Current-controlled creations, deletions, and topological transformations of a single magnetic antiskyrmion in nanostructured cells

Domain: physics
Published: 2025-11-25
Editorial outcome: major_revision

Abstract
Topological magnetic solitons have emerged as promising candidates for information carriers in spintronic devices, thanks to their fascinating electromagnetic properties. For fundamental device applications, the ability to electrically manipulate individual solitons is crucial. However, electrical manipulation of single antiskyrmions has been rarely demonstrated. In this work, we present current-controlled manipulations, encompassing the creation, deletion, and topological transformation of a single antiskyrmion within FeNiPdP nanostructured cells at room temperature. This nanostructure is uniquely designed with dimensions of about 400 nm in width and length, enabling the stabilization of a single antiskyrmion. By simply adjusting the density of nanosecond single-pulsed currents, we achieve the reversible creation and deletion of single antiskyrmions. Moreover, we uncover a rich variety of current-controlled topological transformations among individual antiskyrmions, skyrmions, bubbles, and ferromagnetic states. Our experimental findings are corroborated by micromagnetic simulations, highlighting the pivotal role of current-induced combined effects, such as spin transfer torque and Joule heating. Our results hold potential for advancing antiskyrmion-based device applications.

Introduction
Topological magnetic solitons, embodied by skyrmions and antiskyrmions, are localized particle-like magnetic structures that boast small size, fascinating electromagnetic properties, and tunability through external electrical stimuli1–5. These magnetic solitons have the potential to serve as versatile information carriers for various functions, including memory, storage, and logic operations6–9.

The electrical manipulation of skyrmions and antiskyrmions has been a long-standing area of interest for practical device applications. Recent research has demonstrated diverse electrical control over skyrmions, encompassing their creation10–17, deletion10–14, and movement14–22, which align with the fundamental device functions of writing, deleting, and addressing, respectively. Vortex-like magnetic solitons are typically described by the polarity P, vorticity v, and topological charge Q, and Q=Pv. Magnetic skyrmions and antiskyrmions are distinguished by their vorticity, which is consistent across other condensed matter systems23–25. Magnetic skyrmions are fundamentally categorized by their helicity into two types: Bloch and Néel. In contrast, magnetic antiskyrmions possessing an opposite sign of vorticity, observed in noncentrosymmetric magnets with anisotropic D interactions, possess opposite topological charges Q for the same polarity P26–28. We note that the classification of skyrmions and antiskyrmions in FeGe magnets, as defined in prior work29, is based on topological charge—a scheme that differs fundamentally from the one employed in our present study.

Antiskyrmions have been observed in a handful of noncentrosymmetric magnets, like Mn-Pt-Sn and Fe-Ni-Pd-P alloys30–32. Due to intricate competing magnetic interactions, it has been established that multiple magnetic solitons, including dipolar skyrmions and bubbles, can coexist with antiskyrmions33–37. It is important to note that skyrmion stabilization in antiskyrmion-hosting material systems arises not from the Dzyaloshinskii-Moriya interaction (DMI), but instead shares the same origin as traditional bubbles in centrosymmetric uniaxial magnets. Magnetic bubbles are typically observed in centrosymmetric uniaxial magnets38,39. They fall into two categories: type-I bubbles and type-II bubbles. Because type-I bubbles share identical polarity, vorticity, and integer topological charge (Q=1 or −1) with chiral-Bloch-twisted skyrmions, they are typically classified as ‘skyrmions’ in antiskyrmion-hosting material systems. Conversely, topologically trivial type-II bubbles (Q=0) retain the conventional ‘bubble’ designation33–37,40,41. Moreover, the additional anisotropic DMI in D2d/S4-symmetric systems distorts type-I and II bubbles from circular to elliptical shapes. Different from the dipolar skyrmions and bubbles, magnetic antiskyrmions with square shapes are mainly supported by DMI.

A pioneering work has demonstrated that coexisting magnetic solitons enable information encoding via distinct topological charges Q42. Consequently, manipulating these solitons topologically represents a promising approach, previously explored using external magnetic fields or thermal gradients33–36,43, these methods lack direct compatibility with high-speed electronic devices. Theoretical studies have revealed intriguing current-induced dynamics of antiskyrmions, such as the antiskyrmion Hall effect and the creation of skyrmion-antiskyrmion pairs42–47. Beyond electrical creation and deletion of antiskyrmions, these systems also enable electrically driven skyrmion-antiskyrmion and antiskyrmion-bubble transformations, a capability not previously achieved in conventional skyrmion-hosting materials.

The experimental electrical manipulation of antiskyrmions remains challenging, with only recent studies exploring the current-induced motion of antiskyrmions confined within a helix48,49. The controlled electrical creation, deletion, and topological transformations of individual magnetic antiskyrmions have yet to be achieved.

In this study, we demonstrate the dynamics of a single antiskyrmion confined within an elemental (Fe0.67Ni0.3Pd0.07)3P (FeNiPdP) lamella nanostructure during the application of nanosecond current pulses. Under a fixed magnetic field, we achieve the creation and deletion of a single antiskyrmion by alternating the density of single current pulses. Additionally, we realize a variety of current-controlled topological magnetic transformations among individual antiskyrmions, skyrmions, bubbles, and ferromagnets (FMs). Our findings showcase the versatility of current-controlled antiskyrmion dynamics, which could pave the way for antiskyrmion-based topological spintronic devices.

Results
Magnetic hysteresis in the nanostructured cuboid
We grew FeNiPdP bulk single crystals using the self-flux method. Magnetization measurements at 100 mT reveal a Curie temperature of approximately 390 K (Supplementary Fig. 1). Magnetic field-dependent magnetization curves along the c-axis and in the ab-plane demonstrate perpendicular magnetic anisotropy across the measured temperature range (2–400 K). The uniaxial magnetic anisotropy constant (Ku) was calculated from the difference in the areas under the magnetization curves ∫MsM(B)dB along the c-axis and perpendicular to it, up to saturation Bsat (Supplementary Fig. 1).

We fabricated highly confined FeNiPdP nanostructured cuboids with [001] out-of-plane orientation. Electron diffraction and high-resolution transmission electron microscopy (TEM) confirm cuboid edges closely aligned with [110] and [1-10] crystallographic directions (Supplementary Fig. 2). Lattice parameters a and b were both determined as 0.92 nm, matching established values37. The period (λ) of zero-field stripe domains in a large FeNiPdP lamella is about 200 nm in the measured temperature range from 95-350 K (Supplementary Fig. 3). Within the rectangle dimension of about 2λ–3λ, the confined FeNiPdP cuboid stabilizes a single magnetic soliton. Around and below the critical size (length/width ~1λ ≈ 200 nm), edge-confined fractional half-antiskyrmion emerges (Supplementary Fig. 4)50. Conversely, dimensions > 3λ permit multiple solitons, including skyrmion-antiskyrmion pairs under field variation (Supplementary Fig. 5).

Initially, we investigated how magnetic fields influence the evolution of magnetism within a 450 nm FeNiPdP nanostructured cuboid at a small tilted field angle 1.5°, defined as the angle between the external magnetic field and the normal [001] axis of the thin cuboid plane, as shown in Fig. 1. At zero magnetic field, we observe a distorted U-shaped spin texture (Fig. 1b). Because the U-shaped spin texture originates from the deformation of the rectangular antiskyrmion during the field-decreasing process and is topologically equivalent to the antiskyrmion, we call it U-antiskyrmion. As we gradually increase the field, the U-shaped antiskyrmion first contracts and morphs into a rectangular antiskyrmion (Fig. 1a). With further increments in the magnetic field, we obtain multiple topological transformations: the antiskyrmion transforms into a bubble, then a skyrmion, and ultimately into FM. Conversely, during the field-decreasing process, we observe notable hysteresis. Specifically, FM remains stable in fields above 380 mT, transitioning back to an antiskyrmion once the field decreases below 380 mT (Fig. 1b). As the field approaches zero, the rectangular antiskyrmion expands and reverts to a U-shaped antiskyrmion. This field-induced magnetic hysteresis (Fig. 1c) hints at the coexistence of four distinct states—antiskyrmion, skyrmion, bubble, and ferromagnet—at a fixed field. Our simulations accurately reproduce the transition from the U-shaped antiskyrmion at low magnetic fields to the rectangular-shaped antiskyrmion at high magnetic fields (Fig. 1e, f). A detailed analysis of the energy terms indicates that the U-shaped antiskyrmion is predominantly stabilized by demagnetization and DMI energies (Supplementary Fig. 6). Moreover, at low magnetic fields, uniaxial anisotropy also contributes to the greater stabilization of the U-shaped antiskyrmion compared to the rectangular-shaped antiskyrmion. The total free energy of the U-shaped antiskyrmion is lower than that of the rectangular-shaped antiskyrmion in the low-magnetic-field regime, explaining the formation of U-shaped antiskyrmions at low magnetic fields.

Typically, such magnetic field-induced topological transformations and magnetic hysteresis are observed across a wide temperature range, from 95 to 340 K (Supplementary Fig. 7). The threshold magnetic fields for topological transformations decrease as the temperature rises (Supplementary Fig. 7). We first show the field-induced magnetic hysteresis. As the field increases from 385 to 510 mT, the initial antiskyrmion transforms into a skyrmion. Moreover, the skyrmion remains stable when the field is decreased back to 385 mT (Supplementary Fig. 8). By utilizing this field-swapping method, we can obtain all four states—antiskyrmion, skyrmion, bubble, and FM—at the same field value (Supplementary Fig. 8). We also explore thermal hysteresis at a fixed field (Supplementary Figs. 9 and 10). We first set an antiskyrmion as the initial state at 95 K. In the temperature-increasing process under the application of a fixed field of 417 mT, the antiskyrmion can transform into a bubble at 245 K, and the bubble state remains stable in the temperature-decreasing process. Similarly, the skyrmion and FM states at 95 K and 417 mT can be achieved in a temperature-decreasing process from 250 K and 261 K, respectively. The field- and thermal-induced magnetic hysteresis proves the coexistence of four distinct states at the same field and temperature, enabling the potential controlled transformations between the four states.

We further characterize field- and temperature-dependent antiskyrmion size, defined as Lx and Ly along the antiskyrmion long axes (Supplementary Figs. 11 and 12). At low fields, antiskyrmions and skyrmions manifest distinct anisotropies (Lx ≠ Ly) arising from dipolar interactions and geometrically tunable via nanostructuring. This anisotropy persists for field tilt angles α ≈ 0°–2.5°, with antiskyrmion long axes consistently aligned to the nanostructure’s long axis. Increasing α at a fixed field first transforms antiskyrmions to bubbles while preserving shape anisotropy (Supplementary Fig. 13); further tilt reorients the bubble’s long axis toward the in-plane field component to minimize Zeeman energy. Field elevation reduces both Lx and Ly, driving convergence toward cubic symmetry at high fields (Supplementary Figs. 11 and 12). Upon increasing the temperature, the transformation field decreases, but the skyrmion/antiskyrmion size follows a similar variation rule in all the measured temperature range. Simulations confirm that nanostructure geometry governs antiskyrmion shape anisotropy (Supplementary Fig. 14).

We then delve into the stability of different magnetic solitons in a strongly confined nanostructure through simulations, at a slight field tilt angle of 2°. By examining magnetic field-dependent evolution and calculating the total free energy, we identify the most stable phases across various field regions (Supplementary Fig. 15). At lower fields, antiskyrmions tend to adopt a distorted U-shaped geometry (Fig. 1d). As the field strengthens, the most stable phase sequentially transitions to a rectangular antiskyrmion, then a bubble, another antiskyrmion, and ultimately the FM state. These field-dependent magnetic profiles (Supplementary Fig. 16) align well with our experimental Fresnel images and retrieve magnetizations of field-driven magnetic evolution (Fig. 1). At low magnetic fields, antiskyrmions are energetically favored over skyrmions due to competing energy contributions (Supplementary Fig. 17). The DMI stabilizes spin twists with anti-vorticity within the domain walls, while exchange energy favors skyrmions because antiskyrmions incur higher exchange costs from Bloch lines. Detailed energy analysis confirms demagnetization and uniaxial anisotropy energies further stabilize antiskyrmions at low fields. Conversely, Zeeman energy preferentially stabilizes skyrmions at low fields. The net energy balance ultimately determines antiskyrmion predominance.

Notably, the field-driven energy evolution can be adjusted by varying the angle of the applied field (Supplementary Fig. 15). A slight tilt is necessary for the four-state transformation. The four-state transformation occurs for field tilt angles of up to approximately 3°. In the absence of a field tilt, the bubble state cannot serve as an intermediate phase during the transformation from antiskyrmion to skyrmion (Supplementary Fig. 15b). Consequently, the field increase yields a direct three-state sequence: antiskyrmion to skyrmion to FM state. Conversely, under a large tilt magnetic field, the skyrmion phase cannot remain the most stable phase across all field regions (Supplementary Fig. 15f), producing a distinct transformation pathway: antiskyrmion to bubble to FM state. The coexistence of different metastable phases within the same field regions accounts for magnetic hysteresis (Fig. 1c). Our experiments confirm the theoretically predicted dependence of magnetic field-driven topological transformations on tilt angle (Supplementary Fig. 18).

Current-controlled dynamics of single antiskyrmions
We delve deeper into the behavior of antiskyrmions in response to external pulsed electrical stimuli. Starting with the FM state as our initial condition at a constant field of 385 mT with a tilted angle of 1.5°, we then subject the FeNiPdP microdevice to pulsed currents with a duration of 40 ns (Fig. 2a and Supplementary Movie 1). The FM state exhibits no dynamic response until the current density j exceeds jc1 (~5.8×1010 A/m2). The creation of an antiskyrmion is observed when the current density j surpasses jc1. As we further elevate the current density, the antiskyrmion transforms into a bubble at j > jc2 (~23.8×1010 A/m2), then into a skyrmion at j > jc3 (~24.4×1010 A/m2), and finally into FM at j > jc4 (~25.5×1010 A/m2). We define jc1, jc2, jc3, and jc4 as the minimum current densities required for the transformations: FM to antiskyrmion, antiskyrmion to bubble, bubble to skyrmion, and skyrmion back to FM, respectively. Such four-state transformations can also be realized when the current orientation is reversed (Supplementary Fig. 19). The current density dependence of topological transformations and magnetic hysteresis suggests the electrical control of deterministic topological states by altering the current density.

We have demonstrated that transitions from FM states to antiskyrmions can be achieved by applying a pulsed current with a density within the range of j ∈ [jc1, jc2] (Fig. 2). Starting with an antiskyrmion as the initial state, we can achieve an antiskyrmion-to-FM transformation by applying a single current pulse with j > jc4. By alternating pulsed currents with densities in the ranges j ∈ [jc1, jc2] and j > jc4, we can reversibly create and delete individual magnetic antiskyrmions (Fig. 3, Supplementary Fig. 20a, and Supplementary Movie 2).

We have shown that during an increase in current density (j-increasing process), an antiskyrmion can transform into a skyrmion through an intermediate bubble state. With an antiskyrmion as the starting point, applying a single current pulse with j ∈ [jc3, jc4] results in an antiskyrmion-to-skyrmion transformation (Fig. 3). However, directly transitioning from a skyrmion to an antiskyrmion through a single electrical pulse is not feasible. Instead, we achieve the skyrmion-to-antiskyrmion transformation through a two-step process: first, we apply a single current pulse with j > jc4 to convert the skyrmion to an FM state, and then we apply another single current pulse with j ∈ [jc1, jc2] to transform the FM state into an antiskyrmion. In summary, using a double-pulsed current with varying density, we can realize the skyrmion-to-FM-to-antiskyrmion transformation (Supplementary Fig. 20b and Supplementary Movie 3).

To achieve skyrmion states, we can consistently apply a single current pulse with j ∈ [jc3, jc4], regardless of whether the initial state is FM, antiskyrmion, or bubble. Similarly, to attain the FM state, we can always use a single current pulse with j > jc4, regardless of the starting state is antiskyrmion, bubble, or skyrmion. In contrast, achieving the antiskyrmion state necessitates starting from an FM state and applying a single current pulse with j ∈ [jc1, jc2]. The bubble state can only be achieved from an initial FM or antiskyrmion state using a single current pulse with j ∈ [jc2, jc3]. By varying the pulsed current density, we can realize all reversible transformations between four distinct states, including bubble-FM (Supplementary Fig. 20c and Movie 4), skyrmion-FM (Supplementary Fig. 20d and Movie 5), antiskyrmion-bubble (Supplementary Fig. 20e and Movie 6), and skyrmion-bubble (Supplementary Fig. 20f and Movie 7).

Our voltage source specifications (2-200 ns pulsed duration range) permit current-controlled ultrafast topological transformations across this full temporal window (Fig. 3b and Supplementary Fig. 21). As w increases, jc1 remains stable around 5.0×1010 A/m2, while jc2, jc3, and jc4 all decrease (Fig. 3b). We also investigate the dependence of threshold current density (jc) on magnetic field (B), as shown in Fig. 3c. As B increases, jc1 rises, while jc2, jc3, and jc4 all decline. These differing trends in jc concerning w and B suggest distinct physical mechanisms underlying the electrically controlled topological transformations. Across a temperature range of 100 to 300 K, the dependence of threshold current densities (jc1, jc2, jc3, and jc4) on pulse duration w and magnetic field B follow similar patterns (Supplementary Fig. 22). Notably, current-controlled topological transformations among individual antiskyrmions, skyrmions, bubbles, and FM states can be reliably reproduced at room temperature (Supplementary Movie 8).

Furthermore, these current-controlled transformations are highly reproducible in similar devices (Supplementary Figs. 22 and 23). For a large nanostructure with a length × width of 730 nm × 730 nm, a current pulse with a high current density (37.9×1010 A/m2) reliably erases all magnetic solitons (Supplementary Fig. 24). However, these larger nanostructures host diverse magnetic states with varying soliton counts and topologies. Consequently, small current pulses applied to high-energy metastable FM states yield stochastic outcomes, generating 2–4 coexisting solitons (antiskyrmions, skyrmions, and bubbles) with unpredictable configurations.

In accordance with field tilt angle dependence on static field-driven transformations, the current-controlled multi-state transformations are also affected by the tilted field. Our results show distinct operational regimes for a fixed field of 417 mT (Supplementary Fig. 25): below 1.5° enables 3-state transformations (Antiskyrmion ⇄ Skyrmion ⇄ FM); between 1.5° and 3.0° enables 4-state transformations (Antiskyrmion ⇄ Skyrmion ⇄ Bubble ⇄ FM); and above 3.0° enables 3-state transformations (Antiskyrmion ⇄ Bubble ⇄ FM). Therefore, antiskyrmion-skyrmion conversion requires a small field tilt angle, antiskyrmion-bubble conversion requires a large field tilt angle, while antiskyrmion-FM conversion is robust across at all measured angular range. The four-state transformations necessitate a small field tilt, achievable with components like rotatable stages, though this adds complexity to device design. In contrast, three-state transformations (skyrmion–antiskyrmion–FM) do not require field tilting, enabling a more streamlined device architecture.

Physical origin of the topological magnetic transformations
We finally explore microscopic mechanisms governing current-induced topological transformations among individual antiskyrmions, skyrmions, bubbles, and FM states. In low-field regions, the rectangular antiskyrmion exhibits the lowest energy, while the FM state has the highest. Starting with the FM state, we investigate its dynamic response to Zhang-Li spin-transfer torque (STT) by applying an in-plane current51, as shown in Fig. 4a, c, and Supplementary Movie 9. Our findings indicate that a nucleation seed forms during the excitation of a spin-polarized current. This seed rapidly expands to create a closed domain with intricate domain walls featuring multiple Bloch points. These complex domain walls do not represent the lowest energy state and eventually transform into an antiskyrmion with Q=1. The oscillation of topological charge observed between 1.4 and 2.4 ns (Fig. 4c) results from annihilation of additional high-energy Bloch points within the initially complex domain walls. Our simulations reveal that the FM-to-antiskyrmion transformation occurs on a very short timescale. For current pulses >2 ns, simulations show pulse-duration-independent threshold current densities for FM-to-antiskyrmion transformation (Supplementary Fig. 26), consistent with our experimental data (Fig. 3b). While prior studies demonstrated ultrafast skyrmion generation using sub-ns pulses11, we find that sub-ns antiskyrmion creation via STT demands higher current densities (Supplementary Fig. 26). Furthermore, as the magnetic field increases, our simulations show an increase in jc1 (Supplementary Fig. 27), which is in line with experimental results (Fig. 3c).

In contrast, we attribute the transformation from antiskyrmion to bubble to skyrmion to FM state to the combined effects of Joule heating and STT. Our experiment has shown magnetic hysteresis during the temperature-varying process at a constant magnetic field (Supplementary Figs. 8 and 9). Applying current pulses also results in a temperature increase due to Joule heating. The larger the current density, the greater the temperature rise52. Once the nanosecond current pulse is turned off, the temperature returns to normal. This process aligns well with the static magnetic evolution observed during temperature changes. Consequently, during ns-duration current pulses, Joule heating contributes significantly to the observed reduction in magnetic soliton size. Upon current termination, both the temperature and soliton size recover. The critical current densities jc2, jc3, and jc4 all decrease as pulse duration w increases (Fig. 3b), which is in line with the typical Joule heating effect. Furthermore, the thermally induced transformation must follow the sequence of antiskyrmion, bubble, skyrmion, and finally FM. States later in the sequence are more stable in high-field regions at a fixed temperature or in high-temperature regions at a fixed field. Here, we establish a current-induced temperature increase based on the experimental temperature dependence of magnetic domain evolution (Supplementary Fig. 9). When the temperature rises from 95 to 245 K at a fixed magnetic field, the antiskyrmion transforms into a bubble. Applying a 40-ns current pulse with a critical current density of about 2.4×1011 A/m2 also induces the antiskyrmion-to-bubble transformation. This equivalence implies that such a current pulse induces a temperature rise of approximately 150 K. Furthermore, using the experimental device geometry and material parameters, we simulated the transient temperature variation during pulsed current injection via multiphysics field simulations (Supplementary Fig. 28)53. Our simulations confirm that a 40-ns pulse at this critical current density generates an average temperature rise of about 200 K, comparable with our experimental estimate (~150 K). Critically, STT efficiency scales with current density, enabling sequential antiskyrmion→bubble→skyrmion→FM transformations through synergistic Joule heating and STT effects. During current pulses, Joule heating dynamically reshapes the magnetic energy landscape, shifting the energy minimum from antiskyrmion to bubble to skyrmion to FM during thermal warming at fixed field (Supplementary Fig. 29). STT subsequently drives transitions from metastable states to the new ground state. Micromagnetic simulations confirm reversibility upon energy landscape modification (Fig. 4d), with field-increase behavior at fixed temperature (Supplementary Fig. 15) mirroring thermal evolution at a fixed field (Supplementary Fig. 29): fields of 310 mT stabilize the FM state, permitting STT-driven antiskyrmion-to-FM transformation. Thus, antiskyrmion→bubble→skyrmion→FM transformations could arise from the two-step mechanism comprising: (1) Joule-heating-induced energy landscape modification and (2) STT-mediated transitions toward equilibrium states.

A low-energy state at high temperatures can persist as a metastable high-energy state even after temperature recovery due to magnetic hysteresis. However, thermal heating effects do not support the reverse transformation from FM to skyrmion, bubble, and then antiskyrmion. Thanks to another mechanism-dominated transformation from FM to antiskyrmion (Fig. 4), we can achieve the reverse transformation from FM to skyrmion or bubble, with the antiskyrmion state serving as an intermediate. The Joule thermal heating is determined only by the density and is not dependent on current orientation. Besides, STT acts as an external stimulus to drive the transformation from the metastable phase to the most stable phase, which is shown not to be dependent on current orientation (Supplementary Fig. 26). Thus, the four-state mutual transformations are not strongly dependent on the current orientation (Supplementary Fig. 19).

Importantly, the definitions of antiskyrmion, skyrmion, and bubble apply exclusively to the middle layers of the FeNiPdP structure. To minimize magnetic dipole-dipole interactions, surface layers consistently adopt Néel-twisted skyrmion configurations with Q=−1 (Supplementary Fig. 30)35,41. Consequently, mutual transformations between antiskyrmion, skyrmion, and bubble states alter the topological charges only in the middle layers, while the surface layers retain their skyrmionic topology. We therefore present the representative 2D magnetization of the middle layer (Figs. 1, 3 and 4), which captures the essential topological transformations. The simulated and observed dynamics of these 3D inhomogeneous states under in-plane current are governed by the interplay of Zhang-Li STT and the system’s free energy landscape, reflecting an ensemble-averaged Néel-twisted skyrmion configurations. In this summary, for the first time, we fulfill the fundamental electrical operations on individual antiskyrmions, including reversible creation, deletion, and topological transformations with skyrmions and bubbles in a nanostructured element. We have established the stabilization mechanisms and mutual topological transformations of individual magnetic solitons in the strongly confined elemental nanostructure as a function of temperature and magnetic field. These current-controlled topological transformations exhibit great versatility and can be achieved over a broad temperature range, including room temperature. The deterministic electrical control of magnetic solitons is explained by current-induced STT, Joule thermal heating, and magnetic hysteresis. Our findings shed light on the potential applications of antiskyrmion-hosting materials, such as in multi-state information processing and memory34,40.

Methods
Bulksamplepreparations
Single FeNiPdP crystals with S4 symmetry were grown by the self-flux method with stoichiometric iron (Alfa Aesar, >99.9%) and Nickel (Alfa Aesar, >99.9%), palladium (Alfa Aesar, >99.9%), and red phosphorus (Alfa Aesar, >99.9%). The sintered bulk FeNiPdP was obtained by heating the mixture at 1100 °C for 4 days. The crystal orientations were further identified using electron diffraction and high-resolution transmission electron microscopy (Supplementary Fig. 2).

Fabrication of FeNiPdP microdevices
We fabricated thin FeNiPdP microdevices from bulk single crystals using a standard lift-off method in a focused ion beam and scanning electron microscopy (FIB-SEM) dual-beam system (Helios Nanolab 600i, FEI). The system was equipped with a gas injection system and a micromanipulator (Omniprobe 200+). We first carved FeNiPdP nanostructure on the surface of the single crystal after milling two trenches. The FeNiPdP nanostructure was then lifted off and transferred close to an electrical chip using the micromanipulator. Each microdevice features two electrical contacts and consists of an FeNiPdP cuboid encased in ion-deposited carbon layers on its top surfaces. The left and right ends of the cuboid were connected to Au electrodes on the chip by fabricating Pt nanosticks. The length and width of the FeNiPdP cuboid are designed to be about 300–700 nm. The FeNiPdP cuboids were all finally thinned to a thickness of approximately 140–150 nm. All main-text data derive from a single 450×420 nm microdevice. Supplementary Figs. include full-dimensional documentation for other devices.

TEM measurements
We used in-situ Lorentz-TEM (Talos F200X, FEI) to investigate the current-induced magnetic domain dynamics in the FeNiPdP nanostructure39,54. The current pulses with pulse durations varying from 2 to 200 ns were provided by a voltage source (AVR-E3-B-PN-AC22, Avtech Electrosystems). The temperature can be adjusted in the range from 95 to 350 K.

Micromagnetic simulations
The zero-temperature micromagnetic simulations were performed using MuMax355. We consider the Hamiltonian exchange interaction energy (εex), 2D chiral DMI energy (εD2d), uniaxial magnetic anisotropy energy (εu), Zeeman energy (εzeeman), and magnetic dipole-dipole interaction energy (εdem)55. The total energy terms are given by:

ε = ∫V (εex + εu + εzeeman + εdem + εD2d) dr (1)

Here, exchange energy εex = A(∂xm2 + ∂ym2 + ∂zm2), εD2d = D2d(m · (∂ymx - ∂xmy)), uniaxial magnetic anisotropy energy εu = -Ku(m · n)2, Zeeman energy εzeeman = -MsB · m, and demagnetization energy εdem = -1/2 MsBd · m. Here, m = m(x, y, z) is the normalized units continuous vector field that represents the magnetization M = Ms m(x, y, z). The parameters A, D2d, Ku, and Ms are the exchange interaction, DMI, uniaxial anisotropy constant, and saturation magnetization, respectively. n is the unit vector field of the uniaxial easy magnetization axis and is set along the (001) z-axis. Bd is the demagnetization field. In the absence of the εD2d energy term, the system’s total energy landscape mirrors that of conventional bubble materials in uniaxial magnets and can stabilize both type-I and type-II bubbles.

We set the exchange stiffness as A = 8.0 pJ/m and chiral interaction as D2d = 0.25 mJ/m3. We set Ku = 110 kJ/m3 and Ms = 617 kA/m based on measured parameters extracted from macroscopic magnetization measurements (Supplementary Fig. 1). Our previous study reveals that the experimental spin textures in FeNiPdP can be well reproduced by simulation based on these magnetic parameters35. These magnetic parameters are close to those widely used in previous studies on similar FeNiPdP materials31,37. Simulation considering thermal fluctuation field indicated a Curie temperature of 420 K (Supplementary Fig. 31), which is close to that of experiments. The cell size was set at 2×2×2 nm3. A Zhang-Li STT is considered for simulating current-driven dynamics. We set the Gilbert damping of 0.05 and the non-adiabatic parameter of 0.

Data availability
The data that support the plots provided in this paper and other findings of this study are available from the corresponding author upon reasonable request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript reports field- and current-driven transformation among different magnetic textures in a plate of FeNiPdP. It is shown that skyrmion/antiskyrmion bubbles and magnetically uniform state can be achieved due to a combination of Lee-Zhang torque and Joule heating effects. Overall, the work seems to be sound, and it will be likely of interest to other researchers in the field of skyrmionics. There are multiple, mostly minor, deficiencies that I believe need to be addressed before the manuscript receives further consideration. 1. I am somewhat disconcerted by the use of antiskyrmion/skyrmion parlance in application to magnetic bubbles, but apparently this is common in studies of magnetic bubbles with chiral domain walls. Perhaps a note on the definitions (e.g. bubbles vs skyrmions) in the introduction could address this issue. A clear illustration of antiskyrmion vs skyrmion vs bubbles would be helpful. The simulations shown in Fig.1d are not sufficiently clear. 2. What mechanism stabilizes the U-shape of the bubble at small field? 3. Are the magnetic properties (e.g. magnetic hysteresis loop, anisotropy) characterized? 4. What is the orientation of the studied crystals? XRD characterization is necessary to ascertain their structure. It is mentioned, but for some reason no data are provided even in the supplemental materials. How is the rectangle oriented relative to the easy magnetic direction(s)? 5. Figure captions do not provide sufficient information about the data, measurement approach and settings (e.g. field tilting, defocusing etc.). The plots show Lorentz images without specifying this in the captions, discussing in the text what the contrast represents and what the reader should focus on to interpret these data. 6. The nanostructure parameters other than the side lengths are not provided. More fabrication details are needed. How were the rectangles obtained? What is their thickness? 7. Are the in-plane magnetization directions indicated by the colored plots in Fig.S6c inferred directly from the data? IMO it may be more appropriate to simulate the grayscale Lorentz data and based on this explain how the conclusions about the magnetic state are made based on the data/simulations. The colorwheel in Fig.1d is indiscernible. 8. It is stated in the main text “Notably, “field-driven energy evolution can be adjusted by varying the angle of the applied field (Supplementary Fig. 5).” But this figure shows only simulations. Is there data supporting this statement? What was the field tilt angle in the experiment? Could it be varied? 9. The observed textures are not isotropic. Is the anisotropy defined by the field tilting direction? If yes, this needs to be specified. If it is the shape, was this confirmed by changing the aspect ratio? 10. It is stated in the text that “The coexistence of different phases within the same field regions accounts for the magnetic hysteresis (Fig. 1c).” But Fig.1c is just a schematic. A different explanation is in order (e.g. metastability and history-dependence). 11. Since Joule heating is one of the mechanisms for current-driven transformations, more relevant details about the electronic properties such as resistivity, and an estimate of the temperature increase based e.g. on Fourier law would be helpful. Does the current direction matter? 12. Figs.S1b,d,f show data for a different device. Are the remaining supplementary figures for this device or for the one shown in the main text? 13. Caption in Fig.3 is unreasonably long. Most of the description should be moved to the main text. Also, the English is generally good, but there still are spelling issues that can be easily checked with a spell-checker. “Summry” in caption of Fig.3 should be Summary, “Fresneal” should be Fresnel, “a single pulsed current” (here and in other places) should be “a single current pulse”. “Nicole” in Methods should be “Nickel”, “lift-out” should be “lift-off”. 14. Line 237, “Q = 1” needs to be defined, as well as “TIE analysis” in caption of Fig.S6", "reviewer_2": "Report on \"Current-controlled creations, deletions, and topological transformations of a single magnetic antiskyrmion in nanostructured cells\" by Yaodong Wu et al. The authors have reported the control of the 2-dimensional spin texture including skyrmion and antiskyrmion by the charge current. They performed the numerical simulation and compared it with the TEM results. I have read it carefully and raised several issues regarding the manuscript below. 1. Why antiskyrmion should be specialized although many skyrmion papers have already been reported. I believe the magnetization dynamics of the skyrmion and antiskyrmion states are understood by the Thiele equation. 2. In the usual skyrmion system, the vortices are determined by the sign of the DM interaction. This should clarify why both skyrmion and antiskyrmion states are stable in this system. The higher topological charge state (e.g. Q=2,3,,,) may be a higher energy state of the fixed DM energy. However, it is not obvious to appear the topological state with the different signs. 3. The inplane magnetization component is crucial for determining the topological states. They should represent the inplane component as well as the simulation results. -Technical issue 4. All videos are hard to distinguish these states for non-specialists, I recommend they add the guide to the eye line. Especially, the contrast of the video is quite low compared with the snapshots of Fig.2C. 5. They should show the definition of the skyrmion and bubble and the value of Q. To conclude, I believe this manuscript is not worth publishing in the Nature Communications. Especially, the general interest concerning comment 1 is crucial for this decision. I recommend the authors transfer the manuscript to a specialized journal.", "reviewer_3": "Skyrmions are nontrivial topological spin textures stabilized by the competition between symmetric exchange interaction, asymmetric Dzyaloshinskii-Moriya interaction (DMI). Skyrmions promise to be the potential candidates for the development of next generation spintronic devices. Antiskyrmions are known as the antiparticles of skyrmions, having topological charges opposite to the skyrmions. For practical application it is quite essential to create, annihilate the skyrmions and antiskyrmions on demand, especially, by electrical current or other electrical means. Electrical creation and annihilation of skyrmions have already been demonstrated experimentally. Although, some theoretical studies are found in literatures on the current-induced dynamics (e.g. antiskyrmion Hall effect, creation of skyrmion-antiskyrmion pairs) of antiskyrmions, the experimental demonstration of the charge current induced creation and annihilation of antiskyrmions are still lacking. In the present work, authors demonstrate charge current-induced creation, annihilation, and topological transformation of a single antiskyrmion stabilized in nanostructured cell made of non-centrosymmetric magnet FeNiPdP at room temperature. The nanostructures are designed with dimensions of about 400 nm in width and length, so that a single antiskyrmion can be stabilization. The magnetic textures are imaged in real space by employing Lorentz transmission electron microscope. The reversible creation and deletion of single antiskyrmions are demonstrated by adjusting the density of single current pulse. The topological transformations among individual antiskyrmions, skyrmions, bubbles, and ferromagnetic states are demonstrated by varying external magnetic field, temperature and charge current density. The experimental findings are corroborated by micromagnetic simulations, which shows the critical role of current-induced spin transfer torque and Joule heating. The presented results are interesting, and should be the current interest of spintronics community. However, the present manuscript lacks experimental data and solid scientific arguments. Overall, the novelty and quality of the work falls short of the standard of Nature Communications. Hence I cannot recommend it for the publication in Nature Communications. However, I think it should more suitable for Communication Physics. Anyway, major revision is required before it can be considered for any other journal. [1] Authors have not cited some important articles as given below. (a) Koshibae, W. & Nagaosa, N. Creation of skyrmions and antiskyrmions by local heating. Nat. Commun. 5, 5148 (2014), doi:10.1038/ncomms6148 (b) Stier, M., Häusler, W., Posske, T., Gurski, G. & Thorwart, M. Skyrmion--Anti-Skyrmion Pair Creation by in-Plane Currents. Phys. Rev. Lett. 118, 267203 (2017). doi:10.1103/PhysRevLett.118.267203 (c) Siegl, P. et al. Creating arbitrary sequences of mobile magnetic skyrmions and antiskyrmions. Phys. Rev. B 106, 014421 (2022), doi:10.1103/PhysRevB.106.014421 (d) Zheng, F. et al. Skyrmion–antiskyrmion pair creation and annihilation in a cubic chiral magnet. Nat. Phys. 18, 863-868 (2022), doi:10.1038/s41567-022-01638-4 (e) Li, S., Ezawa, M. & Zhou, Y. Current-induced dynamics of isolated antiferromagnetic antiskyrmion and antiskyrmionium. Phys. Rev. B 107, 174409 (2023) doi:10.1103/PhysRevB.107.174409 (f) Guang, Y. et al. Confined antiskyrmion motion driven by electric current excitations. Nat. Commun. 15, 7701 (2024), doi:10.1038/s41467-024-52072-4 [2] Authors used non-centrosymmetric magnet FeNiPdP for the observation of skyrmions and antiskyrmions. However, characterization of the crystal structure of material, and its magnetic properties (magnetization, DMI, exchange stiffness constant, anisotropy) as a function of magnetic field, temperature is missing. Moreover, the direction of the applied external magnetic field in all the measurements is also not mentioned. Authors highlight the importance of tilting angle of magnetic field in Supplementary Fig. 5. It appears to me that the magnetic field should be aligned with the accuracy of about 1-2 deg. This can be a bottleneck for practical implication. I was just wondering how that much accuracy can be achieved in practical experiment. [3] Which factors decide the formation of antiskyrmion more preferably over skyrmion in FeNiPdP? [4] I recommend to provide schematics of 3D spin textures of antiskyrmion, skyrmion and bubbles so that nonexperts can understand the difference between them very easily. [5] Authors explained that the transformation from uniform ferromagnetic (FM) state to antiskyrmion state occurs due to the spin-torques. Whereas, the transformation from antiskyrmions to the bubble to skyrmion to FM state occur due to the Joule heating effect. Although authors have tried their best to explain this, I am not convinced with their arguments. I think the spin-torques also increase with the current density. So, the spin-torques must have a critical role even for the transformation from antiskyrmions to the bubble to skyrmion to FM state. The energy landscape, as shown in Fig. 4a for FM and antiskyrmion states, should be modified by considering the thermal effect even for other topological states. Moreover, it is important to know the increment of the temperature with the increment of current density. Authors should use a thermal sensor/camera to determine the increase of the temperature due to current pulse. Additionally, a theoretical estimation would also be very useful. [6] What is U-antiskyrmions? My point is that why do the authors call it as antiskyrmion? I do not see any estimation about the skyrmion/antiskyrmion size and their evolution as a function of magnetic field, temperature and current. [7] Some previous studies show the creation of skyrmion-antiskyrmion pair. However, in the present study either the formation of antiskyrmion or skyrmion is observed. Is that because of the finite size of the magnetic sample? What is the role of finite size of magnetic element in the stabilization of antiskyrmions and skyrmions in this study? Why does topological number oscillate between 1.4 to 2.4 ns in Fig. 4a? [8] The width of the current pulses used in this study seems to be longer than usual. What if the authors use multiple sub-nanosecond current pulses to create antiskyrmions? [9] I think the cell size in FeNiPdP must have an important role in the stabilization of antiskyrmions and skyrmions, and hence determining the critical current densities for creation, annihilations and transformation. Authors tried to make some small variation in the dimensions (supplementary fig. 1), but that is not enough for understanding. Authors should shed some light on this."}, "author_response": "Manuscript ID: NCOMMS-25-13186-T \"Current-controlled creations, deletions, and topological transformations of a single magnetic antiskyrmion in nanostructured cells\" by Y. Wu et al. Note that all page numbers and references without special instructions refer to the newly revised manuscript attached with this response and not to the original version submitted. The added contents are marked in red in the revised manuscript. Response to Reviewer #1: Reviewer #1: The manuscript reports field- and current-driven transformation among different magnetic textures in a plate of FeNiPdP. It is shown that skyrmion/antiskyrmion bubbles and magnetically uniform state can be achieved due to a combination of Lee-Zhang torque and Joule heating effects. Overall, the work seems to be sound, and it will be likely of interest to other researchers in the field of skyrmionics. There are multiple, mostly minor, deficiencies that I believe need to be addressed before the manuscript receives further consideration. Response: We thank you very much for your time and efforts in reviewing our manuscript. Below, please find our detailed response to each of your insightful comments. Comment 1: I am somewhat disconcerted by the use of antiskyrmion/skyrmion parlance in application to magnetic bubbles, but apparently this is common in studies of magnetic bubbles with chiral domain walls. Perhaps a note on the definitions (e.g. bubbles vs skyrmions) in the introduction could address this issue. A clear illustration of antiskyrmion vs skyrmion vs bubbles would be helpful. The simulations shown in Fig.1d are not sufficiently clear. Response: Following your comment, we have added a note on the definitions of magnetic solitons in the Introduction Section, see Lines 50-56: “Vortex-like magnetic solitons are typically described by the polarity P, vorticity v, and topological charge Q, and Q = Pv. Skyrmions and antiskyrmions are distinguished by their vorticity. The Bloch and Néel-twisted skyrmions have been commonly taken as skyrmions. In contrast, magnetic antiskyrmions possessing an opposite sign of vorticity, observed in noncentrosymmetric magnets with anisotropic D interactions, possess opposite 2d topological charges Q for the same polarity P.23-25” And Lines 65-73: “Magnetic bubbles are cylindrical domains typically observed in centrosymmetric uniaxial magnets.35,36 They fall into two categories: type-I bubbles and type-II bubbles. Because type-I bubbles share identical polarity, vorticity, and integer 1 topological charge (Q = 1 or −1) with chiral-Bloch-twisted skyrmions, they are typically classified as 'skyrmions' in antiskyrmion-hosting material systems. Conversely, topologically trivial type-II bubbles (Q = 0) retain the conventional 'bubble' designation.30-34,37,38 Moreover, the additional anisotropic DMI in D /S -symmetric 2d 4 systems distorts type-I and II bubbles from circular to elliptical shapes.” Comment 2: What mechanism stabilizes the U-shape of the bubble at small field? Response: We have clarified the stabilization mechanism of U-shaped antiskyrmions at low fields in our revised manuscript. This (Fig. R1a) reveals that U-shaped configurations are primarily stabilized by demagnetization and DMI energies, while rectangular forms are dominated by exchange and Zeeman energies. Figure R1b-c presents the simulated field-driven evolution from U-shaped to rectangular antiskyrmions, which is consistent with our experiments. Our analysis compares the energy difference 𝜀 (cid:3398)𝜀 throughout the hysteresis cycle, where: u rect  𝜀 (cid:3398)𝜀 > 0 indicates rectangular antiskyrmion stability. u rect  𝜀 (cid:3398)𝜀 < 0 favors U-shaped antiskyrmions. u rect Uniaxial anisotropy further reinforces U-shaped stability at low fields. Critically, the negative Δε values at low fields confirm the thermodynamic preference for U-shaped antiskyrmions. a 5 Rectangle  zeeman  0 u total DM  dem -5 60 70 80 90 b B = 0 mT 60 mT 85 mT 130 mT 200 nm B-increasing c B = 0 mT 60 mT 85 mT 90 mT B-decreasing 2 )3m/Jk( - tcer U U-shape  ex B (mT) Fig. R1 (i.e., Supplementary Fig. 6) Simulated energy landscape and field-driven evolution of antiskyrmion morphologies. a Magnetic field dependence of the energy difference 𝜀 (cid:3398)𝜀 between U-shaped and rectangular antiskyrmions, showing U rect contributions from: total energy (𝜀 ), demagnetization (𝜀 ), exchange (𝜀 ), DMI total demag ex (𝜀 ), anisotropy (𝜀 ), and Zeeman (𝜀 ) terms. b Field-induced morphological D2d anis zeeman evolution starting from a U-shaped antiskyrmion during increasing field. c Morphological evolution starting from a rectangular antiskyrmion during decreasing field. We have added a discussion about the stabilization of the U-shaped antiskyrmion in our revised manuscript, see Lines 134-143: “Our simulations accurately reproduce the transition from the U-shaped antiskyrmion at low magnetic fields to the rectangular- shaped antiskyrmion at high magnetic fields (Supplementary Fig. 6). A detailed analysis of the energy terms indicates that the U-shaped antiskyrmion is predominantly stabilized by demagnetization and DMI energies. Moreover, at low magnetic fields, uniaxial anisotropy also contributes to the greater stabilization of the U-shaped antiskyrmion compared to the rectangular-shaped antiskyrmion. The total free energy of the U-shaped antiskyrmion is lower than that of the rectangular-shaped antiskyrmion in the low-magnetic-field regime, explaining the formation of U-shaped antiskyrmions at low magnetic fields.”. Comment 3: Are the magnetic properties (e.g. magnetic hysteresis loop, anisotropy) characterized? Response: Yes. We have provided temperature dependence of hysteresis loop measurements along and perpendicular to the c axis in our revised manuscript, as shown in Fig. R2. Our FeNiPdP crystals reveal perpendicular anisotropy with easy axis along the c axis in the whole measured temperature range from 2 to 400 K. The anisotropy constant is extracted from the difference in the areas under the magnetization curves (cid:1516) (cid:3003)(cid:3151)(cid:3159)(cid:3178)𝑀(cid:4666)𝐵(cid:4667)d𝐵 along the c-axis and perpendicular to it, up to saturation 𝐵 . The (cid:2868) (cid:2903)(cid:2911)(cid:2930) saturated magnetization M is taken at the magnetization of 2000 mT. The temperature s dependence of magnetization indicates a Curie temperature of about 390 K. 3 160 140 120 100 80 60 40 20 0 Temperature (K) 4 )m/Ak( M s )3m/Jk( K u 10 700 K u B = 10 mT M 600 s 500 5 400 300 200 0 0 100 200 300 400 0 100 200 300 400 )g/ume( M 80 B // c 60 40 20 0 -20 -40 -60 -80 -2000 -1000 0 1000 2000 B // c FC B // c ZFC B // ab FC B // ab ZFC Temperature (K) )g/ume( M 80 B // ab 60 40 20 0 -20 -40 -60 -80 -2000 -1000 0 1000 2000 B (mT) )g/ume( M a b 2K 50K 75K 100K 125K 150K 175K 200K 225K 250K 275K 300K 325K 350K 375K 400K B (mT) c d Fig. R2 (i.e., Supplementary Fig. 1) Fundamental magnetic properties of bulk single crystals. a and b Magnetic field dependence of magnetization along the c axis (a) and ab plane (b). c Temperature dependence of magnetization at 10 mT. d Temperature dependence of saturated magnetization M and uniaxial magnetic anisotropy constant s K . u We have added the discussion about the fundamental magnetic properties of FeNiPdP crystals, see Lines 98-105: “Magnetization measurements at 100 mT reveal a Curie temperature of approximately 390 K (Supplementary Fig. 1). Magnetic field-dependent magnetization curves along the c-axis and in the ab-plane demonstrate perpendicular magnetic anisotropy across the measured temperature range (2 K to 400 K). The uniaxial magnetic anisotropy constant (K ) was calculated from the difference in the u areas under the magnetization curves (cid:1516) (cid:3003)(cid:3268)(cid:3276)(cid:3295)𝑀(cid:4666)𝐵(cid:4667)𝑑𝐵 along the c-axis and (cid:2868) perpendicular to it, up to saturation 𝐵 (Supplementary Fig. 1)”. (cid:3020)(cid:3028)(cid:3047) Comment 4: What is the orientation of the studied crystals? XRD characterization is necessary to ascertain their structure. It is mentioned, but for some reason no data are provided even in the supplemental materials. How is the rectangle oriented relative to the easy magnetic direction(s)? Response: We have clarified the crystal orientation in the revised manuscript. XRD characterization was precluded by insufficient sample volume from our small bulk crystals, which yields weak diffraction intensity. Instead, we provide electron diffraction of thin FeNiPdP plates (Fig. R3c), confirming a noncentrosymmetric tetragonal structure (space group 𝐼4(cid:3364) ) within the (001) plane. High-resolution transmission electron microscopy (HRTEM) measurements (Fig. R3d) further verify rectangular microdevice edges aligned parallel to [110] and [11(cid:3364) 0] crystallographic directions. Lattice parameters a = b = 0.92 nm agree with established values. a b y 200 nm x d c y [1 -1 0] x 10 1/nm [1 1 0] 2 nm Fig. R3 (i.e., Supplementary Fig. 2) Fundamental structural properties of FeNiPdP(001) microdevice. a Scanning electron microscopy of the fabricated microdevice. b Enlarged scanning electron microscopy of the thin FeNiPdP region. c Electronic diffraction pattern of the thin FeNiPdP region, agreeing well with the (001) oriented plane of the noncentrosymmetric tetragonal structure (space group 𝐼4(cid:3364) ). d High-resolution transmission electron microscopy of the thin FeNiPdP plate, confirming two edges of the rectangle along the [110] and [11(cid:3364)0] axes, respectively. We have added a discussion about the crystal characterization in the revised manuscript, see Lines 106-110: “We fabricated highly confined FeNiPdP nanostructured cuboids with [001] out-of-plane orientation. Electron diffraction and high-resolution transmission electron microscopy (TEM) confirm cuboid edges closely aligned with [110] and [1 1(cid:3364) 0] crystallographic directions (Supplementary Fig. 2). Lattice parameters a and b were both determined as 0.92 nm, matching established values34”. Comment 5: Figure captions do not provide sufficient information about the data, measurement approach and settings (e.g. field tilting, defocusing etc.). The plots show Lorentz images without specifying this in the captions, discussing in the text what the contrast represents and what the reader should focus on to interpret these data. 5 Response: Following your insightful comments, we have provided more sufficient information in the Figure captions, including field tilting, defocus distance. Some representative corrections, e.g., Lines 211-212 in the Figure 1 caption: “Field tilt angle, 1.5°. The Lorentz Fresnel images in (a) and (b) were taken at a defocused distance of −500 μm”; Lines 238-239 in the Figure 2 caption: “Pulse duration 40 ns. Magnetic field, 385 mT. Defocus distance, −500 μm. Field tilt angle, 1.5°”, etc. Comment 6: The nanostructure parameters other than the side lengths are not provided. More fabrication details are needed. How were the rectangles obtained? What is their thickness? Response: The thickness of nanostructures is about 140-150 nm. We follow a similar fabrication process that is presented in detail in a previous study (Ref. Song et al. Nat. Commun. 15, 5614 (2024)), which shares some same co-authors as our manuscript. The nanostructures are fabricated using a standard lift-off method using an FIB-SEM system. We have provided more fabrication details in the method section, see Lines 429-441: “We fabricated thin FeNiPdP microdevices from bulk single crystals using a standard lift-off method in a focused ion beam and scanning electron microscopy (FIB-SEM) dual-beam system (Helios Nanolab 600i, FEI). The system was equipped with a gas injection system and a micromanipulator (Omniprobe 200+). We first carved FeNiPdP nanostructure on the surface of the single crystal after milling two trenches. The FeNiPdP nanostructure was then lifted off and transferred close to an electrical chip using the micromanipulator. Each microdevice features two electrical contacts and consists of an FeNiPdP cuboid encased in ion-deposited carbon layers on its top surfaces. The left and right ends of the cuboid were connected to Au electrodes on the chip by fabricating Pt nanosticks. The length and width of the FeNiPdP cuboid are designed to be about 300-700 nm. The FeNiPdP cuboids were all finally thinned to a thickness of approximately 140-150 nm. A detailed fabrication process of microdevices has been presented in a previous study.19”. Comment 7: 7.1 Are the in-plane magnetization directions indicated by the colored plots in Fig.S6c inferred directly from the data? Response: Yes, the in-plane magnetization directions indicated by the colored plots in Fig.S6c are inferred directly from the data, through the TIE analysis of Lorentz-TEM Fresnel images. We have added the Lorentz Fresnel data in Fig. S6c (Fig. S16 in the revised supporting information), as shown in Fig. R4. We have also specified this in the figure caption: “c-d Corresponding experimental in-plane magnetizations (c) and Fresnel images (d) for U-antiskyrmion, rectangle antiskyrmion, bubble, and skyrmion retrieved from transport of intensity equation (TIE) analysis.” 6 Fig. R4 (i.e., Supplementary Fig. 16) a-b Simulated defocused Fresnel contrasts (a) and integral in-plane magnetizations (b) for U-antiskyrmion at 0 mT, rectangle antiskyrmion at 280 mT, bubble at 290 mT, and skyrmion at 300 mT. c-d Corresponding experimental in-plane magnetizations (c) and Fresnel images (d) for U-antiskyrmion, rectangle antiskyrmion, bubble, and skyrmion retrieved from transport of intensity equation (TIE) analysis. Comment 7: 7.2 IMO it may be more appropriate to sim Fresnel images ulate the grayscale Lorentz data and based on this explain how the conclusions about the magnetic state are made based on the data/simulations. The colorwheel in Fig.1d is indiscernible. Response: Thank you for your kind suggestion. We have also provided the simulated grayscale Lorentz data for a direct comparison, as shown in Fig. R4a. The simulations all agree well with our experimental observations. We have also increased the resolution of the colorwheel in Fig. 1d, as shown in Fig. R5. 7 We have discussed the consistency between experiments and simulation in our revised manuscript, see Lines 183-185: “These field-dependent magnetic profiles (Supplementary Fig. 16) align well with our experimental Fresnel images and retrieve magnetizations of field-driven magnetic evolution (Fig. 1)”. d U-Antiskyrmion Antiskyrmion Bubble Skyrmion 200 nm Fig. R5 (i.e., Fig. 1d in the maintext) The colorwheel resolution in the figure has been greatly improved. Comment 8: It is stated in the main text “Notably, “field-driven energy evolution can be adjusted by varying the angle of the applied field (Supplementary Fig. 5).” But this figure shows only simulations. Is there data supporting this statement? What was the field tilt angle in the experiment? Could it be varied? Response: We appreciate your careful review of this point. In the original manuscript, the experimental field tilted angle is fixed at 1.5° and can be varied. The claim regarding field-angle-dependent energy evolution is now experimentally supported in our revised manuscript: Figure R6 shows systematic variation of the field tilt angle (θ) and shows the resulting magnetic state transformations. Key findings include: at θ = 0°, field increase drives antiskyrmion→skyrmion→ferromagnet (FM) transitions; at intermediate θ (1°–2.5°), we observe the complete four-state sequence (antiskyrmion→bubble→skyrmion→FM); for θ > 2.5°, only three-state transformations occur (antiskyrmion→bubble→FM). These experimental results closely match our simulations (Supplementary Fig. 18), confirming that field tilt angle critically controls accessible state-transformation pathways. The tilted field information has been demonstrated in our revised manuscript. We have added related discussion in our revised manuscript, see Lines 201-206: “Our experiments confirm the theoretically predicted dependence of magnetic field-driven topological transformations on tilt angle (Supplementary Fig. 18). At zero tilt angle, field increase produces a direct 3-state transformation sequence: antiskyrmion to skyrmion to FM, with no bubble state observed. At larger tilt angles, field increase yields a distinct 3-state sequence: antiskyrmion to bubble to FM, with no skyrmion state emerging”. 8 a B-increasing 258 mT 346 mT 347 mT 365 mT Antiskyrmion Antiskyrmion Skyrmion FM 200 nm B-decreasing 0 mT 226 mT 282 mT 300 mT U-Antiskyrmion U-Antiskyrmion Antiskyrmion FM Skyrmion U-Antiskyrmion Antiskyrmion FM Antiskyrmion U-Antiskyrmion FM 0 50 100 150 200 250 300 350 400 450 500 550 600 650 B (mT) b B-increasing 336 mT 341 mT 346 mT 365 mT Antiskyrmion Bubble Skyrmion FM 200 nm B-decreasing 0 mT 206 mT 297 mT 320 mT U-Antiskyrmion U-Antiskyrmion Antiskyrmion FM Skyrmion U-Antiskyrmion Antiskyrmion FM Bubble U-Antiskyrmion Antiskyrmion FM 0 50 100 150 200 250 300 350 B (mT) c B-increasing 274 mT 305 mT 329 mT 363 mT Antiskyrmion Antiskyrmion Bubble FM 200 nm B-decreasing 0 mT 234 mT 292 mT 320 mT U-Antiskyrmion Antiskyrmion Bubble FM Antiskyrmion U-Antiskyrmion FM Bubble U-Antiskyrmion Antiskyrmion FM 0 50 100 150 200 250 300 350 B (mT) Fig. R6 (i.e., Supplementary Fig. 18) Tilted field effects on the field-driven magnetic evolution. Magnetic evolutions and summary of stable diagram in the field-increasing and field-decreasing processes. (a) 0°. (b) 1.0°.(c) 2.9°. 9 Comment 9: The observed textures are not isotropic. Is the anisotropy defined by the field tilting direction? If yes, this needs to be specified. If it is the shape, was this confirmed by changing the aspect ratio? Response: We thank you very much for bringing to our attention the anisotropic shape of spin textures. We believe that the anisotropic magnetic textures are mainly determined by the aspect ratio of rectangular nanostructures originating from magnetic dipole-dipole interactions. For a direct comparison, we fabricated two geometries with a length (cid:3400) width of 530(cid:3400)440 and 425(cid:3400)530 nm2, as shown in Fig. R7. The long edge of antiskyrmions always aligns with the long edge of the rectangle. In our experiments, we always apply a field tilted fixed at 1.5° with an in-plane component along the x-axis. Thus, we do not think that the field tilt determines the anisotropy in small tilt angles (< 2°). The experimental effect of geometry shape on the shape anisotropy of the antiskyrmion is well reproduced in our simulation, as shown in Fig. R8. B = 214 mT 288 mT 329 mT 360 mT 530 nm 10 440 nm y x B = 235 mT 315 mT 389 mT 401 mT 425 nm 530 nm a b y x c d 400 300 200 100 300 400 500 600 )mn( L 500 400 300 200 100 300 400 500 B (mT) )mn( L e 530 nm ×440 nm 425 nm ×530 nm 4 530 nm ×440 nm 9 9 1 1 2 2 2 2 2 2 5 5 5 5 0 0 5 5 9 9 0 0 0 0 0 0 5 5 K K K K K K K K K K L L L L L L L L L L x y x y x y x y x y 2 3 425 nm ×530 nm 1 0 300 400 500 600 B (mT) L/L y x 9 1 2 2 2 9 1 2 2 2 5 5 0 5 9 5 5 0 5 9 0 0 0 5 0 0 0 5 K K K K K K K K K K L L x x L L L L L L L L / / x x x x x x x x L L / / / / / / / / L L L L L L L L y y y y y y y y y y B (mT) Fig. R7 (i.e., Supplementary Fig. 12) Experimental effect of geometry shape on the shape anisotropy of antiskyrmions. a Magnetic evolution in the field-increasing process in a rectangle with a length (cid:3400) width of 530 (cid:3400) 440 nm2. b Magnetic evolution in the field-increasing process in a rectangle with a length (cid:3400) width of 425 (cid:3400) 530 nm2. c Magnetic field dependence of length L and width L of antiskyrmion in the rectangle x y with a length (cid:3400) width of 530 (cid:3400) 440 nm2. d Magnetic field dependence of length L and width L of antiskyrmion in the rectangle with a length (cid:3400) width of 425 (cid:3400) 530 x y nm2. e Magnetic field dependence of the aspect ratio of antiskyrmions. Thickness, 140 nm. B = 0 mT 150 mT 250 mT 330 mT 450 nm 11 400 nm y x B = 0 mT 150 mT 250 mT 330 mT 400 nm 450 nm y x 2.0 1.5 1.0 0.5 100 200 300 L/L y x 400 400 nm X 450 nm 450 nm X 400 nm 300 200 100 0 100 200 300 B (mT) )mn( L 400 L 300 x L y 200 100 0 100 200 300 B (mT) )mn( L a L x b c 450 nm (cid:3400) 400 nm d 400 nm (cid:3400) 450 nm e L x L y B (mT) Ly Fig. R8 (i.e., Supplementary Fig. 14) Simulated effect of geometry shape on the shape anisotropy of antiskyrmions. a Magnetic evolution in the field-increasing process in a rectangle with a length (cid:3400) width of 450 (cid:3400) 400 nm2. b Magnetic evolution in the field-increasing process in a rectangle with a length (cid:3400) width of 400 (cid:3400) 450 nm2. c Magnetic field dependence of length L and width L of antiskyrmion in the rectangle with a x y length (cid:3400) width of 450 (cid:3400) 400 nm2. d Magnetic field dependence of length L and width L of antiskyrmion in the rectangle with a x y length (cid:3400) width of 400 (cid:3400) 450 nm2. e Magnetic field dependence of the aspect ratio of antiskyrmions. Thickness, 140 nm. Finally, we also explore the effect of a field tilt on the shape of antiskyrmions, as shown in Fig. R9. The antiskyrmion maintains its shape in the field tilt range of about 0-2.5°. For a larger field tilt angle, the antiskyrmion transforms to a bubble without change of the shape anisotropy. But for the bubble with its long axis along the y-axis, its shape anisotropy changes when the in-plane x-axis field component increases. At a field tilt angle larger than 4.5°, we observe that the long axis of the bubble changes from the y-axis to the x-axis to minimize the Zeeman energy. a 𝛼 = 0° 2.04° 4.65° 8.14° 9.90° y 200 nm x b 𝛼 = 0° 2.30° 5.34° 7.25° 9.49° 200 nm Fig. R9 (i.e., Supplementary Fig. 13) Experimental field tilt effect on the shape anisotropy of antiskyrmions. a Fresnel contrast in the nanostructure with a length of 530 nm and a width of 440 nm. Magnetic field 320 mT with a tilt toward the −x axis. b Fresnel contrast in the nanostructure with a length of 425 nm and a width of 530 nm. Magnetic field 295 mT with a tilt toward the −x axis. Defocus distance, −350 μm. We have added a discussion about the shape of antiskyrmion in the revised manuscript, see Lines 162-176: “We further characterize field- and temperature-dependent antiskyrmion/skyrmion dimensions, defined as lengths L and L along the [110] and x y [11(cid:3364)0] crystallographic axes (Supplementary Fig. 11 and Supplementary Fig. 12). At low fields, antiskyrmions and skyrmions manifest distinct anisotropies (L ≠ L ) arising x y from dipolar interactions and geometrically tunable via nanostructuring. This anisotropy persists for field tilt angles 𝛼 ≈ 0°–2.5°, with antiskyrmion long axes consistently aligned to the nanostructure's long axis. Increasing 𝛼 at fixed field first transforms antiskyrmions to bubbles while preserving shape anisotropy (Supplementary Fig. 13); further tilt reorients the bubble's long axis toward the in-plane field component to minimize Zeeman energy. Field elevation reduces both L and x L , driving convergence toward cubic symmetry at high fields (Supplementary Fig. 11 y and Supplementary Fig. 12). Upon increasing the temperature, the transformation field decreases, but the skyrmion/antiskyrmion size follows a similar variation rule in all the measured temperature range. Simulations confirm that nanostructure geometry governs antiskyrmion shape anisotropy (Supplementary Fig. 14)”. Comment 10: It is stated in the text that “The coexistence of different phases within the same field regions accounts for the magnetic hysteresis (Fig. 1c).” But Fig.1c is just a schematic. A different explanation is in order (e.g. metastability and history-dependence). Response: We thank you very much for your nice suggestion. We have provided the field and temperature history dependence of magnetic evolution in our manuscript, as 12 shown in Fig. R10. See the discussion about magnetic hysteresis in our manuscript in Lines 147-161: “We first show the field-induced magnetic hysteresis. As the field increases from 385 to 510 mT, the initial antiskyrmion transforms into a skyrmion. Moreover, the skyrmion remains stable when the field is decreased back to 385 mT (Supplementary Fig. 8). By utilizing this field-swapping method, we can obtain all four states—antiskyrmion, skyrmion, bubble, and FM—at the same field value (Supplementary Fig. 8). We also explore thermal hysteresis at a fixed field (Supplementary Fig. 9 and Supplementary Fig. 10). We first set antiskyrmion as the initial state at 95 K. In the temperature-increasing process under the application of a fixed field of 417 mT, the antiskyrmion can transform into a bubble at 245 K, and the bubble state remains stable in the temperature-decreasing process. Similarly, the skyrmion and FM states at 95 K and 417 mT can be achieved in a temperature-decreasing process from 250 and 261 K, respectively. The field- and thermal-induced magnetic hysteresis proves the coexistence of four distinct states at the same field and temperature, enabling the potential controlled transformations between the four states”. Fig. R10 (i.e., Supplementary Fig. 8 and Fig. 9) Left: Magnetic field history dependence of hysteresis at a fixed temperature of 95 K. Right: Temperature history dependence of hysteresis at a fixed magnetic field of 417 mT. Comment 11: 11.1 Since Joule heating is one of the mechanisms for current-driven transformations, more relevant details about the electronic properties such as resistivity, and an estimate of the temperature increase based e.g. on Fourier law would be helpful. Response: We thank you very much for your insightful comment. Here, we present an estimate of the current-induced temperature rise using the multiphysics software COMSOL simulation, as shown in Fig. R11. The resistance value is taken from a previous study (Ref. Nakamura et al. Phys. Rev. B 108, 104403 (2023)) on a similar FeNiPdP crystal. We build a corresponding geometry in simulation as experiments, and the time and current density dependence of Joule heating effects are discussed. The temperature increases during the application of current pulses, and then quickly relaxes to the initial temperature once the current is off. The maximum temperature rise nonlinearly increases as the current density increases. A 40-ns current pulse with a density of 2.4 × 1011 A/m2 can contribute to an average temperature rise of about 200 13 K, which is comparable with our experiments (150 K), estimated based on static temperature-driven magnetic domain evolutions (Fig. R10). a b 300 K 250 K 200 K 150 K 200 nm 100 K 400 300 200 100 0 10 20 30 14 )K( >T< c d 400 j (1010 A/m2) 300 200 100 0 20 40 60 80 j (1010 A/m2) )K( >T< 5 7 13 15 17 20 22 24 28 t (ns) edortcele-tP edortcele-tP C-capping FeNiPdP Fig. R11 (i.e., Supplementary Fig. 28) Simulated temperature rise induced by Joule thermal heating effects based on parameters shown in Supplementary Table 1. a Real-time temperature distribution in the microdevice induced by current-induced Joule thermal heating after applying a 40-ns duration current with a density of 2.4(cid:3400)1011 A/m2. b Enlarged temperature distribution in the thin FeNiPdP plate. c Time t dependence of average temperature <T> in the thin FeNiPdP region (b) by applying a 40-ns duration current pulse with different current densities. d Current density j dependence of average temperature <T> in the thin FeNiPdP region after applying a 40-ns current pulse. We have added a discussion about Joule heating in our revised manuscript, see Lines 353-365: “Here, we establish a current-induced temperature increase based on the experimental temperature dependence of magnetic domain evolution (Supplementary Fig. 9). When the temperature rises from 95 K to 245 K at a fixed magnetic field, the antiskyrmion transforms into a bubble. Applying a 40-ns current pulse with a critical current density of about 2.4 (cid:3400) 1011 A/m2 also induces the antiskyrmion-to-bubble transformation. This equivalence implies that such a current pulse induces a temperature rise of approximately 150 K. Furthermore, using the experimental device geometry and material parameters, we simulated the transient temperature variation during pulsed current injection via multiphysics field simulations (Supplementary Fig. 28).50 Our simulations confirm that a 40-ns pulse at this critical current density generates an average temperature rise of about 200 K, comparable with our experimental estimate (~150 K)”. Comment 11: 11.2 Does the current direction matter? Response: Following your nice comment, we have added a comparison for the current applied in two directions of the x axis, as shown in Fig. R12. Our results demonstrate that the four-state transformation can also be achieved by reversing the current orientation. Our manuscript demonstrates that the combined effects of spin transfer torque (STT) and Joule thermal heating contributed to the transformation. Joule thermal heating is not determined by the orientation. STT acts as an external stimulus to trigger the transformation from the metastable phase to the most stable phase. Our simulation also suggests that STT-driven FM-to-antiskyrmion is not affected by the current orientation. Thus, these explain that the current direction does not affect four-state transformations. Fig. R12 (i.e., Supplementary Fig. 19) Current-orientation dependence of four-state transformations induced by sequential current pulses with densities: 29.8, 31.1, 32.2, and 35.4 × 1010 A/m². a Current is applied along the x-axis. b Current is applied along the −x-axis We have added discussion about current orientation in our revised manuscript, see Lines 229-230: “Such four-state transformations can also be realized when the current orientation is reversed (Supplementary Fig. 19)”, and Lines 383-389: “The Joule thermal heating is determined only by the density and is not dependent on current orientation. Besides, STT acts as an external stimulus to drive the transformation from the metastable phase to the most stable phase, which is shown not to be dependent on current orientation (Supplementary Fig. 26). Thus, the four-state mutual transformations are not strongly dependent on the current orientation (Supplementary Fig. 19)”. Comment 12: 12. Figs.S1b,d,f show data for a different device. Are the remaining supplementary figures for this device or for the one shown in the main text? Response: We thank you very much for your careful reading. In the original manuscript, the remaining Figures in the supplementary and main text are all taken from device A. 15 We have added the description for the device source for each figure in our revised manuscript. We have specified the device origin for all figures in the revised manuscript, see Lines 441-443: “All main-text data derive from a single 450 nm × 420 nm microdevice. Supplementary figures include full dimensional documentation for other devices”. Comment 13: 13. Caption in Fig.3 is unreasonably long. Most of the description should be moved to the main text. Also, the English is generally good, but there still are spelling issues that can be easily checked with a spell-checker. “Summry” in caption of Fig.3 should be Summary, “Fresneal” should be Fresnel, “a single current pulse” (here and in other places) should be “a single current pulse”. “Nicole” in Methods should be “Nickel”, “lift-out” should be “lift-off”. Response: We thank you very much for your careful reading. We have greatly shortened the caption of Fig. 3a, see Lines 274-283: “a Summry for current-controlled topological transformations among single antiskyrmion, skyrmion, bubble, and FM. Insets shows the corresponding defocused Fresneal images. To write an antiskyrmion, a single pulsed current within the range of j ∈ [j , j ] is used. Deleting an c1 c2 antiskyrmion requires a single pulsed current with j > j . For writing a skyrmion, a c4 single pulsed current within the range of j ∈ [j , j ] is applied. Deleting a skyrmion c3 c4 necessitates a single pulsed current with j > j . Creating a bubble involves using a single c4 pulsed current within the range of j ∈ [j , j ]. To delete a bubble, a single pulsed c2 c3 current with j > j is utilized. Transforming an antiskyrmion into a skyrmion can be c4 achieved using a single pulsed current within the range of j ∈ [j , j ]. Conversely, c3 c4 converting a skyrmion to an antiskyrmion requires two sequential pulsed currents: first with j > j and then with j ∈ [j , j ]. To transform an antiskyrmion into a bubble, a c4 c1 c2 single pulsed current within the range of j ∈ [j , j ] is employed. Switching a bubble c2 c3 back to an antiskyrmion involves two sequential pulsed currents: first with j > j and c4 then with j ∈ [j , j ]. Transforming a bubble into a skyrmion can be done using a c1 c2 single pulsed current within the range of j ∈ [j , j ]. Lastly, converting a skyrmion to c3 c4 a bubble requires two sequential pulsed currents: first with j > j and then with j ∈ [j , c4 c2 j ]. c3 a Summary for current-controlled topological transformations among single antiskyrmion, skyrmion, bubble, and FM. Insets show the corresponding defocused Fresnel images. A single current pulse with j > j deletes antiskyrmions, skyrmions, or c4 bubbles. Writing requires single pulses: antiskyrmions with j ∈ [j , j ], bubbles with c1 c2 j ∈ [j , j ], and skyrmions with j ∈ [j , j ]. Single-pulse transformations include: c2 c3 c3 c4 antiskyrmion to skyrmion (j ∈ [j , j ]), antiskyrmion to bubble (j ∈ [j , j ]), and c3 c4 c2 c3 bubble to skyrmion (j ∈ [j , j ]). Two-step transformations require sequential pulses: c3 c4 skyrmion to antiskyrmion (first j > j then j ∈ [j , j ]), bubble to antiskyrmion (first c4 c1 c2 j > j then j ∈ [j , j ]), and skyrmion to bubble (first j > j then j ∈ [j , j ])”. c4 c1 c2 c4 c2 c3 16 We have carefully proofread our manuscript, and wrong spellings have been corrected, e.g., Lines 212-213: “c Summary Summry of stable diagram in the field-increasing and field-decreasing processes”. Lines 274-276: “Summary Summry for current-controlled topological transformations among single antiskyrmion, skyrmion, bubble, and FM. Insets show the corresponding defocused Fresnel Fresneal images”. Lines 242-244: “Starting with an antiskyrmion as the initial state, we can achieve an antiskyrmion-to-FM transformation by applying a single current pulse pulsed current with 𝑗 (cid:3408) 𝑗 ”. (cid:3030)(cid:2872) Lines 422-423: “Single FeNiPdP crystals with S symmetry were grown by the self-flux 4 method with stoichiometric iron (Alfa Aesar, >99.9%) and Nicole Nickel (Alfa Aesar, >99.9%)”. Lines 429-431: “We fabricated thin FeNiPdP microdevices from bulk single crystals using a standard lift-out lift-off method in a focused ion beam and scanning electron microscopy (FIB-SEM) dual-beam system (Helios Nanolab 600i, FEI)”. Comment 14: Line 237, “Q = 1” needs to be defined, as well as “TIE analysis” in caption of Fig.S6. Response: Thank you for your careful reading. “Q” has been defined in Lines 50-51: “Vortex-like magnetic solitons are typically described by the polarity P, vorticity v, and topological charge Q”. We have also defined TIE in the caption of original Fig. S6: “c-d Corresponding experimental in-plane magnetizations (c) and Fresnel images (d) for U-antiskyrmion, rectangle antiskyrmion, bubble, and skyrmion retrieved from transport of intensity equation (TIE) analysis.” 17 Response to Reviewer #2: Reviewer #2: The authors have reported the control of the 2-dimensional spin texture including skyrmion and antiskyrmion by the charge current. They performed the numerical simulation and compared it with the TEM results. I have read it carefully and raised several issues regarding the manuscript below. Response: We sincerely appreciate your efforts in reviewing our manuscript. Below, you will find our detailed responses to each of your insightful questions. Comment 1: Why antiskyrmion should be specialized although many skyrmion papers have already been reported. I believe the magnetization dynamics of the skyrmion and antiskyrmion states are understood by the Thiele equation. Response: We agree with your assessment that “the magnetization dynamics of both skyrmions and antiskyrmions are governed by the Thiele equation”. A key distinction of antiskyrmions is their ability to coexist with other magnetic solitons—including skyrmions and bubbles—due to complex magnetic interactions in D and S - 2d 4 symmetric antiskyrmion host materials. This enables information encoding using solitons of differing topological charges and the fundamental topological operations (Siegl et al. Phys. Rev. B 106, 014421 (2022)), such as skyrmion-antiskyrmion interactions and transformations. Compared to prior studies on antiskyrmion systems (Peng et al., Nat. Nanotechnol. 15, 181 (2020); Jena et al., Nat. Commun. 11, 1115 (2020); Yasin et al., Nat. Commun. 14, 7094 (2023)), our work advances the antiskyrmionics in the following aspects: First demonstration of topological transformations induced by ns-current pulses; First realization of electrical control over individual solitons in device-relevant confined geometries; First elucidation of stabilization mechanisms and field/temperature-driven transformations of individual solitons in confined antiskyrmion-hosting nanostructures. In summary, antiskyrmion-host systems enable electrically controlled topological transformations—including skyrmion-antiskyrmion interconversion—unachievable in conventional skyrmion materials. Our manuscript presents the first systematic study of both static stabilization and electrical control of single magnetic solitons in nanoconfined antiskyrmion-host geometries. We have specified the specialty for antiskyrmions in the introduction part, see Lines 74-83: “A pioneering work has demonstrated that coexisting magnetic solitons enable information encoding via distinct topological charges Q.39 Consequently, manipulating these solitons topologically represents a promising approach, previously explored using external magnetic fields or thermal gradients,30-33,40 these methods lack direct compatibility with high-speed electronic devices. Theoretical studies have revealed intriguing current-induced dynamics of antiskyrmions, such as the antiskyrmion Hall 18 effect and the creation of skyrmion-antiskyrmion pairs.39-44 Beyond electrical creation and deletion of antiskyrmions, these systems also enable electrically driven skyrmion- antiskyrmion and antiskyrmion-bubble transformations, a capability not previously achieved in conventional skyrmion-hosting materials”. Comment 2: In the usual skyrmion system, the vortices are determined by the sign of the DM interaction. This should clarify why both skyrmion and antiskyrmion states are stable in this system. The higher topological charge state (e.g. Q=2,3,,,) may be a higher energy state of the fixed DM energy. However, it is not obvious to appear the topological state with the different signs. Response: We appreciate your insightful comment. We agree that vortex chirality is determined by the sign of the Dzyaloshinskii-Moriya interaction (DMI). Examining the physical origin of topological states through the total energy expression for antiskyrmion-hosting materials (Equation 1): 𝜀 (cid:3404) (cid:1516) (cid:4668)𝜀 (cid:3397)𝜀 (cid:3397)𝜀 (cid:3397)𝜀 (cid:3397)𝜀 (cid:4669)d𝒓 (1) (cid:3023)(cid:3294) ex (cid:2931) zeeman dem D2d Where, exchange energy 𝜀 , uniaxial magnetic anisotropy energy 𝜀 , Zeeman energy ex u 𝜀 , demagnetization energy 𝜀 , and DMI energy 𝜀 . zeeman dem D2d When 𝜀 is excluded (Equation 2), the energy landscape mirrors conventional bubble D2d materials in uniaxial magnets, supporting stabilization of both bubble types: 𝜀 (cid:3404) (cid:1516) (cid:4668)𝜀 (cid:3397)𝜀 (cid:3397)𝜀 (cid:3397)𝜀 (cid:4669)d𝒓 (2) (cid:3023)(cid:3294) ex (cid:2931) zeeman dem Type-I bubbles are classified as 'skyrmions' in these systems because they share identical polarity, vorticity, and topological charge Q with chiral Bloch skyrmions. Conversely, topologically trivial type-II bubbles (Q = 0) retain the standard 'bubble' designation. Critically, the D distorts both bubble types from circular to elliptical shapes, distinguishing them from traditional uniaxial-magnet bubbles. In summary, antiskyrmion formation is governed by DMI, while the 'skyrmions' in these materials originate from magnetic dipolar interactions, analogous to conventional magnetic bubbles. We have clarified the definition of skyrmion in antiskyrmion-hosting materials, see Lines 62-73: “It is important to note that skyrmion stabilization in antiskyrmion-hosting material systems arises not from the Dzyaloshinskii-Moriya interaction (DMI), but instead shares the same origin as traditional bubbles in centrosymmetric uniaxial magnets. Magnetic bubbles are cylindrical domains typically observed in centrosymmetric uniaxial magnets.35,36 They fall into two categories: type-I bubbles and type-II bubbles. Because type-I bubbles share identical polarity, vorticity, and integer topological charge (Q = 1 or −1) with chiral-Bloch-twisted skyrmions, they are typically classified as 'skyrmions' in antiskyrmion-hosting material systems. Conversely, topologically trivial type-II bubbles (Q = 0) retain the conventional 'bubble' designation.30-34,37,38 Moreover, the additional anisotropic DMI in D /S -symmetric 2d 4 systems distorts type-I and II bubbles from circular to elliptical shapes.” And Lines 464-466: “In the absence of the 𝜀 energy term, the system's total energy D2d landscape mirrors that of conventional bubble materials in uniaxial magnets and can stabilize both type-I and type-II bubbles.” Comment 3: The inplane magnetization component is crucial for determining the topological states. They should represent the inplane component as well as the simulation results. Response: Following your nice suggestions, we have presented typical in-plane magnetization components of different magnetic textures in both simulation and experiments for a direct comparison, as shown in Fig. R13. The experimental Fresnel contrasts and in-plane magnetization components are both consistent with our simulations. We have discussed the consistency between experiments and simulation in our revised manuscript, see Lines 183-185: “These field-dependent magnetic profiles (Supplementary Fig. 16) align well with our experimental Fresnel images and retrieve magnetizations of field-driven magnetic evolution (Fig. 1)”. 20 Fig. R13 (i.e., Supplementary Fig. 16) a-b Simulated defocused Fresnel contrasts (a) and integral in-plane magnetizations (b) for U-antiskyrmion at 0 mT, rectangle antiskyrmion at 280 mT, bubble at 290 mT, and skyrmion at 300 mT. c-d Corresponding experimental in-plane magnetizations (c) and Fresnel images (d) for U-antiskyrmion, rectangle antiskyrmion, bubble, and skyrmion retrieved from transport of intensity equation (TIE) analysis. -Technical issue Comment 4: All videos are hard to distinguish these states for non-specialists, I recommend they add the guide to the eye line. Especially, the contrast of the video is quite low compared with the snapshots of Fig.2C. Response: We have added annotations “antiskyrmion”, “Bubble”, “skyrmion”, and “FM” in the video to show the displayed configurations for a better guide, as shown in Fig. R14. The Fresnel contrasts shown in Fig. 2c are photos taken with a long exposure time of 2 s, which could show better resolution than that shown in real-time videos. Fig. R14 (i.e., snapshots of Video 1) The annotations “antiskyrmion”, “Bubble”, “skyrmion”, and “FM” have been added in all videos. Comment 5: They should show the definition of the skyrmion and bubble and the value of Q. Response: Following your nice suggestions, we have added the definition and the value Q of skyrmion/bubbles in our revised manuscript, see Lines 65-71: “Magnetic bubbles are cylindrical domains typically observed in centrosymmetric uniaxial magnets. They fall into two categories: type-I bubbles and type-II bubbles. Because type-I bubbles share identical polarity, vorticity, and integer topological charge (Q = 1 or −1) with chiral-Bloch-twisted skyrmions, they are typically classified as 'skyrmions' in antiskyrmion-hosting material systems. Conversely, topologically trivial type-II bubbles (Q = 0) retain the conventional 'bubble' designation.30-34,37,38” To conclude, I believe this manuscript is not worth publishing in the Nature Communications. Especially, the general interest concerning comment 1 is crucial for this decision. I recommend you transfer the manuscript to a specialized journal. Response: We express our great gratitude for your thoughtful feedback and the opportunity to address your concerns. Regarding the question of broad interest: 21 antiskyrmion-hosting materials exhibit unique magnetic interactions that enable the coexistence of multiple topological solitons - including antiskyrmions, dipolar skyrmions, and bubbles. This distinctive property facilitates the investigation of topological transformations (e.g., skyrmion-antiskyrmion and antiskyrmion-bubble) that advance both basic topological magnetism and potential applications in spintronic devices. Our work could represent an advance toward electrically controlled magnetic dynamics in antiskyrmion-hosting material systems, demonstrating the following results: 1. First achievement of electrically driven mutual transformations between four states, i.e., antiskyrmion, skyrmion, bubble, and uniform ferromagnet. 2. First individual soliton-level control in nanostructured cells of antiskyrmion-hosting materials. 3. First elucidation of stabilization mechanisms and field/temperature-driven transformations of four states in confined nanostructures of antiskyrmion-hosting materials. We believe that our electrically controlled four-state transformations could represent an important advance beyond existing skyrmion manipulation capabilities. Our work establishes great diversity for electrically controlled dynamics in antiskyrmion systems and meets Nature Communications' criteria for broad interdisciplinary interest. We respectfully request your reconsideration of our manuscript's suitability for publication. 22 Response to Reviewer #3: Reviewer #3: Skyrmions are nontrivial topological spin textures stabilized by the competition between symmetric exchange interaction, asymmetric Dzyaloshinskii-Moriya interaction (DMI). Skyrmions promise to be the potential candidates for the development of next generation spintronic devices. Antiskyrmions are known as the antiparticles of skyrmions, having topological charges opposite to the skyrmions. For practical application it is quite essential to create, annihilate the skyrmions and antiskyrmions on demand, especially, by electrical current or other electrical means. Electrical creation and annihilation of skyrmions have already been demonstrated experimentally. Although, some theoretical studies are found in literatures on the current-induced dynamics (e.g. antiskyrmion Hall effect, creation of skyrmion-antiskyrmion pairs) of antiskyrmions, the experimental demonstration of the charge current induced creation and annihilation of antiskyrmions are still lacking. In the present work, authors demonstrate charge current-induced creation, annihilation, and topological transformation of a single antiskyrmion stabilized in nanostructured cell made of non-centrosymmetric magnet FeNiPdP at room temperature. The nanostructures are designed with dimensions of about 400 nm in width and length, so that a single antiskyrmion can be stabilization. The magnetic textures are imaged in real space by employing Lorentz transmission electron microscope. The reversible creation and deletion of single antiskyrmions are demonstrated by adjusting the density of single current pulse. The topological transformations among individual antiskyrmions, skyrmions, bubbles, and ferromagnetic states are demonstrated by varying external magnetic field, temperature and charge current density. The experimental findings are corroborated by micromagnetic simulations, which shows the critical role of current-induced spin transfer torque and Joule heating. The presented results are interesting, and should be the current interest of spintronics community. However, the present manuscript lacks experimental data and solid scientific arguments. Overall, the novelty and quality of the work falls short of the standard of Nature Communications. Hence I cannot recommend it for the publication in Nature Communications. However, I think it should more suitable for Communication Physics. Anyway, major revision is required before it can be considered for any other journal. Response: We sincerely appreciate your recognition of our results as “interesting” and “relevant to the spintronics community”. In direct response to your insightful critique, we have substantially strengthened the manuscript by adding: 1. Comprehensive experimental data, including fundamental magnetic/structural measurements of bulk crystals, field tilt angle dependence of static topological magnetic transformations and current-controlled dynamics, and device-size dependence of static and dynamic transformations. 2. Robust scientific arguments supported by theoretical modeling of temperature effects, detailed analysis of ultrashort current pulse mechanisms. 23 Antiskyrmion-host materials uniquely permit the coexistence of skyrmions and bubbles, enabling topological manipulations (e.g., skyrmion-antiskyrmion transformations) crucial for advancing fundamental topological magnetism and spintronic applications. While this rapidly evolving field has garnered significant attention, existing demonstrations primarily rely on external magnetic fields (e.g., Peng et al., Nat. Nanotechnol. 15, 181 (2020); Jena et al., Nat. Commun. 11, 1115 (2020)). Our enhanced manuscript establishes two transformative advances: 1. First electrical control of individual antiskyrmion transformations (creation/deletion/interconversion) with skyrmions, bubbles, and ferromagnetic states; 2. Fundamental stabilization mechanisms governing isolated solitons in confined nanostructures. This work reveals great diversity in electrically driven topological transformations within antiskyrmion-host systems, presenting a compelling case that meets Nature Communications' standards. We respectfully request your reevaluation of the manuscript's suitability for publication. Below, we submit our thorough responses to your valuable comments. Comment 1: Authors have not cited some important articles as given below. (a) Koshibae, W. & Nagaosa, N. Creation of skyrmions and antiskyrmions by local heating. Nat. Commun. 5, 5148 (2014), doi:10.1038/ncomms6148 (b) Stier, M., Häusler, W., Posske, T., Gurski, G. & Thorwart, M. Skyrmion--Anti-Skyrmion Pair Creation by in-Plane Currents. Phys. Rev. Lett. 118, 267203 (2017). doi:10.1103/PhysRevLett.118.267203 (c) Siegl, P. et al. Creating arbitrary sequences of mobile magnetic skyrmions and antiskyrmions. Phys. Rev. B 106, 014421 (2022), doi:10.1103/PhysRevB.106.014421 (d) Zheng, F. et al. Skyrmion–antiskyrmion pair creation and annihilation in a cubic chiral magnet. Nat. Phys. 18, 863-868 (2022), doi:10.1038/s41567-022-01638-4 (e) Li, S., Ezawa, M. & Zhou, Y. Current-induced dynamics of isolated antiferromagnetic antiskyrmion and antiskyrmionium. Phys. Rev. B 107, 174409 (2023) doi:10.1103/PhysRevB.107.174409 (f) Guang, Y. et al. Confined antiskyrmion motion driven by electric current excitations. Nat. Commun. 15, 7701 (2024), doi:10.1038/s41467-024-52072-4. Response: We thank you very much for bringing these important references to our attention. The ref. (f) has been cited (Ref. 38) in our original manuscript. We have incorporated and appropriately cited them in the revised manuscript. See Lines 74-80: “A pioneering work has demonstrated that coexisting magnetic solitons enable information encoding via distinct topological charges Q.39 [Ref. Phys. Rev. B 106, 014421 (2022)]. Consequently, manipulating these solitons topologically represents a promising approach, previously explored using external magnetic fields or thermal gradients30-33,40[Ref. Nat. Commun. 5, 5148 (2014)], these methods lack direct compatibility with high-speed electronic devices. Theoretical studies have revealed intriguing current-induced dynamics of antiskyrmions, such as the antiskyrmion Hall 24 effect and the creation of skyrmion-antiskyrmion pairs39-44[Ref. Phys. Rev. Lett. 118, 267203 (2017)， Phys. Rev. B 107, 174409 (2023)]”, and Lines 56-58: “We note that antiskyrmions in FeGe magnets, as defined in prior work26 [Nat. Phys. 18, 863-868 (2022)], exhibit identical vorticity but opposite polarity P compared to those studied here”. References: 26. Zheng, F. et al. Skyrmion–antiskyrmion pair creation and annihilation in a cubic chiral magnet. Nat. Phys. 18, 863-868 (2022). (Ref. d) 39. Siegl, P. et al. Creating arbitrary sequences of mobile magnetic skyrmions and antiskyrmions. Phys. Rev. B 106, 014421 (2022). (Ref. c) 40. Koshibae, W. & Nagaosa, N. Creation of skyrmions and antiskyrmions by local heating. Nat. Commun. 5, 5148 (2014). (Ref. a) 41. Stier, M., Hausler, W., Posske, T., Gurski, G. & Thorwart, M. Skyrmion-Anti-Skyrmion Pair Creation by in-Plane Currents. Phys. Rev. Lett. 118, 267203 (2017). (Ref. b) 43. Li, S., Ezawa, M. & Zhou, Y. Current-induced dynamics of isolated antiferromagnetic antiskyrmion and antiskyrmionium. Phys. Rev. B 107, 174409 (2023). (Ref. e) 46. Guang, Y. et al. Confined antiskyrmion motion driven by electric current excitations. Nat. Commun. 15, 7701 (2024). (Ref. f) Comment 2: 2.1 Authors used non-centrosymmetric magnet FeNiPdP for the observation of skyrmions and antiskyrmions. However, characterization of the crystal structure of material, and its magnetic properties (magnetization, DMI, exchange stiffness constant, anisotropy) as a function of magnetic field, temperature is missing. Response: Following your suggestions, we have characterized the structure and fundamental magnetic properties of bulk crystals in our revised manuscript. The structure of the thin microdevice is characterized by electronic diffraction and high-resolution transmission electron microscopy. We also mark the in-plane orientation according to the structure characterization, as shown in Fig. R15. 25 a b y x 200 nm c d y [1 -1 0] x 10 1/nm [1 1 0] 2 nm Fig. R15 (i.e., Supplementary Fig. 2) Fundamental structural properties of FeNiPdP(001) microdevice. a Scanning electron microscopy of the fabricated microdevice. b enlarged scanning electron microscopy of the thin FeNiPdP region. c electronic diffraction pattern of the thin FeNiPdP region, agreeing well with the (001) oriented plane of the noncentrosymmetric tetragonal structure (space group 𝐼4(cid:3364) ). d High-resolution transmission electron microscopy of the thin FeNiPdP plate, confirming two edges of the rectangle along the [110] and [11(cid:3364)0] axes, respectively. We have added a discussion about the crystal characterization in the revised manuscript, see Lines 106-110: “We fabricated highly confined FeNiPdP nanostructured cuboids with [001] out-of-plane orientation. Electron diffraction and high-resolution transmission electron microscopy (TEM) confirm cuboid edges closely aligned with [110] and [1 1(cid:3364) 0] crystallographic directions (Supplementary Fig. 2). Lattice parameters a and b were both determined as 0.92 nm, matching established values.34” We have measured magnetization during the field cooling process at 10 mT, which indicates a Curie temperature of approximately 390 K. We have also measured the magnetic field dependence of magnetization in the temperature range from 2-400 K along and perpendicular to the c axis, as shown in Fig. R16. According to the magnetization measurements, we could derive the temperature dependence of saturated magnetizations and magnetic anisotropies, as shown in Fig. R16. The anisotropy constant K is extracted from the difference in the areas under the magnetization curves u (cid:1516) (cid:3003)(cid:3151)(cid:3159)(cid:3178)𝑀(cid:4666)𝐵(cid:4667)d𝐵 along the c-axis and perpendicular to it, up to a saturated field 𝐵 . (cid:2868) (cid:2903)(cid:2911)(cid:2930) The saturated magnetization M is taken at the magnetization of 2000 mT. s 26 160 140 120 100 80 60 40 20 0 Temperature (K) 27 )m/Ak( M s )3m/Jk( K u 10 700 K u B = 10 mT M 600 s 500 5 400 300 200 0 0 100 200 300 400 0 100 200 300 400 )g/ume( M 80 B // c 60 40 20 0 -20 -40 -60 -80 -2000 -1000 0 1000 2000 B // c FC B // c ZFC B // ab FC B // ab ZFC Temperature (K) )g/ume( M 80 B // ab 60 40 20 0 -20 -40 -60 -80 -2000 -1000 0 1000 2000 B (mT) )g/ume( M a b 2K 50K 75K 100K 125K 150K 175K 200K 225K 250K 275K 300K 325K 350K 375K 400K B (mT) c d Fig. R16 (i.e., Supplementary Fig. 1) Fundamental magnetic properties of bulk single crystals. a-b Magnetic field dependence of magnetization along the c axis (a) and ab plane (b). c Temperature dependence of magnetization at 10 mT. d Temperature dependence of saturated magnetization M and uniaxial magnetic anisotropy constant s K . u Temperature dependence of macroscopic magnetization measurements is added in our revised manuscript, see Lines 98-105: “Magnetization measurements at 100 mT reveal a Curie temperature of approximately 390 K (Supplementary Fig. 1). Magnetic field- dependent magnetization curves along the c-axis and in the ab-plane demonstrate perpendicular magnetic anisotropy across the measured temperature range (2 K to 400 K). The uniaxial magnetic anisotropy constant (K ) was calculated from the difference u in the areas under the magnetization curves (cid:1516) (cid:3003)(cid:3268)(cid:3276)(cid:3295)𝑀(cid:4666)𝐵(cid:4667)𝑑𝐵 along the c-axis and (cid:2868) perpendicular to it, up to saturation 𝐵 (Supplementary Fig. 1)”. (cid:3020)(cid:3028)(cid:3047) We regret that it is not easy to derive the exchange stiffness and DMI directly from macroscopic magnetization measurements. Temperature has mainly two effects on spin exchange interactions: lattice variation and thermal fluctuation. Under the thermal fluctuation, the scaling of exchange stiffness and DMI at a finite temperature T is considered as 𝐴 (cid:4666)𝑇(cid:4667) ∝ 𝑀 (cid:4666)𝑇(cid:4667)(cid:3080) and 𝐷 (cid:4666)𝑇(cid:4667) ∝ 𝑀 (cid:4666)𝑇(cid:4667)(cid:3081) with 𝛼 = 1.5 and 𝛽 = 1.5 (cid:3032)(cid:3051) (cid:3046) (cid:2870)(cid:3031) (cid:3046) [Ref. Raimondo et al. Phys. Rev. Appl. 18, 024062 (2022)]. In our simulation, we use the exchange stiffness A and DMI as 8 pJ/m and 0.25 mJ/m2, respectively, which are ex comparable with the values widely used in previous studies [Ref. Karube et al. Nat. Mater. 20, 335 (2021) and Karube et al. Adv. Mater. 34, 2108770 (2022)]. These simulated parameters in our previous work [Ref. Tang et al. Science Bulletin 68, 3000 (2023)] also well reproduces the experimental spin textures in the same material. Here, by taking the cell size (0.25 nm) as the nearest neighbor magnetic ions of FeNiPdP crystals, we also perform additional Mumax3 simulations on temperature dependence of magnetization by considering A = 8 pJ/m, which suggests a Curie temperature of ex 420 K, agreeing well with experiments, as shown in Fig. R17. In this simulation, the finite temperature is provided by the thermal fluctuation field. Fig. R17 (i.e., Supplementary Fig. 31) Simulated temperature dependence of magnetization at a field of 10 mT in a warming process. We increase the temperature from 0 K with a step of 5 K with a duration of 100 ps, and the magnetization is recorded before switching to the next temperature. World size 50 nm (cid:3400) 50 nm (cid:3400) 25 nm. Cell size, 0.25 nm (cid:3400) 0.25 nm (cid:3400) 0.25 nm. We have added a discussion about the parameters A and D in our revised manuscript, ex 2d see Lines 467-474: “We set the exchange stiffness as A = 8.0 pJ/m and chiral interaction ex as D = 0.25 mJ/m3. We set K = 110 kJ/m3 and M = 617 kA/m based on measured 2d u s parameters extracted from macroscopic magnetization measurements (Supplementary Fig. 1). Our previous study reveals that the experimental spin textures in FeNiPdP can be well reproduced by simulation based on these magnetic parameters.32 These magnetic parameters are close to those widely used in previous studies on similar FeNiPdP materials.28,34 Simulation considering thermal fluctuation field indicated a Curie temperature of 420 K (Supplementary Fig. 31), which is close to that of experiments.” Comment 2: 2.2 Moreover, the direction of the applied external magnetic field in all the measurements is also not mentioned. Authors highlight the importance of tilting angle of magnetic field in Supplementary Fig. 5. It appears to me that the magnetic field should be aligned with the accuracy of about 1-2 deg. This can be a bottleneck for practical implication. I was just wondering how that much accuracy can be achieved in practical experiment. Response: We appreciate your point on magnetic field alignment precision. Our instrument achieves a minimum tilt angle control accuracy of 0.01° (Fig. R18), significantly exceeding the ~1-2° requirement. In the original manuscript, the experimental field tilted angle is fixed at 1.5°. We have added the external field orientation details and new experimental data on the tilted-angle dependence of static topological magnetic transformations and electrically controlled dynamic transformations (Fig. R19 and Fig. R20) to the revised manuscript. 28 Fig. R18 Control panel of our Lorentz-TEM. The field tilt angle is shown in the red box. 29 a B-increasing 258 mT 346 mT 347 mT 365 mT Antiskyrmion Antiskyrmion Skyrmion FM 200 nm B-decreasing 0 mT 226 mT 282 mT 300 mT U-Antiskyrmion U-Antiskyrmion Antiskyrmion FM Skyrmion U-Antiskyrmion Antiskyrmion FM Antiskyrmion U-Antiskyrmion FM 0 50 100 150 200 250 300 350 400 450 500 550 600 650 B (mT) b B-increasing 336 mT 341 mT 346 mT 365 mT Antiskyrmion Bubble Skyrmion FM 200 nm B-decreasing 0 mT 206 mT 297 mT 320 mT U-Antiskyrmion U-Antiskyrmion Antiskyrmion FM Skyrmion U-Antiskyrmion Antiskyrmion FM Bubble U-Antiskyrmion Antiskyrmion FM 0 50 100 150 200 250 300 350 B (mT) c B-increasing 274 mT 305 mT 329 mT 363 mT Antiskyrmion Antiskyrmion Bubble FM 200 nm B-decreasing 0 mT 234 mT 292 mT 320 mT U-Antiskyrmion Antiskyrmion Bubble FM Antiskyrmion U-Antiskyrmion FM Bubble U-Antiskyrmion Antiskyrmion FM 0 50 100 150 200 250 300 350 B (mT) Fig. R19(i.e., Supplementary Fig. 18) Tilted field effects on the field-driven magnetic evolution. Magnetic evolutions and summary of stable diagram in the field-increasing and field-decreasing processes. (a) 0°. (b) 1.0°.(c) 2.9°. 30 Our results show distinct operational regimes: below 1.0° enables 3-state transformations (Antiskyrmion ⇄ Skyrmion ⇄ FM); between 1.0° and 2.5° enables 4-state transformations (Antiskyrmion ⇄ Skyrmion ⇄ Bubble ⇄ FM); and above 2.5° enables 3-state transformations (Antiskyrmion ⇄ Bubble ⇄ FM). Crucially, antiskyrmion-skyrmion conversion requires angles <2.5°, antiskyrmion-bubble conversion requires >1.0°, while antiskyrmion-FM conversion is robust across all the measured angular range. 31 FM Antiskyrmion Skyrmion FM 1.0 0.5 0.0 -0.5 -1.0 0 5 25 30 Q Current density j (1010 A/m2) FM Antiskyrmion Bubble FM 1.0 0.5 0.0 -0.5 -1.0 0 5 25 30 Q Current density j (1010 A/m2) FM Antiskyrmion Bubble Skyrmion FM 1.0 0.5 0.0 -0.5 -1.0 0 5 25 30 Q a 𝛼 (cid:3404) 0° b 𝛼 (cid:3404) 1.5° Current density j (1010 A/m2) c 𝛼 (cid:3404) 3° Fig. R20 (i.e., Supplementary Fig. 25) Field Tilted effects on the current-controlled topological magnetic transformations. a 0°. b 1.5°. c 3°. We have added a discussion about the effect of tilted field angle on field-driven topological transformations, see Lines 201-206: “Our experiments confirm the theoretically predicted dependence of magnetic field-driven topological transformations on tilt angle (Supplementary Fig. 18). At zero tilt angle, the field increase produces a direct 3-state transformation sequence: antiskyrmion to skyrmion to FM, with no bubble state observed. At larger tilt angles, the field increase yields a distinct 3-state sequence: antiskyrmion to bubble to FM, with no skyrmion state emerging”. We have added a discussion about the effect of tilted field angle on current-driven topological transformations, see Lines 308-317: “In accordance with field tilt angle dependence on static field-driven transformations, the current-controlled multi-state transformations are also affected by the tilted field. Our results show distinct operational regimes for a fixed field of 417 mT (Supplementary Fig. 25): below 1.5° enables 3-state transformations (Antiskyrmion ⇄ Skyrmion ⇄ FM); between 1.5° and 3.0° enables 4-state transformations (Antiskyrmion ⇄ Skyrmion ⇄ Bubble ⇄ FM); and above 3.0° enables 3-state transformations (Antiskyrmion ⇄ Bubble ⇄ FM). Therefore, antiskyrmion-skyrmion conversion requires a small field tilt angle, antiskyrmion- bubble conversion requires a large field tilt angle, while antiskyrmion-FM conversion is robust across at all measured angular range”. Comment 3: Which factors decide the formation of antiskyrmion more preferably over skyrmion in FeNiPdP? Response: We appreciate your insightful comments. We have analyzed the antiskyrmion-skyrmion energy difference (E – E ) in Fig. R21. The total energy anti skyr difference increases and undergoes sign reversal during field ramping, indicating a transition from antiskyrmion to skyrmion stability. This finding confirms our experimental observations. We further deconvolve individual energy contributions: demagnetization (𝜀 ), exchange (𝜀 ), DMI (𝜀 ), anisotropy (𝜀 ), and Zeeman demag ex D2d anis (𝜀 ) energy. zeeman Fig. R21 (i.e., Supplementary Fig. 17) Magnetic field dependence of the antiskyrmion-skyrmion energy difference ε – ε , showing contributions from: total (𝜀 ), anti skyr total demagnetization (𝜀 ), exchange (𝜀 ), DMI (𝜀 ), anisotropy (𝜀 ), and Zeeman demag ex D2d anis (𝜀 ) energy terms. Positive values indicate skyrmion stability, while negative zeeman values favor antiskyrmions. The relative stability of antiskyrmions versus skyrmions emerges from competing energy contributions. Dzyaloshinskii-Moriya interaction (DMI) stabilizes anti-type spin twists, while the Bloch lines containing magnetic singularities in antiskyrmion domain walls incur substantial exchange energy penalties. Consequently, exchange energy favors skyrmion stabilization. At low fields, DMI, demagnetization, and uniaxial anisotropy energies collectively stabilize antiskyrmions, whereas Zeeman and exchange energies preferentially support skyrmions. We have added a discussion on the energy difference between antiskyrmion and skyrmion in our revised manuscript, see Lines 186-193: “At low magnetic fields, antiskyrmions are energetically favored over skyrmions due to competing energy 32 contributions (Supplementary Fig. 17). The DMI stabilizes spin twists with anti- vorticity within the domain walls, while exchange energy favors skyrmions because antiskyrmions incur higher exchange costs from Bloch lines. Detailed energy analysis confirms demagnetization and uniaxial anisotropy energies further stabilize antiskyrmions at low fields. Conversely, Zeeman energy preferentially stabilizes skyrmions at low fields. The net energy balance ultimately determines antiskyrmion predominance”. Comment 4: I recommend to provide schematics of 3D spin textures of antiskyrmion, skyrmion and bubbles so that nonexperts can understand the difference between them very easily. Response: Following your nice suggestion, we have added schematics of 3D spin textures for magnetic solitons (antiskyrmions, skyrmions, and bubbles) in the revised manuscript (Fig. R22). Detailed 3D spin textures in FeNiPdP alloys were previously characterized in Tang et al. Sci. Bull. 68, 2919 (2023) and Yasin et al. Adv. Mater. 36, 2311737 (2024) – with the former study sharing some co-authors with our current work. Notably, while the middle layers retain distinct antiskyrmion, skyrmion, and bubble characteristics, the surface layers consistently form Néel-twisted skyrmions to minimize dipole-dipole interactions. Fig. R22 (i.e., Supplementary Fig. 30) Simulated 3D magnetic configurations of magnetic soliton: antiskyrmion, skyrmion, and bubble. Each configuration displays cross-sectional magnetization (top, middle, bottom layers) and the m = 0 iso-surface. z Simulations were performed in a confined 400 nm × 400 nm × 140 nm geometry at 210 mT. We have added related discussion about 3D spin textures in our revised manuscript, see Lines 390-393: “Importantly, the definitions of antiskyrmion, skyrmion, and bubble apply exclusively to the middle layers of the FeNiPdP structure. To minimize magnetic dipole-dipole interactions, surface layers consistently adopt Néel-twisted skyrmion configurations (Supplementary Fig. 30).32,38” 33 Comment 5: 5.1 Authors explained that the transformation from uniform ferromagnetic (FM) state to antiskyrmion state occurs due to the spin-torques. Whereas, the transformation from antiskyrmions to the bubble to skyrmion to FM state occur due to the Joule heating effect. Although authors have tried their best to explain this, I am not convinced with their arguments. I think the spin-torques also increase with the current density. So, the spin-torques must have a critical role even for the transformation from antiskyrmions to the bubble to skyrmion to FM state. The energy landscape, as shown in Fig. 4a for FM and antiskyrmion states, should be modified by considering the thermal effect even for other topological states. Response: We thank you very much for pointing out the role of spin torque in other topological transformations. We agree with you that “the spin-torques also increase with the current density”. We also agree with you that “the energy landscape for different states could be modified by considering thermal heating effects”. Therefore, we think the transformation from antiskyrmion to bubble to skyrmion to FM could be considered a result of combined spin-torque and thermal heating effects. Initially, the antiskyrmion is the most stable state with the lowest total energy. During the increase in current density at a fixed magnetic field, because of the temperature increase, the energy landscape changes and the most stable phase varies following a sequence of bubble, skyrmion, and FM, as shown in Fig. R23. The spin-transfer torque (STT) can then trigger the transformation from the metastable antiskyrmion phase to the most stable phase (Fig. R24). In our simulation, we also reproduce the transformation of STT-driven antiskyrmion- to-FM transformations if the energy landscape is changed, as shown in Fig. R23. The field-increase behavior at a fixed temperature mirrors thermal evolution at a fixed field. At a high magnetic field, FM becomes the more stable phase. Thus, under the current pulse stimuli, STT could further drive the transformation from the antiskyrmion to the FM state. 34 FM STT Antiskyrmion Antiskyrmion STT Bubble STT Skyrmion STT FM 35 Temperature increasing Fig. R23 (i.e., Supplementary Fig. 29) Schematic energy landscape variation in the warming process at a fixed magnetic field with a slight field tilt. The most stable phase changes following a sequence of antiskyrmion, bubble, skyrmion, and FM. STT acts as an external stimulus to trigger the transformation from the metastable phase to the most stable phase. Fig. R24 (i.e., Fig. 4 in the main text) Simulated STT-induced FM-antiskyrmion transformations. a-b Time t dependence of total free energy and topological charge Q during the FM-antiskyrmion transformation by applying an in-plane current with j = 5.0 (cid:3400) 1011 A/m2. (a) FM-to-antiskyrmion. Magnetic field B, 85 mT. (b) Antiskyrmion- to-FM. Magnetic field B, 310 mT. c-d Representative middle-layer magnetic configurations during the FM-antiskyrmion transformation. (c) FM-to-antiskyrmion. (d) Antiskyrmion-to-FM. Field tilt angle, 2°. We have added a discussion about the combined Joule heating and STT effects in our revised manuscript, see Lines 365-377: “Critically, STT efficiency scales with current density, enabling sequential antiskyrmion→bubble→skyrmion→FM transformations through synergistic Joule heating and STT effects. During current pulses, Joule heating dynamically reshapes the magnetic energy landscape, shifting the energy minimum from antiskyrmion to bubble to skyrmion to FM during thermal warming at fixed field (Supplementary Fig. 29). STT subsequently drives transitions from metastable states to the new ground state. Micromagnetic simulations confirm reversibility upon energy landscape modification (Fig. 4d), with field-increase behavior at fixed temperature (Supplementary Fig. 15) mirroring thermal evolution at a fixed field (Supplementary Fig. 29): fields of 310 mT stabilize the FM state, permitting STT-driven antiskyrmion- to-FM transformation. Thus, antiskyrmion→bubble→skyrmion→FM transformations could arise from the two-step mechanism comprising: (1) Joule-heating-induced energy landscape modification and (2) STT-mediated transitions toward equilibrium states”. Comment 5: 5.2 Moreover, it is important to know the increment of the temperature with the increment of current density. Authors should use a thermal sensor/camera to determine the increase of the temperature due to current pulse. Additionally, a theoretical estimation would also be very useful. Response: We thank you very much for these valuable comments. We regret that the detection of temporal temperature rise on an ns time scale is difficult to achieve, because we have no access to ultrafast characterization on an ns time scale. But we can present an estimation of temperature rise based on the temperature dependence of magnetic domain evolution. For an initial antiskyrmion at a fixed magnetic field, our experiments show that the antiskyrmion-to-bubble transformation occurs when the temperature increases from 95 to 245 K. Meanwhile, a 40-ns pulsed current with a critical density of 2.4(cid:3400)1011 A/m2 can trigger the antiskyrmion-to-bubble transformation (Fig. 2 in the maintext). Thus, the 40-ns current pulse with a density of 2.4(cid:3400)1011 A/m2 A/m2 could induce a temperature rise of about 150 K. Moreover, following your nice suggestions, we have also performed multiple physics field COMSOL simulations on temperature rise induced by pulsed current, as shown in Fig. R25. We build a corresponding geometry in simulation as experiments, and the time and current density dependence of Joule heating effects are discussed. The temperature increases during the application of current pulses, and then quickly relaxes to the initial temperature once the current is off. The maximum average temperature 36 rise nonlinearly increases as the current density increases. A 40-ns current pulse with a density of 2.4(cid:3400)1011 A/m2 can contribute to an average temperature rise of about 200 K, which is comparable with our experiments (150 K), estimated based on static temperature-driven magnetic domain evolutions (Fig. R10). a b 300 K 250 K 200 K 150 K 200 nm 100 K 37 edortcele-tP edortcele-tP C-capping FeNiPdP Fig. R25 (i.e., Supplementary Fig. 28) Simulated temperature rise induced by Joule thermal heating effects. a Real-time temperature distribution in the microdevice induced by current-induced Joule thermal heating after applying a 40-ns duration current with a density of 2.4(cid:3400)1011 A/m2. b Enlarged temperature distribution in the thin FeNiPdP plate. c Time t dependence of average temperature <T> in the FeNiPdP region (b) by applying a 40-ns duration current pulse with different current densities. d Current density j dependence of average temperature <T> in the FeNiPdP region after applying a 40-ns current pulse. We have added a discussion about Joule heating in our revised manuscript, see Lines 353-365: “Here, we establish a current-induced temperature increase based on the experimental temperature dependence of magnetic domain evolution (Supplementary Fig. 9). When the temperature rises from 95 K to 245 K at a fixed magnetic field, the antiskyrmion transforms into a bubble. Applying a 40-ns current pulse with a critical current density of about 2.4 1011 A/m2 also induces the antiskyrmion-to-bubble transformation. This equivalence implies that such a current pulse induces a temperature rise of approximately 150 K. Furthermore, using the experimental device geometry and material parameters, we simulated the transient temperature variation during pulsed current injection via multiphysics field simulations (Supplementary Fig. 28).50 Our simulations confirm that a 40-ns pulse at this critical current density generates an average temperature rise of about 200 K, comparable with our experimental estimate (~150 K)”. Comment 6: 6.1 What is U-antiskyrmions? My point is that why do the authors call it as antiskyrmion? Response: The U-antiskyrmion is the spin texture with a U-shape and a topological charge equal to the antiskyrmion. We call it an antiskyrmion because it forms due to the deformation of the antiskyrmion during the field-decreasing process and is topologically equivalent to the antiskyrmion. We have added more discussion on the definition of antiskyrmion in our revised manuscript, see Lines 122-124: \"Because the U-shaped spin texture originates from the deformation of the rectangular antiskyrmion during the field-decreasing process and is topologically equilibrium to the antiskyrmion, we call it U-antiskyrmion\". a 5 Rectangle  zeeman  0 u total DM  dem -5 60 70 80 90 b B = 0 mT 60 mT 85 mT 130 mT 200 nm B-increasing c B = 0 mT 60 mT 85 mT 90 mT B-decreasing 38 )3m/Jk( - tcer U U-shape  ex B (mT) Fig. R26 (i.e., Supplementary Fig. 6) Simulated energy landscape and field-driven evolution of antiskyrmion morphologies. a Magnetic field dependence of the energy difference 𝜀 (cid:3398)𝜀 between U-shaped and rectangular antiskyrmions, showing u rect contributions from: total energy (𝜀 ), demagnetization (𝜀 ), exchange (𝜀 ), DMI total demag ex (𝜀 ), anisotropy (𝜀 ), and Zeeman (𝜀 ) terms. b Field-induced morphological D2d anis zeeman evolution starting from a U-shaped antiskyrmion during increasing field. c Morphological evolution starting from a rectangular antiskyrmion during decreasing field. The details discussed in the stability of the U-shaped antiskyrmion over the rectangular- shaped antiskyrmion have also been added in our revised manuscript (Fig. R26), see Lines 134-143: “Our simulations accurately reproduce the transition from the U- shaped antiskyrmion at low magnetic fields to the rectangular-shaped antiskyrmion at high magnetic fields (Supplementary Fig. 6). A detailed analysis of the energy terms indicates that the U-shaped antiskyrmion is predominantly stabilized by demagnetization and DMI energies. Moreover, at low magnetic fields, uniaxial anisotropy also contributes to the greater stabilization of the U-shaped antiskyrmion compared to the rectangular-shaped antiskyrmion. The total free energy of the U-shaped antiskyrmion is lower than that of the rectangular-shaped antiskyrmion in the low-magnetic-field regime, explaining the formation of U-shaped antiskyrmions at low magnetic fields”. Comment 6: 6.2 I do not see any estimation about the skyrmion/antiskyrmion size and their evolution as a function of magnetic field, temperature and current. Response: Following your insightful comments about the antiskyrmion and skyrmion size, we have provided magnetic field and temperature dependence of skyrmion/antiskyrmion size in the confined cuboid, as shown in Fig. R27 and Fig. R28. Antiskyrmion/skyrmion show anisotropic shapes with the long axis parallel to the long axis of the nanostructure. As the magnetic field increases, the size decreases and the shape becomes more isotropic. We have added the discussion about field and temperature effects on skyrmion/antiskyrmion size in our revised manuscript, see Lines 162-176: “We further characterize field- and temperature-dependent antiskyrmion/skyrmion dimensions, defined as lengths L and L along the [110] and x y [11(cid:3364)0] crystallographic axes (Supplementary Fig. 11 and Supplementary Fig. 12). At low fields, antiskyrmions and skyrmions manifest distinct anisotropies (L ≠ L ) arising x y from dipolar interactions and geometrically tunable via nanostructuring. This anisotropy persists for field tilt angles 𝛼 ≈ 0°–2.5°, with antiskyrmion long axes consistently aligned to the nanostructure's long axis. Increasing 𝛼 at fixed field first transforms antiskyrmions to bubbles while preserving shape anisotropy (Supplementary Fig. 13); further tilt reorients the bubble's long axis toward the in-plane field component to minimize Zeeman energy. Field elevation reduces both L and x L , driving convergence toward cubic symmetry at high fields (Supplementary Fig. 11 y and Supplementary Fig. 12). Upon increasing the temperature, the transformation field decreases, but the skyrmion/antiskyrmion size follows a similar variation rule in all the measured temperature range. Simulations confirm that nanostructure geometry governs antiskyrmion shape anisotropy (Supplementary Fig. 14)”. 39 400 95 K Lx 95 K Ly 150 K Lx 300 150 K Ly 200 K Lx 200 K Ly 200 250 K Lx 250 K Ly 300 K Lx 100 300 K Ly 330 K Lx 330 K Ly 200 300 400 500 600 40 )mn( L a 217 mT 278 mT 306 mT 329 mT L x b 223 mT 306 mT 322 mT 351 mT 200 nm c Antiskyrmion d Skyrmion 95 K Lx 95 K Ly 150 K Lx 150 K Ly 200 K Lx 200 K Ly 250 K Lx 250 K Ly 300 K Lx 300 K Ly 330 K Lx 330 K Ly 200 300 400 500 600 B (mT) B (mT) Ly Fig. R27 (i.e., Supplementary Fig. 11) Magnetic field and temperature dependence of antiskyrmion and skyrmion size in a 410 nm × 400 nm rectangle. a-b Fresnel image of antiskyrmion (a) and skyrmion (b) size evolution in the field-increasing process at 295 K. Defocus distance, −350 μm. c-d Magnetic field dependence of length L and width x L of antiskyrmion (c) and skyrmion (d) in the temperature range from 95 to 330 K. x B = 214 mT 288 mT 329 mT 360 mT 530 nm 440 nm y x B = 235 mT 315 mT 389 mT 401 mT 425 nm 530 nm a b y x c d 400 300 200 100 300 400 500 600 )mn( L 500 400 300 200 100 300 400 500 B (mT) )mn( L e 530 nm ×440 nm 425 nm ×530 nm 4 530 nm ×440 nm 11222222 9955005599 5500000055 KK KKKKKKKK LL LLLLLLLL xyxyxyxyxy 2 3 425 nm ×530 nm 1 0 300 400 500 600 B (mT) L/L y x 1222 1222 9 9 5059 5059 5 5 0005 0005 K K KKKK KKKK L L LLLL LLLL x x / / xxxx xxxx L L //// //// LLLL LLLL y y yyyy yyyy B (mT) Fig. R28 (i.e., Supplementary Fig. 12) Magnetic field and temperature dependence of antiskyrmion size in two nanostructured rectangles (530 nm × 440 nm and 425 nm × 530 nm). a Fresnel images in the field-increasing process at 295 K in the 530 nm × 440 nm rectangle. Defocus distance, −300 μm. b Fresnel images in the field-increasing process at 295 K in the 425 nm × 530 nm rectangle. Defocus distance, −350 μm. c Magnetic field dependence of length L and width L in the temperature range from 95 x x to 295 K in the 530 nm × 440 nm rectangle. d Magnetic field dependence of length L and width L in the temperature range from 95 to 295 K in the 425 nm × 530 nm x rectangle. e Magnetic field dependence of astropic ratio L /L in the temperature range x y from 95 to 295 K. Current-driven thermal effects reduce antiskyrmion/skyrmion sizes during electrical pulsing, as experimentally verified. Upon current termination, temperature recovery restores soliton dimensions to their initial values. We have added a discussion about the current effect on skyrmion size, see Lines 346-349: “Consequently, during ns-duration current pulses, Joule heating contributes significantly to the observed reduction in magnetic soliton size. Upon current termination, both the temperature and soliton size recover”. Comment 7: 7.1 Some previous studies show the creation of skyrmion-antiskyrmion pair. However, in the present study either the formation of antiskyrmion or skyrmion is observed. Is that because of the finite size of the magnetic sample? What is the role of finite size of magnetic element in the stabilization of antiskyrmions and skyrmions in this study? Response: Yes, the finite sample size limits stabilization to a single soliton. Nanostructure dimensions primarily govern the maximum soliton density, as confirmed by additional size-effect experiments. The zero-field stripe period λ ≈ 200 nm in a large FeNiPdP lamellae (Fig. R29) establishes our scaling framework. Single solitons form reliably in rectangles with dimensions ≈ 2λ - 3λ. Around and below the critical size (length/width ∼1λ ≈ 200 nm), edge-confined fractional half-antiskyrmion emerges (Fig. R30) [Jena et al., Nat. Commun. 13, 2348 (2022)]. Conversely, dimensions > 3λ permit multiple solitons, including skyrmion-antiskyrmion pairs under field variation (Fig. R31). Fig. R29 (i.e., Supplementary Fig. 3) Magnetic stripe domains at zero magnetic field in a large FeNiPdP thin plate. a Fresnel image of zero-field stripe domains at 300 K. Defocus distance, −500 μm. b Temperature T dependence of zero-field stripe period 𝜆. 41 Fig. R30 (i.e., Supplementary Fig. 4) Magnetic domain evolution in small rectangular nanostuctures. a Experimental Fresnel images in a 200 nm(cid:3400) 180 nm rectangular nanostructure at 295 K. Defocus distance, −250 μm. b Simulated middle-layer magnetization and defocus Fresnel image in a 200 nm (cid:3400) 200 nm rectangular nanostructure. Fig. R31 (i.e., Supplementary Fig. 5) Magnetic domain evolution in large rectangular nanostuctures. a Experimental Fresnel images in a 730 nm(cid:3400) 730 nm rectangular nanostructure at 95 K. Defocus distance, −300 μm. b Simulated middle-layer 42 magnetization and defocus Fresnel image in a 700 nm (cid:3400) 700 nm rectangular nanostructure. We have added a size discussion on the stabilization of antiskyrmions and skyrmions in our revised manuscript, see Lines 110-117: “The period (𝜆 ) of zero-field stripe domains in a large FeNiPdP lamella is about 200 nm in the measured temperature range from 95-350 K (Supplementary Fig. 3). Within the rectangle dimension of about 2λ-3λ, the confined FeNiPdP cuboid stabilizes a single magnetic soliton. Around and below the critical size (length/width ∼1λ ≈ 200 nm), edge-confined fractional half-antiskyrmion emerges (Supplementary Fig. 4) [Jena et al., Nat. Commun. 13, 2348 (2022)]. Conversely, dimensions > 3λ permit multiple solitons, including skyrmion-antiskyrmion pairs under field variation (Supplementary Fig. 5)”. Comment 7: 7.2 Why does topological number oscillate between 1.4 to 2.4 ns in Fig. 4a? Response: The topological number oscillations in the simulation are attributed to the annihilation of magnetic singularities in the domain wall. The initial seed domain emerges but shows multiple magnetic singularities (Bloch points) and is unstable (Fig. R32). During the application of STT, those high-energy magnetic singularities gradually annihilate and contribute to the variation of topological charge. We have added a discussion about the topological charge oscillation in our revised manuscript, see Lines 328-330: “The oscillation of topological charge observed between 1.4 and 2.4 ns (Fig. 4c) results from annihilation of additional high-energy Bloch points within the initially complex domain walls”. Fig. R32 (i.e., shown in Fig. 3c) Initial seed domains possessing multiple magnetic singularities (Bloch points) around the domain wall triggered by STT. 43 Comment 8: The width of the current pulses used in this study seems to be longer than usual. What if the authors use multiple sub-nanosecond current pulses to create antiskyrmions? Response: We thank you very much for bringing us attention to ultrafast electrical operations on antiskyrmions. The shortest width of the current pulses is limited by our voltage source. Our voltage source only supports the application of current pulses with a duration between 2 and 200 ns. Our results have shown the ultrafast operations using single current pulses with a duration of 2-10 ns, as shown in Fig. R33. Moreover, we also compare the width of current pulses between our antiskyrmion creation and previous skyrmion creation. We find the shortest width (2 ns) of current pulses for our antiskyrmion creation is smaller or comparable with some previous experimental studies on skyrmion creation, e.g., 10 ns in Ref. Woo et al. Nat. Electron. 1, 288 (2018), 20 ns in Ref. Wang et al. Nat. Commun. 13, 1593 (2022), 300 ms in Ref. Yang et al. Adv. Mater. 33, 2104406 (2021) and 7 ns in Ref. Hrabec et al. Nat. Commun. 8 15765 (2017). We noted that previous ultrafast skyrmion creation can be achieved by applying sub-ns current pulses (Ref. Buttner et al. Nat. Nanotechnol. 12, 1040 (2017). In our revised manuscript, we have added simulated current-driven dynamics with a duration smaller than 1 ns. Our simulation shows that the creation of antiskyrmions can be achieved using sub-ns current pulses but requires a larger current density. Fig. R33 (i.e., Supplementary Fig. 21) Experimental pulse duration w dependence of threshold current density for multi-state transformations. Magnetic field, 415 mT. Temperature, 95 K. Device geometry, 410 nm (cid:3400) 400 nm. 44 Fig. R34 (i.e., Supplementary Fig. 26) Simulated pulse duration w dependence of threshold current density for the FM-to-antiskyrmion transformation. Mgantic field, 85 mT. The current orientation does not affect the transformation. We have added a discussion about the effect of sub-ns pulse duration on antiskyrmion creation in our revised manuscript, see Lines 287-289: “Our voltage source specifications (2-200 ns pulse duration range) permit current-controlled ultrafast topological transformations across this full temporal window (Fig. 3b and Supplementary Fig. 21)”, and Lines 330-336: “Our simulations reveal that the FM-to-antiskyrmion transformation occurs on a very short timescale. For current pulses >2 ns, simulations show pulse-duration-independent threshold current densities for FM-to-antiskyrmion transformation (Supplementary Fig. 26), consistent with our experimental data (Fig. 3c). While prior studies demonstrated ultrafast skyrmion generation using sub-ns pulses,11 we find that sub-ns antiskyrmion creation via STT demands higher current densities (Supplementary Fig. 26).” Comment 9: I think the cell size in FeNiPdP must have an important role in the stabilization of antiskyrmions and skyrmions, and hence determining the critical current densities for creation, annihilations and transformation. Authors tried to make some small variation in the dimensions (supplsementary fig. 1), but that is not enough for understanding. Authors should shed some light on this. Response: Following your suggestion, we have added results about the effect of cell size on current-controlled magnetic dynamics, as shown in Fig. R35 and R36. 45 a 480 nm 46 450 nm FM Antiskyrmion Bubble Skyrmion FM 200 nm 400 nm 410 nm FM Antiskyrmion Bubble Skyrmion FM 200 nm 540 nm 510 nm FM Antiskyrmion Bubble FM j c1 j c2 j c3 j c4 j c1 j c2 j c3 j c4 b 1.0 0.5 0.0 -0.5 -1.0 0 5 30 35 j c1 j c2 j c4 c 200 nm Q 1.0 0.5 0.0 -0.5 -1.0 0 5 25 30 Current density j (1010 A/m2) Q Current density j (1010 A/m2) 1.0 0.5 0.0 -0.5 -1.0 0 5 10 15 20 25 Q Current density j (1010 A/m2) Fig. R35 (i.e., Supplementary Fig. 23) Current-induced multi-state transformation in different geometries at 95 K and under a fixed magnetic field. a 410 nm × 400 nm at 417 mT. b 480 nm × 450 nm at 436 mT. c 540 nm × 510 nm at 453 mT. Field tilt angle, 1.5°. Pulse duration, 40 ns. 37.9 37.9 11.4 11.4 11.4 𝑗 (1010 A/m2) 200 nm Fig. R36 (i.e., Supplementary Fig. 24) Current-induced magnetic domain dynamics in a 730 nm × 730 nm rectangular nanostructure at 95 K under 417 mT field. Fresnel imaging (defocus distance, −300 μm) captures domain evolution under single 40-ns current pulses (density, 11.4 and 37.9 × 1010 A/m²). Field tilt angle, 1.5°. We have addressed the static magnetic configurations in Response 7.1. Antiskyrmion dynamic control proves unachievable in sub-300 nm nanostructures due to incomplete stabilization (Fig. R30). Our fabricated microdevices (400–700 nm range) demonstrate size-dependent effects. The reliable four-state transformations are well reproduced in geometry size within the range of 400-500 nm. In a 540 nm × 510 nm rectangular nanostructure, only three-state transformations (antiskyrmion, bubble, FM) occur, even at a small tilt angle of 1.5°. In a larger (~730 nm × 730 nm) rectangle, a current pulse with a high current density (37.9 × 1010 A/m²) reliably erases all magnetic solitons. However, these larger nanostructures host diverse magnetic states with varying soliton counts and topologies. Consequently, small current pulses applied to uniform FM states yield stochastic outcomes, generating 2-4 coexisting solitons (antiskyrmions, skyrmions, and bubbles) with unpredictable configurations. We have added a discussion on the size effects on current-induced dynamics in the revised manuscript, see Lines 300-307: “Furthermore, these current-controlled transformations are highly reproducible in similar devices (Supplementary Fig. 22 and Supplementary Fig. 23). For a large nanostructure with a length (cid:3400) width of 730 nm (cid:3400) 730 nm, a current pulse with a high current density (37.9 × 1010 A/m²) reliably erases all magnetic solitons (Supplementary Fig. 24). However, these larger nanostructures host diverse magnetic states with varying soliton counts and topologies. Consequently, small current pulses applied to high-energy metastable FM states yield stochastic outcomes, generating 2-4 coexisting solitons (antiskyrmions, skyrmions, and bubbles) with unpredictable configurations”. 47 Manuscript ID: NCOMMS-25-13186A \"Current-controlled creations, deletions, and topological transformations of a single magnetic antiskyrmion in nanostructured cells\" by Y. Wu et al. Note that all page numbers and references without special instructions refer to the newly revised manuscript attached with this response and not to the original version submitted. The added contents are marked in red in the revised manuscript. Response to Reviewer #1: Reviewer #1: In the rebuttal and the revised manuscript, the authors have comprehensively addressed my comments, and in my opinion also the technical comments of the other two Reviewers. I recommend that the manuscript is published, provided that the authors can satisfactorily address one potentially major issue that arose on my reading of the revised manuscript and the response to the comment 5 of Reviewer 3 is the confusion regarding the surface effects vs bulk, as discussed starting on line 383. Response: Thank you very much for your time and effort in reviewing our manuscript. We are pleased to know that we have “comprehensively addressed your comments”. Below, please find our detailed response to your helpful remaining comments. If the magnetic structure at the surface is different from the bulk, what is the meaning of the topological indices? How should one think about the STT in such inhomogeneous states? Does the simulation in Supplementary Fig.30 essentially invalidate the quasi-2D picture presented throughout most of the manuscript? It seems that the magnetic textures as shown in this Figure are substantially different from the simplified 2D picture. In particular, the top and the bottom surfaces appear to form a Neel skyrmion dipole. Response to Comment “If the magnetic structure at the surface is different from the bulk, what is the meaning of the topological indices?”: We thank you for raising this important point regarding the interpretation of topological indices in non-uniform 3D structures. The topological charge Q, defined as 𝑄 = 1/(4π)(cid:1516)(cid:1516)d𝟐𝐫𝐦∙( (cid:2986)𝐦 × (cid:2986)𝐦 ) , is (cid:2986)(cid:3051) (cid:2986)(cid:3052) fundamentally a property of a two-dimensional magnetization texture. Therefore, it can be computed layer-by-layer for a 3D system. Our analysis confirms that the middle layers of the 3D structures (Supplementary Fig. 30) exhibit topological charges corresponding to the intended solitons: 𝑄 (cid:3404) (cid:3398)1 for the antiskyrmion, 𝑄 (cid:3404) (cid:3397)1 for the skyrmion, and 𝑄 (cid:3404) 0 for the bubble. In contrast, the surface layers of these 3D structures all stabilize as Néel-twisted skyrmions, each 1 with a charge of 𝑄 (cid:3404) (cid:3398)1. To provide a complete depth-resolved picture, we have now included a detailed layer-by-layer decomposition of the topological charge for each magnetic structure shown in Fig. R1, explicitly showing how the topology evolves through the film thickness. Fig. R1 (i.e., Supplementary Fig. 30b) Depth z dependence of topological charge Q of 3D magnetic configurations. Response to Comment “How should one think about the STT in such inhomogeneous states?”: Our simulations employ the Zhang-Li STT model [Zhang & Li, Phys. Rev. (cid:2869) Lett. 93, 127204 (2004)], described by the torque term: 𝛕 (cid:3404) (cid:4668)(cid:4666)1(cid:3397)𝛽𝛼(cid:4667)𝐦(cid:3400) (cid:2910)(cid:2896) (cid:2869)(cid:2878)(cid:3080)(cid:3118) (cid:4670)𝐦(cid:3400)(cid:4666)𝐮∙∇(cid:4667)𝐦(cid:4671)(cid:3397) (cid:4666)𝛽 (cid:3398)𝛼(cid:4667)𝐦(cid:3400)(cid:4666)𝐮∙∇(cid:4667)𝐦(cid:4669) , with 𝐮 (cid:3404) (cid:3091)(cid:3251)(cid:3091)(cid:3116) 𝑃𝐉 . Here, the (cid:2870)(cid:3032)(cid:3082)(cid:3116)(cid:3003)(cid:3294)(cid:3276)(cid:3295) (cid:4666)(cid:2869)(cid:2878)(cid:3081)(cid:3118)(cid:4667) charge current density 𝐉 is applied along the in-plane 𝑥-axis. Physically, the Zhang- Li torque represents the transfer of spin angular momentum from conduction electrons to the local magnetization texture, acting predominantly along the one-dimensional current path. The resulting dynamical response we simulate and observe is a collective outcome governed by the interplay between this STT and the system's total free energy landscape, representing an ensemble-averaged behavior across the entire layer. This complex interplay in 3D inhomogeneous states can yield emergent phenomena. For instance, in a previous study from our group [Tang et al., Sci. Bull. 68, 2919 (2023)], simulations of the hybrid 3D antiskyrmion tube revealed a \"Hall balance\" effect (Fig. R2). This behavior arises from the compensation of opposite Hall shifts from surface layers (𝑄 (cid:3404) (cid:3398)1) and middle layers (𝑄 (cid:3404) (cid:3397)1). 2 Fig. R2 Left: Theoretical Hall angle as a function of layers for the 3D hybrid antiskyrmion tube with Neel-twisted skyrmions at surface layers. Right: Simulated dynamical trajectories of the 3D hybrid antiskyrmion tube to an in-plane current along the x-axis. The Hall balance (i.e., Hall shift ~ 0) represents the average effects over the whole layer. We have added a discussion about STT in inhomogeneous magnetizations in the revised manuscript, see Lines 415-419: “The simulated and observed dynamics of these 3D inhomogeneous states under in-plane current are governed by the interplay of Zhang- Li STT and the system's free energy landscape, reflecting an ensemble-averaged response. For instance, a hybrid antiskyrmion tube with surface Néel-type skyrmions can exhibit a Hall balance, as previously identified.35” Response to Comment “Does the simulation in Supplementary Fig.30 essentially invalidate the quasi-2D picture presented throughout most of the manuscript? It seems that the magnetic textures as shown in this Figure are substantially different from the simplified 2D picture. In particular, the top and the bottom surfaces appear to form a Neel skyrmion dipole.”: The 2D picture presented in the main manuscript remains valid, as these figures are the magnetization of the middle layers within our full 3D simulations. We have chosen to focus on these middle-layer configurations for a clearer and more consistent narrative, as the key topological transformations—between antiskyrmion, bubble, and skyrmion states—are primarily manifested through the evolution of these central layers. Crucially, the surface-layer magnetization remains stable, consistently maintaining a Néel-type skyrmion state across all three topological configurations (hybrid antiskyrmion, bubble, and skyrmion tubes). Therefore, while the full 3D structure is more complex, the essential physics of the transformations is accurately and completely captured by the 2D middle-layer representations. We have clarified in the relevant figure captions that all 2D images represent the middle-layer magnetization of the simulated 3D structures, e.g., caption of Fig. 1d “Corresponding middle-layer magnetizations of simulated magnetic U-antiskyrmion at 0 mT, antiskyrmion at 290 mT, bubble at 295 mT, and skyrmion at 300 mT”, and caption of Fig. 4c, d “Representative middle-layer magnetic configurations during the FM- antiskyrmion transformation.” 3 We have explained the presentation of 2D configurations in our maintext, see Lines 407-414: “Importantly, the definitions of antiskyrmion, skyrmion, and bubble apply exclusively to the middle layers of the FeNiPdP structure. To minimize magnetic dipole-dipole interactions, surface layers consistently adopt Néel-twisted skyrmion configurations with Q = −1 (Supplementary Fig. 30).35,41 Consequently, mutual transformations between antiskyrmion, skyrmion, and bubble states alter the topological charges only in the middle layers, while the surface layers retain their skyrmionic topology. We therefore present the representative 2D magnetization of the middle layer (Figs. 1, 3, 4), which captures the essential topological transformations.” Comment 1.1: My original comment 1: The explanation about skyrmions/bubbles added to the manuscript in response to this comment is somewhat confusing, and I believe should be revised. On page 65 of the revised manuscript they state “Magnetic bubbles are cylindrical domains…” This is indeed a common definition of magnetic bubbles. However, the discussed magnetic textures are clearly not cylinder shaped – they are either rectangular of U-shaped. Do the authors still define them as (anti)skyrmion bubbles? Response: We thank you for this insightful comment regarding the terminology of skyrmions and bubbles. The terms \"skyrmion\" and \"bubble\" are established nomenclature within the literature on antiskyrmion-host materials (see Refs. 33–37, 40, 41 in our manuscript). In the FeNiPdP system, the inherent D₂d-symmetric Dzyaloshinskii-Moriya interaction (DMI) distorts these solitons from a circular shape into an elliptical one. This provides a crucial distinction: the \"skyrmions\" and \"bubbles\" we refer to are dipolar-stabilized solitons with elliptic distortion. In contrast, the rectangular and U- shaped textures are antiskyrmions, which are uniquely stabilized by the DMI itself. To avoid possible misleading, we have revised the statement, see Lines 68-69: “Magnetic bubbles are cylindrical domains typically observed in centrosymmetric uniaxial magnets.38,39 ” The shape variation under the influence of DM interaction has been specified in our manuscript, see Lines 74-77: “Moreover, the additional anisotropic DMI in D /S - symmetric 2d 4 systems distorts type-I and II bubbles from circular to elliptical shapes. Different from the dipolar skyrmions and bubbles, magnetic antiskyrmions with square shapes are mainly supported by DMI.” Comment 1.2: The phrasing is also confusing, for example the sentence “The Bloch and Néel-twisted skyrmions have been commonly taken as skyrmions” is not grammatically correct and confusing, which can be easily rectified by using a proof- reading/editing tool such as ChatGPT or Deepseek. Response: We thank you for your careful reading and valuable suggestion. The sentence has been revised as recommended, see Lines 54-56: \"Magnetic skyrmions are fundamentally categorized by their helicity into two types: Bloch and Néel.\" Comment 1.3: The statement “We note that antiskyrmions in FeGe magnets, as defined in prior work,26 exhibit identical vorticity but opposite polarity P compared to those studied here.” on lines 56-58 is also confusing. Doesn’t the product of vorticity and polarity uniquely determine whether the texture is a skyrmion or anti-skyrmion? Response: The distinction between magnetic skyrmions and antiskyrmions is fundamentally based on their vorticity type, not the product of vorticity and polarity. This definition by vorticity is consistent across other condensed matter systems, such as vortex-antivortex pairs in superconductors [Geurts et al. Phys. Rev. Lett. 97, 137002 (2006)] and skyrmion-antiskyrmion pairs in ultracold atomic gases [Price & Cooper, Phys. Rev. A 83, 061605(R) (2011)] and ferroelectrics [Gómez-Ortiz et al. Phys. Rev. B 111, L180104 (2025)]. The reference in our manuscript (Ref. 26) represents a special case within this framework, where the distinction is made through the topological charge 𝑄 (the product of vorticity and polarity). We acknowledge that this specific case may have caused confusion, and we have clarified this point in the revised text to ensure consistency with the broader, field-standard definition based on vorticity. We have also added a discussion to this part of our manuscript, see Lines 53-54: “Magnetic skyrmions and antiskyrmions are distinguished by their vorticity, which is consistent across other condensed matter systems.23-25” And Lines 58-61: “We note that the classification of skyrmions and antiskyrmions in FeGe magnets, as defined in prior work,29 is based on topological charge—a scheme that differs fundamentally from the one employed in our present study exhibit identical vorticity but opposite polarity P compared to those studied here. ” Comment 2: My original comment 10. I am afraid that my comment was not sufficiently clear, resulting in unsatisfactory response/changes. I pointed out that magnetic hysteresis is not a direct consequence of the coexistence of different phases at the same field, which seems to be implied by the statement cited in my comment. For example, the fraction of each phase can be uniquely determined by the field, in which case there will be no hysteresis even though different phases coexist. The minimal change that could address my comment would be to simply add “metastable” between “different” and “phases” in the sentence I cited. Response: Thank you for your helpful comments. We have added the word “metastable” to the sentence, see Lines 208-209: “The coexistence of different metastable phases within the same field regions accounts for magnetic hysteresis (Fig. 1c).” Comment 3: The discussion starting on line 177 is confusing, as it does not make it clear that the discussed results are simulations. Response: We have revised this sentence to explicitly state that the following discussion is based on simulation results, see Lines 182-183: “We then delve into the stability of different magnetic solitons in a strongly confined nanostructure through simulations, at a slight field tilt angle of 2°.” Comment 4: The paragraph inserted on lines 201-206 of revised manuscript to address one of the Reviewer’s comments is redundant, it essentially repeats the previous paragraph. These should be streamlined/merged. Response: We have merged this paragraph into the previous discussion, see Lines 202- 211: “In the absence of a field tilt, the bubble state cannot serve as an intermediate phase during the transformation from antiskyrmion to skyrmion (Supplementary Fig. 15b). Consequently, the field increase yields a direct three-state sequence: antiskyrmion to skyrmion to FM state. Conversely, under a large tilt magnetic field, the skyrmion phase cannot remain the most stable phase across all field regions (Supplementary Fig. 15f), producing a distinct transformation pathway: antiskyrmion to bubble to FM state. The coexistence of different metastable phases within the same field regions accounts for magnetic hysteresis (Fig. 1c). Our experiments confirm the theoretically predicted dependence of magnetic field-driven topological transformations on tilt angle (Supplementary Fig. 18).” The initial discussion is deleted: “At zero tilt angle, the field increase produces a direct 3-state transformation sequence: antiskyrmion to skyrmion to FM, with no bubble state observed. At larger tilt angles, the field increase yields a distinct 3-state sequence: antiskyrmion to bubble to FM, with no skyrmion state emerging.” Comment 5: The revised manuscript still has grammatical issues. For instance, “topologically equilibrium to the antiskyrmion” on line 124 should be “topologically equivalent to the antiskyrmion”. I recommend that the authors use widely available editing tools to find and correct such issues. Response: We thank you for your careful review. We have corrected the word “equilibrium” to “equivalent”, avoiding this grammatical issue. See lines 127-128: “during the field-decreasing process and is topologically equilibrium equivalent to the antiskyrmion”. We have also checked the whole manuscript, ensuring no such issues appear again. 6 Response to Reviewer #2: Reviewer #2: The authors have revised the manuscript properly. The revision made it clear the assertion. Now I believe this manuscript is ready to publish on the Nature Communications. Response: We are delighted to receive your recommendation for our manuscript's publication in Nature Communications. We would like to take this chance to express our profound gratitude for your efforts in reviewing our manuscript. 7 Response to Reviewer #3: Reviewer #3: I have carefully gone through the authors responses and revised manuscript. I found that the authors have satisfactorily addressed all my queries/critics and significantly modified the manuscript. The quality of the work is now suitable for Nature Communications. However, I still have couple of minor suggestions. The manuscript may be published after addressing those suggestions. Response: We sincerely appreciate your positive assessment of our revisions and your recommendation for publication. We have addressed the remaining points below as suggested. Comment 1: In page 3, line 52-53, \"The Bloch and Néel-twisted skyrmions have been commonly taken as skyrmions\". This sentence should be reformulated. Response: Thank you very much for your careful reading. We have corrected this sentence, see Lines 54-56: “Magnetic skyrmions are fundamentally categorized by their helicity into two types: Bloch and Néel.” Comment 2: The direction or geometry of the applied magnetic field should be clearly shown in Fig. 1. I understand that the small tilt angle of the magnetic field is necessary. However, the tolerance of the tilt angle (i.e. maximum tilt angle) should be mentioned. According to the authors, how can a magnetic field with a small tilt angle be applied in practical devices? Response to “The direction or geometry of the applied magnetic field should be clearly shown in Fig. 1”: We have added a schematic to Fig. 1 illustrating the direction of the tilted magnetic field, as shown in Fig. R3. Fig. R3 The inset shows a schematic of the experimental field tilt angle, α. The-plane magnetic field component is along the in-plane x-axis. 8 Response to “I understand that the small tilt angle of the magnetic field is necessary. However, the tolerance of the tilt angle (i.e., maximum tilt angle) should be mentioned”: We have specified the maximum tilted angle allowed for four-state transformations in the revised manuscript, see Lines 201-202: “The four-state transformation occurs for field tilt angles of up to approximately 3°.” Response to “According to the authors, how can a magnetic field with a small tilt angle be applied in practical devices?”: The four-state transformations (skyrmion– antiskyrmion–bubble–FM) indeed require a tuned field tilt, which could be achieved experimentally using rotatable stages or similar components. While this adds complexity to device design, it enables a higher number of distinct topological states. Importantly, we also demonstrate robust three-state transformations (skyrmion– antiskyrmion–FM) that proceed without any field tilt (Fig. R4). This tilt-free protocol offers a more straightforward path to practical implementation while still enabling key topological transitions. We have added this discussion to the revised manuscript (Lines 328-332): \"The four-state transformations necessitate a small field tilt, achievable with components like rotatable stages, though this adds complexity to device design. In contrast, three-state transformations (skyrmion–antiskyrmion–FM) do not require field tilting, enabling a more streamlined device architecture.\" Fig. R4 (i.e., Supplementary Fig. 25a) Current-controlled 3-state transformation without field tilt. Comment 3: I suggest to move Supplementary figures 6(b,c) to Figure 1 after Figure 1(d). Response: Following your nice suggestion, we have moved Supplementary Figures 6b and 6c to Figure 1 after Figure 1d, as shown in Fig. R5. 9 Fig. R5 (i.e., Fig. 1d-f in the maintext) d Corresponding middle-layer magnetizations of simulated magnetic U-antiskyrmion at 0 mT, antiskyrmion at 290 mT, bubble at 295 mT, and skyrmion at 300 mT. e Field-induced morphological evolution starting from a U-shaped antiskyrmion during increasing field. f Morphological evolution starting from a rectangular antiskyrmion during decreasing field. The color in (d)-(f) represents magnetization orientation according to the colorwheel. 10 Manuscript ID: NCOMMS-25-13186B \"Current-controlled creations, deletions, and topological transformations of a single magnetic antiskyrmion in nanostructured cells\" by Y. Wu et al. Note that all page numbers and references without special instructions refer to the newly revised manuscript attached with this response and not to the original version submitted. Response to Reviewer #1: Reviewer #1: The authors have thoroughly addressed my latest comments. I agree with the other two reviewers that the revised manuscript is suitable for publication. Response: We greatly appreciate your support in recommending its publication in Nature Communications. Response to Reviewer #3: Reviewer #3: The authors have satisfactorily responded to rest of my concerns and made the necessary changes in the revised manuscript. I believe that the manuscript should be suitable for publication after addressing the concerns from other reviewers. Response: We sincerely appreciate your recommendation for publication."}, {"round": 2, "reviewer_comments": {"reviewer_1": "In the rebuttal and the revised manuscript, the authors have comprehensively addressed my comments, and in my opinion also the technical comments of the other two Reviewers. I recommend that the manuscript is published, provided that the authors can satisfactorily address one potentially major issue that arose on my reading of the revised manuscript and the response to the comment 5 of Reviewer 3 is the confusion regarding the surface effects vs bulk, as discussed starting on line 383. If the magnetic structure at the surface is different from the bulk, what is the meaning of the topological indices? How should one think about the STT in such inhomogeneous states? Does the simulation in Supplementary Fig.30 essentially invalidate the quasi-2D picture presented throughout most of the manuscript? It seems that the magnetic textures as shown in this Figure are substantially different from the simplified 2D picture. In particular, the top and the bottom surfaces appear to form a Neel skyrmion dipole. My remaining comments/questions on the revised manuscript are minor and intended to improve the readability of the paper. i) My original comment 1: The explanation about skyrmions/bubbles added to the manuscript in response to this comment is somewhat confusing, and I believe should be revised. On page 65 of the revised manuscript they state “Magnetic bubbles are cylindrical domains…” This is indeed a common definition of magnetic bubbles. However, the discussed magnetic textures are clearly not cylinder shaped – they are either rectangular of U-shaped. Do the authors still define them as (anti)skyrmion bubbles? The phrasing is also confusing, for example the sentence “The Bloch and Néel-twisted skyrmions have been commonly taken as skyrmions” is not grammatically correct and confusing, which can be easily rectified by using a proof-reading/editing tool such as ChatGPT or Deepseek. The statement “We note that antiskyrmions in FeGe magnets, as defined in prior work,26 exhibit identical vorticity but opposite polarity P compared to those studied here.” on lines 56-58 is also confusing. Doesn’t the product of vorticity and polarity uniquely determine whether the texture is a skyrmion or anti-skyrmion? ii) My original comment 10. I am afraid that my comment was not sufficiently clear, resulting in unsatisfactory response/changes. I pointed out that magnetic hysteresis is not a direct consequence of the coexistence of different phases at the same field, which seems to be implied by the statement cited in my comment. For example, the fraction of each phase can be uniquely determined by the field, in which case there will be no hysteresis even though different phases coexist. The minimal change that could address my comment would be to simply add “metastable” between “different” and “phases” in the sentence I cited. iii) The discussion starting on line 177 is confusing, as it does not make it clear that the discussed results are simulations. iv) The paragraph inserted on lines 201-206 of revised manuscript to address one of the Reviewer’s comments is redundant, it essentially repeats the previous paragraph. These should be streamlined/merged. v) The revised manuscript still has grammatical issues. For instance, “topologically equilibrium to the antiskyrmion” on line 124 should be “topologically equivalent to the antiskyrmion”. I recommend that the authors use widely available editing tools to find and correct such issues.", "reviewer_2": "The authors have revised the manuscript properly. The revision made it clear the assertion. Now I believe this manuscript isready to publish on the Nature Communications.", "reviewer_3": "I have carefully gone through the authors responses and revised manuscript. I found that the authors have satisfactorily addressed all my queries/critics and significantly modified the manuscript. The quality of the work is now suitable for Nature Communications. However, I still have couple of minor suggestions. The manuscript may be published after addressing those suggestions. [1] In page 3, line 52-53, \"The Bloch and Néel-twisted skyrmions have been commonly taken as skyrmions\". This sentence should be reformulated. [2] The direction or geometry of the applied magnetic field should be clearly shown in Fig. 1. I understand that the small tilt angle of the magnetic field is necessary. However, the tolerance of the tilt angle (i.e. maximum tilt angle) should be mentioned. According to the authors, how can a magnetic field with a small tilt angle be applied in practical devices? [3] I suggest to move Supplementary figures 6(b,c) to Figure 1 after Figure 1(d)."}, "author_response": "Manuscript ID: NCOMMS-25-13186A \"Current-controlled creations, deletions, and topological transformations of a single magnetic antiskyrmion in nanostructured cells\" by Y. Wu et al. Note that all page numbers and references without special instructions refer to the newly revised manuscript attached with this response and not to the original version submitted. The added contents are marked in red in the revised manuscript. Response to Reviewer #1: Reviewer #1: In the rebuttal and the revised manuscript, the authors have comprehensively addressed my comments, and in my opinion also the technical comments of the other two Reviewers. I recommend that the manuscript is published, provided that the authors can satisfactorily address one potentially major issue that arose on my reading of the revised manuscript and the response to the comment 5 of Reviewer 3 is the confusion regarding the surface effects vs bulk, as discussed starting on line 383. Response: Thank you very much for your time and effort in reviewing our manuscript. We are pleased to know that we have “comprehensively addressed your comments”. Below, please find our detailed response to your helpful remaining comments. If the magnetic structure at the surface is different from the bulk, what is the meaning of the topological indices? How should one think about the STT in such inhomogeneous states? Does the simulation in Supplementary Fig.30 essentially invalidate the quasi-2D picture presented throughout most of the manuscript? It seems that the magnetic textures as shown in this Figure are substantially different from the simplified 2D picture. In particular, the top and the bottom surfaces appear to form a Neel skyrmion dipole. Response to Comment “If the magnetic structure at the surface is different from the bulk, what is the meaning of the topological indices?”: We thank you for raising this important point regarding the interpretation of topological indices in non-uniform 3D structures. The topological charge Q, defined as 𝑄 = 1/(4π)(cid:1516)(cid:1516)d𝟐𝐫𝐦∙( (cid:2986)𝐦 × (cid:2986)𝐦 ) , is (cid:2986)(cid:3051) (cid:2986)(cid:3052) fundamentally a property of a two-dimensional magnetization texture. Therefore, it can be computed layer-by-layer for a 3D system. Our analysis confirms that the middle layers of the 3D structures (Supplementary Fig. 30) exhibit topological charges corresponding to the intended solitons: 𝑄 (cid:3404) (cid:3398)1 for the antiskyrmion, 𝑄 (cid:3404) (cid:3397)1 for the skyrmion, and 𝑄 (cid:3404) 0 for the bubble. In contrast, the surface layers of these 3D structures all stabilize as Néel-twisted skyrmions, each 1 with a charge of 𝑄 (cid:3404) (cid:3398)1. To provide a complete depth-resolved picture, we have now included a detailed layer-by-layer decomposition of the topological charge for each magnetic structure shown in Fig. R1, explicitly showing how the topology evolves through the film thickness. Fig. R1 (i.e., Supplementary Fig. 30b) Depth z dependence of topological charge Q of 3D magnetic configurations. Response to Comment “How should one think about the STT in such inhomogeneous states?”: Our simulations employ the Zhang-Li STT model [Zhang & Li, Phys. Rev. (cid:2869) Lett. 93, 127204 (2004)], described by the torque term: 𝛕 (cid:3404) (cid:4668)(cid:4666)1(cid:3397)𝛽𝛼(cid:4667)𝐦(cid:3400) (cid:2910)(cid:2896) (cid:2869)(cid:2878)(cid:3080)(cid:3118) (cid:4670)𝐦(cid:3400)(cid:4666)𝐮∙∇(cid:4667)𝐦(cid:4671)(cid:3397) (cid:4666)𝛽 (cid:3398)𝛼(cid:4667)𝐦(cid:3400)(cid:4666)𝐮∙∇(cid:4667)𝐦(cid:4669) , with 𝐮 (cid:3404) (cid:3091)(cid:3251)(cid:3091)(cid:3116) 𝑃𝐉 . Here, the (cid:2870)(cid:3032)(cid:3082)(cid:3116)(cid:3003)(cid:3294)(cid:3276)(cid:3295) (cid:4666)(cid:2869)(cid:2878)(cid:3081)(cid:3118)(cid:4667) charge current density 𝐉 is applied along the in-plane 𝑥-axis. Physically, the Zhang- Li torque represents the transfer of spin angular momentum from conduction electrons to the local magnetization texture, acting predominantly along the one-dimensional current path. The resulting dynamical response we simulate and observe is a collective outcome governed by the interplay between this STT and the system's total free energy landscape, representing an ensemble-averaged behavior across the entire layer. This complex interplay in 3D inhomogeneous states can yield emergent phenomena. For instance, in a previous study from our group [Tang et al., Sci. Bull. 68, 2919 (2023)], simulations of the hybrid 3D antiskyrmion tube revealed a \"Hall balance\" effect (Fig. R2). This behavior arises from the compensation of opposite Hall shifts from surface layers (𝑄 (cid:3404) (cid:3398)1) and middle layers (𝑄 (cid:3404) (cid:3397)1). 2 Fig. R2 Left: Theoretical Hall angle as a function of layers for the 3D hybrid antiskyrmion tube with Neel-twisted skyrmions at surface layers. Right: Simulated dynamical trajectories of the 3D hybrid antiskyrmion tube to an in-plane current along the x-axis. The Hall balance (i.e., Hall shift ~ 0) represents the average effects over the whole layer. We have added a discussion about STT in inhomogeneous magnetizations in the revised manuscript, see Lines 415-419: “The simulated and observed dynamics of these 3D inhomogeneous states under in-plane current are governed by the interplay of Zhang- Li STT and the system's free energy landscape, reflecting an ensemble-averaged response. For instance, a hybrid antiskyrmion tube with surface Néel-type skyrmions can exhibit a Hall balance, as previously identified.35” Response to Comment “Does the simulation in Supplementary Fig.30 essentially invalidate the quasi-2D picture presented throughout most of the manuscript? It seems that the magnetic textures as shown in this Figure are substantially different from the simplified 2D picture. In particular, the top and the bottom surfaces appear to form a Neel skyrmion dipole.”: The 2D picture presented in the main manuscript remains valid, as these figures are the magnetization of the middle layers within our full 3D simulations. We have chosen to focus on these middle-layer configurations for a clearer and more consistent narrative, as the key topological transformations—between antiskyrmion, bubble, and skyrmion states—are primarily manifested through the evolution of these central layers. Crucially, the surface-layer magnetization remains stable, consistently maintaining a Néel-type skyrmion state across all three topological configurations (hybrid antiskyrmion, bubble, and skyrmion tubes). Therefore, while the full 3D structure is more complex, the essential physics of the transformations is accurately and completely captured by the 2D middle-layer representations. We have clarified in the relevant figure captions that all 2D images represent the middle-layer magnetization of the simulated 3D structures, e.g., caption of Fig. 1d “Corresponding middle-layer magnetizations of simulated magnetic U-antiskyrmion at 0 mT, antiskyrmion at 290 mT, bubble at 295 mT, and skyrmion at 300 mT”, and caption of Fig. 4c, d “Representative middle-layer magnetic configurations during the FM- antiskyrmion transformation.” 3 We have explained the presentation of 2D configurations in our maintext, see Lines 407-414: “Importantly, the definitions of antiskyrmion, skyrmion, and bubble apply exclusively to the middle layers of the FeNiPdP structure. To minimize magnetic dipole-dipole interactions, surface layers consistently adopt Néel-twisted skyrmion configurations with Q = −1 (Supplementary Fig. 30).35,41 Consequently, mutual transformations between antiskyrmion, skyrmion, and bubble states alter the topological charges only in the middle layers, while the surface layers retain their skyrmionic topology. We therefore present the representative 2D magnetization of the middle layer (Figs. 1, 3, 4), which captures the essential topological transformations.” Comment 1.1: My original comment 1: The explanation about skyrmions/bubbles added to the manuscript in response to this comment is somewhat confusing, and I believe should be revised. On page 65 of the revised manuscript they state “Magnetic bubbles are cylindrical domains…” This is indeed a common definition of magnetic bubbles. However, the discussed magnetic textures are clearly not cylinder shaped – they are either rectangular of U-shaped. Do the authors still define them as (anti)skyrmion bubbles? Response: We thank you for this insightful comment regarding the terminology of skyrmions and bubbles. The terms \"skyrmion\" and \"bubble\" are established nomenclature within the literature on antiskyrmion-host materials (see Refs. 33–37, 40, 41 in our manuscript). In the FeNiPdP system, the inherent D₂d-symmetric Dzyaloshinskii-Moriya interaction (DMI) distorts these solitons from a circular shape into an elliptical one. This provides a crucial distinction: the \"skyrmions\" and \"bubbles\" we refer to are dipolar-stabilized solitons with elliptic distortion. In contrast, the rectangular and U- shaped textures are antiskyrmions, which are uniquely stabilized by the DMI itself. To avoid possible misleading, we have revised the statement, see Lines 68-69: “Magnetic bubbles are cylindrical domains typically observed in centrosymmetric uniaxial magnets.38,39 ” The shape variation under the influence of DM interaction has been specified in our manuscript, see Lines 74-77: “Moreover, the additional anisotropic DMI in D /S - symmetric 2d 4 systems distorts type-I and II bubbles from circular to elliptical shapes. Different from the dipolar skyrmions and bubbles, magnetic antiskyrmions with square shapes are mainly supported by DMI.” Comment 1.2: The phrasing is also confusing, for example the sentence “The Bloch and Néel-twisted skyrmions have been commonly taken as skyrmions” is not grammatically correct and confusing, which can be easily rectified by using a proof- reading/editing tool such as ChatGPT or Deepseek. Response: We thank you for your careful reading and valuable suggestion. The sentence has been revised as recommended, see Lines 54-56: \"Magnetic skyrmions are fundamentally categorized by their helicity into two types: Bloch and Néel.\" Comment 1.3: The statement “We note that antiskyrmions in FeGe magnets, as defined in prior work,26 exhibit identical vorticity but opposite polarity P compared to those studied here.” on lines 56-58 is also confusing. Doesn’t the product of vorticity and polarity uniquely determine whether the texture is a skyrmion or anti-skyrmion? Response: The distinction between magnetic skyrmions and antiskyrmions is fundamentally based on their vorticity type, not the product of vorticity and polarity. This definition by vorticity is consistent across other condensed matter systems, such as vortex-antivortex pairs in superconductors [Geurts et al. Phys. Rev. Lett. 97, 137002 (2006)] and skyrmion-antiskyrmion pairs in ultracold atomic gases [Price & Cooper, Phys. Rev. A 83, 061605(R) (2011)] and ferroelectrics [Gómez-Ortiz et al. Phys. Rev. B 111, L180104 (2025)]. The reference in our manuscript (Ref. 26) represents a special case within this framework, where the distinction is made through the topological charge 𝑄 (the product of vorticity and polarity). We acknowledge that this specific case may have caused confusion, and we have clarified this point in the revised text to ensure consistency with the broader, field-standard definition based on vorticity. We have also added a discussion to this part of our manuscript, see Lines 53-54: “Magnetic skyrmions and antiskyrmions are distinguished by their vorticity, which is consistent across other condensed matter systems.23-25” And Lines 58-61: “We note that the classification of skyrmions and antiskyrmions in FeGe magnets, as defined in prior work,29 is based on topological charge—a scheme that differs fundamentally from the one employed in our present study exhibit identical vorticity but opposite polarity P compared to those studied here. ” Comment 2: My original comment 10. I am afraid that my comment was not sufficiently clear, resulting in unsatisfactory response/changes. I pointed out that magnetic hysteresis is not a direct consequence of the coexistence of different phases at the same field, which seems to be implied by the statement cited in my comment. For example, the fraction of each phase can be uniquely determined by the field, in which case there will be no hysteresis even though different phases coexist. The minimal change that could address my comment would be to simply add “metastable” between “different” and “phases” in the sentence I cited. Response: Thank you for your helpful comments. We have added the word “metastable” to the sentence, see Lines 208-209: “The coexistence of different metastable phases within the same field regions accounts for magnetic hysteresis (Fig. 1c).” Comment 3: The discussion starting on line 177 is confusing, as it does not make it clear that the discussed results are simulations. Response: We have revised this sentence to explicitly state that the following discussion is based on simulation results, see Lines 182-183: “We then delve into the stability of different magnetic solitons in a strongly confined nanostructure through simulations, at a slight field tilt angle of 2°.” Comment 4: The paragraph inserted on lines 201-206 of revised manuscript to address one of the Reviewer’s comments is redundant, it essentially repeats the previous paragraph. These should be streamlined/merged. Response: We have merged this paragraph into the previous discussion, see Lines 202- 211: “In the absence of a field tilt, the bubble state cannot serve as an intermediate phase during the transformation from antiskyrmion to skyrmion (Supplementary Fig. 15b). Consequently, the field increase yields a direct three-state sequence: antiskyrmion to skyrmion to FM state. Conversely, under a large tilt magnetic field, the skyrmion phase cannot remain the most stable phase across all field regions (Supplementary Fig. 15f), producing a distinct transformation pathway: antiskyrmion to bubble to FM state. The coexistence of different metastable phases within the same field regions accounts for magnetic hysteresis (Fig. 1c). Our experiments confirm the theoretically predicted dependence of magnetic field-driven topological transformations on tilt angle (Supplementary Fig. 18).” The initial discussion is deleted: “At zero tilt angle, the field increase produces a direct 3-state transformation sequence: antiskyrmion to skyrmion to FM, with no bubble state observed. At larger tilt angles, the field increase yields a distinct 3-state sequence: antiskyrmion to bubble to FM, with no skyrmion state emerging.” Comment 5: The revised manuscript still has grammatical issues. For instance, “topologically equilibrium to the antiskyrmion” on line 124 should be “topologically equivalent to the antiskyrmion”. I recommend that the authors use widely available editing tools to find and correct such issues. Response: We thank you for your careful review. We have corrected the word “equilibrium” to “equivalent”, avoiding this grammatical issue. See lines 127-128: “during the field-decreasing process and is topologically equilibrium equivalent to the antiskyrmion”. We have also checked the whole manuscript, ensuring no such issues appear again. 6 Response to Reviewer #2: Reviewer #2: The authors have revised the manuscript properly. The revision made it clear the assertion. Now I believe this manuscript is ready to publish on the Nature Communications. Response: We are delighted to receive your recommendation for our manuscript's publication in Nature Communications. We would like to take this chance to express our profound gratitude for your efforts in reviewing our manuscript. 7 Response to Reviewer #3: Reviewer #3: I have carefully gone through the authors responses and revised manuscript. I found that the authors have satisfactorily addressed all my queries/critics and significantly modified the manuscript. The quality of the work is now suitable for Nature Communications. However, I still have couple of minor suggestions. The manuscript may be published after addressing those suggestions. Response: We sincerely appreciate your positive assessment of our revisions and your recommendation for publication. We have addressed the remaining points below as suggested. Comment 1: In page 3, line 52-53, \"The Bloch and Néel-twisted skyrmions have been commonly taken as skyrmions\". This sentence should be reformulated. Response: Thank you very much for your careful reading. We have corrected this sentence, see Lines 54-56: “Magnetic skyrmions are fundamentally categorized by their helicity into two types: Bloch and Néel.” Comment 2: The direction or geometry of the applied magnetic field should be clearly shown in Fig. 1. I understand that the small tilt angle of the magnetic field is necessary. However, the tolerance of the tilt angle (i.e. maximum tilt angle) should be mentioned. According to the authors, how can a magnetic field with a small tilt angle be applied in practical devices? Response to “The direction or geometry of the applied magnetic field should be clearly shown in Fig. 1”: We have added a schematic to Fig. 1 illustrating the direction of the tilted magnetic field, as shown in Fig. R3. Fig. R3 The inset shows a schematic of the experimental field tilt angle, α. The-plane magnetic field component is along the in-plane x-axis. 8 Response to “I understand that the small tilt angle of the magnetic field is necessary. However, the tolerance of the tilt angle (i.e., maximum tilt angle) should be mentioned”: We have specified the maximum tilted angle allowed for four-state transformations in the revised manuscript, see Lines 201-202: “The four-state transformation occurs for field tilt angles of up to approximately 3°.” Response to “According to the authors, how can a magnetic field with a small tilt angle be applied in practical devices?”: The four-state transformations (skyrmion– antiskyrmion–bubble–FM) indeed require a tuned field tilt, which could be achieved experimentally using rotatable stages or similar components. While this adds complexity to device design, it enables a higher number of distinct topological states. Importantly, we also demonstrate robust three-state transformations (skyrmion– antiskyrmion–FM) that proceed without any field tilt (Fig. R4). This tilt-free protocol offers a more straightforward path to practical implementation while still enabling key topological transitions. We have added this discussion to the revised manuscript (Lines 328-332): \"The four-state transformations necessitate a small field tilt, achievable with components like rotatable stages, though this adds complexity to device design. In contrast, three-state transformations (skyrmion–antiskyrmion–FM) do not require field tilting, enabling a more streamlined device architecture.\" Fig. R4 (i.e., Supplementary Fig. 25a) Current-controlled 3-state transformation without field tilt. Comment 3: I suggest to move Supplementary figures 6(b,c) to Figure 1 after Figure 1(d). Response: Following your nice suggestion, we have moved Supplementary Figures 6b and 6c to Figure 1 after Figure 1d, as shown in Fig. R5. 9 Fig. R5 (i.e., Fig. 1d-f in the maintext) d Corresponding middle-layer magnetizations of simulated magnetic U-antiskyrmion at 0 mT, antiskyrmion at 290 mT, bubble at 295 mT, and skyrmion at 300 mT. e Field-induced morphological evolution starting from a U-shaped antiskyrmion during increasing field. f Morphological evolution starting from a rectangular antiskyrmion during decreasing field. The color in (d)-(f) represents magnetization orientation according to the colorwheel. 10 Manuscript ID: NCOMMS-25-13186B \"Current-controlled creations, deletions, and topological transformations of a single magnetic antiskyrmion in nanostructured cells\" by Y. Wu et al. Note that all page numbers and references without special instructions refer to the newly revised manuscript attached with this response and not to the original version submitted. Response to Reviewer #1: Reviewer #1: The authors have thoroughly addressed my latest comments. I agree with the other two reviewers that the revised manuscript is suitable for publication. Response: We greatly appreciate your support in recommending its publication in Nature Communications. Response to Reviewer #3: Reviewer #3: The authors have satisfactorily responded to rest of my concerns and made the necessary changes in the revised manuscript. I believe that the manuscript should be suitable for publication after addressing the concerns from other reviewers. Response: We sincerely appreciate your recommendation for publication."}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have thoroughly addressed my latest comments. I agree with the other two reviewers that the revised manuscript is suitable for publication.", "reviewer_3": "The authors have satisfactorily responded to rest of my concerns and made the necessary changes in the revised manuscript. I believe that the manuscript should be suitable for publication after addressing the concerns from other reviewers."}, "author_response": "Manuscript ID: NCOMMS-25-13186B \"Current-controlled creations, deletions, and topological transformations of a single magnetic antiskyrmion in nanostructured cells\" by Y. Wu et al. Note that all page numbers and references without special instructions refer to the newly revised manuscript attached with this response and not to the original version submitted. Response to Reviewer #1: Reviewer #1: The authors have thoroughly addressed my latest comments. I agree with the other two reviewers that the revised manuscript is suitable for publication. Response: We greatly appreciate your support in recommending its publication in Nature Communications. Response to Reviewer #3: Reviewer #3: The authors have satisfactorily responded to rest of my concerns and made the necessary changes in the revised manuscript. I believe that the manuscript should be suitable for publication after addressing the concerns from other reviewers. Response: We sincerely appreciate your recommendation for publication."}]

Decision letter