Unconventional magnon-mediated spin torque enabled by ferroelectric domain engineering in multiferroic BiFeO_3

Domain: physics
Published: 2026-04-10
Editorial outcome: major_revision

Abstract
Spin current provides an energy-efficient approach for manipulating magnetization, when its spin polarization aligns with the magnetization direction. However, conventional spin-source materials possess high crystalline symmetry, restricting spin polarization to be orthogonal to both spin and charge current directions. Here, we overcome this limitation by utilizing the concept of magnon-mediated spin-orbit torque through integration of the insulating multiferroic BiFeO with a conventional spin-source material. We observe that spin polarization generated by conventional spin-source material can excite unconventional magnon polarization due to the interplay between cycloidal antiferromagnetic order and the ferroelectric domain structure in BiFeO . This produces an unconventional magnon torque that allows deterministic, field‑free switching of in‑plane magnetization collinear with the current direction, unattainable with conventional spin-source materials. Our results establish multiferroic-based heterostructure as a symmetry‑engineered magnon spin source, paving the way for low-power spintronic devices.

Introduction
Spin currents, flows of spin angular momentum characterized by their spin polarization (𝝈 enable efficiently manipulating magnetization via spin-orbit torques1, crucial for developing emerging magnetic logic and memory devices2-6. Electron-mediated spin currents can be induced by the spin Hall effect7,8 (SHE or Rashba-Edelstein effect9 (REE in spin-source materials. Nevertheless, the most commonly used spin-source materials, such as polycrystalline heavy metals10, exhibit high crystalline symmetry, constraining spin polarization 𝛔 to be orthogonal to both the charge and spin current directions. Specifically, when a charge current (𝐽 flowing along the x-axis generates a spin current (𝐽 propagating along the z-axis, the spin polarization is confined strictly to the y-axis, producing only a conventional damping-like spin torque 𝛕 𝑦 ∝ 𝐌×(𝐲×𝐌) (Fig. 1a . As a result, efficient field-free magnetization switching is limited exclusively to the y-axis11. Achieving efficient field-free switching along other axes, which is desirable for low-power, high density magnetic devices, requires unconventional spin polarization (with 𝛔 deviating from the y-axis 2. Such unconventional spin polarizations have been observed in spin-source materials with reduced crystalline symmetry (Fig. 1b 12-16, or materials with non-collinear antiferromagnetic17-21 or altermagnetic orders22-24.

Alternatively, spin angular momentum can be carried by magnons, the collective excitations of magnetic orders, which efficiently propagate magnon currents (𝐽 through magnetically-ordered insulators over long distances without involving charge transport25-32. In heterostructures of spin-source/antiferromagnetic-insulator/ferromagnet, spin currents from a spin-source layer excite magnons in the antiferromagnetic insulator, generating a magnon current that subsequently exerts magnon torque on an adjacent ferromagnetic layer33-35. This approach presents an attractive pathway toward more energy-efficient spintronic devices36. More importantly, this magnon-mediated spin torque can leverage the symmetry of the antiferromagnetic layer, offering an additional degree of freedom for spin torque engineering. Recent studies have shown that the amplitude of magnon torque can be tuned by controlling the ferroelectric order in heterostructure incorporating multiferroic BiFeO 37-39. However, controlling the magnon spin polarization direction to generate unconventional magnon torques remains unexplored.

In this work, we experimentally demonstrate that two-variant ferroelectric domains with distinct spin cycloid structure in BiFeO enable control over magnon spin polarization (Fig. 1c . In epitaxial SrRuO /BiFeO /Ni Fe heterostructures, we observe efficient generation of unconventional magnon torque 𝛕𝑥 ∝𝐌×(𝐱×𝐌), with spin polarization rotated by up to 11° from the conventional y-axis direction dictated by symmetry. This unconventional magnon torque strongly depends on the orientation of the ferroelectric domains and is absent in samples with disordered domains, consistent with symmetry analysis of BiFeO possessing ferroelectrically coupled spin cycloid structures. We further demonstrate deterministic, field-free magnetization switching along the x-axis which is prohibited by symmetry with conventional spin torque. These results reveal that control of the ferroelectric domain structures in multiferroic materials provide a route to leverage hidden symmetries within the antiferromagnetic order, opening pathways for advanced functionalities in future magnon-based spintronic devices.

Results
Symmetry analysis of BiFeO with spin cycloid structure
Bulk BiFeO possesses a pseudocubic perovskite lattice with a slight rhombohedral distortion40. The breaking of inversion symmetry in BiFeO induces robust ferroelectric polarization 𝐏41 (approximately 100 μC/cm2 oriented along one of the eight possible pseudocubic [111] directions, forming eight ferroelectric variants (𝐏± , as illustrated in Fig. 2a. These eight ferroelectric variants give rise to three possible types of ferroelectric domain walls (71°, 109° and 180° 42. The inversion symmetry breaking also leads to a strong Dzyaloshinskii–Moriya (DM interaction characterized by a pseudovector 𝐃 that is perpendicular to 𝐏37. For instance, when 𝐏 points along [111], 𝐃 oriented along [112̅ ] cants the antiferromagnetically coupled Fe3+ magnetic moments, leading to a spin cycloid structure that couples strongly to the magnon band structure and magnon transport43-46. This cycloid rotates within the plane perpendicular to 𝐃 and and propagates along the vector 𝐤 [11̅0]41, satisfying the orthogonality condition 𝐃∝𝐏×𝐤, as illustrated in Fig. 2b. Another intrinsic DM interaction parallel to 𝐏 accounts for non-compensation of the magnetic moments in BiFeO , though this contribution is relatively small47,48. Therefore, the chirality of the Fe3+ spin cycloid is predominantly determined by 𝐃. The cycloidal rotation in BiFeO can be described by a pseudovector 𝛀 =(𝐧∙𝐤)𝐃49 (𝒏 denotes an arbitrary real-space direction .

We exploit the symmetries of the cycloidal spin structure to control magnon-mediated spin currents by engineering the ferroelectric domain structure in BiFeO . In two-variant domain BiFeO that can be stabilized through strain50 or substrate vicinality51, the cycloidal propagation vector 𝐤 is constrained within the sample plane and remains orthogonal to 𝐏50,52. As illustrated in Fig. 2c, domain 1 exhibits polarization 𝐏− along [11̅1̅], 𝐤 along [1̅1̅0 ], and 𝐃 along [1̅1I2̅ ]; similarly, domain 2 exhibits polarization 𝐏− along [111̅ ], 𝐤 along [11̅0], and 𝐃 along [1̅1̅2̅].

To understand the symmetry implications of this two-variant domain structure for magnon-mediated spin transport, we perform a symmetry analysis by considering symmetry operations 𝒪 acting on the cycloidal antiferromagnetic order49 (Fig. 2d . The identity operations show the directions of vectors in each domain. Because 𝐏 inherently breaks the four-fold symmetry about the [001] axis, we focus our analyze on mirror operations (ℳ , ℳ and ℳ defined relative to planes perpendicular to the pseudocubic axes [100], [100] [010] [001] [010], and [001], as well as an out-of-plane two-fold rotation operation along the [001] axis (𝒞2 . We investigate how these operations affect the cycloidal rotation pseudovectors 𝛀 , 𝛀 , and 𝛀 , as these vectors determine magnon chirality via DM interactions37. We find that ℳ , ℳ and 𝒞2 are not valid symmetries for the two-variant domain structure, as they alter the cycloidal rotation vectors 𝛀 , 𝛀 , and 𝛀 . In contrast, the mirror operation ℳ swaps the cycloid rotation between domains relative to the identity operation (Fig. 2c, d . Therefore, the combination of ℳ with a half-period translation symmetry constitutes the only valid symmetry for the system. This low-symmetry configuration permits an unconventional in-plane damping-like torque of the form 𝛕𝑥 ∝𝐌×(𝐱×𝐌) , provided that the applied charge current is neither parallel nor perpendicular to the [010] axis16. We also analyzed the symmetry of other achievable domain structures (see Supplementary Note 1 .

Measurement of unconventional magnon torque
To experimentally confirm the presence of unconventional magnon torque, we fabricated epitaxial heterostructures consisting of 11 nm SrRuO /40 nm BiFeO /5 nm Ni Fe on orthorhombic (o DyScO substrates with (110 orientation (see Methods . The slight in-plane compressive strain introduced by the (110 -oriented DyScO substrate leads to a well-defined, two-variant ferroelectric domain structure in BiFeO , separated by 71° domain walls50. A bulk-like spin cycloid structure in the BiFeO thin film is stabilized, with propagation vectors 𝐤 ([1̅1̅0] and 𝐤 ([11̅0] corresponding to the two domain variants53. SrRuO exhibiting significant spin Hall conductivity, serves as the spin-source layer that excites magnons in the BiFeO 54-57. The crystalline quality of the SrRuO and BiFeO layers was characterized by X-ray diffraction (XRD , and the two-variant domain structure was characterized using reciprocal space mapping (RSM and piezoelectric force microscopy (PFM (see Supplementary Fig. 2 , consistent with previous studies50. All spin torque measurements were performed at room temperature, well above the Curie temperature of SrRuO (~160 K .

To quantify the magnon torque, we employed spin-torque ferromagnetic resonance (ST-FMR measurements (see Methods . Devices were patterned as microstrips (16 μm wide and 80 μm long aligned along various crystalline orientations, characterized by the angle 𝜑 between the applied microwave current 𝐼 direction and the [100] axis (Fig. 3a . Since the device dimensions are much larger than individual ferroelectric domains (about 200 nm 50, the measured magnon torque reflects the overall symmetry of the two-variant domain structure. For ST-FMR measurements, 𝐼 with a fixed frequency 𝑓 was applied, and the external magnetic field 𝐻 was swept in-plane at different angles 𝜑 relative to the current axis.

A representative ST-FMR spectrum for the 𝜑 = 45° device at 𝜑 = 40° is shown in Fig. 3b. The symmetric 𝑉 and antisymmetric 𝑉 voltage components were extracted using Equation (1 in Methods. To differentiate conventional and unconventional magnon torque contributions, we analyzed the magnetic angular 𝜑 dependence of the voltage signal components17,22 (see Eqs. (2 and (3 in Methods . For the 𝜑 = 0° device (𝐼 along [100] , the angular dependence of the symmetric voltage 𝑉 can be described by the form 𝑐𝑜𝑠𝜑 𝑠𝑖𝑛 𝜑 (Fig. 3c , corresponding exclusively to a conventional damping-like torque 𝛕 𝑦 . This behavior is consistent with symmetry constraints that forbid unconventional magnon torque generation when the current is aligned with the mirror plane ℳ .

In contrast, the 𝜑 = 45° device shows a distinctly different angular dependence (Fig. 3d , in which the fitting of 𝑉 requires including an additional component proportional to 𝑠𝑖𝑛𝜑 𝑠𝑖𝑛 𝜑 , consistent with an unconventional damping-like torque 𝛕𝑥 with spin polarization along the x-axis (𝛔 . Notably, this unconventional component 𝑠𝑖𝑛𝜑 𝑠𝑖𝑛 𝜑 reverses sign for the 𝜑 = 135° device (Fig. 3e . In all devices, the 𝑉 components were consistent with conventional out-of-plane field-like torque 𝛕 ∝𝐌×𝐲 (Supplementary Note 3 and Supplementary Fig. 3 .

We then systematically characterized the damping-like torque efficiencies, 𝜉 𝑦 (conventional torque with 𝛔 and 𝜉𝑥 (unconventional torque with 𝛔 across devices with 𝜑 varying from 0° to 165° (Supplementary Note 4 and Supplementary Figs. 4 and 5 . The dependences of 𝜉 𝑦 on 𝜑 show modest 𝑐𝑜𝑠2(𝜑 ) anisotropy, attributed to the orthorhombic symmetry of the DyScO substrate54, with magnitudes consistent with previously reported magnon torque efficiencies in similar SrRuO systems (Fig. 3f 38,39,54,55. The unconventional torque efficiency 𝜉𝑥 reaches a maximum at 𝜑 = 45° and 135°, well fitted to sin ( 𝜑 ) anisotropy (Fig. 3g , consistent with our symmetry analysis (see Fig. 2 . The uncertainties for the torque efficiencies come mainly from possible layer-thickness variations, see the analysis in Supplementary Note 5, Supplementary Fig. 6. The maximum ratio of 𝜉𝑥 /𝜉 𝑦 (20% corresponds to an approximately 11° rotation of the spin polarization from the conventional y-axis direction, comparable to values reported in low symmetry spin-source materials12-24. Independent second harmonic Hall measurements performed on the same sample further confirmed the angular (𝜑 dependence of both 𝛕 𝑦 and 𝛕𝑥 consistent the ST-FMR results (see Supplementary Note 6, Supplementary Figs. 7 and 8 .

To confirm the role of the ferroelectric domains in enabling unconventional torque, we fabricated a control sample with a thinner BiFeO layer (11 nm SrRuO /20 nm BiFeO /5 nm Ni Fe on (110 -oriented DyScO substrate , in which the ferroelectric domain structure collapses into a disordered state due to reduced crystal anisotropy or random pinning42. We found that 𝜉𝑥 fluctuates near the noise level, indicating negligible 𝛕𝑥 (see Supplementary Note 7 and Supplementary Fig. 9 . Additional control measurements ruled out contributions from either SrRuO or BiFeO alone in heterostructures of 11 nm SrRuO /5 nm Ni Fe and 40 nm BiFeO /5 nm Ni Fe grown on (110 -oriented DyScO substrates (see Supplementary Notes 8 and 9, Supplementary Figs. 10 and 11 . These experimental results demonstrate that the symmetry of ferroelectric domains dominates the 𝛕x generation, likely through the exchange interaction between the injected magnon current and the noncollinear spin texture37,38,43 and can potentially be extended to other multiferroic materials58,59.

Deterministic, field-free type-x magnetization switching
Finally, we demonstrate that this unconventional magnon torque 𝛕𝑥 can drive deterministic field-free switching of magnetization along the x-axis (referred to as type-x switching , as schematically shown in Fig. 4a. Conventionally, deterministic type-x switching using damping-like torque 𝛕 𝑦 requires an external out-of-plane magnetic field to break symmetry60. To understand the role of 𝛕𝑥 in switching dynamics, we performed macro-spin simulations for field-free type-x switching, incorporating a damping-like magnon torque with an in-plane spin polarization canted by 11°, consistent with that observed in our sample (see Methods . Figure 4b shows the simulated trajectories of magnetization with initial magnetization along +x direction. Under a 1 ns current pulse, magnetization aligns toward the direction of 𝛔 , with suppressed processional amplitudes due to damping cancellation by 𝛕𝑥 . Upon pulse termination at 10 ns, the magnetization relaxes into the −𝑥 direction, resulting in deterministic, field-free switching. Control simulations without 𝛔 failed to produce switching, confirming the critical role of 𝛕𝑥 for enabling type-x switching (see Supplementary Note 10 and Supplementary Fig. 12 .

We then experimentally validated the field-free type-x switching in the 11 nm SrRuO /40 nm BiFeO /5 nm Ni Fe sample. To monitor the magnetization state, we utilized the second-harmonic Hall voltage (𝑉2𝜔 , which arises from the spin Seebeck effect (SSE 61 in the Ni Fe layer due to a thermal gradient ∇𝑇 perpendicular to sample plane. This generates a spin current with spin polarization parallel to the magnetization which propagates through the BiFeO and produces 𝑉2𝜔 ∝∇𝑇×𝐌 in SrRuO via the inverse spin Hall effect62. An example of a hysteresis loop in 𝑉2𝜔, corresponding to reversal of 𝐌 in response to sweeping an in-plane field along the x-axis is presented in Supplementary Note 11 and Supplementary Fig. 13.

Figure 4c shows deterministic, field-free switching of 𝐌 driven by a 500 μs current pulse 𝐼 , in a Hall bar device oriented at 𝜑 = 30°, where symmetry permits the unconventional magnon torque 𝛕𝑥 . (Shape anisotropy causes the magnetic easy axis to be in the x direction. The critical switching current is about 22 mA, corresponding to a current density of about 4.6×106 A/cm2 (Supplementary Note 4 . The switching polarity is reversed for the φ = 5 device (see Supplementary Fig. 14 , consistent with the reversal of 𝛕𝑥 . In contrast, no field-free switching is observed in Hall bar devices with 𝜑 = 90° (Fig. 4d , where symmetry forbids the generation of unconventional torque 𝛕𝑥 . In this case, magnetization reversal requires a 3 mT out-of-plane magnetic field (Supplementary Fig. 13 . The realization of field-free type-x switching enabled by magnon current in BiFeO could provide potential for developing high-density, energy efficient and fast-switching magnetic devices (see Supplementary Note 12, Supplementary Fig. 15 and Supplementary Table 1 .

Methods
Sample growth
Epitaxial SrRuO /BiFeO heterostructures were deposited on (110 -oriented DyScO substrates using pulsed laser deposition (PLD with a 248 nm KrF excimer laser. SrRuO and BiFeO were deposited at substrate temperature of 670 ℃ and 700 °C, under an oxygen partial pressure of 110 mTorr and 150 mTorr, respectively. The laser fluence at the target surfaces was approximately 1.5 J/cm2 with a pulse repetition rate of 5-7 Hz. Subsequently, the samples were cooled to room temperature in an oxygen rich atmosphere and transferred through air to a magnetron sputtering chamber with a base pressure of 1×10-8 Torr for the deposition of ferromagnetic metals. The ferromagnetic Ni Fe layer was deposited at an argon pressure of 3 mTorr, followed by the deposition of a 3 nm Ti capping layer to prevent oxidation. Film thicknesses were measured using X-ray reflectivity.

Device fabrication
Devices for ST-FMR and second harmonic Hall measurements were fabricated on the same sample chip using standard photolithography, followed by argon ion milling. Subsequently, 10 nm Ti / 150 nm Cu bilayers were deposited for electrode contacts using standard lift-off process. ST-FMR devices were patterned into 16 μm-wide and 80 μm-long microstrips with ground-signal-ground (GSG electrodes, while devices for second harmonic Hall measurements were patterned into 16 μm-wide and 80 μm-long Hall bars with 4 μm-wide Hall contacts.

Magnon torque measurements
For ST-FMR measurements, a Keysight E8257D microwave generator was used to provide a 15 dBm microwave excitation, modulated by an internal oscillator at 1713 Hz. The mixing voltage signal was detected using a DSP 7265 lock-in amplifier. For second harmonic Hall measurements, an AC current at 2333 Hz was supplied by the internal voltage source of the DSP 7265 lock-in amplifier. Both the first and second harmonic Hall voltage signals were simultaneously recorded using a single DSP 7265. Magnetic fields for both ST-FMR and second harmonic Hall measurements were applied using a GMLW projected-field magnet mounted on a Newport motion-controlled stage.

Vector components of magnon torque extracted from ST-FMR measurements
The alternating magnon torque acting on the Ni Fe layer induces magnetization procession and leads to resistance oscillation due to the anisotropic magnetoresistance of the device. Mixing between the device resistance oscillation and 𝐼 generates a resonance in the d.c. voltage V , expressed as63:
𝑉 =𝑉 𝑉 0 0 0 (1
where Δ is the resonant linewidth, 𝜇 is the vacuum permittivity, and 𝐻 is the magnet resonant field. 𝑉 and 𝑉 are the symmetric and antisymmetric coefficient of the Lorentzian functions, related to the in-plane and out-of-plane magnon torques, respectively.

If the magnon carries spin polarization components 𝜎 , 𝜎 and 𝜎 , along the x, y and z axis, respectively, the induced magnon torque has components along all of the x, y and z axis. The corresponding angle 𝜑 dependences for the 𝑉 and 𝑉 coefficients are expressed as22:
𝑉 =𝑉𝑥𝑠𝑖𝑛𝜑 𝑠𝑖𝑛 𝜑 𝑉 𝑦 𝑐𝑜𝑠𝜑 𝑠𝑖𝑛 𝜑 𝑉𝑧 𝑠𝑖𝑛 𝜑 (2
𝑉 =𝑉𝑥 𝑠𝑖𝑛𝜑 𝑠𝑖𝑛 𝜑 𝑉 𝑦 𝑐𝑜𝑠𝜑 𝑠𝑖𝑛 𝜑 𝑉𝑧 𝑠𝑖𝑛 𝜑 (3
Here, 𝑉𝑥 , 𝑉 𝑦 and 𝑉𝑧 are coefficients for the damping-like torque generated by the 𝜎 , 𝜎 and 𝜎 , respectively. 𝑉𝑥, 𝑉 𝑦 and 𝑉𝑧 are the field-like-torque counterparts. We note that 𝑉 𝑦 in principle can have contributions from both a field-like magnon torque and a current-induced Oersted field.

Macrospin simulation
We performed macro-spin simulation of type-x magnetization switching by numerically solving spin-orbit torque modified LLG equation with damping-like torque64-66:
𝜕𝐦 𝜕𝐦
=𝛾𝐦×𝐇 𝛼𝐦× 𝛾𝐻 (𝐦×𝛔×𝐦) (4
𝜕𝑡 𝐞𝐟𝐟 𝜕𝑡 𝐷𝐿
where m is the unit magnetization, which can be written as (𝑚 ,𝑚 ,𝑚 ), 𝛾 is the gyromagnetic ratio, 𝐇 = 𝛿(−𝐻 𝑘 𝑥(𝐦⋅𝐱)2−𝐻 𝑘 𝑧(𝐦⋅𝐳)2) is the effective field mainly contributed by the anisotropy field with 𝜇 𝐻𝑥 = 5 mT, 𝜇 𝐻𝑧 = 0.8 T. 𝛼 = 0.014 is the Gilbert damping coefficient, 𝐻 is damping-like torque effective field induced by magnon-mediated spin current 𝐽 =𝜉𝐽 𝛔 with 𝛔=(−𝑠𝑖𝑛𝜓,𝑐𝑜𝑠𝜓, ) as the normalized spin polarization and 𝜓 = 11°. A magnon torque efficiency of 𝜉 = 0.015 was extracted from the device capable of achieving field-free type-x switching. In our simulation, 𝐽 = 1.1×106 A/cm2, which is on the same order of magnitude as the experimental current density required for magnetization switching.

Magnon-torque-induced magnetization switching measurements
Field-free magnetization switching induced by magnon torque was measured using a probe station under zero applied magnetic field. Magnetization switching assisted by an out-of-plane magnetic field, as described in Supplementary Note 9, was performed in a Physical Property Measurement System (PPMS). All measurements were conducted at room temperature. A Keithley 6221 source meter was used to generate a single square wave with a 1 ms period and a 50% duty cycle, corresponding to a pulse duration of 500 μs. Following the application of the current pulse, the system waited for 8 s before measuring the second harmonic Hall voltage using a DSP 7265 lock-in amplifier at a frequency of 2333 Hz and a current amplitude of 2 mA.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Liang et al. report an unconventional magnon-mediated spin torque in BiFeO3-based heterostructures with a two-variant ferroelectric domain structure. The authors demonstrate that reduced symmetry permits an unconventional spin polarization collinear with the applied charge current, enabling deterministic, field-free switching of magnetization.\nMagnon transport in multiferroics is of considerable interest nowadays because the magnon torque can be tuned by controlling the ferroelectric order. In addition, symmetry-breaking routes to unconventional spin polarization and associated field-free spin-orbit-torque switching are currently central topics in spin-orbitronics. By combining ferroelectric-order-dependent symmetry breaking with magnon torque to realize field-free switching, this work is both important and timely. We support publication of this manuscript in Nature Communications after the authors have considered the following minor comments:\n1. While discussed elsewhere, a concise in-paper explanation of the microscopic mechanism for the unconventional spin polarization $\\sigma_x$ would greatly help readers.\n2. What is the role of having “TWO” ferroelectric domains? Is the TWO-variant state essential for the observed effect or is a single-domain state with an appropriate orientation sufficient?\n3. In line 108,’ $D_1$ along $[\\overline{1}\\ 1\\ 2]$’ seems to be a typo. It should read ‘$D_1$ along $[\\overline{1}\\ 1\\ \\overline{2}]$’.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "This manuscript presents a highly significant and compelling study on the generation of an unconventional magnon-mediated spin torque in SrRuO₃/BiFeO₃/Ni₈₀Fe₂₀ heterostructures. The authors expertly leverage ferroelectric domain engineering in the multiferroic insulator BiFeO₃ to break the crystalline symmetry constraints that typically limit spin polarization in conventional spin-source materials. The experimental demonstration of a magnon torque with a spin polarization rotated by ~11° from the conventional y-axis, enabled by the specific spin cycloid structures in BiFeO₃, is a notable achievement. Furthermore, the subsequent demonstration of deterministic, field-free magnetization switching along the current direction (type-x switching) provides a crucial proof-of-concept for advanced, low-power spintronic devices. The work is meticulously executed, combining sophisticated symmetry analysis, thorough spin-torque ferromagnetic resonance (ST-FMR) measurements, and convincing switching experiments. The potential impact of this work on the fields of magnonics and spintronics is substantial. While the work is compelling and of high value, its impact could be further strengthened by addressing the following aspects:\n1. While the authors provide a superb symmetry analysis proving that an in-plane unconventional torque is allowed, the manuscript lacks a detailed discussion on the specific microscopic mechanism that generates this non-y polarization. How exactly does the interaction between the spin current from SrRuO₃ and the unique spin cycloid in BiFeO₃ lead to a magnon current with a tilted spin polarization? A deeper physical explanation, potentially discussing the role of the Dzyaloshinskii-Moriya vector, the coupling efficiency to different magnon modes, or the spin-to-magnon conversion process at the interface, would greatly enhance the fundamental understanding and impact of this work.\n2. The experiments are conducted at room temperature, which is above the Curie temperature of SrRuO₃ (~160 K). The authors should include a brief discussion or citation to justify that SrRuO₃ retains sufficient spin-Hall conductivity in its paramagnetic state at 300 K to generate the observed effects.\n3. A critical observation from Figures 3f and 3g is that the measurement uncertainties (error bars) for the unconventional torque efficiency appear to be an order of magnitude smaller than those for the conventional torque efficiency . Given that both are extracted from fitting the same set of ST-FMR curves, this significant discrepancy requires a clear explanation. The precise measurement of the torque efficiency is the direct experimental proof of the unconventional torque, and such a large difference in uncertainty could raise questions about the fitting procedure or the robustness of the signal. Is this due to a higher signal-to-noise ratio for the sinφHsin2φH angular dependence? Or does it stem from the fitting model itself, where the conventional torque component is more susceptible to confounding factors (e.g., Oersted fields, variations in anisotropy)? A discussion on the origin of these error bars and the reasons for their disparity is essential to firmly establish the credibility of the central finding.\n4. The work on field-free switching is impressive. However, the explanation of the switching mechanism could be further strengthened to clarify the specific roles of the different polarization components. It is necessary for the authors to provide a clearer explanation, either in the theoretical analysis or discussion section, regarding the relative contributions and influence of the y-polarization and x-polarization components in driving the field-free switching process. In addition, the authors effectively contrast the switching behavior at φE = 30° and φE = 90° to demonstrate the deterministic role of the x-polarization component. To further solidify this claim, a complementary experimental data point at φE = 135° would be highly informative. Would the switching polarity be expected to reverse at this angle? Including this result could serve as another direct and compelling evidence for the existence and critical role of the x-polarization component.", "reviewer_4": "Liang et al. reported the observation of unconventional magnon torque in SrRuO3/BiFeO3/NiFe heterostructures, where the unconventional magnon spin polarization is governed by the ferroelectric domain structure of multiferroic BiFeO3. The authors analyzed the symmetry of the two-variant ferroelectric domain structure and demonstrated that the ferroelectric domains can break magnetic mirror symmetry for unconventional torque. They then fabricated devices with controlled ferroelectric domains and observed the in-plane unconventional magnon torque through STFMR and harmonic measurements, and further demonstrated field-free type-x magnetization switching. The underlying physics is interesting and the topic is timely, supported by convincing results.\nI would recommend publication of this manuscript in Nature Communications if the authors address the following points:\n1. Could the authors provide additional symmetry analyses for other possible ferroelectric domain structures, such as the single-domain and four-variant domain configurations that are commonly observed in BiFeO3 thin films? Including these cases would help readers better understand and generalize the presented results.\n2. According to the symmetry analysis, only one mirror plane exists in the two-variant domain structure, why only sigma_x is observed?\n3. Can the authors exclude the interfacial origin of the unconventional torque?\n4. Will field-like torque affect the switching?\n5. There are some typos that authors should check, for example in Supplementary Fig. 8c the y-axis label is wrong."}, "author_response": "Response to referees\nReviewer #1 (Remarks to the Author):\nLiang et al. report an unconventional magnon-mediated spin torque in BiFeO3-based\nheterostructures with a two-variant ferroelectric domain structure. The authors\ndemonstrate that reduced symmetry permits an unconventional spin polarization\ncollinear with the applied charge current, enabling deterministic, field-free switching\nof magnetization.\nMagnon transport in multiferroics is of considerable interest nowadays because the\nmagnon torque can be tuned by controlling the ferroelectric order. In addition,\nsymmetry-breaking routes to unconventional spin polarization and associated field-free\nspin-orbit-torque switching are currently central topics in spin-orbitronics. By\ncombining ferroelectric-order-dependent symmetry breaking with magnon torque to\nrealize field-free switching, this work is both important and timely. We support\npublication of this manuscript in Nature Communications after the authors have\nconsidered the following minor comments:\nResponse: We thank the reviewer for the positive assessment of our and for supporting\npublication after revisions.\n1. While discussed elsewhere, a concise in-paper explanation of the microscopic\nmechanism for the unconventional spin polarization $\\sigma_x$ would greatly help\nreaders.\nResponse:\nWe appreciate this insightful comment. We have actually worked out most of a\nmicroscopic picture, extending some of the ideas from previous work by other groups\nfor how magnon transport will be affected by a spatially non-uniform magnetic texture\nset by the DM interaction (e.g., Nat. Mater. 23, 898-904 (2024); Nat. Commun. 15,\n5975 (2024). Phys. Rev. B 77, 012406 (2008)). In short, we find that one can express\nthe effects of a cycloidal spin texture as giving rise to an emergent Berry curvature that\nwill induce a magnon spin reorientation. However, a full explanation of this picture\nis somewhat involved, and so we would prefer to present it in a separate paper (under\npreparation), while keeping the focus for the current paper on our experimental results.\nWe have added references on page 10 to some of the previous microscopic work:\n‘These experimental results demonstrate that the symmetry of ferroelectric domains\ndominates the 𝝉𝑥 generation, likely through the exchange interaction between the\n𝐷𝐿\ninjected magnon current and the noncollinear spin texture37,38,43. ’\n2. What is the role of having “TWO” ferroelectric domains? Is the TWO-variant state\nessential for the observed effect or is a single-domain state with an appropriate\norientation sufficient?\nResponse:\nWe thank reviewer for this comment. We studied the two-variant structure because\nit was more straightforward for us to grow, and it yielded the interesting, non-trivial\neffects described in the manuscript.\nIn addition, based on our symmetry analysis, a properly oriented single-domain\nconfiguration (𝐏− = [11̅1], 𝐤− = [1̅1̅0], 𝐃 = [1̅12̅], as shown in Figure R1a)\n1 1 1\nshould also permit an unconventional component. By calculating the cycloidal rotation\ndescribed by pseudovector 𝛀 , 𝛀 and 𝛀 , We found there is only one\n[100] [010] [001]\nmirror symmetry ℳ exists, as shown in Figure R1b. Therefore, we anticipate that\n[110]\nthe two-variant state is not the only possible route for observing an unconventional\ntorque component.\nWe have added references on page 6 of the revised manuscript concerning the\nmeans for stabilizing the two-variant structure: ‘In two-variant domain BiFeO that can\n3\nbe stabilized through strain50 or substrate vicinality51, …’. We have also added a\nsymmetry analysis for the single-domain configuration in in the Supplementary Note 1\nof the revised Supplementary Materials, and on page 6 of the manuscript we point the\nreader to this Supplementary Note.\nFigure R1. Additional analysis on the symmetry of single-domain BiFeO . a,\n1\nℳ (gray plane). b, Table summarizing the effects of various symmetry operations\n[110]\non 𝐏, 𝐤, 𝐃 for the P− single domain, as well as the corresponding cycloid\n1\ncomponents 𝛀 , 𝛀 and 𝛀 . Blue check marks indicate that the global spin\n[100] [010] [001]\ncycloid symmetry under ℳ is preserved and equivalent to the identity operation.\n[110]\n3. In line 108,’ $D_1$ along $[\\overline{1}\\ 1\\ 2]$’ seems to be a typo. It should read\n‘$D_1$ along $[\\overline{1}\\ 1\\ \\overline{2}]$’.\nResponse:\nWe appreciate this comment. We have corrected this typo in the revised\nmanuscript.\nReviewer #2 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nReviewer #3 (Remarks to the Author):\nThis manuscript presents a highly significant and compelling study on the generation\nof an unconventional magnon-mediated spin torque in SrRuO /BiFeO /Ni Fe\n3 3 80 20\nheterostructures. The authors expertly leverage ferroelectric domain engineering in the\nmultiferroic insulator BiFeO₃ to break the crystalline symmetry constraints that\ntypically limit spin polarization in conventional spin-source materials. The\nexperimental demonstration of a magnon torque with a spin polarization rotated by ~11°\nfrom the conventional y-axis, enabled by the specific spin cycloid structures in BiFeO₃,\nis a notable achievement. Furthermore, the subsequent demonstration of deterministic,\nfield-free magnetization switching along the current direction (type-x switching)\nprovides a crucial proof-of-concept for advanced, low-power spintronic devices. The\nwork is meticulously executed, combining sophisticated symmetry analysis, thorough\nspin-torque ferromagnetic resonance (ST-FMR) measurements, and convincing\nswitching experiments. The potential impact of this work on the fields of magnonics\nand spintronics is substantial. While the work is compelling and of high value, its\nimpact could be further strengthened by addressing the following aspects:\nResponse:\nWe thank for the reviewer for the highly positive and thoughtful assessment of our\nwork and for recognizing its potential impact on the fields of magnonics and spintronics.\nWe address each point in detail as follows.\n1. While the authors provide a superb symmetry analysis proving that an in-plane\nunconventional torque is allowed, the manuscript lacks a detailed discussion on the\nspecific microscopic mechanism that generates this non-y polarization. How exactly\ndoes the interaction between the spin current from SrRuO and the unique spin cycloid\n3\nin BiFeO lead to a magnon current with a tilted spin polarization? A deeper physical\n3\nexplanation, potentially discussing the role of the Dzyaloshinskii-Moriya vector, the\ncoupling efficiency to different magnon modes, or the spin-to-magnon conversion\nprocess at the interface, would greatly enhance the fundamental understanding and\nimpact of this work.\nResponse:\nWe appreciate this insightful comment. We have actually worked out most of a\nmicroscopic picture, extending some of the ideas from previous work by other groups\nfor how magnon transport will be affected by a spatially non-uniform magnetic texture\nset by the DM interaction (e.g., Nat. Mater. 23, 898-904 (2024); Nat. Commun. 15,\n5975 (2024). Phys. Rev. B 77, 012406 (2008)). In short, we find that one can express\nthe effects of a cycloidal spin texture as giving rise to an emergent Berry curvature that\nwill induce a magnon spin reorientation. However, a full explanation of this picture\nis somewhat involved, and so we would prefer to present it in a separate paper (under\npreparation), while keeping the focus for the current paper on our experimental results.\nWe have added references on page 10 to some of the previous microscopic work:\n‘These experimental results demonstrate that the symmetry of ferroelectric domains\ndominates the 𝝉𝑥 generation, likely through the exchange interaction between the\n𝐷𝐿\ninjected magnon current and the noncollinear spin texture37,38.’\n2. The experiments are conducted at room temperature, which is above the Curie\ntemperature of SrRuO₃ (~160 K). The authors should include a brief discussion or\ncitation to justify that SrRuO₃ retains sufficient spin-Hall conductivity in its\nparamagnetic state at 300 K to generate the observed effects.\nResponse:\nWe thank for reviewer’s suggestion. According to the temperature dependent\nresistivity measurements of SrRuO , the Curie temperature of our SrRuO films is about\n3 3\nthe spin-Hall conductivity of SrRuO increases upon cooling into the ferromagnetic\n3\nstate, a substantial spin-Hall conductivity persists in the paramagnetic state at room\ntemperature (Y. Ou et al., Nano Lett. 19, 3663-3670 (2019)). To quantitatively confirm\nthis in our samples, we measured the spin-Hall conductivity for an 11 nm SrRuO /5 nm\n80 20\napplied along [001] direction (𝜑 = 0°), we obtain a room-temperature 𝜎 =\no 𝐸 𝑆𝐻𝐶\n(5.0±0.8)×103 ℏ Ω−1𝑚−1, consistent with previous studies (ref. 54 and ref. 55 of the\n2𝑒\nrevised paper).\nWe added a reference to the Y. Ou et al. Nano Letters paper into our revised\nmanuscript (ref. 57) and note our result for 𝜎 in the revised Supplementary Note 8,\n𝑆𝐻𝐶\nℏ 𝑦\nas ‘The conventional spin Hall conductivity 𝜎 = 𝜎∙𝜉 for the 𝜑 = 0° device\n𝑆𝐻𝐶 2𝑒 𝐷𝐿 𝐸\nis 𝜎 = (5.0±0.8)×103 ℏ 𝛺−1𝑚−1, consistent with previous studies1,2.’.\n𝑆𝐻𝐶\n2𝑒\n3. A critical observation from Figures 3f and 3g is that the measurement uncertainties\n(error bars) for the unconventional torque efficiency appear to be an order of magnitude\nsmaller than those for the conventional torque efficiency. Given that both are extracted\nfrom fitting the same set of ST-FMR curves, this significant discrepancy requires a\nclear explanation. The precise measurement of the torque efficiency is the direct\nexperimental proof of the unconventional torque, and such a large difference in\nuncertainty could raise questions about the fitting procedure or the robustness of the\nsignal. Is this due to a higher signal-to-noise ratio for the sinφHsin2φH angular\ndependence? Or does it stem from the fitting model itself, where the conventional\ntorque component is more susceptible to confounding factors (e.g., Oersted fields,\nvariations in anisotropy)? A discussion on the origin of these error bars and the reasons\nfor their disparity is essential to firmly establish the credibility of the central finding.\nResponse:\nWe thank the reviewer for this question. The absolute uncertainty in the\nconventional torque efficiency (Fig. 3f) is indeed larger than the absolute uncertainty\nin the unconventional efficiency (Fig. 3g), but the size of the uncertainties relative to\nthe size of the two signals are actually the same (That is, 𝛿𝜉 𝑦 /𝜉 𝑦 and 𝛿𝜉𝑥 /𝜉𝑥\n𝐷𝐿 𝐷𝐿 𝐷𝐿 𝐷𝐿\nare same.). This is because of the way the uncertainties are calculated. We have\nchecked that we did not make an error in the plotting.\nBoth the conventional and unconventional torque components are extracted from\nthe same ST-FMR spectra and exhibit comparable fitting uncertainties in the\ncorresponding voltage amplitudes (see details in Supplementary Note 4). The dominant\ncontribution to the total uncertainty in the torque efficiencies arises from estimating the\nrf current density in the SrRuO layer, which is sensitive to possible thickness variations\n3\nof both the SrRuO and Ni Fe layers. To quantify this effect, we explicitly evaluated\n3 80 20\nall plausible cases corresponding to 1 nm thickness fluctuations in both layers and\ncalculated the resulting distributions of 𝜉 𝑦 and 𝜉𝑥 . The calculated 𝜉 𝑦 and 𝜉𝑥\n𝐷𝐿 𝐷𝐿 𝐷𝐿 𝐷𝐿\nare shown in Figure R2a and Figure R2b, respectively. The rf current calibration\n𝑦 𝑦\nenters the calculation as a multiplicative factor, so that it affects 𝛿𝜉 /𝜉 and\n𝐷𝐿 𝐷𝐿\n𝛿𝜉𝑥 /𝜉𝑥 the same way. Because the unconventional torque efficiency has a smaller\n𝐷𝐿 𝐷𝐿\nabsolute magnitude, its absolute uncertainty is smaller than that of the conventional\ntorque.\nWe clarify the origin of the uncertainty of 𝜉 𝑦 and 𝜉𝑥 in the revised manuscript\n𝐷𝐿 𝐷𝐿\nas ‘The uncertainties for the torque efficiencies come mainly from possible layer-\nthickness variations, see the analysis in Supplementary Note 5, Supplementary Fig. 6.’\n𝑦\nin page 8 of revised manuscript, and also add this part for detailed calculation of 𝜉\n𝐷𝐿\nand 𝜉𝑥 , as well as the uncertainties in Supplementary Note 5 in revised Supplementary\n𝐷𝐿\nMaterials.\nFigure R2. Clarification of error bars. a, Dependence of the conventional\ndamping-like torque efficiency on the angle 𝜑 for all possible 1 nm thickness\n𝐸\nfluctuations, with the averaged 𝜉 𝑦 fitted to 𝜉 𝑦 = 𝜉0 +𝜀 ∙𝑐𝑜𝑠2(𝜑 ) (blue solid\n𝐷𝐿 𝐷𝐿 𝑦 𝑦 𝐸\nline). b, Dependence of the unconventional damping-like torque efficiency on the angle\n𝜑 for all possible 1 nm thickness fluctuations, with the averaged 𝜉𝑥 fitted to 𝜉 𝑦 =\n𝐸 𝐷𝐿 𝐷𝐿\n𝜉0 ∙𝑠𝑖𝑛(2𝜑 ) (red solid line). The red dashed line indicates the baseline 𝜉𝑥 = 0. The\n𝑥 𝐸 𝐷𝐿\nerror bars come from the statistical uncertainty of 𝜉 𝑦 and 𝜉𝑥 for all possible 1 nm\n𝐷𝐿 𝐷𝐿\nthickness variations.\n4. The work on field-free switching is impressive. However, the explanation of the\nswitching mechanism could be further strengthened to clarify the specific roles of the\ndifferent polarization components. It is necessary for the authors to provide a clearer\nexplanation, either in the theoretical analysis or discussion section, regarding the\nrelative contributions and influence of the y-polarization and x-polarization\ncomponents in driving the field-free switching process. In addition, the authors\neffectively contrast the switching behavior at φ = 30° and φ = 90° to demonstrate the\nE E\ndeterministic role of the x-polarization component. To further solidify this claim,\na complementary experimental data point at φE = 135° would be highly informative.\nWould the switching polarity be expected to reverse at this angle? Including this result\ncould serve as another direct and compelling evidence for the existence and critical role\nof the x-polarization component.\nResponse:\nWe thank the reviewer for this insightful comment. To clarify the switching\nmechanism, we performed macro-spin simulation that separate the roles of the\nconventional 𝜏 𝑦 and unconventional torque 𝜏𝑥 components. The simulation shows\n𝐷𝐿 𝐷𝐿\nthat unconventional magnon torque 𝜏𝑥 plays a critical role in the type-x switching\n𝐷𝐿\nbecause the magnetization becomes aligned with the total applied torque vector during\nthe current pulse, so that the direction of the subsequent relaxation of the magnetization\ntoward the x-axis after the pulse is removed is controlled by the sign of 𝜏𝑥 . In contrast,\n𝐷𝐿\n𝑦\nsimulations including only 𝜏 preserve symmetry between the +M and -M states\n𝐷𝐿 x x\nand therefore do not yield deterministic field-free switching, consistent with our\nexperimental observations a 𝜑 = 90° device.\n𝐸\nIn addition, we conducted additional type-x magnetization switching with the\ncurrent applied along 𝜑 = 135° device. As anticipated from symmetry analysis and\n𝐸\nST-FMR measurements, the sign of 𝜏𝑥 reverses at this angle. Correspondingly, we\n𝐷𝐿\nobserved deterministic field-free magnetization switching with the opposite polarity\n(Figure R3) compared to 𝜑 = 30°.\n𝐸\nWe mentioned this part in the revised manuscript, as ‘Figure 4b shows the\nsimulated trajectories of magnetization with initial magnetization along +x direction.’\nand ‘the switching polarity is reversed for the 𝜑 = 135° device (see Supplementary\n𝐸\nFig. 14), consistent with the reversal of 𝝉𝑥 ’ in page 11 of revised manuscript. This\n𝐷𝐿\nresult is also included into Supplementary Fig. 14 of the revised Supplementary\nMaterials.\n=135°\nFigure R3. Field-free type-x switching induced by magnon torque in 𝝋 = 𝟏𝟑𝟓°\n𝑬\ndevice.\nReviewer #4 (Remarks to the Author):\nLiang et al. reported the observation of unconventional magnon torque in\nSrRuO3/BiFeO3/NiFe heterostructures, where the unconventional magnon spin\npolarization is governed by the ferroelectric domain structure of multiferroic BiFeO3.\nThe authors analyzed the symmetry of the two-variant ferroelectric domain structure\nand demonstrated that the ferroelectric domains can break magnetic mirror symmetry\nfor unconventional torque. They then fabricated devices with controlled ferroelectric\ndomains and observed the in-plane unconventional magnon torque through STFMR\nand harmonic measurements, and further demonstrated field-free type-x magnetization\nswitching. The underlying physics is interesting and the topic is timely, supported by\nconvincing results.\nI would recommend publication of this manuscript in Nature Communications if the\nauthors address the following points:\nResponse:\nWe sincerely thank the reviewer for the insightful and constructive evaluation of\nour work, and for acknowledging its potential significance in the magnon physics. We\nprovide detailed responses to each point below.\n1. Could the authors provide additional symmetry analyses for other possible\nferroelectric domain structures, such as the single-domain and four-variant domain\nconfigurations that are commonly observed in BiFeO3 thin films? Including these cases\nwould help readers better understand and generalize the presented results.\nResponse:\nWe thank the reviewer for the critical comments. For a four-variant domain\nstructure, the unconventional magnon spin polarization is forbidden by the higher\nsymmetry operations (four-fold rotation), which is consistent by our control sample (11\nnm SrRuO /20 nm BiFeO /5 nm Ni Fe ) showing negligible unconventional torque\n3 3 80 20\n(see Supplementary Note 9).\nBased on our symmetry analysis, a properly oriented single-domain configuration\n(𝐏− = [11̅1], 𝐤− = [1̅1̅0], 𝐃 = [1̅12̅], as shown in Figure R4a) can also permit an\n1 1 1\nunconventional component. By calculating the cycloidal rotation described by\npseudovector 𝛀 , 𝛀 and 𝛀 , We found there is only one\n[100] [010] [001]\nmirror symmetry ℳ exists, as shown in Figure R4b. These results suggest that the unconventional\n[110]\nmagnon torque could also by induced in single-domain BiFeO .\nthe symmetry of other achievable domain structures (see Supplementary Note 1).’ in\npage 6, and included the further discussion in the Supplementary Note 1 of revised\nSupplementary Materials.\nFigure R4. Additional analysis on the symmetry of single-domain BiFeO . a,\n1\nℳ (gray plane). b, Table summarizing the effects of various symmetry operations\n[110]\non 𝐏, 𝐤, 𝐃 for the P− single domain, as well as the corresponding cycloid\n1\ncomponents 𝛀 , 𝛀 and 𝛀 . Blue check marks indicate that the global spin\n[100] [010] [001]\ncycloid symmetry under ℳ is preserved and equivalent to the identity operation.\n[110]\n2. According to the symmetry analysis, only one mirror plane exists in the two-variant\ndomain structure, why only sigma_x is observed?\nResponse:\nWe thank reviewer for this comment. The reduced symmetry from the spin texture\nis a necessary but not sufficient condition for the generation of unconventional magnon\ntorque components. For the four-variant domain structures, the unconventional magnon\nspin polarization is forbidden by the higher symmetry operations (four-fold rotation),\nwhich is consistent with the results from our control sample (11 nm SrRuO /20 nm\n3 80 20\nNote 9). For the two-variant domain structures, by our understanding the\nunconventional spin polarization components 𝜎 and 𝜎 should both be allowed by\n𝑥 𝑧\nsymmetry. We observe a 𝜎 component clearly, but do not observe a 𝜎 component\n𝑥 𝑧\nabove our noise level. If any 𝜎 component is present, it may be swamped by a large\n𝑧\n𝑦\ncontribution to the antisymmetric ST-FMR voltage 𝐴 generated by the Oersted\n𝐹𝐿\nfield (Supplementary Note 6).\n3. Can the authors exclude the interfacial origin of the unconventional torque?\nResponse:\nWe thank for this comment. We performed spin-torque measurements on a control\nBiFeO /Ni Fe sample (see Supplementary Note 9 of the revised Supplementary\n3 80 20\nMaterials). Neither the conventional nor the unconventional torques were observed,\nthereby excluding the interfacial origin of the unconventional torque.\n4. Will field-like torque affect the switching?\nResponse:\nWe thank for this critical comment. We performed harmonic Hall voltage\nmeasurements and extracted a field-like torque efficiency of approximately −0.04, as\ndiscussed in Supplementary Note 6. However, according to our macro-spin simulations,\nthe unconventional magnon torque 𝜏𝑥 dominates the observed magnetization\n𝐷𝐿\nswitching, as it aligns magnetization with the applied torque polarization during the\ncurrent pulse, allowing the magnetization to deterministically relax into the opposite\nin-plane remanent state after the pulse is removed. Consistent with this picture, field-\nfree type-x magnetization switching is experimentally observed only in devices\nexhibiting a finite 𝜏𝑥 (𝜑 = 30∘), and is absent in devices where 𝜏𝑥 is not present\n𝐷𝐿 𝐸 𝐷𝐿\n(𝜑 = 90∘). The switching polarity is reversed in device with opposite 𝜏𝑥 (𝜑 =\n𝐸 𝐷𝐿 𝐸\n135∘), see Figure R5. These observations suggest that the field-like torque plays a\nminor role in the switching.\nWe mentioned this part in the revised manuscript, as ‘Figure 4b shows the\nsimulated trajectories of magnetization with initial magnetization along +x direction.’\nand ‘the switching polarity is reversed for the 𝜑 = 135° device (see Supplementary\n𝐸\nFig. 14), consistent with the reversal of 𝝉𝑥 ’ in page 11 of revised manuscript. This\n𝐷𝐿\nresult is also included into Supplementary Fig. 14 of the revised Supplementary\nMaterials.\n=135°\nFigure R5. Field-free type-x switching induced by magnon torque in 𝝋 = 𝟏𝟑𝟓°\n𝑬\ndevice.\n5. There are some typos that authors should check, for example in Supplementary Fig.\n8c the y-axis label is wrong.\nResponse:\nWe thank for this critical comment. We checked and corrected the typo."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors' responses to our comments are reasonable. We support publication of this work in Nature Communications.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "I have reviewed the authors’ responses to my previous comments. All my concerns have been adequately addressed, and the revisions are satisfactory. I recommend acceptance of the manuscript in its present form.", "reviewer_4": "Upon reviewing the revised manuscript, it is confirmed that the authors have adequately addressed and elaborated on all comments and concerns from the initial review. All revisions are logically sound and targeted, effectively resolving key issues in the original submission. The following issues need the author’s attentions:\n1. Could the author clarify the “unconventional magnon-mediated spin torque” phenomenon, as well as other multiferroic materials that may exhibit similar phenomena?\n2. The authors should thoroughly review all symbols to ensure consistent boldface formatting for required symbols. For example, “Mx” on Page 11.\n3. The authors are recommended to refine the language throughout the text to improve accessibility for readers. For example, the proof of \"field-free type-x magnetization switching\" on Page 10 should be streamlined with a clearer logical progression.\nIn conclusion, upon completing the aforementioned revisions, the manuscript is recommended for formal acceptance and publication."}, "author_response": "Response to referees\nReviewer #1 (Remarks to the Author):\nThe authors' responses to our comments are reasonable. We support publication of this\nwork in Nature Communications.\nResponse: We thank the reviewer for supporting publication after revisions.\nReviewer #2 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nReviewer #3 (Remarks to the Author):\nI have reviewed the authors’ responses to my previous comments. All my concerns\nhave been adequately addressed, and the revisions are satisfactory. I recommend\nacceptance of the manuscript in its present form.\nResponse: We thank the reviewer for their careful evaluation of our revisions and for\nrecommending the manuscript for publication.\nReviewer #4 (Remarks to the Author):\nUpon reviewing the revised manuscript, it is confirmed that the authors have adequately\naddressed and elaborated on all comments and concerns from the initial review. All\nrevisions are logically sound and targeted, effectively resolving key issues in the\noriginal submission. The following issues need the author’s attentions:\nResponse: We thank the reviewer for acknowledging our previous revisions. We have\naddressed the remaining points of attention as detailed below, which we believe have\nfurther strengthened the clarity of the manuscript.\n1. Could the author clarify the “unconventional magnon-mediated spin torque”\nphenomenon, as well as other multiferroic materials that may exhibit similar\nphenomena?\nResponse:\nBy “unconventional magnon-mediated spin torque” we mean that the magnon\nmediated spin torque has a damping-like component in the unconventional x and/or z\ndirection (parallel to the charge current or in the out-of-plane direction), and not only\nin the conventional y direction. This is explained in the first paragraph of the\nIntroduction. As for other multiferroic materials that might exhibit similar\nphenomena, that requires some speculation going beyond the experimental results\nestablished in our paper. We anticipate that our results should be generalizable to other\nmaterials which possess magnetoelectric coupling between a spiral spin texture and\nferroelectric order (e.g., CuO, Nat. Mater. 7, 291–294 (2008); TbMnO , Sci. Adv. 8,\n3\neadd6984 (2022)). We have included additional references on page 10 of the revised\nmanuscript, “…likely through the exchange interaction between the injected magnon\ncurrent and the noncollinear spin texture37,38,43 and can potentially be extended to other\nmultiferroic materials58,59.”\n2. The authors should thoroughly review all symbols to ensure consistent boldface\nformatting for required symbols. For example, “Mx” on Page 11.\nResponse:\nWe have corrected the typo.\n3. The authors are recommended to refine the language throughout the text to improve\naccessibility for readers. For example, the proof of \"field-free type-x magnetization\nswitching\" on Page 10 should be streamlined with a clearer logical progression.\nResponse:\nWe thank the Referee for the suggestion. We have provided additional clarification;\nsee the revised manuscript.\nIn conclusion, upon completing the aforementioned revisions, the manuscript is\nrecommended for formal acceptance and publication."}, {"round": 3, "reviewer_comments": {"reviewer_4": "All comments have been satisfactorily addressed, and I recommend formal acceptance and publication of this manuscript."}, "author_response": "Response: We thank the reviewer for supporting publication after revisions."}]

Decision letter