Voltage-based magnetization switching and reading in magnetoelectric spin-orbit nanodevices

As CMOS technologies face challenges in dimensional and voltage scaling, the demand for novel logic devices has never been greater, with spin-based devices offering scaling potential, at the cost of significantly high switching energies. Alternatively, magnetoelectric materials are predicted to enable low-power magnetization control, a solution with limited device-level results. Here, we demonstrate voltage-based magnetization switching and reading in nanodevices at room temperature, enabled by exchange coupling between multiferroic BiFeO3 and ferromagnetic CoFe, for writing, and spin-to-charge current conversion between CoFe and Pt, for reading. We show that, upon the electrical switching of the BiFeO3, the magnetization of the CoFe can be reversed, giving rise to different voltage outputs. Through additional microscopy techniques, magnetization reversal is linked with the polarization state and antiferromagnetic cycloid propagation direction in the BiFeO3. This study constitutes the building block for magnetoelectric spin-orbit logic, opening a new avenue for low-power beyond-CMOS technologies.

After 50 years of continuous transistor size downscaling and increased performance 1 , future iterations of logic circuits will require beyond-CMOS alternatives 2 that explore new physical effects through non-conventional materials.While Moore's law is still sustained by increasingly complex transistor designs and lithography advances 3 , the last decade saw a clear breakdown of Dennard's scaling, where smaller transistors no longer mean smaller operational voltages, compromising the energy efficiency and performance of future chips.In recent years, a flurry of new logic devices has emerged, driven by the usage of alternative state variables, such as spin, polarization, strain, and orbital 4 .Among these options, spin-based solutions have shown tremendous promise and applicability 5 .Owing to their non-volatile nature, effects like spintransfer torque (STT) and spin-orbit torque (SOT) brought major improvements in stand-by power, as well as in terms of endurance, writing speed, and compatibility with back-end of line (BEOL) fabrication processes 6,7 .Yet, controlling magnetization states using these methods still requires rather large currents, preventing their usage as a realistic non-volatile logic solution.Alternatively, voltage-based methods gained some traction in recent years 8 , mainly pushed by voltage-controlled magnetic anisotropy (VCMA) 9 , where voltage-induced dynamic switching of magnetization has been reported 10 .However, an external magnetic field is normally required to control the magnetization precession, making it unsuitable for circuit applications.
A pathway for field-free voltage-based switching of magnetism has been proposed using magnetoelectric multiferroics 11 .Among several possible combinations, the coexistence of ferroelectricity and ferromagnetism is expected to allow the control of magnetization through switching of the ferroelectric polarization with an electric field.In this category, BiFeO3 has been the most studied material, exhibiting a tight coupling between antiferromagnetic (AF) and ferroelectric (FE) orders at room temperature.One of the most notable results towards multiferroic-based devices was the demonstration of magnetization reversal by 180º in a CoFe element, exchange coupled with BiFeO3, upon application of an electric field 12 .The result was interpreted considering weak ferromagnetism arising from canting of the Fe 3+ magnetic moments in BiFeO3 [13], which can couple to the magnetization of the CoFe.Upon a two-step switching of the polarization and canted magnetization in BiFeO3, the magnetization of the CoFe is expected to follow this motion and reverse 14 .
Since then, the road to multiferroic-based devices has been long and tortuous, with sparse results reported 15 .Yet, it is expected that such devices can bring magnetization writing energies down to the aJ range 16 , an improvement of several orders of magnitude when compared with state-of-the-art current-based devices.This driving force led to the recent proposal of magnetoelectric spin-orbit (MESO) logic 16 , suggesting a spin-based nanodevice adjacent to a multiferroic, where the magnetization is switched solely with a voltage and is electrically read using spin-to-charge current conversion (SCC) phenomena.In this article, we demonstrate the experimental implementation of such a device.We fabricate SCC nanodevices on BiFeO3 and analyze the reversibility of the magnetization of CoFe using a combination of piezoresponse (PFM) and magnetic force microscopy (MFM), where the polarization state of the BiFeO3 and the magnetization of CoFe are imaged upon switching.
We then correlate this with all-electrical SCC experiments where voltage pulses are applied to switch the BiFeO3 and reverse the magnetization of CoFe (writing), and SCC outputs different voltages depending on the magnetization direction (reading).Lastly, we investigate the magnetic textures at the surface of BiFeO3 using scanning nitrogen-vacancy (NV) magnetometry, where the coupling between CoFe and BiFeO3 is linked with the AF cycloid propagation direction.
In Fig. 1a, we show a sketch of the fabricated MESO nanodevice.The MESO concept can be described as an assembly of a magnetoelectric (ME) module used for writing, and a spin-orbit (SO) module used for reading 17 .The ME module comprises the multiferroic and an adjacent ferromagnet, here BiFeO3 and CoFe, respectively.Voltages pulses (Vp) are applied between a metallic La0.7Sr0.3MnO3/SrRuO3bottom electrode and the CoFe, so that the polarization (P) and the AF order (L) in the BiFeO3 can be switched, as exemplified in Fig. 1b.Here, the magnetization direction of CoFe (MCoFe) is also reversed, following the reversal of P and L, due to exchange coupling at the CoFe/BiFeO3 interface.The SO module is based on a Tshaped nanostructured device composed of CoFe and the spin-orbit material Pt, following a recent study on SCC for magnetic logic readout 18 .A spin-polarized current (Iin) is electrically driven from CoFe to Pt, where, at the Pt/CoFe junction, the spins are converted into a charge current through the inverse spin Hall effect (ISHE) and picked up as a transverse voltage VSO.
Depending on the magnetization direction, spins  are deflected either to the right or left, as shown in Fig. 1b, enabling a fully electrical method of magnetization state readout, that generates an electromotive force that can drive another circuit element.The device is based on a Pt(10 nm)/CoFe(2.5 nm)/BiFeO3(30 nm)/La0.7Sr0.3MnO3(4nm)/SrRuO3(10 nm) stack grown on a DyScO3 (110) substrate, using a combination of pulsed laser deposition and sputtering (see details in Methods).The fabrication of the device comprises positive nanolithography processes using e-beam lithography, Ar-ion milling, and sputtering, used to define both the CoFe wire (500 nm x 150 nm in lateral size), the Pt T-shaped electrode, and contacts.The device is capped with SiO2(5 nm) to prevent oxidation of the CoFe.Details of the fabrication process flow can be found in Supplementary Information Note 1.A scanning electron microscopy (SEM) top image of the integrated MESO nanodevice is shown in Fig. 1c, and a cross-sectional image of the Pt/CoFe junction area, taken by transmission electron microscopy (TEM) after device fabrication, is shown in Fig. 1d.We observe highly ordered epitaxial growth of the oxide heterostructure, as well as clean and sharp interfaces between BiFeO3, CoFe, and Pt.From the energy dispersive X-ray spectroscopy (EDX) maps shown in Fig. 1e, we observe minimal interdiffusion between the three layers.
We start by investigating the magnetization orientation of CoFe upon polarization reversal of the BiFeO3 using a combination of PFM and MFM.In Fig. 2a, we observe that the polarization of the bare BiFeO3 can be poled up (dark area) and down (bright area) with positive (2 V) and negative (−2 V) voltages, respectively.Then, a CoFe/Pt disk 5 μm in diameter (patterned similarly to the MESO devices) was used to measure the current and polarization vs. voltage loops, as shown in Fig. 2b and 2c, respectively.These capacitors based on a 30-nm-thick BiFeO3 show large saturation polarization (close to the bulk value), with low leakage, as well as low switching voltages.Indeed, we observe switching voltages of −0.5 V and 1.5 V underneath the metallic disk.A relatively large imprint, normally observed in thin ferroelectric films due to top and bottom contact electrostatic asymmetries, is still present, even though largely improved by the La0.7Sr0.3MnO3buffer layer 19 .As illustrated in Fig. 2d, disks 300 nm in diameter were then used to evaluate both the out-of-plane (Pout) and in-plane (Pin) polarization direction in the BiFeO3 underneath the disk, as well as the direction of MCoFe, labeled as V-PFM, L-PFM, and MFM in Fig. 2e, respectively (setup details in Methods).
From V-PFM data, we observe that Pout can be reversed between down and up states, after applying voltage pulses of −1.8 V and 2 V, respectively.Small unswitched patches were occasionally observed, either caused by incomplete switching after Vp is applied or by relaxation back to the P down state after the voltage pulse is applied (V = 0 V) due to the BiFeO3 imprint.While Pout reverses consistently, we observe from L-PFM data that Pin remains split into randomly distributed FE domains for the three voltage pulses applied.For 9 different devices probed in the same sample, Pout is always switched, while Pin exhibits mostly slight changes in the FE domain structure, suggesting a combination of local 71º/109º/180º switch of the polarization 12 .From MFM, we observe that after poling the BiFeO3 down with Vp=−1.8V, MCoFe points diagonally to the bottom right.Poling the BiFeO3 up with Vp=2 V reverses the magnetization of CoFe by nearly 180º.Poling the polarization back down with Vp=−1.8V drives a rotation of MCoFe by ~90º.Out of the 9 devices tested, the magnetization could always be switched in 3 of them (33.5%), could be partially/randomly switched in 4 (44.5%), and could never be switched in 2 (22%).Out of 24 out-of-plane polarization switching events, we observed that the magnetization switched 13 times (54%) and did not switch 11 times (46%).
Extended data and additional switching experiments can be found in Supplementary Information Note 2.
Given these results, we conclude that the reversal of MCoFe is still possible even though there is a lack of control of Pin, which should be intimately related to the in-plane component of the AF order and canted magnetization in BiFeO3.Moreover, Pout switching seems to be driving the reversal/rotation of MCoFe, but does not always guarantee it, indicating that the magnetic configuration in a uniformly out-of-plane polarized region may be more complex, a hypothesis investigated further ahead in this article.Regardless, these results reveal that the magnetization can be manipulated in nanoscale magnets interfaced with BiFeO3 using only a voltage pulse and without external magnetic fields, experimentally demonstrating the MESO writing capabilities.
We now move to the electrical experiments on the MESO nanodevices.First, we investigate the switching ability of the BiFeO3 by applying voltage pulses with a duration of 200 μs between the CoFe element and the bottom of the BiFeO3.After each pulse, we perform SCC experiments on the nanodevice, as illustrated in Fig. 1c, by applying Iin=20 A and measuring the output voltage VSO, hereinafter shown as a resistance RSO=VSO/Iin.As shown in Fig. 3a, upon switching the BiFeO3, the baseline of the SCC signal acquires two stable states, −3.48  and −3.42 .This baseline resistance reflects the slight misalignment of the CoFe element with respect to the Pt T-shaped electrode, giving rise to either a positive or negative transverse voltage 18 .The shift in baseline resistance can be explained by slight modulation of the resistivity of CoFe, either due to a static field effect from the remanent polarization in the BiFeO3 (Ref. 20), or strain induced by different ferroelastic domains.While this resistance vs. voltage loop does not give quantitative information about the polarization, we observe that the BiFeO3 directly underneath the nanodevices switches at −350 mV and 750 mV, in fair agreement with the results from PFM.As shown in Fig. 3b, the leakage current measured through the BiFeO3 layer during the voltage pulses was minimized to about 0.5-1 A (for Vp=2 V), largely due to the reduced fabricated area of CoFe and Pt in direct contact with BiFeO3.
To fully characterize the SCC results with respect to the expected MCoFe orientation, we measure RSO as a function of a rotating in-plane external magnetic field Bext=1 T, enough to fully saturate the CoFe element (Fig. 3c).Grey arrows indicate the MCoFe orientation as seen from above.RSO is dominated by the ISHE at 90º and 270º (in violet) when MCoFe points along the easy axis of the CoFe element, following a sin(), and by the planar Hall effect (PHE) at diagonal orientations (45º, 135º, 225º, and 315º) (in green), following a sin(2).Similar behavior was identified in Ref. 21 .In Fig. 3 d-f, we show RSO as a function of Bext along the CoFe long (easy) axis (90º), after voltage pulses of Vp=2 V. Voltage pulses are applied without any external magnetic field, and the loops are taken by sweeping Bext from −500 Oe to 500 Oe (in blue) and back (in green).These loops only provide information on the inherent interactions between MCoFe and BiFeO3, while the MCoFe direction manipulation right after different Vp is investigated further ahead.After applying Vp=2 V, the Bext sweep reveals that RSO decreases when Bext approaches zero, indicating that, when mapped to the angle dependence, the magnetization tilts up (Fig. 3d).After applying Vp=−2 V, we observe two possible states.In the first case, MCoFe also tilts up around Bext=0 (Fig. 3e).We postulate that given the occasional incompleteness of the polarization switching observed from PFM, the area underneath the CoFe element may be at times split into different domains, giving rise to inhomogeneous coupling.However, in Fig. 3f the magnetization loop is reversed, and MCoFe tilts down around Bext=0.Additional data concerning the reproducibility of the two fully switched magnetization loops and their correspondence with the angle dependence can be found in Supplementary Information Note 3 and 4. Unlike T-shaped devices fabricated on Si/SiO2 substrates where at zero external magnetic field MCoFe points to the right (90º) or to the left (270º) due to shape anisotropy 18 , on BiFeO3 the CoFe magnetization may be pulled in any direction, depending on the magnetic textures underneath the CoFe.The observed tilt of MCoFe in our devices suggests that the exchange energy is larger than the shape anisotropy, leading to non-trivial MCoFe orientations in the absence of external magnetic fields.Additionally, we show in Fig. 3g that the CoFe coercivity Hc, obtained by the difference between switching fields, changes deterministically between ~500 Oe and 200 Oe, as observed in previous reports of exchange coupling at CoFe/BiFeO3 interfaces 22,23 .However, no evident correlation is seen between Vp and the exchange bias HEB (Fig. 3h), obtained by the sum of the switching fields, suggesting prevalent exchange coupling with the AF order 24 , rather than the weak ferromagnetism in BiFeO3, that would pull the magnetization in opposite directions depending on the polarization state.
Moving towards a scenario that is closer to the full implementation of MESO logic, we now investigate the MCoFe orientation right after applying Vp=2 V. We note that, since MCoFe is tilted when Bext=0 T, the reading function of the MESO device will mostly rely on the PHE instead of the ISHE.While this may reduce the overall output reading voltage, it is still sufficient to electrically probe the magnetization direction in our experiments.
In Fig. 4a, we initialize the magnetization direction in the top right direction (black arrow) by applying a Vp=−2 V and sweeping the external magnetic field from 0 to 400 Oe and back.From this known state, we apply Vp=2 V at zero magnetic field and measure RSO as a function of Bext, to see to which branch of the full loop (of Fig. 3d) this half sweep corresponds.As shown in Fig. 4b, a higher initial RSO is observed, corresponding to a magnetization rotation by 90º counterclockwise (in blue).Out of eight attempts, this behavior was observed four times (in the same device), with the remaining attempts showing no noticeable change in RSO (in grey).
We then initialize the magnetization direction in the top left direction (Fig. 4c), by applying Vp=2 V and sweeping the magnetic field from 0 to −400 Oe and back.From this state, we observe that a negative voltage pulse Vp=−2 V can lead to two outcomes, as shown in Fig. 4d.In the first one, after applying Vp=−2 V the magnetization shows no rotation (in grey).The magnetization is then realigned to the top left, by sweeping the magnetic field from 0 to −400 Oe and back, and a second Vp=−2 V is applied.This time, RSO starts with a higher RSO, corresponding to a 180º reversal of MCoFe.This behavior was observed in eight out of nine switching attempts.The full switching data and statistics can be found in Supplementary Information Notes 5 and 6.All-in-all, these results demonstrate magnetization rotation/reversal We further investigate the nature of the coupling between CoFe and BiFeO3, which is expected to be responsible for the switchable MCoFe.While the switching mechanism may be explained by coupling between MCoFe and the canted magnetization in BiFeO3 (Ref. 12), the spin cycloid, reported in BiFeO3 thin films grown on DyScO3 substrates 25,26 , may complicate this interpretation.Indeed, through scanning nitrogen-vacancy (NV) magnetometry, we show in Fig. 5a that the cycloid is also present in our 30-nm-thick BiFeO3, with a rotating AF order propagating in diagonal directions with a period of about ~70 nm, and changing its propagation direction (Q) by 90º in neighboring FE domains 27 .Here, the periodic variation of the magnetic stray field comes from the spin-density wave that is locked to the cycloid and perpendicular to the cycloidal plane defined by Q and P (Ref. 26,28).As exemplified in Fig. 5b, given the dimensions of the CoFe nanostructured element in our MESO devices, represented by the white rectangle, five full rotations of the AF order within each one of the single FE domain stripes are expected to interact with MCoFe, with two of these rotations within the Pt/CoFe junction area (black rectangle).Within this area, the canted magnetization in BiFeO3 should, in principle, average to zero.Since the magnetization in the CoFe is shown to be pulled in diagonal directions in the absence of external fields, as seen from the MFM and the electrical read-out characterization, we infer that MCoFe may in fact couple with Q (Fig. 5c).Through this type of coupling, a rotation of Q by ~90º/180º, for a partially or fully switched BiFeO3, respectively, may be responsible for the reversal/rotation of MCoFe.
We finish by discussing the reproducibility and non-deterministic aspects of our results, in light of the complex ferroelectric and magnetic textures of BiFeO3.For two identical devices fabricated over different regions of the BiFeO3, MCoFe may interact with completely different magnetic textures.Depending on this interaction, MCoFe may initially be pulled in different directions, so that the same voltage pulse polarity will drive different rotation/reversal paths, as observed in the PFM/MFM data in Supplementary Information Notes 2. This lack of correspondence between positive and negative voltage pulses with specific directions of MCoFe makes device-to-device reproducibility a real challenge.Not only that, but due to "maze-like" magnetic regions observed in Fig. 5a, some devices may not even exhibit a clear coupling with the BiFeO3.These issues may potentially be solved by better control of the ferroelectric domain structure of BiFeO3 itself (or another multiferroic), ideally culminating in controlled single macroscopic domain regions with a coherent cycloid propagation 29,30 that can be effectively switched 31 .Alternatively, the overall absence of the cycloid could simplify the coupling mechanism, where MCoFe would couple with a uniform AF order in the multiferroic.
Besides these fundamental issues, the future implementation of MESO logic will require additional improvements on both the ME and SO modules.Unlike STT or SOT current-based solutions, the reliability of the writing on MESO devices does not improve with larger input signals.In fact, as long as the BiFeO3 can be engineered to switch robustly at lower voltages, the writing energies can be progressively reduced without compromising the reliability of the writing.The key elements to consider are the coupling between the magnet and the BiFeO3, together with a soft magnet that can easily "follow" the magnetic motion in the multiferroic, while maintaining an overall thermally stable magnetization state and FE domain structure.
Further miniaturization of the magnetic and spin-orbit elements to sub-100-nm features, together with the reduction of BiFeO3 thickness, switching voltages (through La doping 32,33 ), leakage currents (through Mn doping 34 ) and switching pulse duration (down to tens of ns 35 ) are pathways to reduce the switching energies to fJ and aJ ranges.In terms of endurance, the bottleneck comes from the degradation of the CoFe/BiFeO3 interface with voltage cycling, given the possible formation of an oxidized or intermixed interfacial magnetic layer, as well as the degradation of BiFeO3 itself.Solutions such as all-oxide epitaxial structures are one possible avenue to improve this 36 .On the SO module side, SCC output voltages between opposite magnetization states need to be at least comparable with the switching voltages of BiFeO3, and ideally based on the SHE instead of PHE, to make it scalable 18 .For an input reading current of 100 μA, our SCC devices only show Vout=1 μV, while optimized Pt-and Ta-based devices reaching 30 μV and 0.35 mV, respectively, have been reported 18,37 .
Nevertheless, additional efforts are required to reach hundreds of mV, potentially through allelectrical SCC in more exotic systems, such as topological insulators 38 and oxide heterostructures.
In conclusion, we have shown voltage-based writing and reading of magnetic states in a CoFe nanostructured element coupled with multiferroic BiFeO3, representing the proof-of-principle for the MESO logic concept.Through a combination of PFM and MFM, we observe that the magnetization of CoFe can undergo 90º and 180º rotation/reversal, when the out-of-plane FE polarization of BiFeO3 is switched using voltage pulses of 2 V. Using CoFe and Pt-based Tshaped nanostructures, we electrically detected the magnetization rotation/reversal, which leads to different voltage output states depending on the direction of CoFe magnetization.The presence of a spin cycloid with a period smaller than the size of the nanostructured magnet suggests that the magnetization control is driven by coupling with the propagating AF cycloid in BiFeO3.While further work is required in terms of controllability and reproducibility of the switching, specifically regarding the ferroelectric and magnetic textures in BiFeO3, these results provide a key step forward towards voltage-control of magnetization in nanoscale magnets, essential for future low-power spin-based logic and memory devices.

Sample preparation
The DyScO3(110) substrates were purchased from MTI Corporation and were cleaned with 20 min sonication at room temperature in acetone.The DySsO3 substrates were bonded onto an Inconel carrier using silver paint.The silver paint was cured on a hot plate heated to 185ºC.The SrRuO3, La0.3Sr0.7MnO3,and BiFeO3 were deposited using pulsed laser deposition with a laser fluence of approximately 1.5 J/cm 2 at 10 Hz and oxygen pressure of 150 mTorr.The SrRuO3 was deposited at 690ºC and the La0.3Sr0.7MnO3and BiFeO3 were deposited at 650ºC to minimize the Mn diffusion.The Co and Pt were deposited by physical vapor deposition in an in-situ magnetic field of ~300 to 400 Oe.A short vacuum break after the pulsed laser deposition (less than 45 seconds) was used to place the DyScO3 Inconel carrier onto the physical vapor deposition sample holder configured with permanent magnets.

Nanodevice fabrication
The devices were fabricated on Pt(10 nm)/CoFe(2.5 nm)/BiFeO3(30 nm)/ La0.7Sr0.3MnO3(4nm)/SrRuO3(10 nm)/DyScO3(110) samples (described above) with a multiple-step e-beam lithography, metal and oxide sputtering deposition, Ar-ion milling and lift-off process.Milling of the initial CoFe/Pt is performed with the ion gun at 10º with respect to the sample surface normal, an Ar flow of 15 s.c.c.m., an acceleration voltage of 50 V, a beam current of 50 mA and a beam voltage of 300 V. Side wall milling of nanostructures after lift-off is performed in the same conditions, with an angle of the ion gun at 80º.Control of the milling rates is achieved through real time end-point mass spectrometer and resistivities of milled films.Pt T-shaped nanostructures are fabricated using a positive PMMA 950A2 e-beam resist and deposited by magnetron sputtering with a rate of 1.25 Å.s −1 , 80 W of power, 1.010 −8 mtorr of base pressure, 3 mtorr of Ar pressure.Isolation layer for wire bonder contact pads of Al2O3 is fabricated with a double-layer PMMA 495A4 + PMMA 950A2 resists and deposited with RF magnetron sputtering with a rate of 0.2 Å.s −1 , 300 W of power, 1.0×10 −8 mtorr of base pressure, 3 mtorr of Ar pressure.All lift-offs were performed using acetone.

Transmission electron microscopy and EDX
STEM and EDX studies were performed on Titan 60-300 Electron Microscope (FEI, Netherlands) at 300 kV accelerating voltage.The microscope was equipped by x-FEG, gun monochromator, retractable RTEM EDX detector (EDAX, USA) and HAADF detector.STEM images were acquired at nominal spot size 9, 10 mrad convergence angle, and −50 V relative gun lens potential.EDX mapping was done at a nominal spot size of 6 and −15 V gun lens potential to provide a sufficient count rate.The cross-sections of the devices were prepared by a standard FIB lamellae fabrication technique: a protective Pt layer was deposited first by e-beam followed by ion-beam deposition, lamellae of ~2 μm thickness were undercut and transferred onto a copper half-grid, thinned there to ~200 nm by 30 keV Ga + beam, and finally polished to ~20 nm at 5 keV.

Piezoresponse force microscopy
PFM experiments were conducted with an atomic force microscope (Nanoscope V multimode, Bruker).Two external lock-in detectors (SR830, Stanford Research) were used to simultaneously acquire vertical and lateral piezoresponses.An external source (DS360, Stanford Research) was used to excite the La0.7Sr0.3MnO3/SrRuO3bottom electrode (ac 0.6 V peak-to-peak at 35 kHz) while the conducting Pt-coated tip was grounded.Pt-coated tips (Budget Sensors) with 40 Nm -1 cantilevers were chosen for these images.For the experiments on the bare BiFeO3 surface (Fig. 2a), the same source was used to write domains with a dc voltage while scanning.For the experiments on devices (Fig. 2c), write voltage pulses (1 sec) were applied while the tip was in contact with Pt/CoFe top electrode but not scanning.

Magnetic force microscopy
The MFM observation of the Pt/CoFe nanostructures has been performed in a setup under low pressure, of the order of P = 10 -6 mbar.Images were obtained at room temperature using magnetic tips in a double-pass tapping-lift mode, detecting the phase shift of the second pass after a topographic measurement and thus probing the magnetic field gradient along the vertical direction.Tips were fabricated in our laboratory by depositing a magnetic coating on commercial silicon tips with magnetic sputtering, whose thicknesses were in the range 3-23 nm for CoFeB, which we selected for their particularly low degree of perturbation on the magnetic configurations under observation and improved signal-to-noise ratio, with quality factor Q = 1,500 and spring constant k = 0.4 N m −1 .

Electrical characterization
Transport measurements are performed in a Physical Property Measurement System from Quantum Design, using a "d.c.reversal" technique with a Keithley 2182 nanovoltmeter and a 6221 current source at 300 K.The input current Iin for the measurements is 20 μA.Gate voltage pulses are applied with a Keithley 2636B Sourcemeter, with pulse duration of 200 μs.Samples are mounted in a rotatable sample stage and the external magnetic field Bext is applied with a superconducting solenoid magnet.Devices are contacted using a wire bonder, with Au wire heated at 70 ºC and a force of 20 cN.

Scanning NV magnetometry
The antiferromagnetic spin textures of BiFeO3 are imaged using a commercial scanning N-V magnetometer (ProteusQ™, Qnami AG) operated under ambient conditions.In our setup, the scanning tip is a commercial all-diamond probe with a single N-V defect at its apex integrated on a quartz tuning fork (Quantilever™ MX, Qnami AG).The diamond tip is integrated into a tuning-fork-based atomic force microscope combined with a confocal microscope optimized for single N-V defect spectroscopy.

Figure 1 -
Figure 1 -MESO nanodevice and material characterization.a, MESO device configuration composed of a DyScO3 substrate, La0.7Sr0.3MnO3/SrRuO3bottom electrodes, multiferroic BiFeO3, magnetic CoFe element and a high spin-orbit material Pt.The logic state variable is given by the magnetization direction in CoFe.b, Writing is achieved by applying voltage pulses Vp between the CoFe and the bottom electrode, switching the polarization P and AF order L of BiFeO3, which reverses the magnetization MCoFe of CoFe.Reading is achieved through SCC phenomena, where a spin-polarized current Iin is injected into Pt, leading to different transverse output voltages VSO, depending on the initial orientation of the injected spins . c, SEM topview image of the fabricated nanodevice.Iin is applied between lead 1 and ground GND, and VSO is detected between leads 2 and 3. d, TEM cross-sectional image at the Pt/CoFe junction region on the fabricated nanodevice.e, EDX elemental maps of Bi (from the BiFeO3 layer), Co (from the CoFe layer) and Pt at the Pt/CoFe junction region.

Figure 2 -
Figure 2 -PFM and MFM characterizations.a, Out-of-plane polarization Pout after a box-inbox switching experiment on the bare BiFeO3 surface.Dark and bright areas correspond to polarization poled up and down, respectively.b, Current and c, polarization vs. voltage loops on Pt/CoFe disks 5 m in diameter over BiFeO3/SrRuO3/DyScO3, collected with a frequency of 5 kHz.d, Sketch of the PFM and MFM experiments.Dashed line corresponds to the area scanned with PFM and MFM.e, Out-of-plane (V) and in-plane (L) PFM phase images after applying voltage pulses of −1.8 V, 2 V, and −1.8 V to a Pt/CoFe disk 300 nm in diameter, showing the FE domains in BiFeO3 underneath the disk.Corresponding MFM images showing the magnetization direction of the CoFe after each pulse, represented by the grey arrows.

Figure 3 -
Figure 3 -Electrical characterization of MESO nanodevices.a, Baseline of the output resistance RSO and b, leakage current Ileak as a function of the voltage pulse Vp applied between the Pt/CoFe nanodevice and the back of the BiFeO3.Two resistance states are visible depending on the polarization P. Resistances are collected 1 s after the pulse is applied.c, RSO as a function of the angle of an in-plane external magnetic field Bext=1 T (black curve), after Vp = −2 V.The data is decomposed in an inverse spin Hall effect (SHE, in violet) and a planar Hall effect (PHE, in green) component.Grey arrows represent the magnetization of CoFe as seen from the top (see top-view sketch above).RSO as a function of Bext applied along the long axis of CoFe, after d, Vp=2 V, e, Vp=−2 V (inhomogeneous coupling) and f, Vp=−2 V (fully reversed).The blue and green curves correspond to a Bext sweep from −500 Oe to 500 Oe and back, respectively.Arrows represent MCoFe as seen from the top.g, Coercivity Hc and h, exchange bias HEB of the CoFe element as function of different voltage pulses alternating between Vp=2 V and Vp=−2 V (grey bars).

Figure 4 -
Figure 4 -Voltage-based magnetization switching and reading in MESO nanodevices.a, Initialization of MCoFe after Vp=−2 V. RSO as a function of Bext applied along the long axis of CoFe, swept from 0 Oe to 400 Oe and back to 0 Oe, where the magnetization finally points to the top right (black arrow).Dashed line illustrates the other branch of the full RSO loop, as seen in Fig. 3e.b, RSO as a function of Bext, swept from 0 Oe to 400 Oe, after applying Vp=2 V.The blue curve shows a switch of MCoFe (arrow pointing to the top left), with a higher initial RSO that then reverts to the initial state with increasing Bext.The grey curve represents a nonswitch.c, Initialization of MCoFe after Vp=2 V, with Bext swept from 0 Oe to −400 Oe and back to 0 Oe, where the magnetization finally points to the top left (black arrow).Dashed line illustrates the other branch of the full RSO loop, as seen in Fig. 3d.d, RSO as a function of Bext, swept from 0 Oe to −400 Oe, after applying two Vp=−2 V.After the first pulse, MCoFe is not switched (grey curve).After the second pulse, the red curve shows a switch of MCoFe (arrow pointing to the bottom right), with a higher initial RSO that then reverts to the initial state with increasing negative Bext.Sketches of the MCoFe direction after each voltage pulse are shown below.

Figure 5 -
Figure 5 -Magnetic textures and spin cycloid in BiFeO3.a, NV magnetometry images on the bare BiFeO3 surface where the MESO nanodevice was fabricated.b, Zoomed region with a superimposed sketch (to scale) of the MESO nanodevice, revealing the possible complex magnetic behavior underneath the CoFe element.c, Suggested coupling mechanism between MCoFe and the propagation direction of the cycloid Q.