Exchange-mediated spin–electric control of single molecules on surfaces

MainElectron and nuclear spins in single molecules have attracted substantial interest as potential building blocks for applications in spintronics, quantum sensing, and quantum computing1. Magnetic molecular systems are of nanoscopic size, benefit from self-assembly and offer unique structural as well as chemical tunability via modern synthetic chemistry2,3. A key challenge lies in achieving reliable and local control over individual spin centres. A potential solution is the use of electric fields, which—in contrast to magnetic fields—can be efficiently applied in a confined region4. Thus, spin–electric coupling (SEC) in molecules has in recent years emerged as a promising control mechanism, which has been discussed theoretically5,6,7 and realized experimentally8,9,10,11,12,13,14,15,16 in a variety of systems. These specifically tailored molecular platforms typically rely on structural distortions that modulate key parameters of the spin Hamiltonian, such as zero-field splitting, g-factor, orbital angular momentum, hyperfine interaction or exchange coupling. Often, effective SEC requires a soft, electrically polarizable molecular environment and spin energy levels that are highly sensitive to structural changes. However, the experimentally observed shifts \(\Delta f\) in spin resonance frequencies due to electric fields have so far remained relatively modest, amounting to less than \(\frac{\Delta f}{{f}_{0}}\) 0\) used for the simulation. b, ESR map \(\Delta I(f,\,{V}_{{\rm{DC}}})\) analogous to a, but with a different magnetic tip with \(P 0)\) and negative \((P 300\,{\rm{mV}}\) remains challenging. Nevertheless, the spin complex is generally easier to use in coherent control experiments than pristine FePc (see ref. 33 and Supplementary Section 5). The pulse scheme used for Rabi oscillation measurements is depicted in Fig. 3b (refs. 21,22). The resulting coherent oscillation of the spin state leads to a change in tunnel current \(\Delta I\) as a function of the radio-frequency (RF) pulse duration \(\tau\) (ref. 21):$$\Delta I=A \sin \left(\varOmega \tau +\phi \right) {{\rm{e}}}^{-\tau /{T}_{2}}.$$ (3) Fig. 3: Spin–electric Rabi detuning on an Fe–FePc complex.Full size imagea, ESR colour map \(\Delta I\left(f,\,{V}_{{\rm{DC}}}\right)\) on the Fe site of an Fe–FePc complex (ESR conditions: \({I}_{\mathrm{set}}=6\,\mathrm{pA},\,{V}_{\mathrm{set}}=-60\,\mathrm{mV},B=469\,\mathrm{mT},\,{V}_{\mathrm{RF}}=10\,\mathrm{mV}\)). The chemical structure of the Fe–FePc is overlaid on the inset topography. The added Fe atom is highlighted by a red arrow, marking the site at which the measurements shown in c and d were performed. White arrows indicate the detuning in frequency \({\rm{\delta }}f=f-{f}_{\mathrm{res}}\) and voltage \({\rm{\delta }}V={V}_{\mathrm{DC}}-{V}_{\mathrm{set}}\) from the resonance. b, Left: schematic drawing of the Rabi pulse scheme. The RF signal consists of an RF pulse with duration \(\tau\) and amplitude \({V}_{{\rm{RF}}}\) followed by an off-time \({\tau }_{{\rm{off}}}\). The total cycle time \({\tau }_{{\rm{cycle}}}=\tau +{\tau }_{{\rm{off}}}\) is kept constant, and a d.c. voltage \({V}_{{\rm{DC}}}\) is applied continuously for readout. Right: Bloch sphere representation of the spin evolution on resonance (orange) and off resonance (purple). c, Rabi oscillations for different frequency detuning \({\rm{\delta }}f\) (Rabi conditions: \(\,{I}_{\mathrm{set}}=4\,\mathrm{pA},\,{V}_{\mathrm{set}}=-60\,\mathrm{mV},\,\)\(B=473\,\mathrm{mT},\,{V}_{\mathrm{RF}}=60\,\mathrm{mV},\,\)\(f=14.04\,\mathrm{GHz},\,{\tau }_{\mathrm{cycle}}=\,250\,\mathrm{ns}\)). Left: colour map of \(\Delta I\) as a function of \({\rm{\delta }}f\) and \(\tau\). The arrows refer to the traces shown on the right. Right: single traces on (orange) and off (purple) resonance, plotting \(\Delta I\) as a function of \(\tau\). Solid lines are fits based on equation (3) (see Extended Data Table 1 for the parameters). Traces are vertically shifted for clarity. d, Rabi oscillations for detuning the voltage \({\rm{\delta }}V\) instead of \({\rm{\delta }}f\) (Rabi conditions: \({I}_{\mathrm{set}}=5\,\mathrm{pA},\,{V}_{\mathrm{set}}=-60\,\mathrm{mV},\,\)\(B=450\,\mathrm{mT},\,{V}_{\mathrm{RF}}=20\,\mathrm{mV},\,\)\(f=14.25\,\mathrm{GHz},\,{\tau }_{\mathrm{cycle}}=\,400\,\mathrm{ns}\)). Left: colour map of \(\Delta I({\rm{\delta }}V,\tau )\). Right: single traces analogous to c.With the amplitude \(A\), the Rabi rate \(\varOmega\), the Rabi phase \(\phi\) and phase coherence time \({T}_{2}\). Moreover, detuning from resonance \({\rm{\delta }}f=f-{f}_{\mathrm{res}}\) leads to a change in both amplitude \(A\) and Rabi rate \(\varOmega\) of the observed oscillation:$$\begin{array}{cc}\varOmega =\sqrt{{\varOmega }_{0}^{2}+{{\rm{\delta }}f}^{2}}, & A={A}_{0}\frac{{\varOmega }_{0}^{2}}{{\varOmega }^{2}}\end{array}.$$ (4) Here \({A}_{0}\) and \({\varOmega }_{0}\) are the parameters at \({f}_{{\rm{res}}}\). Consequently, the Rabi oscillations \(\Delta I(\tau )\) can be tuned by \({\rm{\delta }}f\), resulting in the typical chevron pattern (Fig. 3c). Utilizing the SEC, we now realize an all-electrical detuning via a change in voltage \({\rm{\delta }}V={V}_{\mathrm{DC}}-{V}_{\mathrm{set}}\) (Fig. 3d) while keeping \({\rm{\delta }}f=0\). We obtain a chevron pattern as well for \(\Delta I(\tau ,{\rm{\delta }}V)\), in which the amplitude \(A\) (Rabi rate \(\varOmega\)) decreases (increases) for increasing |\({\rm{\delta }}{V|}\). Compared with the frequency tuning, the pattern is slightly distorted. We attribute this to a linear contribution to \({\varOmega }_{0}\propto {V}_{\mathrm{DC}}\) predicted for spin resonance in the exchange bias model29,30. In addition, we expect a dependence of the amplitude with tunnelling current \(A\propto I\propto\) \({V}_{{\rm{DC}}}\) (see Supplementary Section 10 for details).Coherent control of a molecule dimerFinally, we realize the SEC detuning in a two-spin system. In Fig. 4a, two complexes are brought into proximity using tip-assisted manipulation to establish a coupled spin system. The resulting configuration (Fig. 4b) consists of a readout spin \({S}_{1}\) that is ferromagnetically coupled to the second spin \({S}_{2}\) mainly through Heisenberg exchange interaction \(J\) (Extended Data Fig. 7 and Supplementary Section 11). Because the coupling is substantially smaller than the Zeeman energy, the system exhibits four distinct energy levels (Fig. 4c). The two resulting ESR transitions \({f}_{{\rm{I}}}\) and \({f}_{{\rm{II}}}\) (Fig. 4c,d) primarily reflect the alignments of \({S}_{2}\) in either |↑〉 and |↓〉 state43,44. \({f}_{{\rm{I}}}\) and \({f}_{{\rm{II}}}\) shift again as a function of \({V}_{{\rm{DC}}}\), with the exchange bias from the tip acting on \({S}_{1}\). The energy splitting \({{f}_{\mathrm{II}}-f}_{{\rm{I}}}\,\approx \,130\,\mathrm{MHz}\) remains constant across the whole voltage range, indicating that the spin–spin coupling between \({S}_{1}\) and \({S}_{2}\) is unaffected by the SEC. In the corresponding Rabi oscillation measurements (Fig. 4e), we now tune from \({f}_{{\rm{I}}}\) to \({f}_{{\rm{II}}}\) by changing \({\rm{\delta }}f\), which leads to two chevron patterns. The weaker intensity of the left chevron arises from the low thermal population of the excited state \(|\downarrow {{\rangle }}\) of \({S}_{2}\). Again, the SEC enables all-electrical detuning via a change in voltage \({\rm{\delta }}V\) (Fig. 4f). The main limitation in this approach is the increased tunnelling current at higher voltages, which induces spin relaxation and decoherence21,22. However, the bias-controlled exchange field still permits to tune from the first transition (\({\rm{\delta }}V\approx 5\,\mathrm{mV}\)) to the second (\({\rm{\delta }}V\approx -80\,\mathrm{mV}\)).Fig. 4: Spin–electric Rabi detuning in a coupled spin system.Full size imagea, Topography of two coupled Fe–FePc complexes (image conditions: \(I=10\,{\rm{pA}},\,{V}_{{\rm{DC}}}=-100\,{\rm{mV}}\)). The black dot marks the tip position of the subsequent measurements. b, Schematic drawing of the two spin ½ with their exchange coupling \(J\) and the tip above the first spin \({S}_{1}\). c, Schematic energy level diagram of the combined spin states with the two ESR transitions \({f}_{{\rm{I}}}\) and \({f}_{{\rm{II}}}\). d, ESR colour map \(\Delta I(f,\,{V}_{{\rm{DC}}})\) measured on the coupled spin system (ESR conditions: \({I}_{{\rm{set}}}=8\,{\rm{pA}},\,{V}_{{\rm{set}}}=-40\,{\rm{mV}},{B}=462\,{\rm{mT}},\,{V}_{{\rm{RF}}}=10\,{\rm{mV}}\)). A single frequency sweep (right) at \(-50\,{\rm{mV}}\) reveals two distinct peaks corresponding to \({f}_{{\rm{I}}}\) and \({f}_{{\rm{II}}}\), that is, transitions corresponding to different spin states of the remote spin \({S}_{2}\). White arrows indicate the detuning in frequency \({\rm{\delta }}f\) and voltage \({\rm{\delta }}V\). e, Frequency detuning of Rabi oscillations (Rabi conditions: \({I}_{{\rm{set}}}=8\,{\rm{pA}},\,{V}_{{\rm{set}}}=-40\,{\rm{mV}},{B}=458\,{\rm{mT}},\,{V}_{{\rm{RF}}}=80\,{\rm{mV}},{f}=13.97\,{\rm{GHz}}\)). Left: colour map of \(\Delta I\) as a function of \({\rm{\delta }}f\) and \(\tau\). The pattern shows two chevrons corresponding to the two ESR transitions. The arrows at the top refer to the single traces to the right. Right: single traces of \(\Delta {I}\) versus \(\tau\) for three \({\rm{\delta }}f\). Solid lines show fits to the circular datapoints based on equation (3) (see Extended Data Table 1 for the parameters). The traces were shifted vertically for clarity. f, Electric detuning of Rabi oscillations, analogous to e (Rabi conditions: \({I}_{{\rm{set}}}=8\,{\rm{pA}},\,{V}_{{\rm{set}}}=-40\,{\rm{mV}},{B}=462\,{\rm{mT}},\,{V}_{{\rm{RF}}}=70\,{\rm{mV}},{f}=14.04\,{\rm{GHz}}\)). Left: colour map of \(\Delta I({\rm{\delta }}V,\tau )\) showing the continuous electrical tuning from one ESR transition to the other. Right: \(\Delta I\) as a function of \(\tau\) for three different \({\rm{\delta }}V\) (also see Supplementary Section 12).ConclusionOur measurements highlight that molecular spin systems can be tuned electrically via the bias voltage \({V}_{{\rm{DC}}}\). In particular, the ESR measurements near the LUMO of FePc suggest that the strong nonlinear SEC arises from the exchange bias due to enhanced virtual tunnelling. While this does not exclude the existence of other contributions, our results indicate that, in the present molecular systems, exchange bias is the dominant effect. Notably, the exchange bias mechanism has several important implications. First, unlike piezoelectric models, it does not require displacement of the molecule or any of its components, which extends applicability to a broader class of molecular systems, including rigid solid-state defects. Second, it permits the integration of molecular spins into devices, where they can be readily tuned via the polarization of nearby ferromagnetic electrodes. Third, the SEC strength observed here reaches close to 30% and is substantially larger than most reported electric tuning effects for molecular spins. In this regime, the resonance peak broadens due to increased decoherence from tunnelling electrons and enhanced electrode coupling. Nevertheless, we believe that, by carefully optimizing both the junction properties and the molecular orbital structure, a good compromise between SEC and preserving spin coherence can be achieved (Extended Data Fig. 8 and Supplementary Section 13).Finally, the results in Figs. 3 and 4 demonstrate not only the feasibility of combining coherent spin control with SEC, but also the ability to electrically tune one spin relative to another with nanometre precision. This precision arises from the particularities of the exchange bias: while a pure electric field from the tip apex would still act over distances exceeding tens of nanometres, the interplay between exchange interaction and the bias voltage—mediated by the magnetic tip electrode—localizes the SEC to the subnanometre scale. Further analysis of the data in Fig. 4 shows that only the molecular spin under the tip is tuned, while the other one stays completely unaffected (Extended Data Fig. 9). Crucially, the ability to tune between two distinct spin resonances represents a key step towards conditional spin control in coupled spin systems. Consequently, the potential for tuning spin dynamics via the exchange bias paves the way for fast all-electrical gate operations in larger molecular quantum systems.MethodsSample preparationSample preparation and all experiments were carried out in a Unisoku USM1600 system with a home-built dilution refrigerator. The data shown in Figs. 1 and 2 were measured at a base temperature of \(1\,{\rm{K}}\), while the data in Figs. 3 and 4 were measured at 50 mK. The in situ sample preparation was performed under ultrahigh vacuum conditions with a base pressure of <5 × 10−10 mbar. The Ag(001) single crystal was first cleaned through multiple cycles of argon ion sputtering and subsequent annealing using an electron beam. MgO was grown by evaporating Mg in an oxygen-rich atmosphere (≈1 × 10−6 mbar) while maintaining the substrate at 510 °C. A deposition time of 10 min resulted in partial coverage (≈50%), with MgO islands ranging from two to five monolayers in thickness. FePc molecules were deposited onto the surface using a home-built Knudsen cell (deposition time 90 s, pressure 9 × 10−10 mbar). Afterwards, Fe atoms were deposited onto the cooled sample by electron-beam evaporation for \(21\,{\rm{s}}\).Experimental set-upFor the ESR and Rabi measurements, we prepared spin-polarized tips by picking up 1–20 Fe atoms from the MgO surface. In most cases, the ESR active tips also showed strong asymmetries in dI/dV spectra around 0 V on FePc molecules due to inelastic electron tunnelling scattering. For the experiments shown, we applied the d.c. and RF voltage to the tip and corrected this to the convention that the voltage is applied to the sample. The RF signal was generated by a Rohde & Schwarz SMB100B generator and mixed with the d.c. bias voltage \({V}_{{\rm{DC}}}\) via a Marki Microwave MDPX-0305 Diplexer. For ESR, a magnetic field \(B\) is applied perpendicular to the sample surface. The presented ESR frequency sweeps were measured with an on/off modulation at 323 Hz, where the RF voltage \({V}_{{\rm{RF}}}\) in continuous-wave mode was present only in the A cycle. The applied \({V}_{{\rm{DC}}}\) was present in both the A and B cycles and therefore applied throughout the entire measurement. During the voltage-dependent frequency sweeps, the feedback of the STM controller was turned off to keep the position of the tip the same when altering \({V}_{{\rm{DC}}}\). The signal was read out via a Stanford Research Systems SR860 digital lock-in amplifier.Data evaluationTo analyse the frequency sweeps of our experiments, we fitted the following Fano function to our resonance peaks:$$\begin{array}{rcl}\Delta I=\frac{A}{{q}^{2}+1}\frac{{\left(q \epsilon +1\right)}^{2}}{1+{\epsilon }^{2}}+c & \mathrm{with} & \epsilon =\frac{f-{f}_{\mathrm{res}}}{0.5 \varGamma }\end{array},$$ (S1) with the amplitude \(A\), the resonance frequency \({f}_{{\rm{res}}}\), the linewidth (full width at half maximum) \(\varGamma\) and the \(q\)-factor, which captures the asymmetry of the resonance peak.For the Rabi measurements presented in Figs. 3 and 4, we followed the detection scheme introduced by ref. 21: instead of a continuous-wave RF signal, we applied pulse trains (Fig. 3b) with on-time \(\tau\) and off-time \({\tau }_{{\rm{off}}}\), keeping the sum (\({\tau }_{\mathrm{cycle}}\)) fixed. The RF pulses were only present in the A cycle and triggered with a Zurich Instruments HDAWG. Therefore, the measured signal presents an average of the spin state-related tunnel current. For each data point \(\tau\), the signal was averaged for 3 s. After the data acquisition, a linear background21 caused by current rectification with increasing pulse duration was subtracted.