# MgO Tunneling Spintronics across Capacitively Coupled Atomic Clusters

Mathieu Lamblin, Victor da Costa, Loïc Joly, Bhavishya Chowrira, Léo Petitdemange, Bertrand Vileno, Romain Bernard, Benoit Gobaut, Samy Boukari, Wolfgang Weber, et al.

► To cite this version:

Mathieu Lamblin, Victor da Costa, Loïc Joly, Bhavishya Chowrira, Léo Petitdemange, et al., MgO Tunneling Spintronics across Capacitively Coupled Atomic Clusters. Nano Letters, 2025, 25 (52), pp.18026-18035. 10.1021/acs.nanolett.5c03672. hal-05457364

HAL Id: hal-05457364

https://hal.science/hal-05457364v1

Submitted on 14 Jan 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
# MgO tunneling spintronics across capacitively-coupled atomic clusters

Mathieu Lamblin,¹, a) Victor Da Costa,¹ Loic Joly,¹ Bhavishya Chowrira,¹ Léo Petitdemange,² Bertrand Vileno,³ Romain Bernard,¹ Benoit Gobaut,¹ Samy Boukari,¹ Wolfgang Weber,¹ Michel Hehn,² Daniel Lacour,² and Martin Bowen¹, b)

¹) Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 CNRS, Université de Strasbourg, 23 Rue du Lœss, BP 43, 67034 Strasbourg, France

²) Institut Jean Lamour UMR 7198 CNRS Université de Lorraine BP 70239, Vandoeuvre les Nancy 54506, France

³) Institut de Chimie UMR 7177 CNRS Université de Strasbourg 4 Rue Blaise Pascal, CS 90032, Strasbourg 67081, France

(Dated: November 6, 2025)

## Abstract

Transport across model junctions built using atomic tip or lateral techniques can generate exotic quantum signatures. However, so far, a viable industrial pathway for atom-driven electronics has been lacking. Here, we demonstrate that a commercialized device platform can help to fill this nanotechnological gap. According to conducting tip atomic force microscopy, inserting C atoms into an ultrathin MgO layer generates nanotransport paths. Across microscale magnetic tunnel junctions, large magnetoresistance peaks result from spin accumulation. We also observe a spectrally localized, nonlinear current noise upon resonant tunneling involving two energetically close nanotransport paths and additional persistent memory effect that we attribute to the charging of a "gating" C nanodot, adjacent to the C nanodot that channels nanotransport. This dual-dot description of quantum transport across spin states within a magnetic tunnel junction should open the door to further research aimed at maturing spintronics into a viable quantum technological track.

**Keywords:** Spintronics, Resonant tunneling, Magnetic tunnel junctions, Random telegraph noise, Resistive switching

Fundamental research on model atomic and molecular junctions has strongly progressed in the last two decades thanks to atomic tip and lateral junction building techniques¹⁻³. Although these technical approaches do not promote industrial nanotechnologies, they have helped reveal intriguing electronic transport mechanisms. Among them are Coulomb blockade inside single-atom transistors⁴, Coulomb drag and co-tunneling effects in capacitively coupled quantum dots⁵, Franck-Condon blockade within carbon nanotubes⁶, spin-phonon coupling in single-molecule magnets⁷, Kondo effect with spin-oriented molecules⁸, memristance and hysteresis linked to resistive switching⁹,¹⁰ and strong current fluctuations caused by vibrational coupling and structural changes¹¹. More recently, quantum phenomena involving internal coherence and superposition have been reported¹²⁻¹⁴, such as phonon interference¹⁵, quantum interference and decoherence¹⁶.

To obtain similar effects in an industrializable device such as a magnetic tunnel junction (MTJ) requires controlling the nature and position of localized states in the ultrathin dilectric layer that separates the vertical pillar device's two ferromagnetic electrodes. In fact, while molecules offer an elegant means of inserting atom-level electronic states within a device, molecular spintronic technologies are still rudimentary and thus very far from industrial deployment¹⁷,¹⁸. This motivates further

investigations of tweaked implementations of the most widely developed industrial spintronic platform: the Fe-CoB/MgO/FeCoB MTJs that already have applications ranging from next-generation memories¹⁹,²⁰, probabilistic computing²¹, true random generators²² and neuro-morphic computing²⁰,²³ to agile microwave emitters and the harvesting of waste energy²⁴.

These applications rely on the MTJ's magnetic properties. In this paper, we showcase several of the aforementioned atomic transport effects by utilizing especially crafted localized states in the MTJ's MgO tunnel barrier. Prior research has shown²⁵⁻³⁰ that introducing states in tunnel junctions can promote some of these effects, including within MgO MTJs²⁷,²⁹. Yet structural defects themselves can generate localized states within a MgO MTJ³¹⁻³⁶. The oxygen vacancies within the tunnel barrier generate discrete electronic states that play a role in spin transfer torque³⁶, and which we have identified³⁵ and controlled³⁷⁻³⁹ in our MgO junctions. These oxygen vacancies are diamagnetic. To achieve discrete, unpaired electron spin states, we introduce carbon atoms onto these oxygen vacancies⁴⁰ (see SI Note 9). We find that they induce hysteretic memory effects, random telegraphic noise and spin accumulation upon resonant transport. These effects underscore the presence of nanotransport paths across discrete spin states, which are borne by clusters of C atoms, and which can take on a 'transport' or a 'gating' role in the MTJ's operation (see schematic in Fig. 1(a)).

<footnote>a) Electronic mail: mathieu.lamblin@lpmmc.cnrs.fr</footnote>

<footnote>b) Electronic mail: martin.bowen@ipcms.unistra.fr</footnote>
<figure><img src="image_2.png" /></figure>

Figure 1. **Atomic nanotransport paths.** (a) Schematic of a nanotransport path formed by a 'transport' C nanodot that bridges the two electrodes of a microscale magnetic tunnel junction. A partly bridged path to a 'gating' C nanodot is also shown. Capacitive coupling is denoted by the green wiggle between the two dots. The C atoms are located 0.9(1.7) nm away from the bottom(top) electrode. The junctions' 20 µm diameter is noted. Conducting tip Atomic Force Microscopy (AFM) scans of a MTJ sample without the top metallic electrode (b) without C atoms in MgO and (c) with C atoms in MgO 0.9 nm away from the lower MgO interface. The interference patterns in panel (b) are due to noise at the background limit. The ~10 nm nanotransport lateral size in panel (c) is the result of tip convolution. Note the different log scales on panels (b-c). a 10 mV bias voltage was applied.

## I. C-BORNE NANOTRANSPORT PATHS ACROSS A MGO TUNNEL BARRIER

We first use conducting Atomic Force Microscopy (AFM) to examine how inserting C alters the nanoscale conductivity across the MgO barrier (see SI Note 9). When C is absent (Fig. 1(b)), the tip does not detect a measurable current. Assuming Gaussian noise, the standard deviation of the measured current is $\sigma \approx 0.065$ pA. Upon inserting C into MgO, we observe a series of current hotspots up to 120 pA that statistically contribute to the tail of the current distribution$^{41}$. The ~10 nm apparent lateral size is due to the convolution of the tip with the nanotransport path over an effective zone that spans several atoms$^{34,39,40}$. Since quantum mechanical tunneling scales exponentially with the barrier's spatial width and energy height, the most prominent hotspot will funnel all the current across a microscale tunnel junction$^{34}$, as schematized in Fig. 1(a). This mechanism therefore supports transport through nanotransport paths generated by the localized states of C atoms despite the device being microscale.

## II. INFORMATION ENCODING ONTO ENERGY LEVELS WITHIN A MICROSCALE DEVICE

Within an MgO MTJ (see SI Note 9), these localized states can be electrically manipulated to encode information. The cyclical *IV* traces in Fig. 2(a) show two ON and OFF current branches that are linked through 'writing' events *E*− and *E*+ during which a current jump occurs, which is typical of the resistive switching effect$^{42,43}$. Below these writing thresholds, the differential conductance (*dI*/*dV*; panel (b)) shows a set of two peaks whose bias positions rigidly shift by $\Delta_W \approx 70$ mV between the ON and OFF branches. Carefully crafted bias sweeps (pan-

els (c-f)) below or above a writing threshold reveal how the writing event causes the conductance peak presence to change. As discussed in SI Note 3 and 4, the constant voltage gap $\Delta_{CG} = 310$ mV between the pair of conductance peaks at positive and negative voltages can be tracked across several other junction states.

These conductance peaks and hysteretic features are absent in our MgO MTJs without C, i.e. when the nanotransport path only involves oxygen vacancies$^{33,35,39}$. This hysteretic behavior induced by conductance jumps closely mimics the electrical responses reported in model molecular junctions$^{44-50}$, which include abrupt switching between two conductance branches due to electron charging$^{47}$, while in single-electron transistors (SETs), featuring Coulomb blockade$^{4}$, the phenomenon of charge trapping is frequent and results in a sudden voltage shift of the entire Coulomb diamond figure$^{51}$.

Given the electronic states in the C delta-doped barrier, the hysteretic nature of this switching, and the localization of the branch jumps in the vicinity of the conductance peaks, charge trapping may thus be the most likely explanation, in line with other nanoscale platforms$^{52}$ (see SI Note 5 for more arguments). In accordance with these related phenomena, we thus infer that electronic transport is occurring through a 'transport' C nanodot that is capacitively coupled to a another 'gating' C nanodot that does not participate in transport but can alter the energy of the 'transport' dot when a charge is removed/added from it, essentially acting as an electrostatic gate (see Figure 1(a)). This is supported in Fig. 2(a) by the presence of noisy regions EA1 and EA2 (semi-transparent datapoints). Indeed, the spectral position and width of these regions do not correspond to conductance peaks in the present dataset, but rather in other datasets acquired on the same junction but with different 'transport' and 'gating' attributions of the C atoms upon thermal cycling. See SI Note 4 for details. We therefore interpret
<figure><img src="image_3.png" /></figure>

**Figure 2. Hysteresis and resonant tunneling.** (a) IV and (b) differential conductance dI/dV data at T = 10 K on junction G10. The *E*<sub>+</sub> and *E*<sub>-</sub> writing events cause a shift Δ*W* = 73 mV in the otherwise constant energy gap Δ*CG* = 310 mV between conductance peaks. Transport noise due to interference with an environmental 'gating' nanodot are shown using semi-transparent datapoints. (c-f) dI/dV data upon sweeping bias to test the interplay between the presence of the conductance peak and the writing events *E*<sub>-</sub> and *E*<sub>+</sub>. Starting in the black-coded junction state, bias is swept (black data of branch 1), and then reversed (red data of branch 2). Reaching a writing event while in the black state impacts the presence of the conductance peak. The blue cross in panel (e) pinpoints the bias and junction state in which the data of Fig. 3(a) was acquired. (g) Magnetoresistance traces at V = -50 mV in the ON/OFF junction states. (h) Hysteretic model of transport involving at least one quantum dot in the transport path (TQD), and at least one environmental 'gating' quantum dot (GQD) that is capacitively linked to the transport dot but doesn't participate directly in electronic transport across the junction (see also Fig 1(a)). The various operations of the hysteretic cycle, showing how charging/discharging the gating dot controls the energy levels of the transport dot, are shown.
the voltage shift $\Delta_W \approx 70$ mV between junction states to the charging of the 'gating' nanodot by one electron. This leads us to infer that it is positioned at twice the radius away from the 'transport' C nanodot (see SI Note 5).

Within this description, the conductance peaks most likely result from the resonant tunneling through an energy level of the 'transport' C nanodot. Additionally, the fact that the gap between the positive and negative conductance peaks remains constant upon the switching of junction states (see SI Note 4) suggests that these two peaks are linked. Using this framework of capacitive coupling to a 'gating' nanodot, this would imply that transport is in both cases influenced by the same electrostatic field difference under charge trapping/detrapping, therefore, these two peaks should be related to the resonant tunneling through the same energy level$^{53}$.

If the 'gating' nanodot was in the same plane, parallel to the junction interfaces that contains the 'transport' nanodot, altering its charge would affect both electrodes equally, and lead to a change in the bias voltage difference but no change in bias offset, as would a standard gate in a lateral device. We thus deduce that our observations regard an 'gating' nanodot that is structurally adjacent to the plane containing the 'transport' nanodot (see Fig. 1a). This asymmetry, along with the asymmetric position of the C delta-layer within MgO (see SI Note 9), might explain why the noise/conductance peak spectroscopic concurrence isn't seen at positive bias.

Inspired by this description, we present in Fig. 2(h) the schematic of a two-quantum dot model that can explain this memory effect in our microjunctions. The upper 'transport' quantum dot (TQD) is connected to both leads, while the lower 'gating' quantum dot (GQD) is connected only to the left lead. Both quantum dots are capacitively coupled together.

Starting at $V = 0$ in the ON branch, the lower-lying levels of the TQD are filled, the upper-lying are empty, and the single level of the GQD is empty (see Fig. 2(h)1). At $V = V_+$ (panel 2), resonant tunneling from the left lead onto the upper level of the TQD occurs, leading to the conductance peak. Increasing the voltage to $V = E_+$ causes potential alignment with the GQD level (panel 3). Electronic charging from the left electrode makes the levels of both QDs rise (step 1): the TQD's higher levels are above the potential, while the lower levels lie between the potential window offered by the electrodes. After equilibration, electron escape from the TQD occurs, and resonant tunneling starts through the lower levels. Within a narrow energy window, either the system trivially returns from 3 to 2, or the new dynamic filling of the TQD's energy levels capacitively lowers the GQD's level (see Fig. 2(h)4). This capacitive back-action traps the electron that filled the GQD level, preventing it from jumping back onto the electrode. This causes a conductance jump from the ON to OFF branch, and only a negative potential can release this trapped electron and revert the junction back to the ON state.

<figure><img src="image_4.png" /><figcaption>Figure 3. Current noise and multistability between nanotransport paths. (a) Intensity as function of temperature at -2000 Oe and -170 mV for junction G10. (b-d): junction C5. (b) Differential conductance at 10 K for the P magnetic state. (c) Color map of the statistic weight of the current deviation from the mean current as a function of applied bias. The junction P magnetic state was used. At each bias value, 800 current measurements were acquired. Datasets at select voltage values are shown in panel (d).</figcaption></figure>

If the voltage is now decreased to $V_+$ (see Fig. 2(h)5), another conductance peak is observed due to resonant tunneling through the lower lying level of the TQD. Then, at $V = 0$ (see Fig. 2(h)6), the gap region is recovered but in an energy window that is shifted by the presence of the electron on the GQD. Similar arguments can describe the process of electron escape from the GQD and the switch from the OFF back to the ON transport regime (see panels 7-10 of Fig. 2(h)). This two-QD capacitive charging cycle, which describes the experimental data of Fig. 2(b), can also be adjusted for other cases. The examples of Fig. 2(d) and SI Fig. S4 are fulfilled if the upper levels of the TQD lie below the empty level of the GQD in the ON state. Then, an electron tunneling from the left electrode would address the GQD level around $V = E_-$ before reaching the edge of the gap region.

### III. BISTABILITY AND CURRENT FLUCTUATIONS

The narrow energy levels of the transport and gating quantum dots give rise to a mutistability of different junction states and inelastic current noise that are circumscribed to specific bias and temperature ranges. We
present in Fig. 3(a) the temperature dependence of the current measured on junction G10 at $V = -170$ mV. As emphasized by the blue cross in Fig. 2(e), the junction is bistable at 10 K at this bias. Upon cooling down from 140 K, the current broadens into two ON/OFF branches, with intermediate spectral weight of low intensity (MID branch). Further evidence of these regimes appears in SI Note 7.

We use bias-dependent current statistics to observe transport branches. We first plot in Fig. 3(b) differential conductance data of junction C5 at $T = 10$ K. On the log scale, we observe sizable increases in conductance, and the clear appearance of noise for $V < -0.4$ V and for $V > 0.3$ V. Within $-0.6 < V$ (V) $< +0.6$, after setting the dc applied bias, we measured the current 800 times. The statistics of a given current deviation from the mean current as a function of applied bias are plotted in panel (c). Within $|V| < 0.2$ V, the current remains essentially stable along the OFF branch. For $|V| > 0.2$ V, the transition to the MID state can appear. This is especially visible within $0.2 < V$ (V) $< 0.4$. While the OFF branch shifts to values below the mean, the MID branch collapses into the dominant branch around $V = 0.4$ V. A higher resolution dataset is shown in SI Note 1. For $V > 0.4$ V, this branch splits into two ON/OFF branches. A similar branching is seen for $V < -0.4$ V. Erratically, each of these two branches can split into two subbranches, for a total of four branches (see Fig. 3(d)). The conductance noise (panel c) thus arises from transport fluctuations between these branches, which are visualized by our current statistics.

Overall, these experimental findings are reminiscent of random telegraph noise (RTN)$^{54}$, which is typical in nanoscale devices such as SETs$^{52,55,56}$, nanoparticule$^{57}$, graphene$^{58}$ and carbon nanotube junctions$^{59}$. This has also been observed in sub-millimetic MTJs with impurities$^{60}$, though without an obvious connection to spectral features as here. In line with the previous interpretation of the hysteretic branch jumps, this phenomenon is also usually caused by charge trapping/de-trapping on impurities that code for the multistable states$^{52,58,60}$ associated with an electron-vibrational coupling that promotes the stochastic transition between states$^{54,59}$.

From a quantum perspective, the theories of Franck-Condon blockade$^{61,62}$ and of out-of-equilibrium polaron dynamics$^{63,64}$, can explain the observed multistability of different states, the telegraphic switching between the different intensity branches, the intermediate inelastic states and hysteresis. This occurs for transport across an impurity with discrete energy levels, such as a quantum dot or a molecular orbital that is strongly coupled to a vibrational degree of freedom and that is tunnel coupled to two leads. The bias voltage acts as an effective temperature and a force that modulates the oscillator potential. Around specific voltage biases, the effective energy potential landscape develops several minima, and thus promotes metastability between different occupation

states. Two scenarios are possible. 1) Thermally activated switching between different intensity branches related to each of the well-separated potential minima can occur$^{10}$. 2) Large fluctuations around a single intensity branch occur when at least two minima are sufficiently degenerate to energetically trigger a $1/f$ noise effect$^{65,66}$. In this latter case, intermediate states outside the well minima are measured.

The various levels of stability suggest that several energy levels are accessible depending on the thermal and electrical energy, such that a only a handful of defects participate directly or indirectly in transport, as described previously.

## IV. SPINTRONIC SIGNATURES

The hysteretic behavior of the conductance peak due to environmental charging represents one level of information encoding, with a write success rate > 80% (see SI Note 3). To examine how the spin polarization of the charge current impacts the memory and noise effects, we compare transport properties upon switching the orientation of the electrodes' magnetization from parallel (P) to antiparallel (AP).

Referring to Fig. S1-2, the plume current noise data is shifted by 33 mV upon switching the MTJ's P/AP magnetic state. A careful comparison of the two P/AP datasets reveals that transport occurs through spin-split energy levels. The simplest scenario is that of resonant transport across a paramagnetic center subjected to an electronically projected magnetic field$^{40,67}$. Although charged oxygen vacancies can be paramagnetic, since we observe this correlation of spectral/noise features only on MgO MTJs with C impurities, it is reasonable to attribute these features to C atoms, which are indeed paramagnetic in MgO by virtue of their unpaired spin$^{40}$.

To further examine this spintronic shift, we consider its bias dependence. We plot in Fig. 4(a) the $IV$ in the MTJ's P and AP states at $T = 10$ K. Both exhibit a series of plateaus and increases that are absent in junctions without C atoms$^{33-35}$. The corresponding differential conductance ($dI/dV$) data (see panel (b)) reveals a series of peaks. While the P and AP datasets share similar traits, the AP plot appears to shift to higher bias as the onset of each conductance increase is reached. This is confirmed through an analysis of the correlated shift between the two datasets in Fig. 4(c) (see SI Note 9).

The tunnel magnetoresistance $TMR = \frac{I_P}{I_{AP}-1}$ characterizes to what extent the two spin channels of current flowing across the device are asymmetric. In our MgO MTJs without C$^{33}$, we observe $TMR \approx 200\%$ at 10 K around $V = 0$, and a mostly monotonous $TMR$ decreasing with increasing $|V|$. When C atoms are introduced into MgO, we observe only a few % $TMR$ around $V = 0$. Instead, due to the shift in AP conductance to higher bias with each succeeding conductance peak, the $TMR$ bias dependence closely mimics the junction con-
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Spin accumulation and magnetoresistance. (a) Current-voltage characteristic for the P and AP junction states, and (b) the resulting dI/dV differential conductance. (c) Voltage shift between the P and AP conductance data (see SI Note 9 for details). (d) Bias dependence of the tunnel magnetoresistance (TMR) calculated from (a). Blue crosses indicate TMR amplitudes obtained from *I*(*H*) experiments. All data: junction G10.</figcaption></figure>

conductance (compare panels (b) and (d) of Fig. 4). This unusual, highly structured TMR bias dependence is confirmed through discrete *I*(*H*) datasets at fixed *V* (crosses in Fig. 4(d)). We observe local TMR maxima precisely on the conductance peaks, with an absolute maximum of 15%.

We present *I*(*H*) data in Fig. 2(g) in both the ON and OFF states of the junction, taken at *V* = −50 mV; i.e. precisely at the bias value corresponding to the hysteretic conductance peak shown in panels (c-e) of Fig. 2. We observe that *I*<sub>P</sub> increases and that *I*<sub>P</sub>−*I*<sub>AP</sub> is multiplied by 7, so that the TMR increases from 0.5% in the OFF state to 3.7% in the ON state due to the peak.

Prior literature has documented unusual bias depen-
dencies of TMR<sup>18,68,69</sup>, which can, for instance, track
junction conductance as a channel opens upon exciting a
spin chain's quantum state<sup>18</sup>. However, in our case, the
TMR peaks due to the P/AP offset in conductance peaks
strongly resemble a theoretical prediction by Barnas and
Fert<sup>70</sup> of spin accumulation onto a Coulomb dot. Since
we do not observe regular bias spacings between conduc-
tance peaks, and given the relatively high temperatures,
our results more likely reflect the impact of spin accumu-
lation upon resonant tunneling across energetically dis-
tinct spin levels. This would constitute a natural ex-
tension at intermediate temperatures of their theory<sup>70</sup>.
Underscoring the spin accumulation is a spin splitting
that arises from the magnetic field that is electronically
projected by the proximate ferromagnetic electrode<sup>40,67</sup>,
and can be altered spintronically<sup>40,71</sup>. This splitting will
differ between the P and AP states of the MTJ due to
different energy alignments of the C electronic levels<sup>40,72</sup>.
Note in our schematic of Fig 2(h) how the splitting is al-
tered upon charging the 'gating' dot. This would explain

the seven-fold TMR enhancement of Fig. 2(g). In turn,
altering the spin splitting through charging the 'gating'
dot would explain the change in TMR SI Notes 1 and 2
provide additional evidence of this spin splitting.

To obtain more insight into the origin of the magnetic
field experienced by the transport C nanodot, we per-
formed nitrogen vacancy (NV) center microscopy exper-
iments on a half-MTJ sample (see SI Note 9), and simu-
lated these data using Mumax3<sup>73,74</sup> to extract micromag-
netic parameters. An example of experimental data and
simulation is shown in Fig. 5(a) for a NV center height
of 90 nm. Using the same parameters, we are able to fit
other NV scans at heights ranging from 60 nm to 180 nm.
This allows us to confidently extrapolate the stray field
at 2.5 nm above the ferromagnetic surface. Figs. 5(b)
(left/right) show the extrapolated maps of the longitu-
dinal B<sub>||</sub> / transverse B<sub>⊥</sub> components of the stray field.
We find that no field component exceeds 20 mT, i.e. or-
ders of magnitude below values inferred by the spintronic
energy shifts observed in magnetotransport (see Fig. 4).
We thus infer that the effect arises from the electronic
magnetic field ≈50 T due to spin-polarized charge trans-
fer from the ferromagnetic metal, in combination with
bias-induced spintronic anisotropy<sup>40</sup>.

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Magnetic stray field on the C atoms due to the ferromagnetic electrode. (a) (left) Experimental data and (right) simulation of a NV center magnetometry scan 90 nm away from the half-MTJ sample surface. The color encodes the stray field absolute value projected onto the NV center axis (100-oriented diamond tip). (b) Simulation of the stray field's longitudinal B|| and transverse B⊥ components, extrapolated from the corresponding experimental magnetometry map.</figcaption></figure>
V. CONCLUSION

To conclude, inserting C atoms into a MTJ’s ultrathin MgO layer generates localized paramagnetic⁴⁰ states that are spin-split by electronic interactions with the MTJ’s ferromagnetic electrodes⁷⁵. Experiments on micronic Fe-CoB/MgO:C/FeCoB magnetic tunnel junctions, which are crafted using straightforward technological processes, show that the effective nanotransport path³⁴ involves a reduced set of C atoms. Their discrete energy levels promote resonant tunneling effects that can be reproducibly shifted in energy by charging events on a neighboring C atom that is along the nanotransport path. The tunnel coupling between these transport and environmental ‘gating’ carbon nanodots promotes a hysteretic memory effect. Spin-polarized transport induces spin accumulation that further lifts the spin degeneracy of the unpaired C electron in MgO. This leads to a voltage shift in conductance peaks between the MTJ’s P and AP datasets, and to a huge enhancement of the spintronic performance, as predicted⁷⁰.

We thus demonstrate how to use both the electron
charge and spin to encode information on just a few
atoms within a solid-state, industrializable device. Our
discussion of experimental results reveals a new level of
insight into the structural and electronic properties of the
effective nanotransport and gating paths across a vertical
MgO microjunction.

These results showcase MgO tunneling spintronics as
a potentially promising industrial platform for quantum
technologies at practical temperatures, to deploy quan-
tum transport effects that are normally only seen in
STM-assembled or lateral junctions. Naturally, com-
pared to research on these model yet non-scalable junc-
tions, the main difficulty here will be to engineer the
C-borne paths embedded into the MTJ pillar so as to
obtain 1) a higher device-to-device reproducibility 2)
with electronic stability at higher temperatures. Possi-
ble approaches include engineering the impedances that
electronically link the transport and gating atoms to
the magnetic tunnel junction electrodes; engineering the
paramagnetic center’s chemical bonds to MgO; and con-
trolling the density of oxygen vacancies³⁹ that are al-
ready present in industrial nanosized MTJs³⁶. Final ap-
plications of quantum spintronics not only encompass in-
formation encoding¹⁸, but also energy harvesting⁴⁰,⁶⁷,⁷⁶
vectors.

SUPPORTING INFORMATION

Current noise time series and current plume; spin ac-
cumulation at negative bias; statistics on the hysteretic
effect; overview of the voltage gaps with evolving junc-
tion state and argumentation for single-atom ‘transport’
and ‘gating’ quantum dots; estimation of the impurities
sizes and distances; reproducibility and other junctions;
resistive switching and temperature dependence; magne-

toresistance; lifetimes.

ACKNOWLEDGEMENTS

We gratefully acknowledge PhD funding for M.L. from
Ecole Polytechnique. We acknowledge financial sup-
port from the ANR (ANR-21-CE50-0039), the Con-
trat de Plan Etat-Region grants in 2006 and 2008, by
"NanoTérahertz", a project co-funded by the ERDF
2014-2020 in Alsace (European Union fund) and by the
Region Grand Est through its FRCR call, by the impact
project LUE-N4S part of the French PIA project "Lor-
raine Université d'Excellence", reference ANR-15IDEX-
04-LUE and by the FEDER-FSE "Lorraine et Massif
Vosges 2014-2020", a European Union Program. This
work of the Interdisciplinary Thematic Institute QMat,
as part of the ITI 2021-2028 program of the University of
Strasbourg, CNRS and Inserm, was supported by IdEx
Unistra (ANR 10 IDEX 0002), and by SFRI STRAT'US
project (ANR 20 SFRI 0012) and EUR QMAT ANR-
17-EURE-0024 under the framework of the French In-
vestments for the Future Program. This work was sup-
ported by France 2030 government investment plan under
grant reference PEPR SPIN–MAT ANR-22-EXSP-0007
and PEPR SPIN–ADAGE ANR-22-EXSP-0006, and by
the ESR/EquipEx+ program (grant number ANR-21-
ESRE-0031).

REFERENCES

<footnote n="1">¹T. Li, V. K. Bandari, and O. G. Schmidt, “Molecular elec-
tronics: Creating and bridging molecular junctions and pro-
moting its commercialization,” *Advanced Materials* **35** (2023),
10.1002/adma.202209088.</footnote>

<footnote n="2">²R. L. McCreery, “Carbon-based molecular junctions for practical molecular electronics,” *Accounts of Chemical Research* **55**, 2766–2779 (2022).</footnote>

<footnote n="3">³W. Peng, H. Wang, H. Lu, L. Yin, Y. Wang, B. Grandidier, D. Yang, and X. Pi, “Recent progress on the scanning tunneling microscopy and spectroscopy study of semiconductor heterojunctions,” *Small* **17** (2021), 10.1002/smll.202100655.</footnote>

<footnote n="4">⁴D. A. Ryndyk, “Electron-Electron Interaction and Coulomb Blockade,” in *Theory of Quantum Transport at Nanoscale*, Vol. 184 (Springer International Publishing, Cham, 2016) pp. 123–147.</footnote>

<footnote n="5">⁵A. Keller, J. Lim, D. Sánchez, R. López, S. Amasha, J. Katine, H. Shtrikman, and D. Goldhaber-Gordon, “Cotunneling Drag Effect in Coulomb-Coupled Quantum Dots,” *Physical Review Letters* **117** (2016), 10.1103/PhysRevLett.117.066602.</footnote>

<footnote n="6">⁶E. Burzurí, Y. Yamamoto, M. Warnock, X. Zhong, K. Park, A. Cornia, and H. S. J. van der Zant, “Franck–condon blockade in a single-molecule transistor,” *14*, 3191–3196 (2014).</footnote>

<footnote n="7">⁷M. Ganzhorn, S. Klyatskaya, M. Ruben, and W. Wernsdorfer, “Strong spin–phonon coupling between a single-molecule magnet and a carbon nanotube nanoelectromechanical system,” *8*, 165–169 (2013).</footnote>

<footnote n="8">⁸J. J. Parks, A. R. Champagne, T. A. Costi, W. W. Shum, A. N. Pasupathy, E. Neuscamman, S. Flores-Torres, P. S. Cornaglia, A. A. Aligia, C. A. Balseiro, G. K.-L. Chan, H. D. Abruña, and D. C. Ralph, “Mechanical control of spin states in spin-1 molecules and the underscreened kondo effect,” *328*, 1370–1373 (2010).</footnote>
⁹T. Miyamachi, M. Gruber, V. Davesne, M. Bowen, S. Boukari, L. Joly, F. Scheurer, G. Rogez, T. K. Yamada, P. Ohresser, E. Beaurepaire, and W. Wulfhekel, “Robust spin crossover and memristance across a single molecule,” *Nature Communications* **3**, 938 (2012).

¹⁰S. J. van der Molen and P. Liljeroth, “Charge transport through molecular switches,” **22**, 133001 (2010).

¹¹D. Secker, S. Wagner, S. Ballmann, R. Härtle, M. Thoss, and H. B. Weber, “Resonant Vibrations, Peak Broadening, and Noise in Single Molecule Contacts: The Nature of the First Conductance Peak,” *Physical Review Letters* **106** (2011), 10.1103/Phys-RevLett.106.136807.

¹²P. Busz, D. Tomaszewski, J. Barnaś, and J. Martinek, “Hanle effect in transport through single atoms in spin-polarized stm,” *Journal of Magnetism and Magnetic Materials* **588**, 171465 (2023).

¹³S. Caneva, P. Gehring, V. M. García-Suárez, A. García-Fuente, D. Stefani, I. J. Olavarria-Contreras, J. Ferrer, C. Dekker, and H. S. J. van der Zant, “Mechanically controlled quantum interference in graphene break junctions,” *Nature Nanotechnology* **13**, 1126–1131 (2018).

¹⁴C. J. Lambert, “Basic concepts of quantum interference and electron transport in single-molecule electronics,” *Chemical Society Reviews* **44**, 875–888 (2015).

¹⁵Y.-J. Zeng, D. Wu, X.-H. Cao, Y.-X. Feng, L.-M. Tang, and K.-Q. Chen, “Significantly enhanced thermoelectric performance of molecular junctions by the twist angle dependent phonon interference effect,” **8**, 11884–11891 (2020).

¹⁶J. E. Greenwald, J. Cameron, N. J. Findlay, T. Fu, S.GNasekaran, P. J. Skabara, and L. Venkataraman, “Highly nonlinear transport across single-molecule junctions via destructive quantum interference,” **16**, 313–317 (2020).

¹⁷C. Barraud, K. Bouzehouane, C. Deranlot, D. J. Kim, R. Rakshit, S. Shi, J. Arabski, M. Bowen, E. Beaurepaire, S. Boukari, F. Petroff, P. Seneor, and R. Mattana, “Phthalocyanine based molecular spintronic devices,” *Dalton Transactions* **45**, 16694–16699 (2016).

¹⁸K. Katcko, E. Urbain, F. Ngassam, L. Kandpal, B. Chowrira, F. Schleicher, U. Halisdemir, D. Wang, T. Scherer, D. Mertz, B. Leconte, N. Beyer, D. Spor, P. Panissod, A. Boulard, J. Arabski, C. Kieber, E. Sternitzky, V. Da Costa, M. Hehn, F. Montaigne, A. Bahouka, W. Weber, E. Beaurepaire, C. Kübel, D. Lacour, M. Alouani, S. Boukari, and M. Bowen, “Encoding Information on the Excited State of a Molecular Spin Chain,” *Advanced Functional Materials* **31**, 2009467 (2021).

¹⁹A. D. Kent and D. C. Worledge, “A new spin on magnetic memories,” *Nature Nanotechnology* **10**, 187–191 (2015).

²⁰A. Hirohata, K. Yamada, Y. Nakatani, I.-L. Prejbeanu, B. Diény, P. Pirro, and B. Hillebrands, “Review on spintronics: Principles and device applications,” *Journal of Magnetism and Magnetic Materials* **509**, 166711 (2020).

²¹W. A. Borders, A. Z. Pervaiz, S. Fukami, K. Y. Camsari, H. Ohno, and S. Datta, “Integer factorization using stochastic magnetic tunnel junctions,” *Nature* **573**, 390–393 (2019).

²²X. Chen, J. Zhang, and J. Xiao, “Magnetic-tunnel-junction-based true random-number generator with enhanced generation rate,” *Physical Review Applied* **18** (2022), 10.1103/physrevap-plied.18.1021002.

²³J. Torrejon, M. Riou, F. A. Araujo, S. Tsunegi, G. Khalsa, D. Querlioz, P. Bortolotti, V. Cros, K. Yakushiji, A. Fukushima, H. Kubota, S. Yuasa, M. D. Stiles, and J. Grollier, “Neuromorphic computing with nanoscale spintronic oscillators,” *Nature* **547**, 428–431 (2017).

²⁴L. Zhang, B. Fang, J. Cai, M. Carpentieri, V. Puliafito, F. Garesci, P. K. Amiri, G. Finocchio, and Z. Zeng, “Ultrahigh detection sensitivity exceeding 10⁵ V/W in spin-torque diode,” *Applied Physics Letters* **113**, 102401 (2018).

²⁵H. R. Zeller and I. Giaever, “ Tunneling, Zero-Bias Anomalies, and Small Superconductors,” *Physical Review* **181**, 789–799 (1969).

²⁶M. Bowen, J.-L. Maurice, A. Barthélémy, P. Prod’homme, E. Jacquet, J.-P. Contour, D. Imhoff, and C. Colliex, “Bias-crafted magnetic tunnel junctions with bistable spin-dependent states,” *Applied Physics Letters* **89**, 103517 (2006).

²⁷D. Halley, H. Majjad, M. Bowen, N. Najjari, Y. Henry, C. Ulhaq-Bouillet, W. Weber, G. Bertoni, J. Verbeeck, and G. Van Tendeloo, “Electrical switching in Fe/Cr/MgO/Fe magnetic tunnel junctions,” *Applied Physics Letters* **92**, 212115 (2008).

²⁸R. Guerrero, F. G. Aliev, R. Villar, T. Santos, and J. Moodera, “Low frequency noise in Co/Al2O3(Si)/Py magnetic tunnel junctions,” *physica status solidi* (a) **205**, 1040–1042 (2008).

²⁹N. Najjari, D. Halley, M. Bowen, H. Majjad, Y. Henry, and B. Doudin, “Electrical switching in Fe/V/MgO/Fe tunnel junctions,” *Physical Review B* **81** (2010), 10.1103/Phys-RevB.81.174425.

³⁰C.-Y. Chen, B.-H. Huang, Y.-H. Tang, C. Gonzalez-Ruano, F. G. Aliev, D.-C. Ling, and J.-Y. Hong, “Stochastic Nature of Voltage-Controlled Charge Dynamics in AlOx Magnetic Tunnel Junctions,” *Nano Letters* **25**, 11776–11781 (2025).

³¹P. P. Freitas, R. Ferreira, S. Cardoso, and F. Cardoso, “Magnetoresistive sensors,” *Journal of Physics-Condensed Matter* **19** (2007), 10.1088/0953-8984/19/16/165221.

³²Y. Lu, M. Tran, H. Jaffrès, P. Seneor, C. Deranlot, F. Petroff, J.-M. George, B. Lépine, S. Ababou, and G. Jézéquel, “Spin-Polarized Inelastic Tunneling through Insulating Barriers,” *Physical Review Letters* **102**, 176801 (2009).

³³F. Schleicher, U. Halisdemir, D. Lacour, M. Gallart, S. Boukari, G. Schmerber, V. Davesne, P. Panissod, D. Halley, H. Majjad, Y. Henry, B. Leconte, A. Boulard, D. Spor, N. Beyer, C. Kieber, E. Sternitzky, O. Cregut, M. Ziegler, F. Montaigne, E. Beaurepaire, P. Gilliot, M. Hehn, and M. Bowen, “Localized states in advanced dielectrics from the vantage of spin- and symmetry-polarized tunnelling across MgO,” *Nature Communications* **5** (2014), 10.1038/ncomms5547.

³⁴M. Studniarek, U. Halisdemir, F. Schleicher, B. Taudul, E. Urbain, S. Boukari, M. Hervé, C.-H. Lambert, A. Hamadeh, S. Petit-Watelot, O. Zill, D. Lacour, L. Joly, F. Scheurer, G. Schmerber, V. D. Costa, A. Dixit, P. A. Guitard, M. Acosta, F. Leduc, F. Choueikani, E. Otero, W. Wulfhekel, F. Montaigne, E. N. Monteblanco, J. Arabski, P. Ohresser, E. Beaurepaire, W. Weber, M. Alouani, M. Hehn, and M. Bowen, “Probing a device’s active atoms,” *Advanced Materials* **29**, 1606578 (2017).

³⁵F. Schleicher, B. Taudul, U. Halisdemir, K. Katcko, E. Monteblanco, D. Lacour, S. Boukari, F. Montaigne, E. Urbain, L. M. Kandpal, J. Arabski, W. Weber, E. Beaurepaire, M. Hehn, M. Alouani, and M. Bowen, “Consolidated picture of tunnelling spintronics across oxygen vacancy states in MgO,” *Journal of Physics D: Applied Physics* **52**, 305302 (2019).

³⁶L. M. Kandpal, B. Taudul, E. Monteblanco, A. Kumar, K. Katcko, F. Schleicher, P. Gupta, S. Boukari, W. Weber, V. Da Costa, J. D. Costa, T. Böhnert, R. Ferreira, P. Freitas, M. Hehn, M. Alouani, P. K. Muduli, D. Lacour, and M. Bowen, “Oxygen vacancy-driven spin-transfer torque across MgO magnetic tunnel junctions,” *npj Spintronics* **3**, 1–7 (2025).

³⁷D. J. Kim, W. S. Choi, F. Schleicher, R. H. Shin, S. Boukari, V. Davesne, C. Kieber, J. Arabski, G. Schmerber, E. Beaurepaire, W. Jo, and M. Bowen, “Control of defect-mediated tunneling barrier heights in ultrathin MgO films,” *Applied Physics Letters* **97**, 263502 (2010).

³⁸F. Schleicher, U. Halisdemir, E. Urbain, D. Lacour, M. Gallart, S. Boukari, F. Montaigne, E. Beaurepaire, P. Gilliot, M. Hehn, and M. Bowen, “MgO magnetic tunnel junctions of enduring F-type upon annealing,” *Journal of Physics D: Applied Physics* **48**, 435004 (2015).

³⁹B. Taudul, E. N. Monteblanco, U. Halisdemir, D. Lacour, F. Schleicher, F. Montaigne, E. Beaurepaire, S. Boukari, M. Hehn, M. Alouani, and M. Bowen, “Tunneling Spintronics across MgO Driven by Double Oxygen Vacancies,” *Advanced Electronic Materials* **3**, 1600390 (2017).
⁴⁰K. Katcko, E. Urbain, B. Taudul, F. Schleicher, J. Arabinski, E. Beaurepaire, B. Vileno, D. Spor, W. Weber, D. Lacour, S. Boukari, M. Hehn, M. Alouani, J. Fransson, and M. Bowen, “Spin-driven electrical power generation at room temperature,” *Communications Physics* **2** (2019), 10.1038/s42005-019-0207-8.

⁴¹V. Da Costa, C. Tiusan, T. Dimopoulos, and K. Ounadjela, “Tunneling phenomena as a probe to investigate atomic scale fluctuations in metal/oxide/metal magnetic tunnel junctions,” *Physical Review Letters* **85**, 876–879 (2000).

⁴²Z. Wang, H. Wu, G. W. Burr, C. S. Hwang, K. L. Wang, Q. Xia, and J. J. Yang, “Resistive switching materials for information processing,” *Nature Reviews Materials* **5**, 173–195 (2020).

⁴³S. Slesazeck and T. Mikolajick, “Nanoscale resistive switching memory devices: a review,” *Nanotechnology* **30**, 352003 (2019).

⁴⁴C. Jia, A. Migliore, N. Xin, S. Huang, J. Wang, Q. Yang, S. Wang, H. Chen, D. Wang, B. Feng, Z. Liu, G. Zhang, D.-H. Qu, H. Tian, M. A. Ratner, H. Q. Xu, A. Nitzan, and X. Guo, “Covalently bonded single-molecule junctions with stable and reversible photoswitched conductivity,” *Science* **352**, 1443–1445 (2016).

⁴⁵E. Lörtscher, J. Ciszek, J. Tour, and H. Riel, “Reversible and controllable switching of a single-molecule junction,” *2*, 973–977 (2006).

⁴⁶F. Schwarz, G. Kastlunger, F. Lissel, C. Egler-Lucas, S. N. Semenov, K. Venkatesan, H. Berke, R. Stadler, and E. Lörtscher, “Field-induced conductance switching by charge-state alternation in organometallic single-molecule junctions,” *Nature Nanotechnology* **11**, 170–176 (2016).

⁴⁷S. W. Wu, N. Ogawa, G. V. Nazin, and W. Ho, “Conductance Hysteresis and Switching in a Single-Molecule Junction,” *The Journal of Physical Chemistry C* **112**, 5241–5244 (2008).

⁴⁸T. Leoni, O. Guillermet, H. Walch, V. Langlais, A. Scheuermann, J. Bonvoisin, and S. Gauthier, “Controlling the Charge State of a Single Redox Molecular Switch,” *Physical Review Letters* **106** (2011), 10.1103/PhysRevLett.106.216103.

⁴⁹L. Gerhard, K. Edelmann, J. Homberg, M. Valášek, S. G. Bahoosh, M. Lukas, F. Pauly, M. Mayor, and W. Wulfhekel, “An electrically actuated molecular toggle switch,” *Nature Communications* **8**, 14672 (2017).

⁵⁰L. Zhang, T. Yang, W. Zhang, D. Qi, X. He, K. Xing, P. K. J. Wong, Y. P. Feng, and A. T. S. Wee, “Bi-stable electronic states of cobalt phthalocyanine molecules on two-dimensional vanadium diselenide,” *Applied Materials Today* **18**, 100535 (2020).

⁵¹D. E. Grupp, T. Zhang, G. J. Dolan, and N. S. Wingreen, “Dynamical offset charges in single-electron transistors,” *Physical Review Letters* **87** (2001), 10.1103/physrevlett.87.186805.

⁵²Z. Li, M. Sotto, F. Liu, M. K. Husain, H. Yoshimoto, Y. Sasago, D. Hisamoto, I. Tomita, Y. Tsuchiya, and S. Saito, “Random telegraph noise from resonant tunnelling at low temperatures,” *Scientific Reports* **8** (2018), 10.1038/s41598-017-18579-1.

⁵³A more complicated explanation might involve two different energy levels located on the same quantum dot.

⁵⁴T. Grasser, “Stochastic charge trapping in oxides: From random telegraph noise to bias temperature instabilities,” *Microelectronics Reliability* **52**, 39–70 (2012).

⁵⁵S. Guo, R. Wang, D. Mao, Y. Wang, and R. Huang, “Anomalous random telegraph noise in nanoscale transistors as direct evidence of two metastable states of oxide traps,” *Scientific Reports* **7** (2017), 10.1038/s41598-017-06467-7.

⁵⁶M. Cowie, P. C. Constantinou, N. J. Curson, T. J. Z. Stock, and P. Grütter, “Spatially resolved random telegraph fluctuations of a single trap at the si/sio2 interface,” *Proceedings of the National Academy of Sciences* **121** (2024), 10.1073/pnas.2404456121.

⁵⁷U. Ghosh, A. Bhaumik, N. Vasudeva, and A. Pandey, “Granular memristors with tunable stochasticity,” *Nanoscale* **17**, 1238–1245 (2025).

⁵⁸J. P. Fried, X. Bian, J. L. Swett, I. I. Kravchenko, G. A. D. Briggs, and J. A. Mol, “Large amplitude charge noise and random telegraph fluctuations in room-temperature graphene single-electron transistors,” *Nanoscale* **12**, 871–876 (2020).

⁵⁹P. Belardinelli, W. Yang, A. Bachtold, M. I. Dykman, and F. Alljani, “Hidden vibrational bistability revealed by intrinsic fluctuations of a carbon nanotube,” *Nano Letters* **25**, 8443–8449 (2025).

⁶⁰C.-Y. Chen, C. Gonzalez-Ruano, I. Martinez, F. G. Aliev, D.-C. Ling, Y.-H. Tang, and J.-Y. Hong, “Bias polarity dependent low-frequency noise in ultra-thin alox-based magnetic tunnel junctions,” *Scientific Reports* **14** (2024), 10.1038/s41598-024-59675-3.

⁶¹J. Koch, F. von Oppen, and A. V. Andreev, “Theory of the Franck-Condon blockade regime,” *Physical Review B* **74** (2006), 10.1103/PhysRevB.74.205438.

⁶²M. Galperin, M. A. Ratner, and A. Nitzan, “Molecular transport junctions: vibrational effects,” *Journal of Physics: Condensed Matter* **19**, 103201 (2007).

⁶³D. Mozyrsky, M. B. Hastings, and I. Martin, “Intermittent polaron dynamics: Born-Oppenheimer approximation out of equilibrium,” *Physical Review B* **73** (2006), 10.1103/PhysRevB.73.035104.

⁶⁴M. Galperin, M. A. Ratner, and A. Nitzan, “Hysteresis, Switching, and Negative Differential Resistance in Molecular Junctions: A Polaron Model,” *Nano Letters* **5**, 125–130 (2005).

⁶⁵M. Wierzbicki and R. Swirkowicz, “Influence of interference effects on thermoelectric properties of double quantum dots,” *Physical Review B* **84** (2011), 10.1103/PhysRevB.84.075410.

⁶⁶S. W. Wu, G. V. Nazin, X. Chen, X. H. Qiu, and W. Ho, “Control of Relative Tunneling Rates in Single Molecule Bipolar Electron Transport,” *Physical Review Letters* **93** (2004), 10.1103/PhysRevLett.93.236802.

⁶⁷B. Chowrira, L. Kandpal, M. Lamblin, F. Ngassam, C. Kouakou, T. Zafar, D. Mertz, B. Vileno, C. Kieber, G. Versini, B. Gobaut, L. Joly, T. Ferté, E. Monteblanco, A. Bahouka, R. Bernard, S. Mohapatra, H. Prima Garcia, S. Elidrissi, M. Gavara, E. Sternitzky, V. Da Costa, M. Hehn, F. Montaigne, F. Choueikani, P. Ohresser, D. Lacour, W. Weber, S. Boukari, M. Alouani, and M. Bowen, “Quantum advantage in a molecular spintronic engine that harvests thermal fluctuation energy,” *Advanced Materials* **34** (2022), 10.1002/adma.202206688.

⁶⁸Q. Xiang, H. Sukegawa, M. Belmoubarik, M. Al-Mahdawi, T. Scheike, S. Kasai, Y. Miura, and S. Mitani, “Realizing room-temperature resonant tunnel magnetoresistance in cr/fe/mgmal2o4 quasi-quantum well structures,” *Advanced Science* **6** (2019), 10.1002/advs.201901438.

⁶⁹R. Suzuki, Y. Tadano, L. D. Anh, M. Tanaka, and S. Ohya, “Unconventional bias dependence of tunnel magnetoresistance induced by the Coulomb blockade effect,” *AIP Advances* **11**, 125029 (2021).

⁷⁰J. Barnaś and A. Fert, “Effects of spin accumulation on single-electron tunneling in a double ferromagnetic microjunction,” *Europhysics Letters* **44**, 85 (1998).

⁷¹M. Misiorny and I. Weymann, “Transverse anisotropy effects on spin-resolved transport through large-spin molecules,” *Physical Review B* **90** (2014), 10.1103/PhysRevB.90.235409.

⁷²A. Plomińska and I. Weymann, “Magnetoresistive properties of a double magnetic molecule spin valve in different geometrical arrangements,” *Journal of Magnetism and Magnetic Materials* **480**, 11–21 (2019).

⁷³J. Leliaert, B. Van de Wiele, A. Vansteenkiste, L. Laurson, G. Durin, L. Dupré, and B. Van Waeyenberge, “Current-driven domain wall mobility in polycrystalline permalloy nanowires: A numerical study,” *Journal of Applied Physics* **115**, 233903 (2014).

⁷⁴A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, and B. Van Waeyenberge, “The design and verification of Mumax3,” *AIP Advances* **4**, 107133 (2014).

⁷⁵B. Chowrira, *Exploring the nano-transport paths across spintronic devices for information enconding and energy harvesting*, Ph.D. thesis, Strasbourg University (2021).

⁷⁶M. Bowen, “Atom-level electronic physicists are needed to develop practical engines with a quantum advantage,” *npj Quantum Information* **9**, 25 (2023).
<figure><img src="image_7.png" /><figcaption>TOC Figure</figcaption></figure>
SUPPORTING INFORMATION

MgO tunneling spintronics across capacitively-coupled
atomic clusters

Mathieu Lamblin¹, Victor Da Costa¹, Loic Joly¹, Bhavishya Chowrira¹, Léo Petitdemange²,
Bertrand Vileno³, Romain Bernard¹, Benoit Gobaut¹, Samy Boukari¹, Wolfgang Weber¹, Michel
Hehn², Daniel Lacour², and Martin Bowen¹,

1) Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 CNRS, Université de Strasbourg, 23 Rue du Lœss, BP 43, 67034 Strasbourg, France

2) Institut Jean Lamour UMR 7198 CNRS Université de Lorraine BP 70239, Vandoeuvre les Nancy 54506, France

3) Institut de Chimie UMR 7177 CNRS Université de Strasbourg 4 Rue Blaise Pascal, CS 90032, Strasbourg 67081, France

**Note 1: Current plume of current noise**

We present in Sup. Fig. S1 a high-resolution dataset of the current distribution plume reported in Fig. 3 of the main text for the junction's P and AP states. We observe a positive 33mV bias shift of the AP dataset due to spin accumulation (see main text).

For each bias voltage we measured 800 times the junction current. An example is shown in panel (a).
The mean current is calculated and subtracted for all points inside the dataset, and finally a histogram is
computed with a bin size of 1 nA. The result of the histogram is represented in Sup. Fig. S1 by a vertical
line of dots at the corresponding voltage bias, the color of a dot representing the number of counts in
every bin of the histogram.
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

Sup. Fig. S1: **Zoom on the plume of current noise.** (a) Example of 800 points of raw data. Bias dependence of the frequency of the deviation from the mean current. Data at T = 10K in the MTJ's P (b) and AP (c) states is shown. Nanojunction C5 was used. Statistics are obtained on 800 points at each bias value.
<figure><img src="image_10.png" /></figure>

Sup. Fig. S2: **Spintronic contrast in the plume of current noise.** (Top) Same data as in Sup. Fig. S. 1, but with a +33 mV shift in the P data. (Bottom) Difference P-AP of the datasets of the top panel. The round dots below the lower branch represent an average of the lower branch difference data. They are centered around the range considered. These points are all blue-leaning: the lower branch is more strongly weighed in the MTJ's AP state.

To distinguish spintronic contrast, we overlap the datasets by manually removing the shift (see Fig. S2a). We note that the OFF branch (lower branch) overlaps rather well. On the other hand, the ON branch (upper branch) exhibits a different deviation from mean current in the MTJ's P and AP states. We attribute this differing deviation to a slight change in the effective potential landscape due to spin-polarized hybridization between the electrodes and the localized paramagnetic barrier states.

To further examine spintronic contrast, we then consider the difference P-AP between the datasets. The results are plotted in the bottom panel of Sup. Fig. S2. We observe that the difference is very pronounced for the OFF branch. To confirm this trend, we're integrated this difference over several bias ranges. The position of the resulting round dots below the OFF branch represents the center of the range, while the color code shows the averaged result. Over the seven bias ranges considered, all averages of the OFF branch reveal that the OFF branch is more prevalent in the MTJ's AP state. We infer that the transport path responsible for the OFF branch is spin-polarized.

The lifetimes of the OFF, MID and ON branches are discussed in Note 10.
Note 2: Spin accumulation at negative bias

<figure><img src="image_11.png" /></figure>

Sup. Fig. S3: **Spin accumulation on the sharpest conductance peak found at V<0. Bias dependence of differential conductance dI/dV at T= 10 K on junction G10 in the MTJ's P (black) and AP (red) states. the AP data in green was bias-shifted by +0.35 mV. This shift enables a qualitatively good overlap of the conductance peak with that seen in the P data. Inset: Overview of the conductance peak in the MTJ's P state, and the bias-shifted AP data.**

In the main text, we present evidence at V>0 of a shift to higher bias values of the conductance peaks when the MTJ's magnetic state is switched from P to AP. We now consider the case of V<0, and focus on the conductance peak shown in Sup. Fig. S3. Its presence can also be switched on/off thanks to writing events E+ and E-, leading to different values of TMR at that bias position (see Fig. 2 of the main text). The data of Sup. Fig. S3 is acquired within -100 < V (mV) < 0, i.e. below the writing events E- and E+ (see inset). An excellent overlap between the P and AP data is seen for bias value below the peak. However, as the peak onset is reached, a bias shift is clearly seen. The very close agreement in the data for the forward and reverse scans underscores that the shift is not the result of trivial charging/heating effects. To qualitatively estimate the small bias shift between the P and AP data, we manually shift the AP data. A reasonable fit is found for a bias shift of 0.35 mV.
Note 3: Statistics on the hysteretic effect

<figure><img src="image_12.png" /></figure>

Sup. Fig. S4: **Overview of the hysteretic voltage shift.** (left) Differential conductance dI/dV vs. bias voltage on junction G10 at 10K. Successive data branches are shifted by 2µS. The E+ and E- writing events cause a shift Δ<sub>W</sub>=73 mV in the constant voltage gap Δ<sub>CG</sub>=310 mV. (Right) Proposed energy diagram of the readout QD in the two E- and E+ states. The justification is provided in the discussion to Sup. Fig. S8.

In the main text, we discuss how current jumps can displace the bias position of pairs of peaks at positive and negative voltages. In this note, we consider the statistics of this electric field-induced voltage shift of the conductance figure. To do so, we first plot an overview of the hysteretic effect in Sup. Fig. S4. We observe that successive forward and reverse branches reveal a set of two conductance peaks separated by the same Δ<sub>CG</sub> = 310 mV. The E+ and E- writing events cause a shift Δ<sub>W</sub>=73 mV in this pair of conductance peaks.
<figure><img src="image_13.png" /><figcaption>Sup. Fig. S5: **Protocol to test junction state writing.** (a) Examples of IV traces showing E- write events that are (top) apparent, with 1 write peak observed, and (bottom) not apparent, i.e. with no write peak observed. (b) Corresponding readouts, with (top) confirmation and (bottom) information that the E-event-driven junction state was written.</figcaption></figure>

To obtain statistical data on the ability to write a junction state, we undertook 1357 measurements on junction C5 at 10 K. Examples of the write and read protocols are shown in Fig. S5. In general, attempting to activate the E- write event at negative bias generates a 81% success rate in the readout at positive bias. As we explain later, this success rate would likely increase if the maximum voltage of the writing IV protocol had been increased.

<figure><img src="image_14.png" /><figcaption>Sup. Fig. S6: **Statistics on the success and failure to write the junction state.** The repeated protocol shown in SI Fig. S5 was used. The statistics are shown as a function of the number of current jumps during the Write current sweep.</figcaption></figure>
Referring to Sup. Fig. S6, we note that the failure to write event E- in the MTJ's P state occurs mostly for one current jump, whereas it is spread over 0-2 jumps for the AP state. There are many AP write attempts without a current jump. Furthermore, for both P and AP MTJ states, cases with an odd number of current jumps dominate even cases.

<table><caption>Sup. Table S1: Statistics of write success/failure according to the sequence of absolute current increase (P) and decrease (N).</caption><thead><tr><th>Current Jump sequence (1<sup>st</sup> ... Last)</th><th>Write Failed: # events</th><th>Write OK: # events</th><th>Write Success (%)</th></tr></thead><tbody><tr><td>PN</td><td>57</td><td>93</td><td>62</td></tr><tr><td>PNPN</td><td>14</td><td>20</td><td>59</td></tr><tr><td>PNPNPN</td><td>2</td><td>2</td><td>50</td></tr><tr><td>P</td><td>88</td><td>548</td><td>86</td></tr><tr><td>PNP</td><td>32</td><td>271</td><td>89</td></tr><tr><td>PNPNP</td><td>5</td><td>43</td><td>90</td></tr><tr><td>PNPNPNP</td><td>1</td><td>4</td><td>80</td></tr><tr><td>No jump</td><td>39</td><td>37</td><td>49</td></tr></tbody></table>

To obtain more insight, we examine the sign of current change and current peak sequences in the entire dataset. We observe that:

- if there is a peak, the first peak is always P. This means that the first current jump is always to more negative current values.

- the sign of succeeding current peaks is always opposite, i.e. there isn't a single PP or NN sequence or subsequence in our entire dataset.

- an odd number of current jumps (i.e. ending in P) has an overall success rate of 87%. This decreases to 61% for an even number of jumps (i.e. ending in N).
<figure><img src="image_15.png" /></figure>

Sup. Fig. S7: **Spectroscopy of current jumps.** Bias dependence of the frequency of a current jump when the writing event (a) fails and (b) succeeds. (c) Bias dependence of junction conductance when no current jump was observed. The average of 60 AP datasets is shown.

We compare in Sup. Fig. S7 the bias dependencies of the baseline $dl/dV$ for the junction's E+ state (i.e. without a current jump / conductance peak), and of the current jump event frequency. We observe that
almost all current jump events occur within the bias range at which a clear conductance increase is observed. We note that the successful write events mimic most closely this dependence/amplitude, while the failed current increase events occur mainly near the peak height. Conversely, very few current jumps, whether successful or not in promoting the E- writing event, are found within the -0.242 < Bias (V) < -0.188 range that exhibits transport noise. We conclude that, for this junction state, the E- writing event begins with the charging of the transport quantum dot, and not with a charging of the environmental quantum dot.

<figure><img src="image_16.png" /><figcaption>Sup. Fig. S8: **Origin of transport noise prior to E- event.** (a) dI/dV traces in E+ state prior to E- event. Data with no current peak was chosen. The use of the log scale removes negative jumps. The average of 60 scans in the AP MTJ state were used. (b) dI/dV in E- state. Arrows indicate the direction of data acquisition.</figcaption></figure>

We plot in Sup. Fig. S8(a) dI/dV traces before the E- event, for which no current peak occurs. We observe an exponential increase in junction conductance starting from V = 0, up to the onset of the very noisy -0.242 < Bias (V) < -0.188 range (red line). Assuming that the conductance exponential increase was to remain the same across this noise range, we see that the conductance at V = 0.242 V would be half that measured (straight red line). We conclude that, in this particular junction state, the quantum interference transport between the readout quantum dot and the environmental quantum dot generates a net increase in current, i.e. that the 'gating' QD participates in transport through higher-order processes.

To verify that readout and environmental QDs with a fortuitously voltage gap (see Sup. Fig. S4(a)) are not simply trading roles in the E- and E+ events, we plot in panel (b) the dI/dV trace after a successful E-write event. We see that this trace's conductance peak does not have a bias range that matches that for the noise seen in panel (a). Furthermore, the two spectral features do not have the same bias extent.
This suggests that the E- and E+ events do not promote different readout QDs, but that the same QD remains as readout, but with an energy landscape that is shifted by the charging of the 'gating' QD (see Sup. Fig. S4(b)). The bias extent and noise envelope of this environmental QD resembles the conductance peak of QD B, but with a +35meV energy shift.

Note 4: Overview of the voltage gaps with evolving junction state and argumentation for 'transport' and 'gating' quantum dots

<figure><img src="image_17.png" /><figcaption>Sup. Fig. S9: **Overview of voltage gap energies with evolving junction state.** (a) Select dI/dV traces for three cooldowns. (b) (top) Endpoints of the voltage gap for select datasets deduced from the bias spacing of pairs of conductance peaks. (bottom) The resulting energy gap of the transport atom. Junction G10 was used. The data from four cooldowns was used.</figcaption></figure>

In our datasets, we observe that heating/cooling our FeCoB/MgO/C/MgO/FeCoB junctions, and bias
cycling, can alter the effective potential landscape inferred at T=10 K from the current derivative. To
illustrate these effects, we focus on junction G10. We plot in Sup. Fig. S9(a) select dI/dV traces obtained
after three cooldowns. We have looked for a pattern of pairs of peaks with the same energy spacing as
thermal and electrical cycling were conducted. This led us to label pairs of peaks and ascribe them to the
charging of a given C atom. In total we identify at least 3, and as many as 5, QDs involved in the device's
electrical response. As described in the main text, these QDs can be in the main transport path. In that
case, charging the atom generates a conduction peak. Alternately, the atom in question can be tunnel
coupled to a C QD that is in the transport path, and thus constitutes an 'gating' QD. Following the
deductions of Sup. Fig. S9 and accompanying text, we assumed that energy motion of a pair of peaks
was due to changes in the environmental charge felt by the 'transport' QD, rather than the reattribution
of 'transport' and 'gating' roles. This logic is supported by the fairly stable energy gap between the
paired peaks (see Sup. Fig. S9(b)).
Using this labeling logic, we find for example, for cooldown #9, that pairs of conductance peaks can be attributed to the same carbon nanodot A, and that, in the course of IV cycling, three absolute energy positions of its voltage gap (see labels A1-, A2-, A3- and A1+, A2+ and A3+ in Sup. Fig. S9(a)) relative to the MTJ electrodes' Fermi level can be tracked as the environmental charge is varied through write events E+ and E- (see main Text). Note how after an E+ writing event the pair of peaks shifts to lower absolute bias. The reverse occurs for an E- writing event. This trend in the bias shift was systematically observed, when a shift indeed occurred (see SI Note 2).

We observe additional conductance peaks at higher absolute bias voltage. In the absence of a clear trend suggesting additional charging of nanodot A, we surmise that these peaks correspond to additional atoms (C, D...) directly in the transport path.

Comparing these cooldowns, we observe that the peak of a dI/dV in one cooldown can spectrally correspond to noise for another cooldown. The best example is, at V ~ -190 mV, that of peak B- in cooldown 2 (black), and of the corresponding noise nB- in cooldown 9 (blue). We infer that atom B is present in the transport path in cooldown 2, but becomes an environmental atom in cooldown 9. This also explains the absence of peaks B- and B+ in cooldowns 3 and 9.

We also observe that, in the junction state defined by cooldowns 3 and 9, the writing event E+ occurs just as the spectral window B+ corresponding to environmental atom B is reached with increasing positive bias around +150 mV. This illustrates the role that the charge state of environmental atom has in the junction write process (see main text).

<figure><img src="image_18.png" /><figcaption>Sup. Fig. S10: **Quantization of the energy shift of the transport atom's voltage gap.** Absolute values are shown.</figcaption></figure>

Within the junction state defined by a cooldown, writing events E- and E+ generate an effective bias shift that can be quantized. A ~75meV shift was observed on transport atom A during the 1357 tests of the E- and E+ event after cooldown 10 (see SI Note 2). A shift of 111meV was observed on atom B in a
transport role, However, those junction states promoted only two pairs of peaks. We present in Sup. Fig. S10 the energy shift $\Delta_w$ data in junction cooldown 9 arising from the presence of 3 pairs of peaks due to transport atom A. Aside from the trivial $\Delta_w = 0$ points due to write failure (see SI Note 2), $\Delta_w$ takes on multiple values of 70-80 meV. Here, we make the reasonable assumption that the charge of an environmental atom can only change by 1 electron, which implies that several environmental atoms can be charged during a write event.

Overall, these data and discussion are consistent with the following picture of the number of nanodots within the transport path(s) of a MgO:C MTJ with 3.2nm barrier thickness and 20 microns in diameter:

- Given how we delta-doped the MgO layer with C, it is reasonable to consider, when discussing the AFM data, that each hotspot that is observed be the result of a single C nanodot.

- As we wrote in the main text: "Since quantum mechanical tunneling scales exponentially with the barrier's spatial width and energy height, the most prominent hotspot will funnel all the current across a microscale tunnel junction, as schematized in Fig. 1(a)." This means that, unless several hotspots share the highest transmission, that MTJ transport will proceed across a single C nanodot.

- In our above discussion, we argue that we are able, by tracking the noise regions in IV data across our junction measurements, to extract an estimate of up to 5 nanodots that can contribute to transport given the junction state. This might be interpreted in terms of the presence of up to 5 hotspots with 'similar' characteristics, such that depending on junction history, one may dominate the others when the junction is in a given state.

**Note 5: Estimation of the impurity's sizes and distances**

Transport across defects in ultrathin oxide tunnel barriers [1-3] can include conductance peaks at zero bias due to surface states at the Fermi level [1] (Zero-Bias Anomaly [4-6]), the prediction of conductance peaks resulting from resonant tunneling through oxygen vacancies [2] and random telegraphic noise (RTN) [31] generated by charge trapping [3,8] or magnetic domain switching [9,10] (see also SI Note 6). However, this literature on transport across vertical pillar devices yields an insight that is generally limited by conjecture as to the precise origin of the localized states.

These transport features are also ubiquitous in nanoscale devices with discrete energy levels such as single-electron transistors (SET) [11,12], molecular junctions [13-16] and scanning tunneling microscopy (STM) experiments [15].
The phenomenon of resistive switching is typically attributed to charge trapping [17,18], tunnel magnetoresistance [19,20], redox and ionic migration (especially of oxygen vacancies) [18,21], ferroelectric polarization switching [19] or phase changes [19]. The last two are very unlikely given the chemical composition of the sample. While O²⁻ electromigration across transition metal oxides can explain resistive switching [21], and has been considered as the cause of hysteretic switches observed between two resistance states in nanoscale oxide MTJs [22], the ionic nature of MgO and low electric fields and temperature here energetically preclude [23,24] this explanation for the writing events. Similarly, since this effect is only weakly impacted by the magnetic field, switching by spin-transfer or spin-orbit torque seems improbable [20].

These arguments thus support a description of conduction through a 'transport' impurity (TQD) directly involved in the flow of current, capacitively coupled to a 'gating' impurity (GQD) whose charge can be electrically modified. This electron/hole trap thus results in a lift of the TQD energy level when a charge is added/removed, such as it triggers this resistive switching effect. Let us then estimate the sizes of the impurities and their distance.

Let us approximate the impurity involved in transport as Ref. 25 a sphere of radius $r$, located at a distance $d$ from the lower electrode, with interelectrode spacing $l$. In the far-field limit, the capacitance $C$ is given in Ref. 25 and reads:

$$C = \frac{4\pi\epsilon\epsilon_0 r}{1 + (\psi^{(0)}(\frac{d}{l}) + \psi^{(0)}(1 - \frac{d}{l}) + 2\gamma)\frac{r}{2l}},$$

where $\psi^{(0)}$ is the polygamma function. Using the relation between the capacitance and the charging energy $E_C = e^2/2C = e\Delta_{CG}$, we obtain the radius of the impurity

$$r = \frac{l}{8\pi\epsilon\epsilon_0\Delta_{CG}/e + 5/3}$$

where $\frac{1}{2}(\psi^{(0)}(d/l) + \psi^{(0)}(1 - d/l) + 2\gamma) \approx -5/3$ with $d = 1$ nm and $l = 3$ nm as approximated from the experimental design of the stack. Taking $\epsilon = 9$ for the relative permittivity of MgO according to Ref. 26, we obtain $r = 0.2$ nm. This shows that the impurities involved in the transport are of atomic sizes and could indeed correspond to single carbon atoms or dimers trapped inside the MgO lattice.

Let us now approximate both the transport and gating quantum dots as two spheres of radius $r$, separated by a distance $d$. The capacitance $C$ of the system is approximately given by:

$$C = \frac{2\pi\epsilon_0\epsilon r}{1 - \frac{r}{d}r}$$

According to the observed shift $\Delta_W = 70$ mV which shall be due to the change of charge of one environmental quantum dot by a quantum of elementary charge, we should then write:

$$e = C\Delta_W.$$
which leads to the distance between the dots:

$$d = r \left( 1 + \frac{1}{1 - \frac{2\pi\epsilon\epsilon_0 r \Delta_W}{e}} \right).$$

With $r = 0.2$ nm as estimated above; we obtain the following approximation:

$$d \approx 2r,$$

such as $d = 0.4$ nm. We thus find that the distance between the transport quantum dots and the charging species is of the order of the diameter of the dots, so the control dot should be a second, third or fourth neighboring site of the transport dot in the MgO lattice. This estimation confirms that we are indeed observing the interaction of a reduced number of atomic formations closely packed inside the MgO barrier which are producing single-electron effects.

## Note 6: Other junctions

<figure><img src="image_19.png" /><figcaption>Sup. Fig. S11: Magnetotransport experiments on other junctions. (a) Differential Conductance for the P (black) and AP (red) states and TMR (blue) plots at 10 K for junction F10. (b) and (c) Intensity-potential (black) and differential conductance (red) plots at 10 K and -2000 Oe for junctions B11 and B5 respectively.</figcaption></figure>

Magnetoresistive properties have also been measured on several of these junctions, of the same kind as G10 and C5 presented in the main text. SI Fig.S11(a) shows that the electrical intensity of the junction F10 differs between the P and the AP configurations of the electrodes. This results in an apparent magnetoresistance of up to 60% that is maximal around 0. The conductance plot features two singular characteristics. First, the V-shaped spike around 0 mV, referred as the Zero-Bias anomaly (ZBA) [27-29], may indicate that an impurity state close to the Fermi level is located inside the MgO barrier [30]. This ZBA seems more pronounced in the P state than in the AP state as the deviation from linearity is more present at -2000 Oe in SI Fig.S11(a). Then, the noise visible in the linear part of the conductance, above 50 mV and below 50 mV should indicate the presence of two or more states close in energy which would result in several interfering nanotransport paths. An asymmetry is also observed in this figure: at negative bias the conductance is higher than at positive bias, in particular in the AP state which suggests
that a structural asymmetry renders the electrodes nonequivalent. The drop in the junction resistance with increasing bias voltage is greater for antiparallel alignment of the magnetic electrodes than for parallel alignment which has been accounted for by spin excitations localized at the interfaces between the electrodes and the tunnel barrier [27].

Of the 58 devices which have been tested, four other junctions displayed hysteretic behaviors, similar to G10 and C5, containing branch jumps and conductance peaks (see Figure SI Fig.S11(c)) which suggests the potential reproducibility of this phenomenon. Five other junctions also presented non-linear intensity-potential characteristics (see SI Fig.S11(b)) translating into sharp conductance peaks, but without branch jumps, looking more like standard MgO junctions without Carbon inside, but with a lower magnetoresistance.

Note 7: Resistive switching and temperature dependence

<figure><img src="image_20.png" /></figure>

Sup. Fig. S12: **Temperature dependence of the resistive switching behavior.** (a) Color plot of the current as a function of the temperature and applied bias for junction G10. (b) Intensity-Voltage characteristic of junction G10 recorded at five different temperatures. Inset: occupation probability of the low (in red) and high (in black) absolute intensity branches as a function of temperature.
## Note 8: Magnetoresistance

<figure><img src="image_21.png" /></figure>

Sup. Fig. S13: **Magnetoresistance.** (a) Plot of the tunnel magnetoresistance as a function of the bias calculated from the intensity-voltage characteristic in the P and AP states of junction G10. The blue crosses represent points that have been confirmed by I(H) experiments. The TMR enhancement due to the different conductance peaks can be observed. (b) Relative intensity compared to the P state as a function of the external field for different applied bias obtained from junction G10.

## Note 9: Methods

### 1. Stack growth, MTJ processing and measurements

Glass//Ta(5)/Co(10)/IrMn(7.5)/CoFeB(4)\//MgO(0.9)/C(0.6)/MgO(1.7)/CoFeB(3)/Ta(2)/Pt(1) samples (all thicknesses in nm) were sputter-grown on Corning 1737 glass substrates [32]. Stacks were post-annealed in an in-plane magnetic field of 200 Oe for one hour at a temperature $T_o$ of 200 °C to magnetically pin the lower electrode thanks to the IrMn antiferromagnetic layer. Samples were then processed by optical lithography [33] into 20 µm-diameter MTJs, and measured on a variable-temperature magnetotransport bench using a Keithley 2636 sourcemeter. 54 junctions were tested on these samples, 35 of them were either metallic or open circuit. Among the other 19 interesting junctions, all the reported effects have been observed in several of them. 8 of them presented memristive properties with branch jumps and conductance peaks, among which at least 3 presented magnetomemristive properties correlating with the conductance, while 7 of them presented jumps and noisy behaviors typical of interferences between several nanotransport paths (see SI Note 6).
The context of this study is that our MgO MTJs without C are stable for T>150K up to 1.3V, and for 30 < T (K) < 150 up to 2V[36]. When C is inserted, our experience has shown that these junctions (memristance effects excluded) remain stable for -0.5 < Bias voltage (V) < 0.5 . Above 0.6 V, junctions can become electrically unstable and can sometimes become short-circuited. This could be due to ion migration within the junction, which can result in the formation of a conducting filament (or pinhole) [18].

## 2. Conducting tip atomic force microscopy

Local probe experiments were carried out on a Si//Ta(3)/Pt(5)/IrMn(8)/CoFeB(5)/MgO(0.4)/C(0.6)/MgO(0.6) stack using an Icon AFM (Atomic Force Microscope) from Bruker. Topography images were acquired in standard contact mode (force constant) and, simultaneously, using an additional TUNA module (Bruker), which allowed current collection via a conductive tip. A voltage bias of 10 mV was applied to conductive AFM tips (Bruker SCM-PIT-V2; PtIr-coated Si with a 3N/m elastic constant) to enable electron collection. The current amplifier gain was set to 10 pA/V.

## 3. NV center scanning magnetometry

We conducted NV scanning magnetometry using a Qzabre microscope, which integrates scanned probe microscopy and optically detected magnetic resonance. This enabled us to image the magnetic field distribution induced by the magnetic texture of the ferromagnetic bottom electrode. The electrode stack configuration is as follows: Glass//Ta(5)/Co(10)/IrMn(7.5)/CoFeB(4)/MgO(2.5)\//Pt(2.5). For this study, we employed a commercial Qzabre tip (QST-100). Scans were carried out at four different heights: 180 nm, 130 nm, 90 nm, and 60 nm. Below 60 nm, the image quality deteriorated, likely due to a fluorescence quenching effect. To simulate the stray field, we used the mumax3 code [34,35], incorporating a random spatial distribution of anisotropy direction with 50 nm magnetic grains. Our mumax3 problem will be made available upon request. Further details will be provided in a more technical paper.

## 4. Voltage shift calculation

The voltage shift between the P and AP conductance data of Fig.4(c) in the main text was calculated by doing a curve fitting of AP data over P data using a rolling window of 40 mV width, with the voltage shift as the only parameter. The fit and estimation of uncertainties were done using the LMFIT python module [31] (Non-Linear Least-Squares Minimization and Curve-Fitting). The calculated voltage shift was then defined as the voltage shift of the mean bias value within the rolling window.
Note 10: Lifetime of the current branches

<figure><img src="image_22.png" /><figcaption>Sup. Fig. S14: **Lifetime of the current branches.** Relaxation time of the OFF, ON and MID current branches, as a function of Voltage in the P state of MTJ's P state (corresponding to Figure 3.(b-c) in the main text).</figcaption></figure>

In Fig.S13. we show the average lifetimes of the the OFF, ON and MID branches of current, calculated using the time series of the current (see e.g. Fig.S1.(a)). At each voltage point, the lifetimes were calculated first by drawing a histogram of the current with 100 bins, then by locating the local maxima of this distribution (which code for the current branch), and finally by calculating the averages of the duration of each branch. Starting from on current branch, a jump to another branch was recorded whenever the current deviated by 0.2 nA from the branch average current (the current corresponding to a local maximum of the current distribution).

This Figure shows four clusters of points:

- For $|U| < 0.2$ V, and right after the current plume $0.25 < U < 0.35$ V, for most voltage points, only one branch is detected (the OFF branch) and the current stays within the tolerated deviation from the average branch current, such that the lifetime of the branch is around 20000 s, corresponding to the total duration of the recording of the time series.
Points located above $10^5$ s are thus artifacts of a state of the junction with a single branch
with a possibly infinite lifetime.

- When two or more branches are detected, the majority branch, called the OFF branch, has a lifetime clustered around $9 \times 10^4$ s.

- For $|U| < 0.5$, when two or more branches are detected, the minority branch, called the ON branch, has a lifetime clustered around 20 s.

- For $|U| > 0.5$, at least two branches are always recorded and the lifetime of the minority branch, the ON branch, gets closer to the lifetime of the OFF branch, reaching around 200 s.

- For some voltage points, a third minority branch, called the MID branch is recorded, with a lifetime similar to the ON branch around 20s.

[1] I. Rungger, A. Reily Rocha, O. Mryasov, O. Heinonen, and S. Sanvito, "Electronic transport through fe/mgo/fe(100) tunnel junctions," *Journal of Magnetism and Magnetic Materials* **316**, 481–483 (2007).

[2] J. P. Velev, M. Y. Zhuravlev, K. D. Belashchenko, S. S. Jaswal, E. Y. Tsymbal, T. Katayama, and S. Yuasa, "Defect-mediated properties of magnetic tunnel junctions," *IEEE Transactions on Magnetics* **43**, 2770–2775 (2007).

[3] A. F. Md Nor, T. Kato, S. J. Ahn, T. Daibou, K. Ono, M. Oogane, Y. Ando, and T. Miyazaki, "Low-frequency noise in MgO magnetic tunnel junctions," *Journal of Applied Physics* **99** (2006).

[4] L. Sheng, D. Y. Xing, and D. N. Sheng, "Theory of the zero-bias anomaly in magnetic tunnel junctions: Inelastic tunneling via impurities," *Physical Review B* **70** (2004).

[5] I. Weymann, J. Barnaś, J. König, J. Martinek, and G. Schön, "Zero-bias anomaly in cotunneling transport through quantum-dot spin valves," *Physical Review B* **72** (2005).

[6] L. Liu, J. Niu, L. Xiang, J. Wei, D.-L. Li, J.-F. Feng, X.-F. Han, X.-G. Zhang, and J. M. D. Coey, "Symmetry-dependent electron-electron interaction in coherent tunnel junctions resolved by measurements of zero-bias anomaly," *Physical Review B* **90** (2014).

[7] Z. Q. Lei, G. J. Li, W. F. Egelhoff, P. T. Lai, and P. W. T. Pong, "Review of noise sources in magnetic tunnel junction sensors," *IEEE Transactions on Magnetics* **47**, 602–612 (2011).

[8] E. R. Nowak, M. B. Weissman, and S. S. P. Parkin, "Electrical noise in hysteretic ferromagnet–insulator–ferromagnet tunnel junctions," *Applied Physics Letters* **74**, 600–602 (1999).

[9] L. Jiang, E. R. Nowak, P. E. Scott, J. Johnson, J. M. Slaughter, J. J. Sun, and R. W. Dave, "Low-frequency magnetic and resistance noise in magnetic tunnel junctions," *Physical Review B* **69** (2004).
[10] K. Hayakawa, S. Kanai, T. Funatsu, J. Igarashi, B. Jinnai, W. Borders, H. Ohno, and S. Fukami, "Nanosecond random telegraph noise in in-plane magnetic tunnel junctions," *Physical Review Letters* 126 (2021).

[11] Z. Li, M. Sotto, F. Liu, M. K. Husain, H. Yoshimoto, Y. Sasago, D. Hisamoto, I. Tomita, Y. Tsuchiya, and S. Saito, "Random telegraph noise from resonant tunnelling at low temperatures," *Scientific Reports* 8 (2018).

[12] J. P. Fried, X. Bian, J. L. Swett, I. I. Kravchenko, G. A. D. Briggs, and J. A. Mol, "Large amplitude charge noise and random telegraph fluctuations in room-temperature graphene single-electron transistors," *Nanoscale* 12, 871–876 (2020).

[13] P. Belardinelli, W. Yang, A. Bachtold, M. I. Dykman, and F. Alijani, "Hidden vibrational bistability revealed by intrinsic fluctuations of a carbon nanotube," *Nano Letters* 25, 8443–8449 (2025).

[14] Y. Kim and H. Song, "Noise spectroscopy of molecular electronic junctions," *Applied Physics Reviews* 8 (2021).

[15] A. Bellec, J. Lagoute, and V. Repain, "Molecular electronics: Scanning tunneling microscopy and single-molecule devices," *Comptes Rendus. Chimie* 21, 1287–1299 (2018).

[16] D. Secker, S. Wagner, S. Ballmann, R. Härtle, M. Thoss, and H. B. Weber, "Resonant Vibrations, Peak Broadening, and Noise in Single Molecule Contacts: The Nature of the First Conductance Peak," *Physical Review Letters* 106 (2011).

[17] T. Grasser, "Stochastic charge trapping in oxides: From random telegraph noise to bias temperature instabilities," *Microelectronics Reliability* 52, 39–70 (2012).

[18] A. Sawa, "Resistive switching in transition metal oxides," *Materials Today* 11, 28–36 (2008).

[19] Z. Wang, H. Wu, G. W. Burr, C. S. Hwang, K. L. Wang, Q. Xia, and J. J. Yang, "Resistive switching materials for information processing," *Nature Reviews Materials* 5, 173–195 (2020).

[20] V. D. Nguyen, S. Rao, K. Wostyn, and S. Couet, "Recent progress in spin-orbit torque magnetic random-access memory," *npj Spintronics* 2 (2024).

[21] I. Hwang, M.-J. Lee, G.-H. Buh, J. Bae, J. Choi, J.-S. Kim, S. Hong, Y. S. Kim, I.-S. Byun, S.-W. Lee, S.-E. Ahn, B. S. Kang, S.-O. Kang, and B. H. Park, "Resistive switching transition induced by a voltage pulse in a Pt/NiO/Pt structure," *Applied Physics Letters* 97, 052106 (2010).

[22] C.-Y. Chen, C. Gonzalez-Ruano, I. Martinez, F. G. Aliev, D.-C. Ling, Y.-H. Tang, and J.-Y. Hong, "Bias polarity dependent low-frequency noise in ultra-thin alox-based magnetic tunnel junctions," *Scientific Reports* 14 (2024).

[23] E. Bertin, D. Halley, Y. Henry, N. Najjari, H. Majjad, M. Bowen, V. DaCosta, J. Arabski, and B. Doudin, "Random barrier double-well model for resistive switching in tunnel barriers," *Journal of Applied Physics* 109, 083712 (2011).

[24] J. M. Aguiar-Hualde and M. Alouani, "Taming the resistive switching in Fe/MgO/V/Fe magnetic tunnel junctions: An ab initio study," *Journal of Magnetism and Magnetic Materials* 372, 167–172 (2014).

[25] A. M. Drews, M. Kowalik, and K. J. M. Bishop, "Charge and force on a conductive sphere between two parallel electrodes: A Stokesian dynamics approach," *Journal of Applied Physics* 116, 074903 (2014).
[26] D. R. Lide, G. Baysinger, S. Chemistry, L. I. Berger, R. N. Goldberg, and H. V. Kehiaian, "CRC Handbook of Chemistry and Physics".

[27] S. Zhang, P. M. Levy, A. C. Marley, and S. S. P. Parkin, "Quenching of Magnetoresistance by Hot Electrons in Magnetic Tunnel Junctions," *Physical Review Letters* 79, 3744–3747 (1997).

[28] A. F. G. Wyatt, "Anomalous Densities of States in Normal Tantalum and Niobium," *Physical Review Letters* 13, 401–404 (1964).

[29] J. A. Appelbaum and L. Y. L. Shen, "Zero-Bias-Conductance Peak Anomaly of Ta-1-Al Tunnel Junctions at 0.3 K and 90 kG," *Physical Review B* 5, 544–553 (1972).

[30] G.-X. Miao, M. Münzenberg, and J. S. Moodera, "Tunneling path toward spintronics," *Reports on Progress in Physics* 74, 036501 (2011).

[31] https://lmfit.github.io/lmfit-py/

[32] J. Bernos, M. Hehn, F. Montaigne, C. Tiusan, D. Lacour, M. Alnot, B. Negulescu, G. Lengaigne, E. Snoeck, and F. G. Aliev, "Impact of electron-electron interactions induced by disorder at interfaces on spin-dependent tunneling in Co-Fe-B/MgO/Co-Fe-B magnetic tunnel junctions," *Physical Review B* 82 (2010).

[33] D. Halley, H. Majjad, M. Bowen, N. Najjari, Y. Henry, C. Ulhaq-Bouillet, W. Weber, G. Bertoni, J. Verbeeck, and G. Van Tendeloo, "Electrical switching in Fe/Cr/MgO/Fe magnetic tunnel junctions," *Applied Physics Letters* 92, 212115 (2008).

[34] J. Leliaert, B. Van de Wiele, A. Vansteenkiste, L. Laurson, G. Durin, L. Dupré, and B. Van Waeyenberge, "Current-driven domain wall mobility in polycrystalline permalloy nanowires: A numerical study," *Journal of Applied Physics* 115, 233903 (2014).

[35] A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, and B. Van Waeyenberge, "The design and verification of Mumax3," *AIP Advances* 4, 107133 (2014).

[36] S. Schleicher et al, "Localized states in advanced dielectrics from the vantage of spin- and symmetry-polarized tunnelling across MgO", *Nature Communications*. 5 4547 (2014).