Electrically controlled nonvolatile switching of single-atom magnetism in a Dy@C84 single-molecule transistor

Single-atom magnetism switching is a key technique towards the ultimate data storage density of computer hard disks and has been conceptually realized by leveraging the spin bistability of a magnetic atom under a scanning tunnelling microscope. However, it has rarely been applied to solid-state transistors, an advancement that would be highly desirable for enabling various applications. Here, we demonstrate realization of the electrically controlled Zeeman effect in Dy@C84 single-molecule transistors, thus revealing a transition in the magnetic moment from 3.8 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu }_{{{{{{\rm{B}}}}}}}$$\end{document}μB to 5.1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu }_{{{{{{\rm{B}}}}}}}$$\end{document}μB for the ground-state GN at an electric field strength of 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-$$\end{document}−10 MV/cm. The consequent magnetoresistance significantly increases from 600% to 1100% at the resonant tunneling point. Density functional theory calculations further corroborate our realization of nonvolatile switching of single-atom magnetism, and the switching stability emanates from an energy barrier of 92 meV for atomic relaxation. These results highlight the potential of using endohedral metallofullerenes for high-temperature, high-stability, high-speed, and compact single-atom magnetic data storage.


Introduction
As scaling the dimensions of magnetic media materials toward the spatial limit, magnetic single atoms are considered the ultimate goal of such downsizing [1][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 singleatom 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 layers [2][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 field 2,[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 barrier 2,3,5 , 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 obtained [10][11][12][13][14][15][16] .Furthermore, in many experiments, the manipulation of magnetic states depends on magnetic fields 2,[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 orientations 17,18 .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) effect [19][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.

Device fabrication and charge transport measurements
We used the precious trivalent EMF Dy@C84 (see the right panel of Fig. 1(a)); 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 cage 26 , 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 capabilities 27,28 .Three-terminal Dy@C84 SMTs were fabricated to allow reliable modulation of the molecular chemical potential by a back gate, as depicted in Fig. 1(a).A Dy@C84 molecule bridges a pair of Au electrodes created by the feedbackcontrolled 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. 17,29for more details).

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 molecule 10,15 (Vg = −7.2V and Vg = −7.9V, marked as red and blue arrows in Fig. 1(d), respectively), and then plot coloured maps of the differential conductance (dIsd/dVsd) around each peak with respect to Vsd and Vg in Fig. 2(a, 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. 2(a) and 2(d), respectively).Figure 2(b, e) shows 2D maps of d 2 Isd/dV 2 sd as a function of Vsd and B, which offer clearer indications of level shifts.In particular, the excited state in Fig. 2(e) 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 d 2 Isd/dV 2 sd curves at different Vg in Fig. 2(b, e) are shown in Fig. 2(c, 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 states 30,31 .
By applying a linear fit to the level shift according to the Zeeman effect, it is possible to determine the effective g-factor 32,33 , which is defined as (where  B is the Bohr magneton).The absolute values of  * range from 2.2 to 8.4 (Table 1).In comparison with the observed  ≈ 2 for a C60 molecule 34,35 , the higher absolute values of  * can be qualitatively attributed to the contribution of the orbitals of Dy 3+ .As the ground state | = 15/2⟩ of free Dy 3+ leads to a  * value of ~10 (Supplementary Note 1), these ground and excited states with  * from 2.2 to 8.4 occur due to either the mixing of different   states or more likely hybridization between orbitals of the carbon cage and the Dy 3+ ion, which is susceptible to the coordination environment.Moreover, there are disparities in  * (and thus disparities in the effective magnetic moments) between the two states in Fig. 2(a) and 2(d), which can be switched by reversible electrical control (see Table 1).Specifically, the magnetic moments of the ground-state GN are 3.8  B and 5.1  B , respectively.We demonstrate that these disparities in  * 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.
Consequently, we designate the state in Fig. 2(a) (red line in Fig. 1(d)) as molecular state 1 (state 1 for short) and the alternative state in Fig. 2(d) (blue line in Fig. 1(d)) as state 2, demonstrating an electrical switching operation between two molecular states and, consequently, the single-atom magnetic moment of Dy 3+ as shown in Fig. 2

(g).
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 () for the GN ground state is approximately 1.3  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. 1(d)) with respect to an external magnetic field.In Fig. 3(a, b), with a fixed Vsd of 5 mV, Isd-Vg curves around the N−1/N resonant tunneling point (in Fig. 2(a, 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. 3(c), 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.
The corresponding ratios of MR are calculated ( MR = (() − (0))/(0) * 100% )) and plotted as a function of B (see inserts in Fig. 3(a, 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 devices [36][37][38][39][40][41][42] in Fig. 3(d), 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 moleculeelectrode interface mechanism being reported in nonresonant tunnelling regions of some organic radicals [36][37][38][39][40] .Furthermore, the effect of spin polarization reported in negative MR systems 42 is also unreasonable for explaining the positive values here.The resulting MR behaviours observed in our device can thus be explained by the metalcage 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 fields 20,[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 control 20,23,25,47 .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 orientations 17,18 , 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 field 28 .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 orbitals 27 .Our DFT calculations show that the HOMO, LUMO, and their adjacent molecular orbitals likely originate from either the 4f orbitals of Dy 3+ or the metal-cage hybrid orbitals (Fig. 4(a, c) and Supplementary Figure 5, Supplementary Figure 6, and Supplementary Table 1).
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 Figure 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. 4(b), 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. 4(a, c,   and 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  B in state 1 to 5.0  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  * values arise from the metal-cage hybrid states, which are sensitive to the coordination environment.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 ∆ * = 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. 3(a, 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 Figure 2 and Supplementary Figure 3).
In addition to their distinct magnetic moments, our calculations reveal that both molecular states exhibit unique electric dipole moments (Table 2 and Fig. 4(d)).When switching the molecular states using an electric field, the coupled magnetic moment of the ground state transforms from 4.16  B for state 1 to 4.55  B for state 2, while the electric dipole moment transforms from 0.70 Å to 0.64 Å.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. 4(e)) and the dipole moment in the z-direction (the lower panel in Fig. 4(e)) 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  B to 5.1  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.

Synthesis and isolation of Dy@C84
Raw soot containing dysprosium EMFs was synthesized using a direct-current arc discharge method 48 .The graphite rods were packed with a mixture of Dy2O3 and graphite powder (molar ratio of Dy/C = 1:12) and annealed at 1000 ℃ 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) separation 26 .

Device fabrication
Three-terminal transistors were fabricated using standard nanofabrication techniques, including UV photolithography, 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 = e 2 /h).The current data from the transport measurements were    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.

Figure captions Figure 1
Figure captions

Figure 2
Figure 2 Electrically controlled nonvolatile switching of single-atom magnetism.

Figure 3
Figure 3 Large MR and multistate operation of Dy@C84 SMTs.

Figure 4
Figure 4 DFT calculations for the two molecular states.

Table 1
Effective g-factors and magnetic moments extracted from the tunneling spectra in each molecular state.