Vibrational detection and control of spin in mixed-valence molecular transistors

We investigate electron transport through a mixed-valence molecular complex in which an excess electron can tunnel between heterovalent transition metal ions, each having a fixed localized spin. We show that in this class of molecules the interplay of the spins and the vibrational breathing modes of the ionic ligand shells allows the total molecular spin to be detected as well as controlled by nonequilibrium transport. Due to a spin-dependent pseudo-Jahn-Teller effect electronic transitions with different spin values can be distinguished by their vibronic conductance side peaks, without using an external magnetic field. Conversely, we show that the spin state of the entire molecule can also be controlled via the nonequilibrium quantized molecular vibrations due to a vibration-induced spin blockade.

Figure 1

(Color online) Sketch: mixed-valence dimer trapped between two electrodes, $L,R$. By applying a bias voltage, $V_b={\mu }_L-{\mu }_R$, electrons can tunnel from one electrode to the other via the molecule. A third gate terminal (not shown), coupled capacitively to the molecule, effectively shifts the molecular energy levels.

Figure 2

(Color online) (a) Differential conductance $\left(dI/d{V}_b\right)$ for $V_g$ vs $V_b$ ($J=2.9\omega$, $t=1.5\omega$, $\lambda =0.5$, $\Gamma =9\times {10}^{-4}\omega$, ${\gamma }_0^v=3.2\times {10}^{-3}\Gamma$, ${\gamma }_0^s={10}^{-4}\Gamma$, and $T={10}^{-2}\omega$) (red: $dI/d{V}_b>0$; blue: $dI/d{V}_b<0$). The double-exchange coupling leads to a spin-dependent gap size of the vibronic spectrum (see arrows). The spectrum of $S=3/2$ is harmonic (signaled by equidistant resonance lines of small energy separation), while the one of $S=1/2$ is anharmonic (nonequidistant lines). (b) Sketch of energy spectrum: the spin multiplets are split due to the intramolecular coupling $J$. For $N=1$, each spin multiplet is split again by approximately twice the spin-dependent intramolecular tunneling, $t_S$, due to the PJT effect. Vibrational/vibronic excitations are omitted for clarity.

Figure 3

(Color online) (a) Differential conductance $\left(dI/d{V}_b\right)$ for $V_g$ vs $V_b$ ($J=0.5\omega$, $t=5.0\omega$, $\lambda =1.5$, $\Gamma =9\times {10}^{-4}\omega$, ${\gamma }_0^v=1.8\times {10}^{-2}\Gamma$, ${\gamma }_0^s={10}^{-4}\Gamma$, and $T={10}^{-2}\omega$). (b) Current vs $V_b$ (red solid) at $V_g=-0.2\omega$ and probability of $S=0$ multiplet with no vibrational/vibronic quanta excited (green dashed line). (c) The energy spectrum of the $N=0,1$ charge states and the spin blockade mechanism. The line-style distinguishes the total spin values $S$ of the states. The longer lines denote a vibrational/vibronic ground state, whereas the shorter ones are excited by at least one such quantum. The molecule is “pumped” by a sequence of tunneling events, each time changing the charge and exciting vibrational and/or vibronic quanta until the $S=1/2$ spin state is reached. From there, the molecule falls into the blocking state ($S=0$ vibrational ground state) via another tunneling process. Since the transition to $S=3/2$ is forbidden by spin-selection rules, $S=0$ cannot relax and the current strongly suppressed.