Introduction

As scaling the dimensions of magnetic media materials toward the spatial limit, magnetic single atoms are considered the ultimate goal of such downsizing1,2,3,4,5, which have thus been an active field of research. However, realizing single-atom magnetic data storage poses significant challenges, including the preservation of unstable single-atom magnetism for prolonged manipulation times. Studies on magnetic single atoms have demonstrated magnetic remanence and relatively high magnetic stability of Ho and Dy atoms for reading and writing on decoupled thin insulating layers2,3,4,5,6,7. The bistability of atomic magnetism significantly depends on the symmetry-protected magnetic ground state placed within a carefully designed coordination field2,6,7,8,9. Additionally, despite the large magnetic anisotropy energies (MAEs) exhibited by individual atoms, the occurrence of quantum tunneling of magnetization (QTM) reduces the energy barrier2,3,5, which results in the loss of useful magnetism and affects the stability of the magnetic state.

In addition, demonstrating single-atom magnetic data storage in solid-state transistors remains challenging. Attempts at single-molecule transistors (SMTs) based on single magnetic atoms coupled with ligands have revealed electronic spin states, magnetic excited states, and atom–ligand exchange coupling; nevertheless, information on switching atomic magnetism has rarely been obtained10,11,12,13,14,15,16. Furthermore, in many experiments, the manipulation of magnetic states depends on magnetic fields2,4,5,6, which hinders the realization of rapid, spatially compact control. An electric field has previously been shown to manipulate the geometrical state of endohedral metallofullerene (EMF), resulting in the transition of two bistable states with different permanent electric dipole orientations17,18. If it is possible to manipulate the coordination around the magnetic atom in EMFs through an electrical field, the resulting magnetic moment should differ, and switching of single-atom magnetism can theoretically be realized through the magnetoelectric coupling (MEC) effect19,20,21,22,23,24,25.

Here, we present the successful switching of single-atom magnetism in Dy@C84 SMTs for nonvolatile data storage. The two electrically controlled molecular states exhibit distinct magnetic moments, as demonstrated by the Zeeman effect. In addition, they display different magnetoresistance (MR) ratios at the resonant tunneling point with values of 600% for molecular state 1 and 1100% for molecular state 2, respectively. Density functional theory (DFT) calculations further confirmed the possibility of switching from one molecular state to another using an electrostatic field, and the coordination around the magnetic Dy atom changed. Therefore, the magnetic moment can be expected to be different to realize magnetism switching.

Results

Device fabrication and charge transport measurements

We used the precious trivalent EMF Dy@C84 (see the right panel of Fig. 1a); its synthesis and purification processes are provided in the Methods section and Ref. 26. The internal Dy atom donates one 4f and two 6s electrons to the outer cage26, which decreases the shielding effect of the cage through hybridization and brings the 4f orbitals of the Dy atom closer to the Fermi level for enhancing the electrical access and manipulation capabilities27,28. Three-terminal Dy@C84 SMTs were fabricated to allow reliable modulation of the molecular chemical potential by a back gate, as depicted in Fig. 1a. A Dy@C84 molecule bridges a pair of Au electrodes created by the feedback-controlled electromigration break junction (FCEBJ) technique, and electrical transport through the Dy@C84 SMTs was investigated at a cryogenic temperature of 1.8 K (see the Methods section and Refs. 17,29. for more details).

Fig. 1: Intrinsic molecular design and electron transport of the Dy@C84 single-molecule transistor (SMT).
figure 1

a Schematic of a three-terminal Dy@C84 SMT and the Dy@C84 molecule. A Dy@C84 molecule falls into the nanogap of ~1 nm created by a feedback-controlled electromigration break junction (FCEBJ) process and forms a Dy@C84 SMT. b Typical source-drain current vs. source-drain voltage (Isd-Vsd) traces of the FCEBJ process. c Representative Isd(Vsd) characteristic curves at different gate voltages (Vg) after electromigration exhibiting Coulomb blockade in the low bias region (within Vsd ~ 20 mV) (T = 1.8 K; all transport measurements were performed at this cryogenic temperature). d The source-drain current Isd recorded with respect to Vg with a fixed Vsd of 5 mV when we sweep Vg back and forth within the range of ±10 V. The curves have been offset vertically for clarity. Two sets of Coulomb oscillations emerge, and we focus on the resonant tunneling points marked by the red and blue arrows.

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Figure 1b shows the source-drain current vs. the source-drain voltage (Isd-Vsd) traces of the FCEBJ process. Representative Isd(Vsd) curves measured at different gate voltages (Vg) reveal apparent nonlinear behaviors and Coulomb blockade in the low bias region (within Vsd ~ 20 mV), as shown in Fig. 1c. We can thus access the single-electron tunnelling regime, in which the source-drain current exhibits Coulomb resonances as a function of Vg when Vsd is held constant (Vsd = 5 mV) (see Fig. 1d). Additionally, upon sweeping Vg forward and backwards over a wide range of up to ±10 V, we observed two distinct sets of Coulomb oscillation patterns. Another device (device B) exhibited the same Coulomb blockade effect, as shown in Supplementary Fig. 1.

Electrically controlled Zeeman effect in Dy@C84 SMTs and the transition of the magnetic moment

The magnetic properties of Dy@C84 SMTs were investigated by tunneling spectroscopy under magnetic fields via the Zeeman effect. We focus on the charge degeneracy point dominated by the resonant tunneling of an electron between the N\(-\)1 and N charge states through an individual molecule10,15 (Vg = \(-\)7.2 V and Vg = \(-\)7.9 V, marked as red and blue arrows in Fig. 1d, respectively), and then plot coloured maps of the differential conductance (dIsd/dVsd) around each peak with respect to Vsd and Vg in Fig. 2a, d, which are obtained through numerical differentiation of the current. The Coulomb diamonds exhibit the N\(-\)1 and N ground states, as well as an excited state ( ~ 30 meV) parallel to the N ground state. To investigate the response of ground and excited states to an external magnetic field (B), Isd(Vsd) curves are recorded while sweeping B perpendicular to the current direction at a constant Vg (Vg = \(-\)7.1 V and Vg = \(-\)7.7 V, as shown by the white dashed lines in Fig. 2a and d, respectively). Figure 2b, e shows 2D maps of d2Isd/dV2sd as a function of Vsd and B, which offer clearer indications of level shifts. In particular, the excited state in Fig. 2e exhibits an apparent split-like behaviour with B, which is attributed to the crossover between the N\(-\)1 and N excited states (rather than the effects of real energy splitting). The relative energies of the ground and excited states extracted from the peaks position of the d2Isd/dV2sd curves at different Vg in Fig. 2b, e are shown in Fig. 2c, f. As B increases, an upwards shift in the relative energy levels of GN−1 ground states occurs, with a corresponding downwards shift in the GN ground states and EN excited states. However, these measurement results of this device do not exhibit energy splitting, indicating that no Kramers doublet is present in these ground states30,31.

Fig. 2: Electrically controlled nonvolatile switching of single-atom magnetism.
figure 2

a, d Colored maps of the differential conductance (dI/dV) near the charge degeneracy point for the transition between N\(-\)1 and N electrons (Vg = \(-\)7.2 V and Vg = \(-\)7.9 V marked as red and blue arrows in Fig. 1d, respectively) for state 1 (a) and state 2 (d) under a zero magnetic field (B = 0 T). The black lines indicate the main resonant excitations of the ground and excited states. Colored maps of d2Isd/dV2sd as a function of B and Vsd for state 1 (b) and state 2 (e) at constant Vg (Vg = \(-\)7.1 V for Fig. 1b and \(-\)7.7 V for Fig. 1e and marked by the white dashed lines parallel to the vertical axis in Fig. 2a, d). The d2Isd/dV2sd maps provide clearer indications of energy shifts in ground and excited states with B. The excited state of state 2 exhibits a clear split-like behavior, likely attributed to the crossover between the N\(-\)1 and N excited states rather than real energy splitting under magnetic fields. c, f The relative energies of the ground and excited states of state 1 and state 2 plotted as a function of B; these energies are extracted from the positions of the d2Isd/dV2sd peaks in (b) and (e). We then fit the data linearly according to the Zeeman effect, and the effective g-factor was defined as\({:g}^{*}=\frac{\triangle E}{{\mu }_{{{{{{\rm{B}}}}}}}\triangle B}\). The values of \({g}^{*}\) are shown in the figure. These states with measured \({g}^{*}\) values are attributed to mixed states of Dy3+ \({m}_{J}\) states or more likely metal-cage hybrid states. g Switching operation of the molecular states in the Dy@C84 SMT. The molecular states represented by two different molecular conformations can be switched by a gate voltage of ±10 V. The right panel shows schematic of a typical electrically controlled nonvolatile switching of single-atom magnetic moment corresponding to the molecular state transition.

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By applying a linear fit to the level shift according to the Zeeman effect, it is possible to determine the effective g-factor32,33, which is defined as \({g}^{*}=\frac{1}{{\mu }_{{{{{{\rm{B}}}}}}}}\frac{\triangle E}{\triangle B}\) (where \({\mu }_{{{{{{\rm{B}}}}}}}\) is the Bohr magneton). The absolute values of \({g}^{*}\) range from 2.2 to 8.4 (Table 1). In comparison with the observed \(g\approx 2\) for a C60 molecule34,35, the higher absolute values of \({g}^{*}\) can be qualitatively attributed to the contribution of the orbitals of Dy3+. As the ground state \(\left|J=15/2\right\rangle\) of free Dy3+ leads to a \({g}^{*}\) value of ~10 (Supplementary Note 1), these ground and excited states with \({g}^{*}\) from 2.2 to 8.4 occur due to either the mixing of different \({m}_{J}\) states or more likely hybridization between orbitals of the carbon cage and the Dy3+ ion, which is susceptible to the coordination environment. Moreover, there are disparities in \({g}^{*}\) (and thus disparities in the effective magnetic moments) between the two states in Fig. 2a and d, which can be switched by reversible electrical control (see Table 1). Specifically, the magnetic moments of the ground-state GN are 3.8 \({\mu }_{{{{{{\rm{B}}}}}}}\) and 5.1 \({\mu }_{{{{{{\rm{B}}}}}}}\), respectively. We demonstrate that these disparities in \({g}^{*}\) between the two molecular states are likely related to changes in the coordination environment and thus the metal-cage hybrid orbitals in the DFT calculations below.

Table 1 Effective g-factors and magnetic moments extracted from the tunneling spectra in each molecular state
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Consequently, we designate the state in Fig. 2a (red line in Fig. 1d) as molecular state 1 (state 1 for short) and the alternative state in Fig. 2d (blue line in Fig. 1d) as state 2, demonstrating an electrical switching operation between two molecular states and, consequently, the single-atom magnetic moment of Dy3+ as shown in Fig. 2g. The right panel illustrates a schematic hysteresis loop that essentially represent a prototypical electrically controlled nonvolatile switching of single-atom magnetism. Considering a silicon oxide layer thickness of ~ 10\(-\)30 nm and a switch gate voltage of 10 V, the variation in magnetic moments (Δμ) for the GN ground state is approximately 1.3 \({\mu }_{{{{{{\rm{B}}}}}}}\) at an electric field strength of ~3\(-\)10 MV/cm. These advancements make corresponding data storage applications more feasible.

Large MR and potential multistate data storage

In this section, we demonstrate the disparity in MR between the two molecular states to highlight its potential for magnetic data storage. We investigated the evolution of the N\(-\)1/N resonance peaks (marked as red and blue arrows in Fig. 1d) with respect to an external magnetic field. In Fig. 3a, b, with a fixed Vsd of 5 mV, Isd-Vg curves around the N\(-\)1/N resonant tunneling point (in Fig. 2a, d) of the two molecular states are plotted at various magnetic fields, revealing a significant reduction in the current intensity as B increases. The current intensities of the two bistable states exhibit distinct responses to magnetic fields, highlighting the versatility of this approach for multistate data storage applications. For example, this approach enables the realization of eight current intensity values from two states, denoted as 11 to 24 in Fig. 3c, which serve as distinct data storage states and facilitate electrical writing through electric field switching of molecular states and magnetic reading by detecting distinct MR using a magnetic field.

Fig. 3: Large MR and multistate operation of Dy@C84 SMTs.
figure 3

a, b Evolution of the N/N\(-\)1 resonant tunneling peaks (marked as red and blue arrows in Fig. 1d) in state 1 (a) and state 2 (b) with respect to magnetic field B when fixing Vsd = 5 mV. The current intensities of these resonance peaks are suppressed by the magnetic field. The inserts show the magnetic field dependence of MR extracted from peak amplitudes of the N/N\(-\)1 resonant tunneling point for state 1 and state 2, indicating high MR ratios of up to 600% for state 1 and 1100% for state 2 at 9 T. c Comparison of the amplitudes of current peaks (labelled 11 to 14 and 21 to 24) in state 1 (S1) and state 2 (S2) under varying magnetic fields (B = 0, 3, 6, 9 T) extracted from (a) and (b). This approach can be used to achieve multistate data storage. (d) Summary of MR values obtained from different molecular devices, namely, FePc (Refs. 36,37), PTM (Ref. 38), Tempo-OPE (Ref. 39), OPT (Ref. 40), Fe4 (Ref. 41), and TbPc2 (Ref. 42), and our device over a range of B. The MR of our study exceeds those of other atomic or molecular devices by nearly an order of magnitude.

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The corresponding ratios of MR are calculated (\({{{{{\rm{MR}}}}}}=(R\left(B\right)-R(0))/R(0)*100\%\))) and plotted as a function of B (see inserts in Fig. 3a, b). In addition to exhibiting high MR ratios of up to 600% for state 1 and 1100% for state 2 at a magnetic field strength of 9 T, the manipulation of molecular states enables MR switching by applying a threshold gate electric field. The MR of state 2 is ~180% larger than that of state 1 under the same magnetic field. Notably, the observed MR of up to 1100% is remarkably high and remains unaffected by the shift in peak position due to the Zeeman effect. We compare the MR of the Dy@C84 SMT with those observed for other molecular devices36,37,38,39,40,41,42 in Fig. 3d, which shows that our device outperforms other molecular systems by nearly an order of magnitude in terms of MR.

Considering the mechanism of MR, we exclude the possibility of the molecule‒electrode interface mechanism being reported in nonresonant tunnelling regions of some organic radicals36,37,38,39,40. Furthermore, the effect of spin polarization reported in negative MR systems42 is also unreasonable for explaining the positive values here. The resulting MR behaviours observed in our device can thus be explained by the metal-cage hybrid state, as discussed in the following section.

DFT calculations further corroborate the electrically nonvolatile switching of single-atom magnetism

The spin‒orbit interaction effect is generally negligible for atomic-scale electron transport, which makes difficult the electrical manipulation of single-atom magnetism without magnetic fields20,43,44,45,46. Additional factors such as electrical modulation of exchange interactions and broken symmetries associated with electric dipole moments have recently been employed for spin‒electric control20,23,25,47. The transition of the encapsulated atom between two different sites in certain EMFs with intrinsic broken inversion symmetries results in two states with different permanent electric dipole orientations17,18, which can be utilized for reversible electrical manipulation of the magnetism of the encapsulated atom.

However, a carbon cage can block the effect of an electric field28. It is therefore somewhat difficult to affect an internal atom. Hybridization between the Dy and cage orbitals decreases the shielding effect of the cage. Previous report has also indicated that the accessible orbitals of Dy@C82 EMFs, when deposited on a Ag surface, are primarily contributed by the 4f orbitals of the Dy atom and the metal-cage hybrid orbitals27. Our DFT calculations show that the HOMO, LUMO, and their adjacent molecular orbitals likely originate from either the 4f orbitals of Dy3+ or the metal-cage hybrid orbitals (Fig. 4a, c and Supplementary Fig. 5, Supplementary Fig. 6, and Supplementary Table 1).

Fig. 4: DFT calculations for the two molecular states.
figure 4

a Calculated density of states (DOSs) of the two molecular states for the free neutral Dy@C84 molecule in the near range of the Fermi level. The Fermi level is shifted to the HOMO. b Calculated energy barriers between two molecular states across the transition state (TS) under various gate electric fields. The gate electric field can effectively lower the energy barrier to a negligible level at ~0.25 V/\(\mathring{\rm A}\), thereby enhancing the transition probability between the two molecular states. The insert shows the interaction between the molecule and the Au16 electrode. c Two possible orbital configurations of metal-cage hybrid states in two molecular states at the HOMO, with magnetic moments 4.16 \({\mu }_{{{{{{\rm{B}}}}}}}\) and 4.55 \({\mu }_{{{{{{\rm{B}}}}}}}\). d Upon switching the molecular states, the coupled magnetic moment of the ground state transforms from 4.16 \({\mu }_{{{{{{\rm{B}}}}}}}\) for state 1 to 4.55 \({\mu }_{{{{{{\rm{B}}}}}}}\) for state 2, while the electric dipole moment transforms from 0.70 eÅ to 0.64 eÅ. The two electric dipoles exhibit a relative angle of 168.4°. e The energy profile with structural diagrams of the Dy ion position (the upper panel) and the dipole moment in the z-direction (the lower panel) when climbing the energy barrier.

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The mechanism of electrically controlled nonvolatile switching between two molecular states is qualitatively validated with theoretical calculations. The bistable molecular states are identified as the two most stable molecular conformations. State 1 is approximately 60 meV more stable than state 2 in free neutral Dy@C84 molecules, while the energy barrier of bistable switching is ~145 meV (see Supplementary Fig. 7 and Supplementary Table 2). The influence of the Au electrodes on molecules was further investigated by considering the coupling between the electrodes and molecules. In this configuration, the energy difference between two molecular states is reduced to 2 meV, while the energy barrier decreases to 92 meV. The charge transfer with the electrodes also influences the energy difference and energy barrier between the bistable states (Supplementary Table 2). As shown in Fig. 4b, the gate electric field effectively reduces the energy barrier to a negligible level when the electric field reaches 0.25 V/Å, leading to a molecular state transition. This transition is accompanied by a displacement of the Dy atom, a modification to the coordination environment, a rearrangement of molecular orbitals and density of states (DOSs), and charge redistribution (Fig. 4a, c, d). Consequently, there is a significant change in orbital angular momentum, which affects the magnetic moment. Specifically, the magnetic moment of the Dy atom switches from 4.4 \({\mu }_{{{{{{\rm{B}}}}}}}\) in state 1 to 5.0 \({\mu }_{{{{{{\rm{B}}}}}}}\) in state 2 (Table 2). The magnetic moment of the Dy@C84 EMF is mainly contributed by the Dy atom according to the calculation results, and the experimentally observed large \({g}^{*}\) values arise from the metal-cage hybrid states, which are sensitive to the coordination environment.

Table 2 Calculated relative energies, electric dipole moments, and effective magnetic moments of state 1 and state 2
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Furthermore, the observed significant MR and the variation in MR between the two molecular states are attributed to the effect of the metal-cage hybrid state. Due to the difference in effective g-factors between the Dy and cage components, an increase in the magnetic field leads to an apparent decrease in the degree of orbital overlap and the density of the hybrid states. For instance, when \({\triangle g}^{*}=5\), a magnetic field of 9 T induces an overlap gap of almost 3 meV between Dy and cage components. According to the Landauer model, a decrease in the DOS of the hybrid state would lead to a drastic reduction in the current intensity, as shown in Fig. 3a, b. Furthermore, the degree of hybridization may influence the MR properties. The smaller MR and variation values may be attributed to a low degree of hybridization (device B in Supplementary Figs. 2 and 3).

In addition to their distinct magnetic moments, our calculations reveal that both molecular states exhibit unique electric dipole moments (Table 2 and Fig. 4d). When switching the molecular states using an electric field, the coupled magnetic moment of the ground state transforms from 4.16 \({\mu }_{{{{{{\rm{B}}}}}}}\) for state 1 to 4.55 \({\mu }_{{{{{{\rm{B}}}}}}}\) for state 2, while the electric dipole moment transforms from 0.70 \(e\mathring{\rm A}\) to 0.64 \(e\mathring{\rm A}\). These two electric dipoles have a relative angle of 168.4°. The energy profile depicting structural diagrams of the molecule (the upper panel in Fig. 4e) and the dipole moment in the z-direction (the lower panel in Fig. 4e) climbing along the energy barrier are investigated to provide comprehensive insights into the bistable state transition. Therefore, as an example of a lanthanide EMF, Dy@C84 demonstrates considerable promise as an innovative platform for showcasing MECs.

Discussion

In summary, we have successfully achieved electrical tuning of the atomic magnetic moment in Dy@C84 SMTs, providing a novel approach to realize single-atom magnetic data storage. Our results demonstrate that by applying a gate electric field of ~ 3\(-\)10 MV/cm, two bistable molecular states can be switched. These bistable molecular states exhibit a significant Zeeman effect with large effective g-factors. Specifically, the magnetic moment of the ground-state GN transformed from 3.8 \({\mu }_{{{{{{\rm{B}}}}}}}\) to 5.1 \({\mu }_{{{{{{\rm{B}}}}}}}\). Moreover, the MR of the N\(-\)1/N resonant tunneling point respectively transitioned from 600% in state 1 to 1100% in state 2. Based on metal-cage hybridization, we manipulate the magnetic properties of the Dy atom within solid-state transistors, paving the way for advances in energy-efficient magnetic data storage and electronics with high integration and low power consumption.

Methods

Synthesis and isolation of Dy@C84

Raw soot containing dysprosium EMFs was synthesized using a direct-current arc discharge method48. The graphite rods were packed with a mixture of Dy2O3 and graphite powder (molar ratio of Dy/C = 1:12) and annealed at 1000 °C for 7 h under an argon atmosphere. Then, these graphite rods were vaporized in an arcing reactor under a 300 Torr helium atmosphere with an arc current of 100 A. The pure Dy@C84 compound was finally obtained through a combination of Lewis acid treatment and high-performance liquid chromatography (HPLC) separation26.

Device fabrication

Three-terminal transistors were fabricated using standard nanofabrication techniques, including UV lithography, electron beam lithography (EBL), and electron beam evaporation (EBE). The gate and external circuitry were defined by UV lithography, while the source and drain electrodes were patterned using EBL. A 30-nm layer of silicon oxide grown by atomic layer deposition (ALD) was used as the dielectric layer of the backgate, on which gold (Au) nanowires (width approximately 50 nm) were deposited by EBE as source and drain electrodes. After cleaning the nanowire transistors using oxygen plasma, a dilute drop of Dy@C84 solution (0.1 mmol/L) was deposited on the device before drying. The device was then cooled to a cryogenic temperature of 1.8 K (all measurements were performed at 1.8 K), and nanogaps were formed using the FCEBJ method by monitoring the current through the nanowire while increasing the applied bias voltage on the source and drain electrodes. The cycle was repeated by increasing the applied voltage from 0 mV again once the current had decreased by 1%, until the conductance reached 0.02 G0 at a voltage of 20 mV (where G0 = e2/h). The current data from the transport measurements were smoothed, and the original data are listed in Supplementary Fig. 4. The molecule-Au couplings were typically greater than the typical intramolecular exchange ( ~ 1 meV)12. Therefore, the intramolecular exchange-induced effects could not be resolved in the transport spectra.

Theoretical calculations

Geometrical optimizations of Dy@C84 were performed using DFT calculations implemented in the program package ADF201949. The Perdew–Burke–Ernzerhof (PBE) functional50 with D3 dispersion correction51 and TZ2P basis set were employed with the scalar relativistic zeroth-order regular approximation (ZORA)52 Hamiltonian for relativistic effects. The frontier molecular orbitals (FMOs) and density of states (DOS) were plotted at the same level of theory with a Gaussian smearing width of 0.3 eV. The magnetic moment was calculated with the Vienna ab initio simulation package (VASP)53 using the PBE-D3 functional. The interaction between valence electrons and ionic cores was considered within the framework of the projector augmented wave (PAW) method54,55. The energy cut-off for the plane wave basis expansion was set to 400 eV, while the criterion for total energy convergence was set at 10–5 eV.