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# Oxygen vacancy-driven spin-transfer torque across MgO magnetic tunnel junctions

L. M. Kandpal, B. Taudul, E. Monteblanco, A. Kumar, K. Katcko, F.

Schleicher, P. Gupta, S. Boukari, W. Weber, V. da Costa, et al.

► To cite this version:

L. M. Kandpal, B. Taudul, E. Monteblanco, A. Kumar, K. Katcko, et al. Oxygen vacancy-driven spin-transfer torque across MgO magnetic tunnel junctions. npj Spintronics, 2025, 3, 10.1038/s44306-024-00067-8. [https://doi.org/10.1038/s44306-024-00067-8](https://doi.org/10.1038/s44306-024-00067-8). [arXiv:2405.00678](https://arxiv.org/abs/2405.00678)

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# Oxygen vacancy-driven spin-transfer torque across MgO magnetic tunnel junctions

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L. M. Kandpal<fnref n="1" />✉, B. Taudul<fnref n="1" />, E. Monteblanco², A. Kumar³, K. Katcko<fnref n="1" />, F. Schleicher², P. Gupta³, S. Boukari<fnref n="1" />, W. Weber<fnref n="1" />, V. Da Costa<fnref n="1" />, J. D. Costa⁴, T. Böhnert⁴, R. Ferreira⁴, P. Freitas⁴, M. Hehn², M. Alouani<fnref n="1" />, P. K. Muduli³, D. Lacour² & M. Bowen<fnref n="1" />✉

Flowing an electrical current that is both of high areal density and large spin polarization across a magnetic tunnel junction (MTJ) can, through spin-transfer torque (STT), alter the relative magnetic orientation of the MTJ's ferromagnetic electrodes. This effect has enabled key next-generation MTJ applications and commercialized products, from memories to artificial synapses and energy harvesters. As MTJs are now downscaled to 2 nm, basic experimental data challenge the accepted understanding of their operation. From transport spectroscopy, ferromagnetic resonance experiments and ab-initio calculations it is revealed that the high conductivity of STT-ready MTJs, and the STT effect therein, is mediated by oxygen vacancy complexes within the MgO barrier. Our work positions the oxygen vacancy at the core of MgO spintronics. This should disrupt the status-quo on STT-MRAM R&D, by generating defect-specific research and new ideas to confer additional functionality to these next-generation electronic devices, as a nanoelectronics platform to industrialize quantum physics.

Research on oxide electronics, which has historically focused on ferroic order parameters<fnref n="1" />, has increasingly highlighted the impact of defects such as oxygen vacancies, and their potential² toward multifunctional behavior, e.g. as memristors³⁻⁵. This nanoscale focus initiated the interdisciplinary field of oxide ionotronics, in which defect motion drives the device state⁶ to emulate biological functions⁷.

However, this atomistic level of insight has thus far not permeated all classes of oxide electronics. Within a segment of green electronics called spintronics⁸, the magnetic tunnel junction (MTJ)⁹ with a MgO oxide barrier represents a crucial component of existing and emerging information and communication technologies. Applications range from magnetic field sensors, microwave radar generation and detection, hard drive read heads, radiation-immune standalone and embedded non-volatile memories (STT-MRAMs), to artificial neurons for stochastic and brain-inspired neuro-morphic computing⁸,¹⁰⁻¹². Furthermore, experiments show that these MTJ devices can also harvest ambient thermal¹³,¹⁴ and waste radio frequency energy⁸. These functionalities arise from the difference in the device's resistances $R_P$ and $R_{AP}$ for the parallel (P) and antiparallel (AP) orientation of ferromagnetic electrode magnetizations. The resulting spintronic

performance is quantified through the tunneling magnetoresistance ratio $TMR = R_{AP} / R_P - 1$¹⁵. One may electrically switch the device's magnetic state using spin-transfer torque (STT)¹⁶, i.e. by flipping one electrode's magnetization thanks to the spin angular momentum imparted by a spin-polarized current.

STT, which underscores many of the aforementioned applications, is observed using sub-350 nm-wide pillars with MgO barrier thickness $d \approx 1$ nm and a resistance-area product $RxA \sim 1-50 \ \Omega \cdot \mu m^{212,17-28}$. The STT effect requires a tunnel current of large density and of high spin polarization. Yet, this large current density appears to be in contradiction with the MgO tunnel barrier's height/width characteristics¹⁸, while an explanation in terms of metal-induced gap states (MIGS) caused by interfacial charge transfer²⁹ cannot account for evidence³⁰,³¹ of metallic conduction in the MTJ's P state and not in the AP state. This latter behavior has phenomenologically been interpreted as the presence of two competing metallic and semiconducting transport channels.

The nature of this metallic channel (i.e. pinholes³²), which decreases TMR at $d = 0.7-1$ nm³³,³⁴, has remained speculative. While recent research into 0 d ferromagnetism in MgO has emphasized the role of magnesium

<footnote n="1">¹Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), UMR 7504 CNRS, Université de Strasbourg, 23 Rue du Lœss, BP 43, 67034 Strasbourg, France. ²Institut Jean Lamour, UMR 7198 CNRS, Université de Lorraine, BP 70239, 54506 Vandœuvre les Nancy, France. ³Department of Physics, Indian Institute of Technology Delhi, New Delhi, 110016, India. ⁴International Iberian Nanotechnology Laboratory (INL), Av. Mestre José Veiga s/n, 4715-330 Braga, Portugal. ✉e-mail: lmkandpal09@gmail.com; bowen@unistra.fr</footnote>
vacancies³⁵, the different growth conditions of MgO when forming MTJ tunnel barriers with a high RxA of 10⁻⁴-10⁶ Ω·µm² where shown to generate single (F center) and double (M center) oxygen vacancies¹⁷,¹⁹,³⁶,³⁷, which can furthermore be filled by the electrodes' B atoms³⁸. The resulting localized states define a nanotransport path³⁷,³⁹ with a barrier height for hole³⁶ tunneling that is much lower than the MgO midgap energy. In particular, the anti-bonding state of the double oxygen vacancy (M*) promotes a 0.4 eV barrier height in FeCoB/MgO/FeCoB MTJs for the Δ₁ electrons that are responsible for spintronic performance here⁴⁰. This is in line with reports indicating that single oxygen vacancies in MgO would degrade TMR²⁸,⁴¹,⁴² from ideal values to those observed experimentally due to incoherent transport⁴⁰,⁴².

The switchover from high RxA semiconducting junctions to low RxA metallic, 'STT-ready' junctions could arise from a larger oxygen vacancy density. Yet, even as low RxA MTJs now reach single nm dimensions⁴³, and as this device class is poised to enjoy breakout applications⁸,¹⁰⁻¹², a nanoscopic accounting of oxygen vacancies in this key green nanotechnology is still lacking. Here, we shall demonstrate that oxygen vacancies constitute a key element of the STT effect across low RxA MgO MTJs. Using MTJs from TDK-Headway (MTJ-H) and (MTJ-INL) INL fablines, thermally-activated transport spectroscopy reveals the presence of a continuum of states extending from the M* center to the Fermi level E<sub>F</sub>. This spectral signature, which is reproduced in ST-FMR experiments, is attributed to oxygen vacancy complexes, and an example is provided using ab-initio calculations. In the process, we rationalize anomalies in the temperature dependence of the critical current density toward STT.

## Results

### Experimental presence of localized states in low RxA MTJs and impact on STT

As background, we present in Fig. 1 typical R(T) data for MTJ-H and MTJ-INL, STT-ready nanopillar devices with in-plane and out-of-plane magnetization, respectively (see Method for growth details). We observe that the MTJ is semiconducting in its AP magnetic state, as expected⁹,²⁹,⁴⁴. However, in the MTJ's P magnetic state, a metallic trend is found, in contrast to that observed in high RxA MTJs¹⁷. Given how solid-state tunneling occurs across MgO²⁹,⁴⁵, this spintronic contrast means that the localized states present at E<sub>F</sub> must be spin- and/or symmetry polarized. The slight increase in R<sub>P</sub> for T < 40 K suggests a thermal activation of transport, i.e. that these states around E<sub>F</sub> are weakly localized or do not transport at the Γ point²⁸,²⁹.

To characterize these states, we first compare the conductance spectroscopy of low RxA junctions with that of high RxA junctions, whose gap states have already been identified³⁶. As seen in Fig. 2a, the bias-induced

<figure><img src="image_5.png" /><figcaption>Fig. 1 | Spintronic origin of metallic and semiconducting transport in low RxA, STT-ready MTJs. The temperature dependence of resistance for V = 100 mV MTJ-INL (black) and MTJ-H (red) nanopillar devices reveals a metallic behavior in the (a) P state, while it is (b) semiconducting in the MTJ's AP state.</figcaption></figure>

change in the high RxA MTJ's conductance strongly increases for |V| > 0.3 V due to the presence of F centers¹⁷,³⁰. However, this is not the case for low RxA MTJs. Instead, past the usual conductance increase due to low-energy inelastic processes (e.g. magnons)⁹, the conductance exhibits a plateau. This trend is particularly visible in the junction's P state, while only a small conductance increase is seen in the AP state. We conclude that there are far fewer F centers in the MgO barrier of low RxA MTJs.

To examine the energy extent of these states, we consider $\hat{I}(V, T_1, T_2) = \{[I(V, T_2)/I(V, T_1)]-1\}$, i.e. the impact on I(V) of increasing temperature by ΔT = T₂-T₁,¹⁷,¹⁹,⁴⁶. At V₀, $\hat{I}(V_0) > 0$ reflects how the additional thermal energy Δk<sub>B</sub>T generates new transport channels thanks to states located ΔeV₀ from E<sub>F</sub> within k<sub>B</sub>(T₂-T₁). Figure 3 depicts $\hat{I}(V, T_2)$ plots with ΔT = 80 K acquired on a MTJ-H MTJ. For both P and AP, an $\hat{I}$ peak centered at V = 0 indicates thermally activated inelastic processes (magnons, localized states, etc...). Beyond this peak, $\hat{I}_P(V)$ is negative while $\hat{I}_{AP}(V)$ is positive, as expected from the R(T) data of Fig. 1.

In the P state, against this $\hat{I} < 0$ background, we observe a $\hat{I}$ peak at 0.6 V and T = 90 K that shifts to 0.4 V at T = 300 K with increasing T. This peak is due to a change in the density of states at 0.4 eV away from E<sub>F</sub> in the barrier. We observe that $\hat{I}_P$ decreases to more negative values for |V| > 0.5 and T > 200 K. This plateau of non-zero, negative $\hat{I}_P$ amplitude suggests the presence of electronic states around E<sub>F</sub> whose thermally activated contribution to transport is complete by 200 K. No such features are found in the MTJ's AP magnetic state (see Fig. 3). As we will see, this is because the enduring tunneling into the metallic counterelectrode due to mismatched electronic symmetries⁴⁵,⁴⁷,⁴⁸ has a thermal activation that overshadows the presence of localized states. Similar $\hat{I}$ results were also obtained on MTJ-INL MTJs (data not shown).

It is known that the magnetic coupling between two FM layers can be altered by the presence of localized states in the tunneling spacer layer⁴⁹,⁵⁰. Since magnetic coupling is the steady-state outcome of spin-polarized currents across the trilayer, one may expect signatures of these localized states in STT experiments. In a first approach, we analyze the bias dependence of STT in nanopillar MTJ devices using spin-torque ferromagnetic resonance (ST-FMR)⁵¹,⁵². This technique probes the onset of magnetization dynamics that lead to STT thanks to an external microwave input (see Methods for details). We plot in Fig. 4a the resulting dc bias voltage as the microwave frequency is swept across the resonance condition, for several values of external bias. By fitting the data (see Methods), we obtain the bias dependence of the parallel and perpendicular torkance (see panels(b) and (c), respectively). The magnitude of the perpendicular torkance is nearly one order of magnitude lower than the parallel torkance, in agreement with previous reports⁵³. Both STT parameters exhibit a marked change in trend at V = 400 mV, which matches the spectroscopic signatures of localized states seen in $\hat{I}_P$ data (see Fig. 3). Note that the corresponding current density is 10x lower than the auto-oscillations threshold current, so that non linearity effects can be discarded here⁵⁴.

A complementary approach is to examine experimental deviations from a barrier-agnostic model⁵⁵ of the critical current density J<sub>C</sub> leading to the STT effect:

$$J_C = 2e\alpha t_F M_S (H_K \pm H_{ext} + 2\pi M_S)/\hbar\eta.$$

Here, α is the effective damping constant, M<sub>S</sub> is the saturation magnetization, t<sub>F</sub> is the free layer thickness, H<sub>K</sub> is the effective anisotropy field including magneto crystalline anisotropy and shape anisotropy, H<sub>ext</sub> is the external field, and η = (P2)(1 + P²cosθ) is the spin-transfer efficiency (a function of spin polarization P and the angle (θ) between the electrode magnetizations).

We plot in Fig. 5a J<sub>C</sub>(T) for the P → AP and AP → P transitions. Within 25 < T(K) < 300, J<sub>C</sub> decreases by a factor of ~2 for P → AP, and by ~30 for AP → P. No temperature dependence of FeCoB properties (M<sub>S</sub> or H<sub>K</sub>) can explain either 1) the huge change in the AP state or 2) that this decrease strongly depend on the MTJ's P/AP state. Note in particular the 10x
**Fig. 2** | Near absence of F centers in low $RxA$ MTJs.
The bias-induced change in conductance for high (blue) and low (red; MTJ-H) $RxA$ junctions in the (a) P and (b) AP states are shown. Initial inelastic tunneling is observed for both junction types up to $|V| < 0.1$ V. The (low) conductance of the high $RxA$ junction strongly increases for $|V| > 0.3$ V due to the F center$^{17,36}$, while the (high) conductance for the low $RxA$ junction remains constant in the P state, and only moderately increases in the AP state. This highlights the near absence of F centers in low $RxA$ MTJs.

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**Fig. 3** | Spectral evidence of localized states involved in transport. $\hat{I}$ plot for the MTJ-H's (left) P and (right) AP magnetic states. Beyond a weak localization/inelastic transport regime at very low bias, thermally activated transport in the P state is metallic due to a band of states that extends 400 meV from $E_F$ at 290 K. Additional states appear beyond 400 mV. No such band is found in the MTJ AP state. The P state curves have been shifted for clarity.

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**Fig. 4** | Localized states impact ST-FMR. A ST-FMR spectra at 300 K on a MTJ-INL device for different bias voltages at $\theta = 185^\circ$ and $H_{ext} = 400$ Oe. The inset shows magnetoresistance (MR) measured at 100 µA. The bias dependence of (b) parallel and (c) perpendicular torkance obtained from fits to the data of (a) change trends at 400 mV.

<figure><img src="image_8.png" /></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 5 | Experimental anomalies in the temperature dependence of the critical current density $J_C$. a Temperature dependence of $J_C$ for $P \to AP$ (black) and $AP \to P$ (red) STT switching. A MTJ-INL device was used. b Experimental and analytical temperature dependencies of $J_C^{P \to AP}/J_C^{AP \to P}(T)$.</figcaption></figure>

reduction in $J_C^{AP \to P}$ within $250 < T < (K) < 300$, even as $J_C^{P \to AP}$ decreases by ~0.5. We also find that the thermal activation coefficient of $J_C$ is 10x higher for $AP \to P$ compared to $P \to AP$ (data not shown). Finally, we plot the experimental and analytical temperature dependencies of $J_C^{P \to AP}/J_C^{AP \to P}(T)$ in Fig. 5b. We observe opposite trends and a clear deviation at high temperature.

## Discussion

Low RxA MTJs now reach a lateral size of 2 nm$^{43}$, and enjoy a broad range of communications$^{10–12}$ and energy$^{8,13,14,56}$ applications, yet understanding the actual nanotransport path$^{37,39}$ across these devices has remained elusive. With this goal in mind, we infer the following facts from our bias-and temperature dependent magnetotransport data, our ST-FMR data and our STT critical current data presented above, obtained on low RxA MTJs and compared with high RxA MTJs:

1. Low RxA MgO MTJs owe their much higher conductance to a much increased density of double oxygen vacancies (M centers) at the expense of single oxygen vacancies (F centers). This is consistent with a prior report demonstrating that switching from ac sputtered MgO to dc sputtered Mg + oxidation – which is also used to form low RxA MTJs$^{51,52,54,57–60}$, increases the ratio of double to single oxygen vacancies$^{19}$.

2. Low RxA MgO MTJs are metallic in the P state due to in-gap states that span $E_F$ and extend up to 0.4 eV. These states aren't visible in the $\hat{I}_{AP}$ thermal activation spectroscopy. Since it is improbable that a mere $P \leftrightarrow AP$ switching of ferromagnetic electrode alignment would extinguish these in-gap states, we infer that transport also proceeds onto these mid-gap states in the MTJ AP state, but that its thermal activation is overshadowed by that of enduring tunneling in the counterelectrode due to mismatched electron spin/symmetry$^{29,45,47,48}$ (within 200 mV, the change in $\hat{I}_{AP}$ ~ 6x $\hat{I}_P$ for $T_2 = 90$ K, see Fig. 3). This would explain the absence of a spectral signature in $\hat{I}_{AP}$.

3. Low RxA MgO MTJs exhibit critical currents toward STT whose temperature dependence cannot be explained by ferromagnetic electrode properties alone.

We point out that the $\hat{I}_P$ and ST-FMR spectroscopies carry the signature$^{36}$ at 400 meV from $E_F$ of the M\* double oxygen vacancy (see Figs. 3 and 4b, c). Its thermal activation is dominant in the $250 < T(K) < 300$ temperature range$^{36}$, in agreement with the $\hat{I}_P$ data (see Fig. 3), and with the $\times 10$ decrease in the $J_C^{AP \to P}(T)$ data (see Fig. 5a). Due to its $\Delta_1$ character$^{19,28}$, transport in the MTJ's AP state across the M\* center would lead to semi-conducting transport due to electron spin/symmetry mismatch in the MTJ counterelectrode. However, the M\* center's density of states does not intersect the Fermi level of a FeCoB/MgO/FeCoB MTJ$^{28,36}$.

An isolated F center generates states 0.7 eV from $E_F$ in a FeCoB/MgO/FeCoB MTJ$^{28,36,38}$. Two F centers, when brought together as a M center form an anti-bonding state 0.4 eV from $E_F$. We propose that, in low RxA MTJs, the localized states that cross $E_F$ and generate spectral weight at 0.4 eV from $E_F$ arise from anti-bonding states of higher energy due to an oxygen vacancy complex comprised of more than two oxygen vacancies$^{17,19,28,36,37,40}$. Put differently, low RxA MTJs should have a comparatively higher density of oxygen vacancies than even moderately high RxA MTJs in which M centers dominate$^{19}$. This picture is consistent with the decrease in F center weight as the RxA product is decreased (see Fig. 2).

To test this premise, and inspired by the phenomenological 'pinhole' description of defect-mediated transport across MTJs, we performed ab-initio calculations of the electronic properties of a Fe/MgO(5 ML)/Fe MTJ in which an oxygen vacancy complex composed of a zig-zag chain of oxygen vacancies that spans the MgO barrier has been inserted (see Fig. 6a and Methods for details). We first observe that, in the defect free-case (panel b), metal-induced gap states (MIGS) appear on the first two ML away from each interface, but promote no DOS at $E_F$ on the 3rd, central MgO layer. We thus dispel the commonly bandied argument that MIGS are responsible for metallic conduction in low RxA MTJs with 5 ML or more of MgO. In contrast, the oxygen vacancy complex we've considered, by virtue of anti-bonding states with a higher energy than those of a M center, does indeed generate a DOS on the MgO 3rd ML that spans $E_F$. This validates our premise. We naturally refrain from explicitly ascribing our experimental data to this particular oxygen vacancy complex, but do note certain spectroscopic resemblances, such as the increase in DOS for $E-E_F < -0.6$ eV (compare the 3rd MgO ML data of Fig. 6c with the $\hat{I}_P$ data of Fig. 3 and the ST-FMR data of Fig. 4b and c, keeping in mind the 0.25 eV Fermi level shift when going from Fe to FeCoB$^{36}$). This candidate also leads to a TMR of ~100%, in broad agreement with experiments. Other oxygen vacancy complex candidates may theoretically yield similar features, but our experimental spectra around $E_F$ are broadened by other effects (e.g. magnon generation) that prevent a more precise discrimination between these theoretical candidates.

To resolve basic contradictions between the conceptual understanding of spin-transfer torque across MgO and experiments on key spintronic green nanotechnology components, we have measured magnetotransport and ST-FMR on low RxA MTJs from two fablines, and compared results with those obtained on high RxA junctions. We attribute the anomalous metallic conductance in the low RxA MTJ's P state to the presence of an oxygen vacancy complex formed of more than two oxygen vacancies. Its density of states spans the Fermi level, and derives from the double oxygen vacancy, which accounts for experimental spectral features in magnetotransport and ST-FMR, and in the thermal dependence of the spin-transfer torque critical current. Ab-initio calculations confirm that a zig-zag chain of
<figure><img src="image_10.png" /><figcaption>**Fig. 6 | An oxygen vacancy complex in a MgO MTJ whose DOS intersects the Fermi level: a possible candidate.** A schematic of the zig-zag chain of oxygen vacancies in 5 ML f.c.c. MgO(001) spanning the bcc Fe(001) electrodes. Density of states calculated for a Fe(MLs 1-4)/MgO(5 ML)/Fe(MLs 5-7) MTJ, with (b) intrinsic/defect-free MgO, and (c) a zig-zag chain of oxygen vacancies that spans the</figcaption></figure>

MgO layer (a). In (c), the P (black) and AP (red) cases are distinguished. In the ideal MTJ, MIGS promote DOS at $E_F$ on the first two MgO MLs away from Fe, but not on the central MgO layer. This prerequisite toward metallic conduction is fulfilled by the zig-zag chain of oxygen vacancies complex, as a possible candidate.

oxygen vacancies that spans the MgO barrier constitutes a possible candidate for this oxygen vacancy complex.

Our work adds MgO MTJs to the burgeoning list of oxide electronic devices whose operation is defect-mediated. This paradigm of oxygen vacancy-driven spin-transfer torque has implications on how small a MgO MTJ can be laterally¹⁹,⁴³,⁶¹,⁶², with an ultimate lateral limit around 7-8 ML MgO¹⁹, i.e. close to the present 2 nm experimental node⁴³. This paradigm also opens new perspectives⁸,⁶³,⁶⁴ on utilizing the oxygen vacancy's properties (e.g. optical absorption) toward additional device functionalities. Mastering oxygen vacancies in industrial MTJs could enable their dual-use not only as memory devices, but also as energy harvesters of ambient heat¹³,¹⁴,⁵⁶. These are examples of using this technological platform, with controlled discrete electronic states, as a vector to industrialize quantum physics⁶⁵. This paradigm of oxygen vacancy-enabled electronic device operation, using the 'simple' MgO oxide, should more broadly inspire the oxide electronics community as it goes nanoscale² to implement 'more than Moore' concepts.

## Methods
### MTJ fabrication

The low $RxA$ stacks nanopillar devices were grown and fabricated using fablines at TDK-Headway Inc. USA (labeled MTJ-H) and International Iberian Nanotechnology Laboratory (INL; labeled MTJ-INL), Portugal, respectively⁴¹,⁵²,⁵⁴,⁵⁷⁻⁶⁰. Details of the MTJ-H nanopillar devices are kept confidential by TDK-Headway Inc. USA. The MTJ-H nanopillar devices feature out-of-plane magnetic anisotropy, whereas MTJ-INL nanopillar devices features in-plane magnetic anisotropy. The nanopillar MTJ-INL devices were processed from the following stack: $Al_2O_3(100)/Ta(3)/CuN(30)/Ta(5)/Pt_{38}Mn_{62}(17)/CoFe_{30}(2)/Ru(0.85)/CoFe_{40}B_{20}(2.6)/MgO$ (wedge=0.6-0.9 nm)/$CoFe_{40}B_{20}(1.4)/Ru(10)/Cu(150)/Ru(30)$ (all numbers in nm)⁵⁴. A typical MTJ-INL device had an elliptical shape with a major (minor) axis of 250 (150) nm and TMR at 293 K (13 K) was 136% (235%). Its $RxA$ product in P (AP) state was 26.71 $\Omega \cdot \mu m^2$ (63.22 $\Omega \cdot \mu m^2$) at 293 K and 26.20 $\Omega \cdot \mu m^2$ (88.37 $\Omega \cdot \mu m^2$) at 13 K. To obtain the temperature dependence of the critical current density ($J_c$) for STT switching, a small magnetic field of 42 Oe was applied to compensate the stray field produced by the bottom electrode to ensure both P and AP states are maintained individually over the temperature range $10 < T(K) < 300$. At a given temperature, each reversal was repeatedly measured, such that a mean $J_c$ and its standard deviation were extracted.

To make high $RxA$ MTJs, $Ta(5)/Co(10)/IrMn(7.5)/FeCoB(4)/MgO(2.5)/FeCoB(4.5)/Ta(5)/Pt(5)$ samples were sputter-grown at the Institute Jean Lamour (Nancy) on Corning 1737 glass substrates. MgO was ac sputtered in a pure Ar partial pressure. All numbers inside parentheses are in nanometers. Stacks were post-annealed in an in-plane magnetic field

of 200 Oe for 1 h at 300 °C to both crystallize the MgO barrier and pin the lower electrode, thanks to the IrMn synthetic antiferromagnetic (SAF) layer. Samples were then processed within the STNano technological platform by optical lithography into 20 µm-diameter junctions with a typical $RxA = 6 \times 10^7 \Omega \cdot \mu m^2$. Typical TMR values are 105% (200%) at 300 K (10 K).

### ST-FMR measurements

ST-FMR measurements were performed on 220 nm-diameter MTJ-INL devices with a $RxA$ product in the MTJ P (AP) state of 13.11 $\Omega \cdot \mu m^2$ (27.59 $\Omega \cdot \mu m^2$) at room temperature. The direction of equilibrium magnetization of the reference layer is taken along the positive x-axis with $\theta = 0^\circ$, where $\theta$ is the in-plane field angle. The AP state is obtained at $H = 0$. We used the radio frequency current modulation spin-torque ferromagnetic resonance (RFM-STFMR) technique: a rf current $I_{rf} \cos(2\pi f) \cdot t$ was modulated onto a reference signal of 98 Hz and fed to the MTJ. A dc current ($I_{dc}$) was simultaneously applied across the MTJ using a bias-tee. The output voltage ($V_{mix}$) is measured across the MTJ by using a lock-in amplifier by sweeping the frequency of $I_{rf}$ signal. We observe two distinct modes, and used the lower frequency mode with higher intensity to calculate torkance⁶⁶.

The detected voltage $V_{mix}(f)$ is given by:

$$V_{\text{mix}}(f) = C + V_S S(f) + V_A A(f) \quad (1)$$

Where, $C = \frac{1}{4} \frac{\partial^2 V}{\partial I^2} I_{rf}^2$ is the non-resonant background signal. $S(f) = \frac{1}{1+(f-f_r)^2/\sigma_r^2}$ is the symmetric Lorentzian and $A(f) = \frac{f-f_r}{\sigma_r}$ is the antisymmetric Lorentzian. $\sigma_r$ is the spectral linewidth (changes with bias current), and $f_r$ and $f$ are the resonance frequency and microwave signal frequencies, respectively. Multiple modes were fitted using additional Lorentzian functions. The amplitudes of Lorentzian function, $V_S$ and $V_A$ depend on the derivative of spin-torque (i.e. torkance) as⁶⁷:

$$V_S = \frac{1}{2} \left( \frac{\partial^2 V}{\partial \theta \partial I} \right) \frac{\hbar \gamma \sin \theta}{4 e M_S V \sigma_r} I_{rf}^2 \left[ \frac{2e}{\hbar \sin \theta} \right] \frac{d\tau_{\parallel}}{dI} \quad (2)$$

and

$$V_A = \frac{1}{2} \left( \frac{\partial^2 V}{\partial \theta \partial I} \right) \frac{\hbar \gamma \sin \theta}{4 e M_S V \sigma_r} I_{rf}^2 \left[ \frac{2e}{\hbar \sin \theta} \right] \Omega_{\perp} \frac{d\tau_{\perp}}{dI} \quad (3)$$

where $M_S = 1.36 \times 10^6$ A/m is the saturation magnetization, $d\tau_{\parallel}/dV$ is the parallel torkance, and $d\tau_{\perp}/dV$ is the perpendicular torkance, $\Omega_{\perp} = \gamma(4\pi M_{\text{eff}} + H_{\text{ext}})/2\pi f_r$ with $4\pi M_{\text{eff}}$ effective magnetic anisotropy, $H_{\text{ext}} = 400$ Oe is the external magnetic field applied during the
measurement, and $f_r = 4.53$ GHz is the resonance frequency of the lower frequency mode. The value of the $I_{rf}$ is calculated by measuring the $S_{11}$ parameter using a vector network analyzer (VNA)$^{68}$. $I_{rf} = \sqrt{\frac{2P_{rf}(1-R_f)}{R_{dc}}}$, with $R_f = 10^{S_{11}/10}$. In the present case, the reflection was found to be 10% within a frequency range of (2–10) GHz.

## Data availability

The data presented in this work is available upon reasonable request.

Received: 2 September 2024; Accepted: 16 November 2024;

Published online: 07 January 2025

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## Acknowledgements

We thank Luc Thomas for providing stacks from the TDK-Headway fabline, and for stimulating discussions. L.M.K. acknowledges Ph.D. fellowship received from 'Centre Franco-Indien pour la Promotion de la Recherche Avancée/Indo-French Center for the Promotion of Advanced Research (CEFIPRA/IFCPAR)'. L.M.K. further acknowledges Olivier Fruchart for his keen interest and constant encouragement in this research work. M.B. and P.K.M. acknowledge support from the 'CEFIPRA/IFCPAR' for this collaborative work via Project No. 5604-3. We acknowledge funding from the Agence Nationale de la Recherche (ANR-09-JCJC-0137, ANR-14-CE26-0009-01), the Labex NIE 'Symmix' (ANR-11-LABX-0058 NIE), MICA Carnot 'Spinterface'. This work is supported by France 2030 government investment plan managed by the French National Research Agency under grant reference PEPR SPIN – SPINMAT ANR-22-EXSP-0007. Calculations were performed using HPC resources from the Strasbourg Mesocenter and from the GENCI-CINES (Grant No gem1100). We acknowledge the use of STNano facilities for some device processing.

## Author contributions

M.B., L.M.K. and P.K.M. conceived the experiment. J.D.C., T.B., R.F., P.F., and M.H. grew the samples and performed nanojunction processing. L.M.K. and E.M performed magnetotransport measurements with the help of K.K., F.S., M.B., D.L., M.H., and A.K. L.M.K. modeled the critical current temperature dependence. B.T. performed DFT calculations with input from M.A. and M.B. L.M.K. plotted and analyzed DFT results with input from B.T., M.A. and M.B. A.K., L.M.K., P.G. and P.K.M. performed and analyzed ST-FMR measurements/results. W.W., V.D.C., S.B. contributed to overall analysis. M.B and L.M.K. wrote the manuscript with input from all authors.

## Competing interests

The authors declare no competing interests.

## Additional information

Correspondence and requests for materials should be addressed to L. M. Kandpal or M. Bowen.

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