Spin-driven electrical power generation at room temperature

ABSTRACT On-going research is exploring novel energy concepts ranging from classical to quantum thermodynamics. Ferromagnets carry substantial built-in energy due to ordered electron spins.

Here, we propose to generate electrical power at room temperature by utilizing this magnetic energy to harvest thermal fluctuations on paramagnetic centers using spintronics. Our spin engine

rectifies current fluctuations across the paramagnetic centers’ spin states by utilizing so-called ‘spinterfaces’ with high spin polarization. Analytical and ab-initio theories suggest that

experimental data at room temperature from a single MgO magnetic tunnel junction (MTJ) be linked to this spin engine. Device downscaling, other spintronic solutions to select a transport

spin channel, and dual oxide/organic materials tracks to introduce paramagnetic centers into the tunnel barrier, widen opportunities for routine device reproduction. At present MgO MTJ

densities in next-generation memories, this spin engine could lead to ‘always-on’ areal power densities that are highly competitive relative to other energy harvesting strategies. SIMILAR

CONTENT BEING VIEWED BY OTHERS OXYGEN VACANCY-DRIVEN SPIN-TRANSFER TORQUE ACROSS MGO MAGNETIC TUNNEL JUNCTIONS Article Open access 07 January 2025 EMERGING FERROMAGNETIC MATERIALS FOR

ELECTRICAL SPIN INJECTION: TOWARDS SEMICONDUCTOR SPINTRONICS Article Open access 28 March 2025 OBSERVATION AND THEORETICAL CALCULATIONS OF VOLTAGE-INDUCED LARGE MAGNETOCAPACITANCE BEYOND

330% IN MGO-BASED MAGNETIC TUNNEL JUNCTIONS Article Open access 12 July 2021 INTRODUCTION A solar cell’s electronic potential landscape is crafted such that, when a photon is absorbed, the

resulting electron and hole (the absence of an electron) flow in opposite directions. Since they carry an electrical charge of opposite sign, this generates an electrical current. Two

low-temperature experiments1,2 have suggested that, by astutely designing the magnetic potential landscape of a quantum dot (QD) device, electrons with a spin ↑ or ↓ quantum property can

flow in opposite directions. This can generate electrical power if the spin ↑ and ↓ current channels are imbalanced, i.e. if the overall current is spin-polarized. This apparent current

imbalance, and the presence of QDs in both systems, are reminiscent of quantum thermodynamical experiments on single electron boxes, which have demonstrated how to harvest thermal

fluctuations3,4 and information5 to perform work at very low temperatures. These heat and information engines are driven by fluctuation-induced quantum tunneling on/off of QDs, with a

transmission asymmetry between left and right leads that can be energy-dependent due to the QD’s discrete energy levels6,7. A few reports have theoretically8 and experimentally (using

nitrogen vacancies in diamond9) taken into account the electron spin. Inspired by the report of Miao et al.2, and by recent progress in quantum thermodynamics3,4,5,6,7,8,9,10,11,12, we

propose that a spin-split paramagnetic (PM) quantum object can enable electrons with a spin ↑ or ↓ quantum property to flow in opposite directions if the transmission rates on either side of

the PM center are spin-dependent. Differing amplitudes in these transport spin channels generate a spontaneous current flow. Measurements across a single MgO magnetic tunnel junction,

backed by analytical and ab-initio theories, indicate that this spin engine can operate at room temperature. We discuss strategies to achieve routine device reproduction. Our work also

confirms the high transport spin polarization at room temperature of the ferromagnetic metal/molecule interface13 inferred from spectroscopy measurements14. RESULTS Figure 1a illustrates our

spin engine in the simplified case of a PM center, characterized by two effectively spin-split energy levels. To achieve a strongly spin-dependent transmission rate Γ, the PM center is

placed between spintronic selectors—materials systems that ideally favor only one transport spin channel while blocking the other. Examples include half metals15,16,17, 2D materials with

half-metallic properties18, a normal metal / ferromagnetic tunnel barrier19 bilayer, and the ferromagnetic metal/molecule interface13, also called a ‘spinterface’. The Fe/MgO system may also

constitute a spintronic selector given either a sufficient MgO thickness20 and/or the presence of oxygen vacancies21,22,23,24. A standard ferromagnetic metal (FM) would also work, albeit

with reduced efficiency. Due to this combination of spintronic selectors and spin-split PM states, a spin ↑(↓) electron may only depart the PM toward the left(right) electrode at the energy

of the PM center’s corresponding spin state. Hai et al.1 used a MnAs ferromagnetic metal with a conventional (~50%) spin polarization of conduction states, and applied a magnetic field to

spin-split their MnAs QDs and obtain power generation at 3K. It is unclear whether this experiment could have worked at higher temperatures. Miao et al.2 filtered the electron spin upon

transport across EuS ferromagnetic tunnel barriers at 1K, i.e. below its ordering temperature TC ~ 16.8 K. Here, spin splitting of the Al QD is induced by electronic coupling to one EuS

barrier. Reports indicate that several spintronic selector tracks include materials science candidates (e.g. the Fe/MgO MTJ class20,22, the half-metallic Co2FeAl17 or the ferromagnetic

tunnel barrier CoFe2O419) that can operate at/beyond room temperature (RT). To obtain RT electrical generation, and in the process demonstrate it to be a RT spintronic selector, we utilize

the spinterface13,14,25,26. This refers to a low energy bandwidth, low density of highly spin-polarized states that arise at room temperature from spin-polarized hybridization between the

highly degenerate electronic states of a FM metal such as Co and the few, energetically discrete states of molecules, including carbon atoms26. The spinterface is weakly conducting, and its

magnetic orientation naturally follows that of the FM metal. To date, only spin-polarized photoemission spectroscopy14,26 suggests that the spinterface may be a spintronic selector at RT. We

now utilize the case of the spinterface to illustrate several key considerations of how spintronic selectors and PM centers can interact to form the spin engine’s transport path. Upon

connecting the spinterface to the PM state (see Fig. 1a), spin-conserved quantum tunneling conditions the resulting spin-polarized landscape in the following significant ways. First, the

spinterface’s density of states (DOS) with a spatially oriented spin polarization generates a corresponding spintronic anisotropy in the PM state’s stochastic spin distribution27,28, thereby

deforming the PM’s Bloch sphere of spin states. This generates an energy difference Δ between the PM center’s spin states and increases the probability that an electron tunnel onto/off of

the PM if its spin is aligned to the spinterface’s spin referential (see Fig. 1b). The ensuing preferential charge flow for that spin channel effectively shifts2 the spinterface/FM metal’s

Fermi level by Δ_ϕ_ toward that spin state of the PM center. We are thus describing how the spinterface can modify a metal’s properties29, namely its Fermi level position, through an

additional mechanism. In a perfectly symmetric magnetic tunnel junction (MTJ) that implements spin-conserved tunneling between these two key ingredients—spinterfaces and a PM site—no net

current (I) should flow in the MTJ’s parallel (P) orientation of electrode magnetizations. However, in the MTJ’s antiparallel (AP) magnetic state (see Fig. 1a), the two FM electrode Fermi

levels are shifted away from one another, each toward the corresponding spinterface-selected spin state of the PM center. The resulting spontaneous bias voltage ΔV between the FM electrodes

thus scales with the amplitude of the spinterface’s spin polarization and the energy difference Δ between the PM center’s spin ↑ and ↓ states. Since an experimental MTJ cannot be exactly

symmetric, one may also anticipate a spontaneous bias, or current, in the MTJ’s P state, albeit of lower amplitude. To generate work, the spin engine harvests energy from the spin

fluctuations that are thermally induced on the PM center. This thermal spin state mixing on the PM center enables current to flow from one spinterface to the other, even against the built-in

ΔV in the MTJ’s AP magnetic state. The spin engine thus requires that Δ ≤ _k_BT, and thus a balance between the tunneling-induced energy shift Δ_ϕ_ of the spinterface state to the PM

center’s spin state and thermal fluctuations, as weighed by the spinterface’s spin polarization (see Fig. 1c). This thermal energy harvesting can be expected to cool the PM center.

Furthermore, the fully spin-polarized current flowing across the spinterface perturbs the FM ground state of the electrode through a spin accumulation-induced interfacial resistance30. The

resulting heat generation in the FM electrode must be dissipated for our spin engine to work. Finally, the spinterface’s low density of highly spin-polarized states may be beneficial to RT

operation. Indeed, it protects the energetically discrete PM spin states against thermal broadening from the FM electrodes. As discussed theoretically in Supplementary Notes 1 and 2, the

thermal fluctuations in current are rectified first upon transport from the FM electrode onto the spinterface, and furthermore upon transport from the spinterface onto the PM center’s spin

state. This, along with the spinterface’s high spin polarization, strongly dampens any energy smearing of the PM center’s discrete spin states. The resulting energetically sharp,

spin-polarized effective current path involving the striped DOS of the FM electrodes and spinterfaces is schematized in Fig. 1c by the yellow band. With the support of analytical and

ab-initio theories, we believe to have observed an experimental realization of this spin engine through measurements across a single MgO MTJ at room temperature (RT; see junction statistics

in Supplementary Note 3). As described hereafter, this MTJ integrates Co/C spinterfaces with nearly total spin polarization26, and paramagnetic C atoms31 on the oxygen vacancy sites of the

MgO tunnel barrier. Referring to Fig. 2a, we observe a negative tunneling magnetoresistance ratio, i.e. TMR = IP/IAP − 1 < 0, at V = +10 mV and T = 295 K through P/AP magnetic states that

are well controlled thanks to an IrMn pinning layer (see Methods). Figure 2b shows the I(H) data acquired at V = +5 mV. Over the ~350 s needed to ramp H down from −2000 Oe to ~0Oe, the MTJ

remains in a P magnetic state, with IP < 0 despite V > 0. In the MTJ’s AP state, IAP > 0 over ~310 s. The abrupt magnetic field dependence of the switch in sign of current clearly

shows that the current sign change originates from the change in the MTJ’s magnetic state, and not the magnetic field amplitude/sweep. Both IP and IAP exceed the maximum 500 pA possible

experimental offset by nearly 2 orders of magnitude (see Supplementary Notes 4 and 5). Thus, in this MTJ, the direction of static current flow can be reversed by simply switching the MTJ’s

spintronic state. Since the external magnetic field is static, and we do not expect a spin texture in our FM electrodes, a spin motive force explanation1,32,33 seems unlikely. In these and

our experiments, no explicit temperature difference between electrodes, or temperature gradient, is applied to the device, such that a spin caloritronics34 explanation, while possible, is

not obvious. We further discuss in the Methods and Supplementary Note 5 how photovoltage/photocurrent and conventional/spintronic thermovoltage17,35 artifacts can be excluded here. These

I(H) datapoints are confirmed through I(V) measurements at RT in the MTJ’s P and AP states (see Fig. 2c), which reveal the following features: (1) at V = 0, IP ≠ IAP ≠ 0, with an amplitude

that also exceeds any experimental offset by nearly 2 orders of magnitude; (2) a non-zero applied bias V leading to a measured I = 0 whose amplitude depends on the MTJ’s magnetic state; (3)

power generation above 0.1 nW whose bias dependence depends on the MTJ’s magnetic state, with a maximum current IAP ≈ −70 nA at V = +1.4 mV (see panel (c) inset using data from Supplementary

Fig. 5a; (4) bias-driven oscillations in current that depend on the MTJ’s P/AP magnetic state, and thus on spin-dependent transport; (5) a bias range for which IP and IAP are of opposite

sign, leading to TMR < −100%. These features of the 0 → +Vmax → −Vmax → +Vmax → −Vmax → 0 I(V) sweep are reproduced with high fidelity in Fig. 2c for another such sweep with differing

maximum applied bias Vmax and bias step (i.e. a differing effective bias sweep rate), as well as by additional datasets (see Supplementary Note 4). This eliminates any junction

instability/memristive/Joule heating explanation36. (6) The numerically derived junction conductance dI/dV of the data of Fig. 2c, shown in Fig. 2d, reveals spintronically determined

conductance jumps, and spectral features as low as 0.25 meV—despite the 2_k_BT ≈ 50 meV thermal smearing expected at 295 K—that are statistically beyond the error bar (see Fig. 2d inset and

Supplementary Note 6 for full dataset and error bars) thanks to an excellent signal-to-noise ratio. This spectral sharpness is also witnessed through a 300% TMR peak with a

full-width-half-max of ~1.3 meV (see Fig. 2e), which arises from a combination of local maxima(minima) in IP(IAP) at V = −3.5 mV. This non-optimized device’s spintronic performance at 295 K

rivals the 600% record for FeCoB/MgO-class MTJs—obtained through a 20-fold performance increase over 7 years37,38 — but since the Co electrodes cannot be _bcc_-oriented here20,39 (see

Methods), this spintronic performance cannot arise from symmetry filtering. Within a simple Jullière model20 interpretation of the TMR amplitude, and from our analytical theory presented

hereafter, this can be ascribed in part to the high transport spin polarization of the Co/C spinterface26 at RT. This spectral sharpness in magnetotransport features at RT despite the

expected thermal broadening, and the excellent signal-to-noise ratio, can be interpreted as an experimental signature of our spin engine at work. Indeed, according to quantum

thermodynamics4,7, the harvesting of spin fluctuations on the PM centers is expected to lower their temperature. From _k_BT ≈ 0.25 meV, we estimate an effective electronic temperature of the

PM centers of 3 K. This cooling is the manifestation of harvesting energy from the PM centers’ spin fluctuations upon spin rectification in the junction. Since a non-zero current is present

at V = 0 across this normally passive component, we observe that the MTJ is intrinsically out of equilibrium. Consequently, to further link our experimental results with our conceptual spin

engine, we analytically consider an out-of-equilibrium nanotransport path across the MTJ comprising two PM centers (see Fig. 3a and the Methods/Supplementary Note 1 for details). Their

initially discrete energy levels (gray lines) are broadened to form a PM dimer as bonding/anti-bonding and spin degeneracies are lifted (see PM 1&2 of Fig. 3a) through a magnetic

exchange coupling that is bias-dependent28,40. To place the junction out of equilibrium, we impose a spin splitting of the FM electrodes’ chemical potential. Following our spin engine

proposal, our analytical model’s magnetic interactions (with Heisenberg, Ising and Dzyaloshinskii–Moriya contributions) result in a spintronic anisotropy27,28 onto PM1 and PM2 due to the

spatially orientated, spin-polarized DOS of each FM electrode, as mediated by spinterfaces (SP1 & SP2). Consistently with our experimental results, we constrain the model’s 7-fold

fitting parameter space using the following physical requirements: 1) the parameters should realistically describe the MTJ’s outer properties (FM electrode + spinterface), including a higher

spin polarization at the lower Co/MgO MTJ interface due to C dusting26 (see Methods); 2) these outer properties should remain identical in the MTJ’s P/AP magnetic states; 3) only minor

changes to the PM dimer’s properties are allowed between the P and AP cases. To account for T = 295 K, the FM electrodes’ Fermi level is broadened by 26 meV (not shown in Fig. 3a). Results

of this analytical model shown in Fig. 3b, c were acquired using a same set of parameters (see Methods for details) for the MTJ’s P/AP outer properties: _sp_ = 8.4, _SP_ = 2, _pL_ = _pR_ = 

0.35, _AP_ = 0.3, _E__0_ = 0, with pR and AP changing sign upon P ↔ AP, while we introduced minor variations in the PM dimer’s starting conditions for P(AP): _e__0_ = −2.5(+0.85) and _ASYM_ 

= 0.5(−0.75). Parameters are described in the Methods. Supplementary Fig. 2 shows the complex bias dependence of this spintronic potential landscape for each spinterface/PM center (SP1, PM1,

PM2 & SP2), depending on the spin channel and the MTJ’s P or AP magnetic state considered. Note how our model fulfills the spin engine’s Δ < _k_BT condition. Referring to Fig. 3b, we

observe a bias anti-symmetric imbalance in the oppositely propagating spin channels of current, which strongly depends on the MTJ’s P/AP magnetic state. This leads to a sizeable spintronic

difference in current, in particular at V = 0. We recopy the IP(V), IAP(V) and TMR(V) experimental data of Fig. 2c/e as Fig. 3d in order to compare them with their analytical counterparts,

shown in Fig. 3c. Despite a skewed bias position that could underscore the simplicity of the bias voltage distribution (see Fig. 3a), our out-of-equilibrium analytical model reproduces all

trends and salient features of the experimental magnetotransport data. This includes the spintronically dependent non-zero current at _V_ = 0, large TMR peak at V < 0 and the bias region

for V > 0 with differing signs of _I_P and _I_AP. A degraded agreement at large V likely reflects how our model only considers sequential transport across the 4 QDs, and not direct

transport between the FM electrodes, which can become significant as the QD levels are energetically shifted away from one another. This agreement between theory and experiment compares

quite favorably with respect to the state of the art21,22,41,42. In general, compared to low-temperature transport across well-characterized quantum objects (e.g. from single atoms and

dimers to molecules and atomic clusters43,44,45,46,47,48,49) thanks to a scanning tunneling microscope (STM), it is thus far difficult to assemble and ascertain the effective nanotransport

path50 in a solid state device, especially for the oxides used as MTJ barriers. Here, uncontrolled imperfections such as oxygen vacancies in the MgO tunnel barrier can concentrate electronic

tunneling transport across a macrojunction onto a nanotransport path50,51, such that the device operates due to a rare tunneling event52. This is what enables53 the spin transfer torque

effect underscoring key MTJ-based technologies54,55. As detailed in Supplementary Notes 7 and 8, while descriptions of the PM dimer in terms of Mn atoms or oxygen vacancies are much less

likely here, paramagnetic C atoms occupying oxygen vacancy sites in MgO are possible considering our MTJ stack with C-dusted MgO interfaces. Indeed, carbon capture by single/double oxygen

vacancies, which are present in our MgO21,23,53, is energetically favorable (see Supplementary Note 7 and the work of Tiusan et al.56) and can yield both paramagnetic monomers (see

Supplementary Note 7) and dimers31. Our ab-initio theory shows that the C–C distance is crucial in order to reproduce our analytical model’s results: only in a 4th nearest-neighbor

positioning does the C dimer simultaneously exhibit AF coupling (favorable over FM by 0.125 eV, i.e. above experimental _k_BT) and generate four states around the Fermi level _E_F of a

Co/MgO/Co MTJ (see Fig. 4 and Supplementary Note 9). On the other hand, C pairs in 1st, 2nd, 3rd, and 5th nearest-neighbor configuration generate a FM state (see Supplementary Note 7), which

would be inconsistent with our analytical model. This stringent C impurity positional requirement on the oxygen sublattice might explain why our spin engine was experimentally observed only

once out of ~200 attempts (see Supplementary Note 3). DISCUSSION To achieve routine experimental reproducibility, we propose that all spintronic selector tracks be attempted (see

introduction), noting that, in addition to the two published reports1,2, similar effects were observed at low temperature on MTJs with manganite half metals57. In all cases, control over the

spatial position and density of the barrier’s PM centers will be required with a precision that, at this time, remains the domain of model STM-assembled junctions43,44,45,46,47,48,49.

Considering that all reports involved microscale devices, this suggests reducing the junction’s lateral size from the micro- to the nano-scale. In an oxide track, one may study tunnel

barriers in which an oxygen vacancy-rich central region—achieved e.g. by varying oxygen concentration in an Ar sputtering plasma during growth51, is nominally seeded with impurities to be

trapped by these vacancies as PM centers. Control over the electronic properties of, and magnetic interactions58 between, PM centers in molecules suggests another, organic-based track using

spintronic nanojunctions59,60. Whatever the route, except for an AF-coupled PM dimer, the PM center(s) should experience dominant tunneling from one spintronic selector in order to adopt

that selector’s spin referential (see Fig. 1b and discussion). This can arise by tuning the selector/PM center tunneling rate through the insertion of an oxide/organic interlayer. Cleverly

crafted operando techniques50 that can directly characterize the PM center’s properties within the device’s nanotransport path can boost research efficiency. Overall, MgO spintronics

represents a compelling route. Indeed, it benefits from both industrial penetration54,61 and knowledge on how oxygen vacancies craft the spintronic nanotransport path21,22,23,24,53, boasts

lateral sizes down to 4.3 nm62, and has been conjugated with half-metallic electrodes operating at RT17. PM centers can be formed in MgO by trapping C, N or Si on oxygen vacancies (see Fig. 

4, the work of Wu et al.31 and Supplementary Note 7). To complement this heat description of our work, we briefly note in the Supplementary Note 10 that the rectification of thermal

fluctuations, which are present experimentally and analytically, can generate work when combined with an increase in the entropy of quantum information11 arising from spin transport onto the

PM center due to its spin fluctuations. A quantum thermodynamical theory along a similar spintronic path has been proposed8, while classical electronic implementations using capacitively

coupled quantum dots have been demonstrated at low temperature3,5,63. Our results should thus generate research initiatives on quantum electronic circuits at the rather unexplored

intersection between quantum thermodynamics3,4,5,6,7,8,9,10,11,12 and spintronics20,34,54. More generally, our work also indicates that the high transport spin polarization, and low density

of states, of spinterfaces represent a compelling approach to integrating the quantum properties of nano-objects within a solid-state device’s operation at room temperature, beyond

proof-of-concept electronic decoupling strategies43,64. The MTJ used to demonstrate our spin engine is an industrial-grade microelectronic device class used as the read head of hard disk

drives, and with promising potential toward low-power information storage54 and bio-inspired computing55. If routine reproducibility can be achieved, then for a typical STT-MRAM61 2D array

of 50 nm-wide MTJs with a pitch of 90 nm, assuming that the 0.1nW occurred through a single conduction channel, the resulting power density would be substantial. As an example, a suitable

series/parallel assembly on a 1 cm2 chip could deliver ~29.4 W of power to a 0.1 Ω load at 3.5 V. See Supplementary Note 11 for more details. Even considering 1% efficiency due to

engineering issues (e.g. managing heat flow, interconnect resistances…), this power density would still exceed the raw solar power density on the earth surface by a factor of three. Further

research may see the MTJ play a key role not only in information & communication, but also renewable energy, technologies. METHODS DEVICE PREPARATION AND BATCH CHARACTERIZATION

Ta(5)/Co(10)/IrMn(7.5)/Co(4)/C(_d_1 = 0, 0.3, 0.6, 0.9)/MgO(2.5 nm)/C(_d_2 = 0, 0.3, 0.6)/Co(10)/Pt(4) samples (all thicknesses in nm) were sputter-grown on Corning 1737 glass substrates65.

Stacks were post-annealed in an in-plane magnetic field of 200 Oe for 1 h at a temperature Ta of 200 °C to magnetically pin the lower electrode thanks to the IrMn antiferromagnetic layer.

This low annealing temperature precludes the diffusion of Mn into the barrier66, though it can promote C diffusion into MgO56. Samples were then processed by optical lithography67 into 20 

μm-diameter MTJs, and measured on a variable-temperature magnetotransport bench. Within the study, 216 MTJs that exhibited neither a short-circuit nor an open circuit had a median R = 4395 Ω

in the MTJ’s P state, i.e. a median R.A. product of 1.38E6 Ω.μm2. Only 1 out of 168 20 μm-diameter MTJs tested at T = 295 K, with _d_1 = 0.9 and _d_2 = 0, a ten-fold larger RA product (R = 

57.7 kΩ, R.A. = 1.81E7 Ω.μm2; standard contact resistances) and anomalous TMR < 0 at V = +10 mV, revealed these peculiar power generation features and high TMR. An additional 48 MTJs did

not exhibit I ≠ 0 at V = 0. We presume that annealing-induced C migration into MgO generated the MTJ’s spinterfaces and PM centers. The lower R found in passive MTJs suggests the presence of

several conduction channels, each with a slightly different nanotransport path, such that electrical generation effects are averaged out. POSSIBLE TRANSPORT ARTIFACTS Measurements on this

MTJ were conducted over 90 min in 4-point measurement mode within a dark cryostat that remained between 295.3 K and 294.5 K with sample heater off. Furthermore, these peculiar transport

features strongly depend on the MTJ’s P/AP magnetic state. We in particular observe that I ≠ 0 at V = 0. We can therefore exclude thermovoltage photovoltage/photocurrent, as well as any

conventional or spintronic thermovoltage explanations. We discuss these discarded artifact sources in more detail in Supplementary Note 5. ANALYTICAL THEORY The analytical model28,40

symmetrically segments the MTJ’s bias drop into 6 zones around the junction mid-point, for which V ≡ 0, using the same bias sign convention as in experiment. Current flow across the

left-hand(right-hand) FM electrode is modeled by a spin-splitting _sp_(_sp_ × _AP_) of its chemical potential. The DOS of the spinterfaces SP1 & SP2 consists in 10meV-wide bands that are

centered around EF at V = 0 and are spin-split by _SP_. A constant E0 = 0 was used. PM 1&2 model the paramagnetic dimer as two spin states S1 and S2 that, initially, are energetically

discrete, are positioned _eo_ away from EF at V = 0, and are energy-split by _ASYM_ but are not spin-split. Current flows between the FM electrodes across SP1/PM1/PM2/SP2 through a tunneling

rate T, which was fixed at [1 1 1] between SP1/PM1; PM1/PM2; PM2/SP2. Finally, pL(pR) describes a possible spin polarization of the tunelling transmission between the left(right) FM lead

and SP1(SP2). The MTJ’s AP state is described by switching the sign of pR and AP, i.e. by flipping the right-hand FM electrode magnetization. This experimentally corresponds to the free Co

layer of the top FM electrode. AP = 0.3 is consistent with an experimentally larger spin polarization of the C-dusted Co lower FM electrode26, and to _d_1 ≠ _d_2. Supplementary Note 1

further details the model’s transport formalism. AB-INITIO THEORY Within density functional theory, the electronic properties of the C dimer within MgO were computed using 64-atom supercells

with a simple cubic structure with two substitutional carbon atoms in various configurations (see Supplementary Note 7 and Supplementary Fig. 8). These calculations were done using VASP

code68 based on the projector augmented wave (PAW) method69 and the Pedrew, Burke, Enzerhof (PBE)70 generalized gradient approximation for the exchange-correlation potential. The kinetic

energy cutoff value of 500 eV for the plane wave basis set and the convergence criterion for the total energy of 10−8 eV is used. The carbon-doped structures are fully relaxed using a

conjugate-gradient algorithm, such that the forces acting on atoms be less than 0.001 eV/Å. A _k_-point mesh of 6 × 6 × 6 with the Methfessel-Paxton method with a smearing τ = 0.1 eV is

used. See Supplementary Note 9 for the determination of EF within a Co/MgO(12 ML, i.e. ~2.5 nm)/Co MTJ. DATA AVAILABILITY The data that support the findings of this study are available from

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_Phys. Rev. Lett._ 77, 3865–3868 (1996). Article  ADS  Google Scholar  Download references ACKNOWLEDGEMENTS We are grateful to H. Thierschmann, K. McKenna and J. Blumberger for useful

discussions, and to Y. Henry for carefully reading our manuscript. Devices were synthesized at the STNano technological platform. We acknowledge financial support from the Institut Carnot

MICA (project ‘Spinterface’), from the ANR (ANR-09-JCJC-0137, ANR-14-CE26-0009-01), the Labex NIE “Symmix” (ANR-11-LABX-0058 NIE) and Vetenskapsrådet. This work was performed using HPC

resources from the Strasbourg Mesocenter and from the GENCI-CINES Grant 2016-gem1100. Open access funding provided by Uppsala University. AUTHOR INFORMATION Author notes * Deceased: E.

Beaurepaire. AUTHORS AND AFFILIATIONS * Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 CNRS, Université de Strasbourg, 23 Rue du Lœss, BP 43, 67034, Strasbourg, France

K. Katcko, E. Urbain, B. Taudul, F. Schleicher, J. Arabski, E. Beaurepaire, D. Spor, W. Weber, S. Boukari, M. Alouani & M. Bowen * Institut Jean Lamour UMR 7198 CNRS, Université de

Lorraine, BP 70239, 54506, Vandœuvre les Nancy, France F. Schleicher, D. Lacour & M. Hehn * Institut de Chimie, UMR 7177 CNRS, Université de Strasbourg, 4 Rue Blaise Pascal, CS 90032,

67081, Strasbourg, France B. Vileno * Department of Physics and Astronomy, Uppsala University, Box 516, 75120, Uppsala, Sweden J. Fransson Authors * K. Katcko View author publications You

can also search for this author inPubMed Google Scholar * E. Urbain View author publications You can also search for this author inPubMed Google Scholar * B. Taudul View author publications

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Boukari View author publications You can also search for this author inPubMed Google Scholar * M. Hehn View author publications You can also search for this author inPubMed Google Scholar *

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Scholar * M. Bowen View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS M.B., E.B. and S.B. conceived the initial experiment. M.H. grew the

sample stack. E.U., F.S., K.K. and J.A. implemented technological processing to make MTJs. E.U., F.S. and K.K. performed magnetotransport measurements. M.B., K.K., S.B., D.L., E.B., M.A. and

W.W. analyzed magnetotransport results. B.V. and D.S. performed auxiliary measurements. J.F. designed the analytical models with input from M.B. K.K. applied the analytical models, with

input from M.B. and J.F. B.T. and M.A. implemented DFT calculations with input from M.B. M.B., K.K. and B.T. prepared the manuscript. All authors commented on the manuscript. CORRESPONDING

AUTHOR Correspondence to M. Bowen. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature remains neutral

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electrical power generation at room temperature. _Commun Phys_ 2, 116 (2019). https://doi.org/10.1038/s42005-019-0207-8 Download citation * Received: 03 May 2019 * Accepted: 01 August 2019

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