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Manipulating chiral-spin transport with ferroelectric polarization 00footnotetext: ∗ E-mail: xzchen@berkeley.edu, rramesh@berkeley.edu
Present and permanent address of Olle Heinonen: Seagate Technology, 7801 Computer Avenue, Bloomington MN 55435

Xiaoxi Huang Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA Xianzhe Chen Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA Materials Sciences Division, Lawrence Berkeley National Laboratory, CA 94720, USA Yuhang Li Department of Electrical and Computer Engineering, University of California, Riverside, CA 92521, USA John Mangeri Materials Research and Technology Department, Luxembourg Institute of Science and Technology (LIST), Avenue des Hauts-Fourneaux 5, L-4362, Esch/Alzette, Luxembourg Hongrui Zhang Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA Maya Ramesh Department of Materials Science and Engineering, Cornell University, Ithaca, NY 14853, USA. Hossein Taghinejad Department of Physics, University of California, Berkeley, CA 94720, USA Peter Meisenheimer Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA Lucas Caretta Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA Sandhya Susarla Materials Sciences Division, Lawrence Berkeley National Laboratory, CA 94720, USA School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85281, USA Rakshit Jain Department of Physics, Cornell University, Ithaca, NY 14853, USA Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY 14853, USA Christoph Klewe Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Tianye Wang Department of Physics, University of California, Berkeley, CA 94720, USA Rui Chen Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA Cheng-Hsiang Hsu Materials Sciences Division, Lawrence Berkeley National Laboratory, CA 94720, USA Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA Hao Pan Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA Jia Yin Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, CA 94720, USA Padraic Shafer Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Ziqiang Qiu Department of Physics, University of California, Berkeley, CA 94720, USA Davi R. Rodrigues Department of Electrical Engineering, Politecnico di Bari, Via Edoardo Orabona, 4, 70126 Bari BA, Italy Olle Heinonen Materials Science Division, Argonne National Laboratory, 9700 S Cass Ave, Lemont, IL 60439, USA Dilip Vasudevan Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, CA 94720, USA Jorge Ín~\tilde{\rm{n}}iguez Materials Research and Technology Department, Luxembourg Institute of Science and Technology (LIST), Avenue des Hauts-Fourneaux 5, L-4362, Esch/Alzette, Luxembourg Department of Physics and Materials Science, University of Luxembourg, 41 Rue du Brill, Belvaux L-4422, Luxembourg Darrell G. Schlom Department of Materials Science and Engineering, Cornell University, Ithaca, NY 14853, USA. Sayeef Salahuddin Materials Sciences Division, Lawrence Berkeley National Laboratory, CA 94720, USA Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA Lane W. Martin Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA Materials Sciences Division, Lawrence Berkeley National Laboratory, CA 94720, USA James G. Analytis Department of Physics, University of California, Berkeley, CA 94720, USA Daniel C. Ralph Department of Physics, Cornell University, Ithaca, NY 14853, USA Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY 14853, USA Ran Cheng Department of Electrical and Computer Engineering, University of California, Riverside, CA 92521, USA Department of Physics and Astronomy, University of California, Riverside, California 92521, USA Zhi Yao Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, CA 94720, USA Ramamoorthy Ramesh Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA Materials Sciences Division, Lawrence Berkeley National Laboratory, CA 94720, USA Department of Physics, University of California, Berkeley, CA 94720, USA
Abstract

A collective excitation of the spin structure in a magnetic insulator can transmit spin-angular momentum with negligible dissipation [1, 2, 3, 4, 5] . This quantum of a spin wave, introduced more than nine decades ago [6] , has always been manipulated through magnetic dipoles [7, 8, 9, 10] , (i.e., time-reversal symmetry). Here, we report the experimental observation of chiral-spin transport in multiferroic BiFeO3, where the spin transport is controlled by reversing the ferroelectric polarization (i.e., spatial inversion symmetry). The ferroelectrically controlled magnons produce an unprecedented ratio of up to 18% rectification at room temperature. The spin torque that the magnons in BiFeO3 carry can be used to efficiently switch the magnetization of adjacent magnets, with a spin-torque efficiency being comparable to the spin Hall effect in heavy metals. Utilizing such a controllable magnon generation and transmission in BiFeO3, an all-oxide, energy-scalable logic is demonstrated composed of spin-orbit injection, detection, and magnetoelectric control. This observation opens a new chapter of multiferroic magnons and paves an alternative pathway towards low-dissipation nanoelectronics.

Intense studies of spin current transport in magnetic insulators [4, 11, 12, 13, 14] have opened various avenues for research on spintronics [15, 16, 17, 18, 19, 20, 21] and their potential use in low-power applications [13] . This trend has also triggered renewed interest in magnon physics, which can be controlled via time-reversal-symmetry design (e.g., magnetic domain walls [7] , spin Hall currents [8, 9] , static magnetic fields [10] ). On the other hand, recent works have shown that broken inversion symmetry and the resulting Dzyaloshinskii-Moriya interaction (DMI) have profound influence on magnon transport in non-centrosymmetric magnets [22, 23, 24] . In this spirit, multiferroics are potentially of great interest, since they display broken inversion symmetry and a ferroelectric polarization that can be switched by the application of an electric field, which in turn allows for control of the magnetism and, potentially, the magnons. The idea that multiferroics could be promising candidates for magnonic manipulation has been considered for some time [13, 25] , but despite this early interest, observation and manipulation of magnon transport in multiferroics - that is, the capability to manipulate spin transport via ferroelectric polarization reversal and resultant DMI switching- remain elusive.

Here, we demonstrate non-volatile, bistable spin transport in multiferroic BiFeO3 upon reversing the ferroelectric polarization. BiFeO3 is a model multiferroic that exhibits multiple order parameters (i.e., antiferromagnetism and ferroelectricity) and intrinsic magnetoelectric coupling of these coexisting order parameters [26, 27] . In the bulk, BiFeO3 possesses a rhombohedrally distorted perovskite structure in which a spin cycloid [28] is formed with a period length of ∼\sim 64 nm [29, 30] and a Néel temperature of ∼\sim 643 K [31] . The DMI in BiFeO3 thin films can influence the spin cycloid order [32, 33, 13] . At the same time, BiFeO3 thin films possess robust ferroelectricity, with a Curie temperature ∼\sim 1100 K and a large polarization >> 90 μ\mu C/cm2 [34] . In turn, BiFeO3 exhibits outstanding magnetoelectric properties which have made it the focus of numerous studies hoping to utilize it as a platform to achieve low-energy (low-voltage) memory devices (e.g., deterministic switching of adjacent ferromagnets [35] ). Specifically, achieving control over changing the magnetization states through ferroelectric polarization switching has always been a keen pursuit in these studies.

As illustrated in Fig. 1a, a spin cycloid propagating along 𝒒=[1​1¯​0]\bm{q}=[1\bar{1}0] is revealed by Nitrogen-Vacancy diamond magnetometry measurements ( Extended Data Fig. 1), which is in good agreement with the pioneering work of Gross et al [29, 30] . The formation of spin cycloid has been explained in terms of a Lifshitz-like invariant [36] which, in the continuum limit, amounts to an effective DMI vector 𝑫0\bm{D}_{0} perpendicular to both the ferroelectric polarization 𝑷\bm{P} (along [111][111]) and the spin cycloid propagating direction 𝒒\bm{q}. In BiFeO3, there is another intrinsic DMI characterized by a global DMI vector parallel to 𝑷\bm{P}, which is responsible for the small magnetization 𝒎\bm{m} everywhere perpendicular to the Néel vector 𝑳\bm{L}. Previous studies have confirmed that the latter mechanism is much weaker so that the spin texture is dominated by 𝑫𝟎\bm{D_{0}} [36, 37] . A reversal of 𝑷\bm{P} is accompanied by the reversal of the octahedral antiphase tilts [35] , which in turn flips the direction of 𝑫0\bm{D}_{0} [33, 36] . In addition, the asymmetric gates, the existence of ferroelectric domain walls [38] , and other asymmetries of external origins generate a built-in potential that induces an additional DMI vector δ​𝑫\delta{\bm{D}}, which remains the same under the reversal of 𝑷\bm{P}. Consequently, the total DMI vector 𝑫0+δ​𝑫\bm{D}_{0}+\delta\bm{D} undergoes a non-180∘180^{\circ} switching, leading to a slight rotation of the propagation direction 𝒒\bm{q}. To intuitively understand the ferroelectric control of magnon spin current, we define the hybrid product (𝑫0×δ​𝑫)⋅𝑲(\bm{D}_{0}\times\delta\bm{D})\cdot\bm{K} where 𝑲\bm{K} is the magnon wave vector (in the thickness direction). It is well-known that the nonreciprocal propagation is allowed not only in magnons but also electrons, electromagnetic waves when they go through materials such as multiferroic materials that host broken time reversal and space inversion symmetry simultaneously. As illustrated in Fig. 1a, reversing 𝑷\bm{P} necessarily flips the sign of (𝑫0×δ​𝑫)⋅𝑲(\bm{D}_{0}\times\delta\bm{D})\cdot\bm{K}, hence the chirality of these three vectors. This hybrid product can also reflect a directional non-reciprocity where the wave vector 𝑲\bm{K} flips sign [39, 22, 23, 24] while the DMI is kept unchanged. In other words, this single quantity captures the common feature of both directional non-reciprocity and ferroelectric modulation of the magnon spin current.

Because the thickness of BiFeO3 is much smaller than the spacial period (∼\sim64 nm) of the spin cycloid, we can ignore any spin texture or magnetic inhomogeneity along the magnon wave vector 𝑲\bm{K}. Then, the transmitted spin current can be phenomenologically expressed as[15]

Js=GL𝒮​∫𝑑𝐫2​[𝑳​(𝒓)⋅𝒔]2+Gm𝒮​∫𝑑𝐫2​[𝒎​(𝒓)⋅𝒔]2,\displaystyle J_{s}=\frac{G_{L}}{\mathcal{S}}\int d{\bf{r}}^{2}[\bm{L}(\bm{r})\cdot\bm{s}]^{2}+\frac{G_{m}}{\mathcal{S}}\int d{\bf{r}}^{2}[\bm{m}(\bm{r})\cdot\bm{s}]^{2}, (1)

where GLG_{L} (GmG_{m}) is the phenomenological spin conductance of the Néel vector (total magnetization), 𝒔=y^\bm{s}=\hat{y} is the polarization of spin injection from the top gate and 𝒮\mathcal{S} is the area of the film. As mentioned above, when the total DMI vector undergoes a non-180∘180^{\circ} switching, the spin cycloid profile functions 𝑳​(𝒓)\bm{L}(\bm{r}) and 𝒎​(𝒓)\bm{m}(\bm{r}) are modulated by 𝑷\bm{P} in a non-trivial way. As calculated in the Supplemental Materials, the resulting spin current JsJ_{s} can be substantially different before and after the reversal of 𝑷\bm{P}. To quantify this difference, we define the rectification ratio as

ξ=Js​(−𝑷)−Js​(𝑷)Js​(−𝑷)+Js​(𝑷)\displaystyle\xi=\frac{J_{s}(-\bm{P})-J_{s}(\bm{P})}{J_{s}(-\bm{P})+J_{s}(\bm{P})} (2)

and plot it against the orientation of the extrinsic δ​𝑫\delta\bm{D} relative to the intrinsic 𝑫0\bm{D}_{0} (along [1¯​1¯​2][\bar{1}\bar{1}2]) in Fig. 1b, where we have marked the experimental value (to be explained below) ξ=0.17857\xi=0.17857.

Based on the predicted potential for chiral-magnon control in BiFeO3, a demonstration of a scalable magnetoelectric spin-orbit logic was investigated. A schematic of this idea is illustrated in Fig. 1d. An electric field is set up in the magnetoelectric capacitor in the −z-z direction, resulting in the vertical component of the ferroelectricity switching from the zz to the −z-z direction. To read the polarization state, a supply voltage is applied into the top spin-orbit coupled (SOC) channel (e.g., SrIrO3 which has a relatively large spin Hall angle [40] ) in the +x+x direction, causing the excitation of magnons in the BiFeO3 via the spin current from the SOC material. The readout of the state of the switch is then enabled by the inverse spin Hall effect using SrIrO3 [41] , where the current direction is along the xx direction. Owing to the magnon propagation with bistable rectification, the output voltage could acquire two stable states, rendering the buffer function of a logic gate. Especially, as compared with the first magneto-electric, spin-orbit (MESO) device proposal [42] , this design makes use of antiferromagnetic magnon to gauge the antiferromagnetism inside the multiferroic itself instead of relying on the adjacent ferromagnet coupled to the multiferroic ( Extended Data Fig. 2). Early efforts on the elimination of the ferromagnet have been devoted to the electric-field controlled spin-orbit interaction [43, 44] , e.g. Rashba effect in two-dimensional electron gas systems [45, 46] . The elimination of the ferromagnet simplifies the readout architecture; furthermore, the implementation of antiferromagnets can favor ultrafast operations frequency up to THz.

Refer to caption
Figure 1: Concept of chiral magnon transport in multiferroics. a, A sketch of spin cycloid that propagates along 𝒒=[1​1¯​0]\bm{q}=[1\bar{1}0]. 𝑷\bm{P} is the ferroelectric polarization pointing along [111][111], 𝑫0\bm{D}_{0} (along [1¯​1¯​2][\bar{1}\bar{1}2]) is the intrinsic DMI vector responsible for the spin cycloid formation, and δ​𝑫\delta\bm{D} is the extrinsic DMI vector induced by the built-in electric field in BiFeO3. The double well is a schematic of the bi-stable states of ferroelectric polarization. Upon the reversal of 𝑷\bm{P}, 𝑫0\bm{D}_{0} switches by 180∘180^{\circ} while δ​𝑫\delta\bm{D} remains unchanged, flipping the sign of the hybrid product (𝑫0×δ​𝑫)⋅𝑲(\bm{D}_{0}\times\delta\bm{D})\cdot\bm{K} with 𝑲\bm{K} the magnon wave vector, hence a chirality flip of the three vectors. b, Rectification ratio of spin current [defined by Eq. (1)] as a function of δ​θ\delta{\theta} and δ​ϕ\delta{\phi}, which are the spherical angles of δ​𝑫\delta\bm{D} relative to the direction of 𝑫0\bm{D}_{0}. The lime solid line marks the experimental value ξ=0.17857\xi=0.17857. c, Buffer logic consists of spin injection in the top SOC layer (dark green), magnetoelectric control of spin transmission in the intermediate ME layer (translucent), and spin detection in the bottom SOC layer (dark green). The switching of the polar order is controlled by 𝑽i​n\bm{V}_{in}. 𝑽s​u​p​p​l​y\bm{V}_{supply} serves as the source for spin Hall current injection. The small (purple) and large (red) output voltages 𝑽o​u​t\bm{V}_{out} in c correspond to spin transport of downward and upward ferroelectric polarization in a respectively.

To experimentally explore the controllable spin transmission enabled by the ferroelectric switch in BiFeO3, we first characterized the strength of spin transmission via magnons in the heterostructures of the form La0.7Sr0.3MnO3/BiFeO3 /SrIrO3 (Methods, Extended Data Fig. 3,4). We performed the measurement using a well-established technique namely spin-torque ferromagnetic resonance (ST-FMR) [40, 47] (Fig. 2a), launching the spin current using the large spin Hall effect of SrIrO3 and detecting the spin torque applied to the magnetic La0.7Sr0.3MnO3 layer [48] . An example ST-FMR spectrum, composed of both symmetric and anti-symmetric components, is shown (Fig. 2b) and indicates the successful detection of the spin currents carried by magnons through the BiFeO3. To manipulate the orientation of the ferroelectric polarization, an external electric field was applied along the out-of-plane [001][001] to set the ferroelectric polarization of the BiFeO3 as illustrated (top panel, Fig. 2c, in which the top SrIrO3 and bottom La0.7Sr0.3MnO3 layers serve as the two electrodes sandwiching the ferroelectric). Specifically, upward- (downward-) pointing polarization (180∘180^{\circ} switching) can be achieved by applying negative (positive) voltage larger than the coercivity of the BiFeO3 on the top SrIrO3 layer (bottom panel, Fig. 2c) [41] . After poling the BiFeO3 in each individual device to the desired polarization state, we then deposited platinum contacts onto the devices (contacting both the SrIrO3 and La0.7Sr0.3MnO3 layers) and performed ST-FMR measurements on the poled devices. By adopting an established analysis method (Methods), the SOT efficiency for the damping-like (DL) torque (symmetric component) is evaluated and summarized (Fig. 2d). We observe that the SOT efficiency can be set at a high value by negative (upward polarization) or at a low value by positive (downward polarization) voltages, indicating the presence of bistable high/low spin transport in BiFeO3. This polarization-dependent spin transmission of BiFeO3 is also verified by interfacial engineering ( Extended Data Fig. 5), time-resolved X-ray ferromagnetic resonance ( Extended Data Fig. 6) and FMR measurements ( Extended Data Fig. 7, 8). The blocking temperature of exchange bias between La0.7Sr0.3MnO3 and BiFeO3 is well below room temperature [49] , and the absence of exchange bias is also confirmed by our magneto-optic Kerr effect measurements ( Extended Data Fig. 9), ruling out the possible contribution from exchange bias on the tuning of spin transmission. It is worthwhile to note that the stability of the ferroelectric polarization reveals another crucial advantage associated with spintronics produced in this manner – non-volatility. By setting the polarization direction, high and low SOT efficiencies of 0.330.33 and 0.230.23 can be achieved, showing a high/low ratio of approximately 0.180.18%. Furthermore, the ferroelectric polarization controlled spin transmission in BiFeO3 is confirmed by ST-FMR measurements on samples with opposite polarizations set by different interface terminations [50] (Extended Data Fig. 5). This is consistent with our theoretical predictions that the polarization state influences magnon propagation and a spin transmission modulation can be achieved upon ferroelectric polarization switching. Further, from the aforementioned experiments it can be inferred that the spin transmission is favorable when the magnon wave vector is anti-parallel to the z-component of the polarization 𝑷\bm{P}.

Refer to caption
Figure 2: Spin transmission controlled by ferroelectric polarization in BiFeO3. a, A 33D schematic illustration for the ST-FMR measurement. Top : SrIrO3, middle : BiFeO3, bottom : La0.7Sr0.3MnO3. 𝑰c\bm{I}_{c} represents the radio frequency microwave current, which flows at a 45∘45^{\circ} angle with respect to the in-plane external magnetic field represented by 𝑩e​x​t\bm{B}_{ext}. A spin cycloid that lies in (1¯​1¯​2)(\bar{1}\bar{1}2) plane, and propagates along [1​1¯​0][1\bar{1}0] direction is dipicted by the double-headed arrows. b, Measured ST-FMR signal at room temperature for 12 dBm of applied microwave power at 44 GHz for a sample La0.7Sr0.3MnO3 (2020 nm)/BiFeO3 (2525 nm)/SrIrO3 (1010 nm) of dimension 50×2550\times 25 μ\mum2. The lines are Lorentzian fits to the mixing voltage as described in methods (ST-FMR analysis section), showing both symmetric and anti-symmetric components. c, A schematic of a La0.7Sr0.3MnO3 (2020 nm) /BiFeO3 (2525 nm) /SrIrO3 (1010 nm) heterostructure subject to an external electric field, along with schematics of the BiFeO3 ferroelectric polarization under negative and positive biases. d, The SOT efficiency measured with the ST-FMR technique as a function of bias voltages applied beforehand for samples of La0.7Sr0.3MnO3 (2020 nm) /BiFeO3 (2525 nm) /SrIrO3 (1010 nm) The open squares (circles) represent the SOT efficiency for the tri-layer with negative (positive) bias voltages applied on the top electrode - SrIrO3.
Refer to caption
Figure 3: Magnetization switching induced by the spin torque in BiFeO3 under the control of ferroelectric polarization. a, A schematic demonstrating the magnetization switching of SrRuO3 by the current-induced torques borne by the magnons transmitted through BiFeO3 for a sample SrRuO3 (55 nm)/BiFeO3 (2525 nm)/SrIrO3 (1010 nm). A spin cycloid that lies in (1¯​1¯​2)(\bar{1}\bar{1}2) plane, and propagates along [1​1¯​0][1\bar{1}0] direction is depicted by the double-headed arrows. The torque carried by the transmitted magnons switches the magnetic moment (dark blue arrows) of the neighboring SrRuO3 layer in the out-of-plane direction. A small assisting magnetic field (𝑯e​x​t\bm{H}_{ext}) is applied along the pulsed current (𝑱C\bm{J}_{C}) direction. b, An optical image of the actual Hall device used in the anomalous Hall effect (AHE) and magnetization switching measurements. Anomalous Hall resistance (𝑹X​Y\bm{R}_{XY}) as a function of the magnetic field at various temperatures for the heterostructure SrRuO3 (55 nm)/BiFeO3 (2525 nm)/SrIrO3 (1010 nm) is shown on the bottom. A dc current of 100 μ\muA is applied during the AHE measurements. c, RX​YR_{XY} as a function of pulsed currents. External magnetic fields with different polarities and strengths are applied along the current pulse direction to assist the magnetization switching. After each current pulse, a dc current of 100 μ\muA is applied to detect the change in 𝑹X​Y\bm{R}_{XY}. The hysteretic magnetization switching loops are shifted with respect to the magnetization switching loop at zero assisting field for display. The current pulses have a pulse width of 1 ms. d, An example IV curve collected during the ferroelectric switching experiments for the heterostructure SrRuO3 (55 nm)/BiFeO3 (2525 nm)/SrIrO3 (1010 nm). e, An example ferroelectric polarization controlled magnetization switching measurement. The magnetization switching behavior for SrRuO3 (55 nm)/BiFeO3 (2525 nm)/SrIrO3 (1010 nm) heterostructure with the polarization of BiFeO3 pointing from the bottom (top) electrode to the top (bottom) electrode is shown in red (blue). The 𝑹X​Y\bm{R}_{XY} is normalized for better display. f, The magnitudes of critical switching current as a function of the applied external magnetic fields are summarized. The critical switching current for SrRuO3 (55 nm)/BiFeO3 (2525 nm)/SrIrO3 (1010 nm) heterostructure with upward (downward) ferroelectric polarization is shown in red (blue). The lines are a guide to the eye.
Refer to caption
Figure 4: Magnetoelectric spin-orbit logic based on controllable magnon transport in BiFeO3. a, Schematic of the non-local device formed with a magnetoelectric test structure. b, Piezo-force microscopy image of the non-local device structure. The channel width is 0.5 μ\mum. c, Hysteresis loop from spin magnon readout in SrIrO3 with first harmonic measurements for a device with a 500 nm channel width. d, Hysteresis loop from thermal magnon readout in SrIrO3 with second harmonic measurements in a device with a 1 μ\mum channel width. e, Output voltage scaling with channel spacing for measurements in nonlocal devices (points for spacings 0.5 μ\mum and above), vertical structure of SIO/BFO/SIO when BFO is 100 nm, and estimates of voltages that could be obtained for vertical transport of magnons through 10 and 15 nm of BiFeO3. The power is fixed at 3 mW.

To corroborate the presence of a magnon transmission modulation in BiFeO3, magnetization switching experiments were carried out to serve as a direct demonstration of the strength of the spin torques under ferroelectric polarization modulation. Here, we investigate deterministic magnetization switching of a SrRuO3 layer with perpendicular magnetic anisotropy (PMA) by the spin torque carried by the BiFeO3. Current-induced magnetization switching measurements were carried out for SrRuO3 (55 nm)/BiFeO3 (2525 nm)/SrIrO3 (1010 nm) heterostructure with BiFeO3 polarized to either upward or downward orientations (Fig. 3a). The switching schematic is also demonstrated (Fig. 3a), where the magnetic moment of the ferromagnetic SrRuO3 is switched between positive and negative directions consistently and reversibly. The magnetic switching was detected by the anomalous Hall effect in the SrRuO3 layer, in which magnetic moments lying on the positive and negative directions can be distinguished by positive and negative values of anomalous Hall resistance. By sweeping an external magnetic field in the out-of-plane direction (Fig. 3b), a hysteretic loop is developed for anomalous Hall resistance (𝑹X​Y\bm{R}_{XY}), when the external magnetic field exceeds the coercivity of SrRuO3(Fig. 3b). Furthermore, 𝑹X​Y\bm{R}_{XY} as a function of magnetic field was repeated at temperatures from 2020 K to 8080 K, confirming the high quality of our heterostructure, and no shift in the hysteretic loop with respect to zero magnetic field is observed, indicating the absence of exchange bias effect between ferromagnetic SrRuO3 and antiferromagnetic BiFeO3. Then magnetization switching measurements were performed in the same device, and 𝑹X​Y\bm{R}_{XY} as a function of current pulses was recorded. Notably, a switching of magnetization was observed by both positive and negative currents, when the magnitudes of current pulses exceed the magnitude of critical switching current, and a saturation of 𝑹X​Y\bm{R}_{XY} is observed with large current pulses, excluding the possible participation of thermal effects in the switching measurements. Moreover, no magnetization switching is observed at zero assisting magnetic field and the switching chirality can be changed by the reversal of polarity of assisting magnetic fields, ruling out the possibility that the magnetization switching is caused by current-induced Oersted field. To further corroborate our observation of ferroelectric polarization-controlled spin transport with ST-FMR, ferroelectric polarization-dependent magnetization switching measurements were carried out. To start with, the polarization of BiFeO3 was switched to either an upward or downward orientation by an external electric field. An example IV curve during the ferroelectric polarization switching measurements is displayed in Fig. 3d, in which the switching of ferroelectric polarization is associated with current peaks in Fig. 3d. Then, the same magnetization switching measurements were conducted on devices with distinct ferroelectric polarization states. A typical switching loop for heterostructures with upward (downward) polarization is displayed in red (blue) solid spheres in Fig. 3e. Strikingly, distinct critical switching currents for upward and downward polarization were observed in both positive and negative current directions. The critical switching currents at different assisting magnetic fields for upward and downward polarization are summarized in Fig. 3f, where upward polarization shows a smaller switching current than downward polarization statistically. Therefore, two conclusions can be drawn based on our experimental observations. First, BiFeO3 has the capability to carry spin information via antiferromagnet magnons, and the spin torque arising from BiFeO3 is sufficiently efficient to switch the magnetization of SrRuO3. More importantly, the spin transmission in BiFeO3 is controlled by ferroelectric polarization, and the smaller critical switching current density for the upward polarization corresponds to a higher spin transmission, in good agreement with the ferroelectric polarization controlled-SOT efficiency study with the ST-FMR technique. The current-induced magnetization switching measurements reinforce the idea that the upward polarization is favorable for magnon transmission.

We further investigated the experimental demonstration of MESO via electrically controllable spin transport using a lateral nonlocal measurement. A schematic of the nonlocal measurement is provided (Fig. 4a); it consists of spin-orbit input and output via parallel source and detector wires, as well as magnetoelectric control. Fig. 4b illustrates well-ordered 71∘71^{\circ} ferroelectric domains, showing the high quality of the BiFeO3 films. A nonlocal, quasi-static measurement was performed (Fig. 4c), varying the magnitude of the electric-field pulse applied in-plane across the channel from negative to positive and back again, and after each pulse measuring (over 100100 seconds) non-local voltage signals due to magnon transport between the source and detector wires (Methods). We observe a butterfly-shaped and hysteretic response in the magnon current launched by the spin Hall effect (first-harmonic voltage, Fig. 4c) and the magnon current launched thermally by the local spin Seebeck effect, respectively (second-harmonic voltage, Fig. 4d), in which the coercive fields match each other. Besides, the electric field modulations of the output voltage can be obtained with dc methods, which can minimize the inductive and capacitive effect ( Extended Data Fig. 10,11). Figure 4e presents measurements of the magnitude of these spin-transport signals as a function of changing the spacing between the source and detector wires from 500 nm to 4 μ\mum. The open squares reflect the magnitude of the signals associated with spin currents launched by the spin Hall effect (first harmonic voltage) and the red circles reflect signals launched thermally by the spin Seebeck effect (second harmonic voltage). Remarkably, the output voltage detected in BiFeO3/SrIrO3 stacks (∼1\sim 1 μ\muV) is approximately one order of magnitude larger than the counterparts in BiFeO3/Pt (∼0.1\sim 0.1 μ\muV) [51] , which is supported by the large spin-torque efficiency of SrIrO3 previously observed with the ST-FMR measurement [40, 52] and the controlled nonlocal measurements of NiFe2O4/Pt and NiFe2O4/SrIrO3 (Extended Data Fig. 13,14). The distance dependence for both types of signals in BiFeO3 fits well to the expectation for diffusive magnon propagation [53]

Rnl=Cλ​exp⁡(d/λ)1−exp⁡(2​d/λ)R_{\rm{nl}}=\frac{C}{\lambda}\frac{\exp(d/\lambda)}{1-\exp(2d/\lambda)} (3)

with effective diffusion lengths ∼0.17\sim 0.17 μ\mum (first harmonic) and ∼0.25\sim 0.25 μ\mum (second harmonic).

Using this result and the spin-torque efficiencies obtained above (Extended Data Fig. 5), we can calculate the inverse-spin-Hall output voltage that would be obtained for a vertical geometry with BiFeO3 thicknesses of 1010 and 1515 nm using [54]

VISHE=θSOT​λSD​tanh⁡(tSIO2​λSD)​LtSIO​σSIO​JSV_{\rm{ISHE}}=\frac{\theta_{\rm{SOT}}\lambda_{\rm{SD}}\tanh(\frac{t_{\rm{SIO}}}{2\lambda_{\rm{SD}}})L}{t_{\rm{SIO}}\sigma_{\rm{SIO}}}J_{\rm{S}} (4)

where we use the values θSOT\theta_{\rm{SOT}} = 0.40.4 is the spin-torque efficiency, λSD=1.4\lambda_{\rm{SD}}=1.4 nm [55] is the spin-diffusion length of SrIrO3, tSIO=10t_{\rm{SIO}}=10 nm is the thickness, σSIO=1×105\sigma_{\rm{SIO}}=1\times 10^{5} Ω−1​m−1\Omega^{-1}m^{-1} is the conductivity, L=10L=10 nm is the wire length. The output voltage is on the order of 1010 mV, which is approaching the MESO target voltage of 100100 mV. A prototypical magnon-mediated MESO logic device and its circuit modeling utilizing this ferroelectrically controlled magnon propagation are shown in Extended Data Fig. 5. This observation sheds light on implementing multiferroics as the potential spin carriers and opens new possibilities of energy-efficient magnonic spin-logic devices.


References

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Methods
Sample and device fabrication
The tri-layers used in this study were grown by RHEED assisted pulsed laser deposition using a KrF laser with a wavelength of 248 nm. A 20 nm La0.7Sr0.3MnO3 (5 nm SrRuO3)layer was first grown at a substrate temperature 700∘C and oxygen partial pressure 150 mTorr (100 mTorr), then a BiFeO3 layer followed with various thicknesses at a substrate temperature 700∘C and oxygen partial pressure 100 mTorr, and finally a 10 nm SrIrO3 layer finished the growth at a substrate temperature 700∘C and oxygen partial pressure 50 mTorr. The films were grown at a repetition of 2 (5 Hz) Hz, 10 Hz and 5 Hz with a laser fluence of 1.5 J/cm2, 1.5 J/cm2 and 1.2 J/cm2, respectively. After the growth, the sample was cooled to room temperature in an oxygen environment of 750 Torr at a cooling rate of 10∘C/min. To make ST-FMR devices, the samples were first spin coated with photoresist (MiR 701), then devices with a 50×2550\times 25 μ\mum2 rectangular dimensions (15×1015\times 10 μ\mum2 for the electric-field-controlled experiment) were made by photolithography (Heidelberg MLA 150) followed by ion milling (Pi scientific) that stopped at the La0.7Sr0.3MnO3 layer. The remaining La0.7Sr0.3MnO3 layer was used as the bottom electrode in the switching experiments; for the ST-FMR measurements this was patterned using a H3PO4 wet etch (H3PO4 : H2O = 1 : 3). Finally, electrical contacts were made from 100 nm of Pt with a ground-signal-ground (GSG) geometry , so that when a GSG high-frequency probe made into contact with the samples the current traveling through the Pt contacts did not produce a net Oersted field at the sample.

Antiferromagnetic spin wave calculations
To perform the spin wave calculations, we first prepare a polar ground state corresponding to 𝐏||[111]\mathbf{P}||[111] and 𝐏||[1¯1¯1¯]\mathbf{P}||[\bar{1}\bar{1}\bar{1}] (along with an order parameter for the octahedral antiphase tilts). We then evolve the LLG-LLB equation to find the magnetic ground state corresponding to 𝐋||[1¯01]\mathbf{L}||[\bar{1}01] with 𝐦||[12¯1]\mathbf{m}||[1\bar{2}1] and 𝐦||[1¯21¯]\mathbf{m}||[\bar{1}2\bar{1}]. To study the spin waves, the homogeneous magnetic ground state is perturbed with an applied field 𝐇||[1¯01]\mathbf{H}||[\bar{1}01] with Gilbert damping α=0\alpha=0, and the spin waves are set to propagate along ±𝐤||[001]\pm\mathbf{k}||[001]. The detectable spin current in the AFM insulating layer[56] are proportional to 𝐣=𝐣𝐥+𝐣𝐦+𝐣𝐦𝐥+𝐣𝐥𝐦\mathbf{j}=\mathbf{j}^{\mathbf{l}}+\mathbf{j}^{\mathbf{m}}+\mathbf{j}^{\mathbf{ml}}+\mathbf{j}^{\mathbf{lm}} where 𝐣𝐥∝𝐥×𝐥˙\mathbf{j}^{\mathbf{l}}\propto\mathbf{l}\times\dot{\mathbf{l}}, 𝐣𝐦∝𝐦×𝐦˙\mathbf{j}^{\mathbf{m}}\propto\mathbf{m}\times\dot{\mathbf{m}}, 𝐣𝐦𝐥∝𝐦×𝐥˙\mathbf{j}^{\mathbf{ml}}\propto\mathbf{m}\times\dot{\mathbf{l}}, and 𝐣𝐥𝐦∝𝐥×𝐦˙\mathbf{j}^{\mathbf{lm}}\propto\mathbf{l}\times\dot{\mathbf{m}}. More details of our simulations are provided in the SM. Calculations are performed using the Ferret module [57] which is part of the open-source MOOSE framework [58].

ST-FMR analysis
The ST-FMR signal, Vm​i​xV_{mix}, is produced across the La0.7Sr0.3MnO3/BiFeO3/SrIrO3 ST-FMR device as rectification of anisotropic magnetoresistance that oscillates at the same frequency as the input microwave current IR​FI_{RF} [59] . A microwave current at frequencies 4-6 GHz and power 12 dBm is applied to the device, with an in-plane external magnetic field oriented 45∘ with respect to the current direction. Finally, Vm​i​x=−14​d​Rd​θ​γ​IR​F​c​o​s​θ2​π​Δ​(d​f/d​H)He​x​t=H0​(τD​L​FS​(He​x​t)+τF​L​FA​(He​x​t))V_{mix}=-\dfrac{1}{4}\dfrac{dR}{d\theta}\dfrac{\gamma I_{RF}cos\theta}{2\pi\Delta(df/dH)_{H_{ext}=H_{0}}}(\tau_{DL}F_{S}(H_{ext})+\tau_{FL}F_{A}(H_{ext})) [59] , where d​R/d​θdR/d\theta is the angle dependent magnetoresistance at θ\theta, γ\gamma is the gyromagnetic ratio, Δ\Delta is the linewidth of the ST-FMR signal, (d​f/d​H)He​x​t=H0(df\textfractionsolidus dH)_{H_{ext}=H_{0}} is the field gradient of the resonance frequency, τD​L\tau_{DL} is the damping-like torque, τF​L\tau_{FL} is the field-like torque, FS​(He​x​t)F_{S}(H_{ext}) is the symmetric Lorentzian function and FA​(He​x​t)F_{A}(H_{ext}) is the anti-symmetric Lorentzian function respectively, is detected by Keithley 2182A nanovoltmeter, from the fits of which the symmetric component VSV_{S} and the anti-symmetric component VAV_{A}, which are associated with damping-like torque (τD​L\tau_{DL}) and field-like torque (τF​L\tau_{FL}) respectively, can be extracted. As a result, spin orbit torque efficiency-ξS​O​T\xi_{SOT} is evaluated using ξD​L=2​e​τD​L​ms​tF​MJc​ℏ\xi_{DL}=\dfrac{2e\tau_{DL}m_{s}t_{FM}}{J_{c}\hbar}, where τD​L=4​Vs​ΔIR​F​c​o​s​θ​d​Rd​θ​1+μ0​Me​f​f2​Br​e​s(1+μ0​Me​f​fBr​e​s)1/2\tau_{DL}=\dfrac{4V_{s}\Delta}{I_{RF}cos\theta\dfrac{dR}{d\theta}}\dfrac{1+\dfrac{\mu_{0}M_{eff}}{2B_{res}}}{(\dfrac{1+\mu_{0}M_{eff}}{B_{res}})^{1/2}} [60, 61] . The SOT efficiency for the samples in this work was measured from 4 GHz to 6 GHz and the error bar in Fig. 2 is a result of SOT efficiencies across different frequencies, while the error bar in extended Fig. 5 is caused by the SOT efficiency distribution across different devices.


Parameters for non-local spin transport measurements
The length of the wire is 100 μ​m\mu m, the applied voltage is   20V, the applied current is 10 μ​A\mu A, the alternating current frequency is 7 Hz.

Data availability
The data that support the findings of this study are available from the corresponding authors on reasonable request.

Acknowledgements
We are grateful for the fruitful discussions with Prof. Albert Fert, Dr. Eric Parsonnet, Dr. Yenlin Huang. X.H., D.C.R. and R.R. acknowledge the support from the SRC-JUMP ASCENT center. R.J. acknowledges the support from the U.S. Department of Energy, under contract No. DE-SC0017671. X.C., P.S., D.V., S.S., L.W.M., Z.Y., and R.R. acknowledge partial support from the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-05-CH11231 (Codesign of Ultra-Low-Voltage Beyond CMOS Microelectronics for the development of materials for low-power microelectronics). Y.L. and R.C. acknowledge the support from the Air Force Office of Scientific Research under Grant No. FA9550-19-1-0307. T.W. and Z.Q.acknowledge the support from US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-05CH11231 (van der Waals heterostructures program, KCWF16). This research used resources of the Advanced Light Source, which is a DOE Office of Science User Facility under contract no. DE-AC02-05CH11231. H.P. acknowledges support from Army Research Office and Army Research Laboratory via the Collaborative for Hierarchical Agile and Responsive Materials (CHARM) under cooperative agreement W911NF-19-2-0119. J.M. has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement SCALES - 897614. D.R.R. acknowledges funding from the Ministerio dell’Università e della Ricerca, Decreto Ministeriale n. 1062 del 10/08/2021 (PON Ricerca e Innovazione). O.H. acknowledges support from the US Department of Energy, Office of Science, Basic Energy Sciences, Division of Materials Sciences and Engineering.

Author contributions
X.C. and R.R. supervised this study. X.H. carried out the synthesis and characterization of heterostructures. X.H. and X.C. fabricated the devices. X.H. and R.J. carried out the ST-FMR measurements. X.H. and X.C. carried out the current induced magnetization switching measurements. C.X. H.T. performed the non-local transport measurements. C.K. performed dynamic XMCD measurements at beamline 4.0.2 of the Advanced Light Source. Y.L. and R.C performed the theoretical calculations. J.M., D.R.R. O.H., and J.I. developed and performed the coupled polar-micromagnetic simulations. X.C., D.V., and Z.Y. devised the electronic model and performed the calculations. S.S. performed the microstructure and electronic structure characterizations. H.Z., T.W., L.C., C.H., I.H., H.P., J.Y., P.M., P.S., Z.Q., S.S., M.R., D.S., L.W.M., D.C.R., and A.F. gave suggestions on the experiments. All authors discussed the results and prepared the manuscript.

Competing interests
The authors declare no competing interests.

Additional information
Correspondence and requests for materials should be addressed to X.C. and R.R. Reprints and permissions information is available at http://www.nature.com/reprints.

Refer to caption
Figure 1: NV magnetometry image for BiFeO3. a, c, Schematic illustrations of ferroelectric domains and the corresponding spin cycloid propagation directions before and after polarization switching. The pink arrows represent the ferroelectric polarization orientations.b, d, Magnetic stray field distribution recorded with scanning NV magnetometer for 100 nm BiFeO3 before and after polarization switching. The blue arrows are the spin cycloid propagation wave vector
Refer to caption
Figure 2: Schematics for magnon-mediated MESO logic device. a, Same schematics duplicated from Fig. 1d. b, Modularized circuit schematics. The top module is the ferroelectric switch module, where the input voltage VincV_{\mathrm{in}}^{c} switches the direction of the ferroelectric polarization PFEP_{\mathrm{FE}} in the magnetoelectric layer. Such polarization change also affects the spin conductance GseG_{\mathrm{se}} and GsfG_{\mathrm{sf}} of the ME layer. The leftmost and rightmost modules represent the spin Hall effect (SHE) process in the top SOC layer (injector) and the inverse spin Hall effect (ISHE) process in the bottom SOC layer (detector), respectively. The current-controlled spin current source ISHESI^{S}_{\mathrm{SHE}} in the SHE module depends on the output charge current of the top SOC layer. Similarly, the current-controlled charge current source IISHECI^{C}_{\mathrm{ISHE}} in the ISHE module depends on the output spin current of the bottom SOC layer. The parameters ηSHE\eta_{\textrm{SHE}} and ηISHE\eta_{\textrm{ISHE}} represent the charge-to-spin and spin-to-charge current conversion rates, respectively. The module in the middle describes the magnon transport process in the ME layer, which is connected to the SHE and ISHE modules through the spin conductance at the interfaces between ME and SOC layers, denoted as GAFM−NMG_{\mathrm{AFM-NM}}. c, Lossy Buffer logic simulation result for the equivalent circuit in Fig. 2.b where the output follows the input pulse signal characteristics.
Refer to caption
Figure 3: Atomic scale control of interface termination by pulsed laser deposition. a, RHEED intensity oscillation of the specularly reflected beam during the growth of SrRuO3 and La0.7Sr0.3MnO3 on TiO2-terminated SrTiO3 [001][001] surface. A growth of 2.5 unit-cell of SrRuO3 on TiO2 terminated SrTiO3 substrate is required in order to achieve the SrO terminated substrate, due to the fact that RuO is highly volatile at high temperatures and SrRuo3 is therefore self-terminated with SrO layer [62] .b, A schematic of the resulting La0.7Sr0.3O-FeO2 interface. c, RHEED intensity oscillation of the specular beam during the growth of La0.7Sr0.3MnO3 by direct on TiO2-terminated SrTiO3 [001][001] surface. d, A schematic of the resulting MnO2-BiO interface.
Refer to caption
Figure 4: Structure, magnetization, ferroelectric domain structure measurements for La0.7Sr0.3MnO3/BiFeO3/SrIrO3 heterostructure. a, HAADF image of La0.7Sr0.3MnO3/BiFeO3/SrIrO3 tri-layer, displaying atomically sharp interfaces and high crystal quality. b, HF etched and thermally annealed SrTiO3 substrate with atomic steps and terraces. c, Magnetization vs applied magnetic field (MH) measurement for La0.7Sr0.3MnO3/BiFeO3/SrIrO3, showing a coercivity of ∼\sim 25 Oe and a saturation magnetization ∼\sim 320 emu/cc. d, In-plane piezoresponse microscopy (PFM) image of the BiFeO3 layer. e, High resolution XRD 2θ\theta-ω\omega scan of the tri-layer
Refer to caption
Figure 5: Ferroelectric control of spin transport enabled by the interface chemistry. a, A schematic for La0.7Sr0.3MnO3/BiFeO3 atomic stacking, where La0.7Sr0.3O-MnO2-BiO-FeO2 is stacked at the interface. b, A schematic for La0.7Sr0.3MnO3/BiFeO3 atomic stacking, where MnO2-La0.7Sr0.3O-FeO2-BiO is stacked at the interface. c, Corresponding piezoresponse for La0.7Sr0.3O-MnO2-BiO-FeO2 stacking (La0.7Sr0.3MnO3(1212 nm)/BiFeO3(5050 nm)), with top and bottom being phase and amplitude respectively. The solid line denotes the shifting of the piezoresponse curves to zero volts, indicating an upward ferroelectric polarization for La0.7Sr0.3O-MnO2-BiO-FeO2 stacking. d, Corresponding piezoresponse for MnO2-La0.7Sr0.3O-FeO2-BiO stacking (La0.7Sr0.3MnO3(1212 nm)/BiFeO3(5050 nm)), with the top and bottom being phase and amplitude respectively. The solid line denotes the shifting of the piezoresponse curves to zero volts, indicating a downward ferroelectric polarization for MnO2-La0.7Sr0.3O-FeO2-BiO stacking. e,f, An artistic illustration for upward and downward ferroelectric polarization. g, Spin orbit torque efficiency for BiFeO3 with different polarization states as a function of BiFeO3 thicknesses. The red (blue) data points represent the spin-orbit torque efficiency for La0.7Sr0.3MnO3/BiFeO3/SrIrO3, where BiFeO3 has an upward (downward) polarization.
Refer to caption
Figure 6: X-ray magnetic circular dichroism spectra for the X-ray Ferromagnetic resonance measurements in LSMO/BFO/Ti/CoFe Stacks. a, b, X-ray absorption spectra (XAS), X-ray magnetic circular dichroism spectra (XMCD), and X-ray ferromagnetic resonance (XFMR) of Mn(a) and Co(b), which correspond to the magnetic element in LSMO and CoFe respectively. The X-FMR measurements confirm the ac spin current transport through BFO.
Refer to caption
Figure 7: FMR measurements for LSMO (20 nm)/BFO (10 nm)/SIO (10 nm) samples with different polarizations. a, b, FMR spectrum for LSMO/BFO/SIO heterostructures with upward and downward ferroelectric polarizations respectively. Arrow K is a representation of spin propagation with respect to the polarization direction for FMR measurements. Resonance fields and frequencies are summarized in c and d for heterostructures with upward and downward respectively. Effective magnetization   402 kA/m and 395 kA/m are determined with Kittel equation fitting. e, f, Peak-to-peak linewidth as a function of frequency is shown for heterostructures with upward and downward polarizations respectively. Effective Gilbert damping constants (α\alpha) of 0.00381 and 0.0116 are estimated for systems with upward and downward polarizations respectively
Refer to caption
Figure 8: FMR measurements for LSMO (20 nm)/BFO (40 nm) samples with different polarizations. a, b, FMR spectrum for LSMO/BFO heterostructures with downward and upward ferroelectric polarizations respectively. Resonance fields and frequencies are summarized in c and d for heterostructures with downward and upward respectively. Effective magnetization   395 kA/m and 389 kA/m are determined with Kittel equation fitting. e, f, Peak-to-peak linewidth as a function of frequency is shown for heterostructures with downward and upward polarizations respectively. Effective Gilbert damping constants of 0.01177 and 0.013335 are deduced for downward and upward polarizations respectively
Refer to caption
Figure 9: Exchange bias in BiFeO3-based heterostructures. MOKE measurements for LSMO (20 nm)/SIO (10 nm) and LSMO (20 nm)/BFO (25 nm)/SIO (10 nm) samples at room temperature.
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Figure 10: dc non-local voltage as a function of applied magnetic field at room temperature. The applied dc current is 10 μ\muA.
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Figure 11: Electric field controlled non-local spin transport measurements with dc current input. A positive electric field of 150 kV/cm and a negative electric field of -300 kV/cm are applied alternately, with dc non-local voltages measured in between the electric fields as shown in the measurement protocol. The corresponding non-local voltage between each electric field is shown below. Each data point is averaged over a time interval of 50 s.
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Figure 12: AFM spin current under 𝐋\mathbf{L} switching. Calculated yy-component of the total spin current for up (blue) and down (red) polarization orientations. The applied magnetic field 𝐇\mathbf{H} to generate the excitation is set along [1¯​01\bar{1}01]. The Néel vector in both polar configurations is different indicative of a possible 180∘180^{\circ} switching scenario of 𝐋\mathbf{L}. The ratio of the time-integrated dc components is +0.978.
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Figure 13: AFM and SQUID characterization. a, An AFM image for SrIrO3 (15 nm) grown on YIG/GGG structure. b, An AFM image for SrIrO3 (15 nm) grown on NiFe2O4/STO structure. c, Magnetization as a function of temperature from 10 – 400 K, with a magnetic field of 1500 Oe applied in the plane. d, Magnetization as a function in-plane magnetic field at 300 K.
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Figure 14: Non-local control experiments on NiFe2O4 (70 nm)/Pt (5 nm) and NiFe2O4 (70 nm)/SrIrO3 (15 nm). First harmonic voltage signal is displayed in a and b for NiFe2O4/Pt and NiFe2O4/SrIrO3 respectively. An ac current with an amplitude of 100 μ\muA and a frequency of 17 Hz was applied in a channel that is separated by 1 μ\mum from the detection channel.