in the Kondo regime in a manner consistent with analytical results, but with a magnitude highly sensitive to the precise electrode-molecule geometry and associated coupling asymmetry.

Figure 1

(a) Device setup for low-temperature transport measurements. (b) SEM image of Ti/Au electrodes contacting a Py* ellipse pair showing a device after electromigration was used to create a tunneling gap between the ellipses. (c) Charge transport is dominated by one energy level at ${\varepsilon }_0$ below the Fermi level ${\varepsilon }_F$, with charging energy $U$, broadened to width $\mathrm{\Gamma }$. The local level is split by an amount proportional to the spin-dependent tunneling-induced exchange field in addition to the external field. Blue $\downarrow$-arrow outline indicates location $\downarrow$-spin electron could occupy.

Figure 2

Sample 1A. (a) Color map plotting $dI/dV$ vs. $V_{sd}$ in steps of $V_G$. Black dashed lines outline Coulomb blockade diamonds. Green dashed lines highlight $V_G$ locations of data shown in (b)–(g). (b)–(d) $dI/dV$ vs. $V_{sd}$ acquired at $T=50\text{mK}$ and $V_G=10\text{V},20\text{V},$ and $30\text{V}$, respectively. Data in (a)–(d) smoothed with five-point adjacent average. (e) Color map of $dI/dV$ vs. $V_{sd}$ in steps of $\mathbf{B}$ at $V_G=20\text{V}$. (f) Separation between spin-resolved resonance peaks in (e) plotted as a function of $\mathbf{B}$. Red line corresponds to $g$ factor $=2.0$. (g) $G(T,V=0)$ vs. $T$ at $V_G=10\text{V},20\text{V},$ and $30\text{V}$, corresponding to the blue squares, red circles, and green diamonds, respectively. Solid gray line is a fit to the empirical form of Eq. (1) using $T_K=8.5\text{K}$

Figure 3

(a) and (b) $dI/dV$ vs. $V_{sd}$ and $V_G$ at $\mathbf{B}=0\text{T}$ for samples 1B and 1C, respectively, which both exhibit same basic features as sample 1A, but with some distinct variations. (c) and (d) $dI/dV$ vs. $V_{sd}$ at $V_G=20\text{V}$ acquired with P (orange) and AP (blue) configurations. (c) The split peaks in the P configuration of sample 1B are transformed into a single resonance peak with enhanced conductance as the effective exchange field is reduced to (nearly) zero. (d) The split peaks evident in the P configuration of sample 1C are not restored into a single resonance in the AP configuration, nor do they increase in conductance, but they do move closer together. Samples 1B and 1C correspond to the same break junction as 1A, but measured after subsequent abrupt changes in transport features. (e) Sample 2 and (f) sample 3 show two more examples of the impact that the switch from P to AP magnetization orientation can have on a Kondo resonance.

Figure 4

Sample 4. (a) $dI/dV$ vs. $V_{sd}$ and $V_G$. Green dashed line at $V_G=-14\text{V}$ signifies location of data shown in (b), (c), and (e). (b) Traces of $dI/dV$ vs. $V_{sd}$ in decreasing steps of $\mathbf{B}$ after increasing field to ${\mathbf{B}}_s$ then slowly decreasing to $60\text{mT}$. Switch to what is inferred to be the AP configuration is apparent only in the zero-bias resonance peak roughly between $-25\text{mT}$ and $-35\text{mT}$. (c) $dI/dV$ vs. $V_{sd}$ acquired near $T_{\mathrm{base}}$ with electrodes in P (red) and AP (blue) configurations. (d) Magnetoconductance ratio over region of stability diagram in (a). (e) $G(V=0,T)$ vs. $T$ for the P (red circles) and AP (blue squares) configurations. The black and gray lines are fits of Eq. (1) to the data with $T_K=6.5\text{K}$ and $4.5\text{K}$ respectively. Inset: $dI/dV$ vs. $V_{sd}$ at multiple values of $T$ between $90\text{mK}$ and $6\text{K}$ while electrodes in AP configuration.

Figure 5

(a) Stability diagram of sample 5 showing transition between Coulomb blockade region and spin-split Kondo resonance. (b) and (c) $G\left(T\right)$ for samples 6 and 7, respectively. Insets: $dI/dV$ vs. $V_{sd}$ while electrodes in AP configuration at multiple values of $T$ from $50\text{mK}$ to $13.2\text{K}$ for (b) and $50\text{mK}$ to $14.3\text{K}$ for (c).