Spontaneous Vortex‐Antivortex Pairs and Their Topological Transitions in a Chiral‐Lattice Magnet

The spontaneous formation and topological transitions of vortex‐antivortex pairs have implications for a broad range of emergent phenomena, for example, from superconductivity to quantum computing. Unlike magnets exhibiting collinear spin textures, helimagnets with noncollinear spin textures provide unique opportunities to manipulate topological forms such as (anti)merons and (anti)skyrmions. However, it is challenging to achieve multiple topological states and their interconversion in a single helimagnet due to the topological protection for each state. Here, the on‐demand creation of multiple topological states in a helimagnet Fe0.5Co0.5Ge, including a spontaneous vortex pair of meron with topological charge N = −1/2 and antimeron with N = 1/2, and a vortex‐antivortex bundle, that is, a bimeron (meron pair) with N = −1 is reported. The mutual transformation between skyrmions and bimerons with respect to the competitive effects of magnetic field and magnetic shape anisotropy is demonstrated. It is shown that electric currents drive the individual bimerons to form their connecting assembly and then into a skyrmion lattice. These findings signify the feasibility of designing topological states and offer new insights into the manipulation of noncollinear spin textures for potential applications in various fields.


Introduction
[5][6] To exploit topological electronic states in natural materials, noncollinear spin textures, such as a proper screw or cycloidal structure arising from broken inversion symmetry of crystal structure, [6] are required instead of the collinear spin-ordering states in ferromagnets (FMs) that exhibit magnetic domains separated by Bloch-type (Figure 1a) or Neel-type domain walls (DWs). [7,8]Upon an external magnetic field to such a spin-noncolinear magnet within a specific temperature range close to the transition temperature T C , a topological state emerges, composed of 2D magnetic skyrmions (Figure 1b). [9]This state is robust and resists transformation into other topological states, except for the collapse of the state induced by external stimuli. [10]The reason for this stability is that the topological state benefits from an invariant topology that remains unchanged under continuous deformations of spin textures, [11] thus providing protection unless the state is affected by strong destructive stimuli.
2D magnetic skyrmions are typical topological spin textures with an integer topological charge N = (1/4) ∫∫n • ((∂n/∂x) × (∂n/∂y)) dxdy = −1 [4] ; n is the unit vector field of the local magnetizations.Skyrmions have been discovered in helimagnets with an intrinsic Dzyaloshinskii-Moriya interaction (DMI) originating from a broken inversion symmetry of crystal structure [4,6,9] or in heterostructured thin films with the artificial DMI. [12][15] Monopoles and antimonopoles are also predicted in meron-antimeron pairs. [16]he (anti)merons (Figure 1c,d) are topological spin textures with a half-integer topological charge.They have recently been observed in helimagnets, [17] heterostructured films, [18] and 2D van der Waals magnets. [19]The sign of topological charge can be either positive (Figure 1d) or negative (Figure 1c) as determined by the magnetization configurations. [17]The meron and antimeron are also treated as half-quantum vortex and antivortex, respectively.They are characterized by a vorticity w = (1/2)∮(∂/∂)d = ±1, where  and  represent the polar and azimuthal angles of the magnetization vector. [4,7]The sign of the vorticity is determined by the so-called "right-hand rule" (Figure 1c,d).The bimeron, as schematically illustrated in Figure 1e, is a topologically stable configuration of a bundle of vortex (a meron with down-core magnetizations) and antivortex (meron with up-core magnetizations).It has been theoretically predicted in frustrated magnets, [20] antiferromagnets, [21] and cubic helimagnets, [22] and observed in epitaxial antiferromagnetic film [23] and multilayered FM film [24] upon external fields.It carries an integer topological charge (N = −1), similar to that of a skyrmion.However, the spontaneous meron-antimeron pair and bimeron (i.e., a bundle of a vortex classified as the type I meron with clockwise (CW) helicity and downward magnetization in the core, and antivortex categorized as the type III meron composed divergent magnetizations and upward magnetizations in the core, as shown in Figure 1c) have not yet been confirmed experimentally.The dynamical switching behaviors of merons, Lorentz TEM micrograph of a meron (dark circular domain on the left side) and an antimeron (bright elliptic domain on the right side) observed in a 40-nm-thick Fe 0.5 Co 0.5 Ge; the helicity is CW for the meron, and CCW for the antimeron, as indicated by the corresponding in-plane field (magnetic induction) maps (d,e).f) 3D vector field map for the meron texture visualized using tomographic Lorentz TEM.The colored arrows show the vector field at every point.g-i) Bimerons observed in a 60-nm-thick Fe 0.5 Co 0.5 Ge plate under a zero field and at 100 K: g) overfocused Lorentz TEM image, and (h,i) the corresponding magnetic induction maps for the squared bimerons in (g).
bimerons, and skyrmions have potential applications to qubits for quantum computing. [25,26]Therefore, the engineering of the spontaneously formed topological states and their mutual transformations in a single material are highly desirable toward future applications.
In this study, we demonstrate the presence of various topological states, including 2D skyrmions, 3D cone-like (anti)merons, and bimerons (the simulated magnetization texture can be observed in Figure 1f, and the corresponding Lorentz transmission electron microscopy (TEM) configuration can be seen in Figure 1g), in the thin helimagnet Fe 0.5 Co 0.5 Ge with a chirallattice structure (Figure 2a).Note that the orientation of bimeron textures in Figure 1f,g is rotated by 90°as compared to that depicted in Figure 1e.We have found that the formation of these multiple topological states can be controlled by adjusting the sample thickness, external magnetic field, and electric current.Additionally, using Lorentz TEM, we have observed reversible transformations between bimerons and skyrmions under a tunable magnetic field.Furthermore, we demonstrate that the application of electric current induces the individual bimerons into bimeron assemblies, which further undergo a transformation into a close-packed skyrmion lattice.The experimental results can be reproduced by micromagnetic simulations.

Multiple States Inherent in the Thin Magnet Fe 0.5 Co 0.5 Ge
With the magnetic properties, as shown in the magnetization (M) versus temperature (T) and external field (H) curves (Figure S1, Supporting Information), reveal that the Curie temperature (T C ) is ≈190 K, and the ground state is a helical state due to the DMI inherent to the chiral-lattice crystal structure of Fe 0.5 Co 0.5 Ge.This helical texture manifests itself as periodic stripes in defocused Lorentz TEM images, with a wavenumber determined by the exchange interaction constant A and DMI constant D. [4,6] However, when the sample thickness is decreased to 20 nm, which is much smaller than the pitch of screws, the screw texture is unexpectedly replaced by an in-plane FM structure (Figure 2b) in the thin Fe 0.5 Co 0.5 Ge.This change implies the existence of a dominant inplane magnetic shape anisotropy, which arises from the demagnetization effect and geometrically affects the magnetic structure.In the real-space Lorentz TEM image (Figure 2b), the dark and bright line contrasts, indicated by orange and black thick arrows, represent the DWs with opposite directions of spin twists, [8] which alternatively appear between the FM domains with opposite in-plane magnetizations (indicated by blue and red arrows). [7]pontaneous dark circular domain and bright elliptic domain (Figure 2c) emerge when the sample thickness is increased up to 40 nm while keeping the condition of constant temperature (T = 100 K).Such vortex-like domains can be considered as a magnetic meron with down-core magnetizations and a CW helicity (the type I meron in Figure 1c) and antimeron with up-core magnetizations and a counterclockwise (CCW) helicity (the type II antimeron in Figure 1d) at zero magnetic field.These identifications are based on the contrasts observed in the corresponding Lorentz TEM images, although determining the direction of core magnetizations at zero field and zero tilt is challenging. [8]To clarify the topological nature of these vortex-like domains, their in-plane magnetic inductions were mapped (see Experimental Section for details), as depicted in Figure 2d,e.Evidently, these vortices exhibit opposite helicities: CW for the meron (the dark circular domain in Figure 2c), while CCW for the antimeron (the bright elliptic domain in Figure 2c).Notably, their core magnetizations should be opposite at zero magnetic field, which was confirmed through an in situ Lorentz TEM movie (see Movie S1, Supporting Information) with normal fields applied along the − zaxis.In this movie, the meron with down-core magnetizations (the dark circular domain exhibiting a magnetization map, as shown in Figure 2d) becomes a field-polarized structure, while the antimeron with up-core magnetizations (the bright elliptic domain with magnetization textures, as shown in Figure 2e) potentially transforms into a skyrmion (the bright circular domain) under a field of −55 mT.
We further clarify the direction of core magnetizations in meron and antimeron and hence unveil their topological characteristics by using an advanced tomographic Lorentz TEM [15] (see details in the Experimental Section).This 3D magnetic imaging involves the procedure of systematically tilting the sample; a portion of the resulting tilted field maps is illustrated in Figure S2b-e (Supporting Information).Figure 2f represents the 3D vector field map for the vortex that reveals a vertical cone structure with down-core magnetizations (dark colors in Figure 2f).In this configuration, the magnetizations within the bulk swirl along the z-axis with a CW helicity and align in the in-plane at the top surface.Thus, this vortex is associated with a topological charge N = − 1 2 , indicating a well-defined meron texture.The details for 3D magnetic imaging protocols are described in the Experimental Section.Furthermore, the bright elliptic domain in the Lorentz TEM micrograph shown in Figure 2c plausibly represents the antimeron textures, which have been confirmed by 3D vector-field maps as shown in Figure S3 (Supporting Information): a type I antimeron, depicted in Figure 1d, with the upward magnetization (indicated by blue arrows in Figure S3h, Supporting Information) in the core; the magnetizations within the bulk swirling along the z-axis with a CCW helicity (see Figure S3g, Supporting Information) and aligning in the in-plane at the top surface.This evidences the bright cone-like domain carrying a topological charge N = 1 2 .When the sample thickness is further increased to 60 nm, bimerons are detected at zero magnetic field.Figure 2g shows spontaneous bimerons observed in an overfocused Lorentz TEM image at zero field, and Figure 2h,i presents the B-field maps of two bimerons indicated by dashed white lines in Figure 2g.The B-field maps are derived from the underfocused and overfocused Lorentz TEM images. [27]Additional details can be found in the Experimental Section and Figure S2f-i (Supporting Information).Compared to the simulated magnetization textures (Figure 1f) and the corresponding Lorentz TEM configuration (Figure 1g) for a bimeron, the observed bimerons here are bundles of merons with reasonably down-core magnetization (vortices, appearing as dark dot contrast in the overfocused Lorentz TEM image) and merons with up-core magnetizations (antivortices, appearing as bright crescent-like lines in the Lorentz TEM image).This configuration of the bimeron gives its total topological charge N = −1, as schematically depicted in Figure 1e.
By systematically investigating the magnetic configurations in the Fe 0.5 Co 0.5 Ge samples by changing their thicknesses t, the multiple state diagrams have been established (Figure S4a, Supporting Information).The in-plane FM state, characterized by an in-plane micrometer-sized domain structure, appears in the thin sample with a thickness of less than 20 nm under zero magnetic field (Figure 2b).A helical structure with periodic stripes (Figure S4b, Supporting Information) is observed under zero field, and isolated skyrmions (Figure S4c, Supporting Information) appear when a 90 mT field is applied perpendicularly to the sample plate at low temperatures, such as 100 K, and a stable skyrmion lattice (Figure S4d, Supporting Information) forms under a 15-mT field near the T C in relatively thick samples with thickness above 100 nm.
The above results indicate that in Fe 0.5 Co 0.5 Ge, under zero magnetic field, the helical state (H) changes into an in-plane FM state mixed with (anti)merons and bimerons when the sample thickness becomes sufficiently smaller than the wavelength of the helical structure (≈120 nm).The emergence of an in-plane FM domain structure and bimerons in thin Fe 0.5 Co 0.5 Ge magnets can be attributed to the in-plane magnetic shape anisotropy induced by the demagnetization effect in thin samples of magnets.Specifically, the formation of both an in-plane FM domain structure and bimerons requires such in-plane magnetic anisotropy. [20]Conversely, achieving a collinear FM structure as well as noncollinear bimeron textures is challenging in bulky helimagnets, wherein the DMI dominates the magnetic textures due to the negligible weak magnetic shape anisotropy.However, the presence of in-plane shape anisotropy destabilizes the helical state (Figure S2j-m, Supporting Information).When the thickness approaches a critical value, the in-plane shape anisotropy begins to dominate over the DMI, resulting in the relative stability of bimerons and an in-plane FM structure.Otherwise, if the sample thickness is comparable to the wavelength of the helical structure, the robust helical state originating from the DMI would prevail.Moreover, a triangular lattice of deformed skyrmions (Figure S5c, Supporting Information) is observed at 160 K below T C , when a normal field ≈ 40 mT is applied to the thick samples.In this case, the ground state exhibits a helical structure (Figure S5a, Supporting Information ).On the other hand, the chiral soliton state [28] is observed under a relatively weak normal field of 30 mT, characterized by the periodically alternating bright/dark stripe domains (Figure S5b, Supporting Information) with relatively larger wavelength than that of the initial helical structure, and a field-polarized state accompanied by sparsely-populated skyrmions (Figure S5d, Supporting Information) are detected at a relatively larger field, such as 60 mT.Magnetization textures of isolated skyrmions (Figure S5d, Supporting Information) and skyrmion lattice (Figure S5c, Supporting Information) have been clarified by their vector-field maps, as shown in Figure S5e,f (Supporting Information).

On-Demand Topological-State Transformation between Bimerons and Skyrmions
Because of the presence of abundant topological states in the thin Fe 0.5 Co 0.5 Ge, transformations among various topological states are expected to occur under external stimuli, such as magnetic field and electric current excitations.Essentially, the on-demand topological state control requires the fine-tuning of both extrinsic and intrinsic parameters.Figure 3 represents magnetic skyrmions, bimerons, and their transformations at 100 K in an 80-nm-thick (1-10) Fe 0.5 Co 0.5 Ge plate.In Figure 3a, a single skyrmion is created in the background of the conical state with a downward-directed wavevector, under a normal magnetic field of −50 mT.It should be noted that the skyrmion appears as a black circular domain in an underfocused Lorentz TEM image.This observation indicates that both the core magnetization and helicity of the skyrmion are reversed compared to skyrmions under fields applied along the +z-axis.This distinction can be confirmed by referring to the corresponding magnetic induction map, as shown in the inset of Figure 3a and Figure S6a (Supporting Information) for the magnified one.Reducing the field strength leads to a transformation of the skyrmion into a bimeron, that is, a bundle of dark circular and bright crescentlike domains in Figure 3b, where the inset shows the magnetic induction map magnified in Figure S6b (Supporting Information).As the field strength is further reduced to −10 mT (Figure 3c), the bimeron undergoes significant elongation and subsequently merges into in-plane helices when the field strength is nearly zero (Figure 3d).Flipping of the direction (sign) of the magnetic field and subsequent increase of its strength result in the inverse transformation of the bimeron (Figure 3e; Figure S6c, Supporting Information) to skyrmion (Figure 3h), via merons and antimerons, as shown in Figure 3f,g.The skyrmion that appears after the transformation is depicted as a bright circular domain in an underfocused Lorentz TEM image, as shown in Figure 3h, and the related magnetic induction map is given in the inset and Figure S6d (Supporting Information) for its magnified image.Note here that the contrast reversals of the skyrmion in Lorentz TEM micrographs (Figure 3a-h) are caused by reversing the external magnetic fields, as mentioned above.The mutual transformations between skyrmions and bimerons, as demonstrated above, indicate that different topological spin textures can be obtained on demand by tuning the external field.Indeed, these experimental observations are further supported by micromagnetic simulations, as shown in Figure 3i,n (see Experimental Section for details).The reversible transformation between skyrmion and bimeron, indicated respectively by a black dashed rectangle (Figure 3i,n) and a yellow dashed rectangle (Figure 3j,m), can be achieved by decreasing and increasing the external out-ofplane magnetic field (Such dynamical transformations can be discerned in Movie S2, Supporting Information).Interestingly, our micromagnetic simulations reveal that the applied out-of-plane magnetic field drives a dimensional topological-state transformation between 2D cylindrical skyrmions (Figure S7, Supporting Information) and 3D bimeron strings (Figure S8, Supporting Information), with the assistance of the magnetic shape anisotropy, that is, the demagnetization effect.The reason is that the in-plane magnetic shape anisotropy, along with DMI, favors the formation of bimeron in a planarly magnetized background, while the outof-plane magnetic field and DMI favor the formation of skyrmion in a perpendicularly magnetized background.

Transformations of Topological Spin Textures via Current-Pulse Stimulations
To investigate the effects of current stimulations on the topological spin textures in Fe 0.5 Co 0.5 Ge, in situ Lorentz TEM was performed.First, a microdevice composed of a thin Fe 0.5 Co 0.5 Ge (Figure S9a, Supporting Information) with a thickness gradient (Figure S9b, Supporting Information) was prepared using a dual-beam system Helios 5UX (see the Experimental Section for details).The device enabled us to systematically explore the occurrence of topological spin textures as the demagnetization field varies.The thickness gradient was introduced perpendicular to the direction of the current flow, resulting in a uniform current density in the horizontal direction.The verification of various magnetization textures in the fabricated Fe 0.5 Co 0.5 Ge was conducted, as demonstrated in the magnetic state diagram (Figure S4a, Supporting Information).The first intriguing dynamical phenomenon observed is the transformation of individual bimerons into bimeron assemblies through a single-pulse stimulation (Figure 4a,d, Movie S3, Supporting Information).
Here the current amplitude is 7 mA (1 mA corresponding to 8 × 10 8 A m −2 ), and the pulse width is 10 μs. Figure 4a,b depicts the Lorentz TEM image and the corresponding magnetic induction map of the individual bimerons, which were formed at 120 K by applying a normal magnetic field of 15 mT prior to the current-pulse stimulation.Following the pulse stimulation, these individual bimerons assemble into bimeron assemblies, as illustrated in Figure 4c,d (Larger-area views of magnetic induction maps are presented in Figure 4e,f, respectively).Such current-induced proliferations of bimerons can be reproducible by micromagnetic simulations in a qualitative manner, as shown in Movie S4 (Supporting Information).The second intriguing phenomenon is observed when the current-pulse amplitude is increased while maintaining a constant pulse width, that  and c,d) in-plane helices in a decreasing of the magnitude of normal fields applied along the −z direction, and the reversible transformation from e) bimerons to h) skyrmions via f,g) (anti)merons in an increasing of the magnitude of normal field applied along the +z direction.Insets show magnetic induction maps for the squared areas.Both Lorentz TEM images shown in Figure 3 were obtained in the underfocused mode.i-n) Micromagnetic simulations of the field-induced transformation between skyrmions and bimeron strings in an 80-nm-thick Fe 0.5 Co 0.5 Ge plate with a square-shaped sample geometry of 1000 × 1000 nm 2 .The snapshots in (i-n) showing the state transformation between skyrmions and bimerons at selected normal magnetic fields during the decreasing and increasing runs.The blue-white-red color scale represents the out-of-plane magnetization component, as indicated by a color bar, while the in-plane magnetization component is indicated by dark arrows.The out-of-plane magnetic field first decreases from 400 to 100 mT, and then reaches to zero field, which is maintained for a long period, and then increases from 0 to 400 mT.The area surrounded by dark dashed rectangular marks skyrmions (i,n) and the area surrounded by yellow dashed rectangular outlines bimeron strings (j,m) whose 3D spin textures are represented in Figure S8 (Supporting Information).
is the transformation of bimerons into close-packed skyrmions arranged in a triangular lattice form (Figure 4g).Consequently, these outcomes demonstrate the current-induced metastability of topological spin textures, causing the proliferation of bimerons and their subsequent transformation into a skyrmion lattice due to the attractive force between topological spin textures in a fieldpolarized background. [21]

Conclusion
In summary, we have successfully demonstrated the ability to create desired topological states, such as pairs of merons and antimerons, vortex-antivortex bundles (bimerons), and skyrmions, as well as the mutual switching among these states within the helimagnet Fe 0.5 Co 0.5 Ge.This was achieved by adjusting the mag-netic shape anisotropy through variations in sample thickness, applying an external magnetic field, and/or utilizing current pulses.Furthermore, we have found a method to assemble individual bimerons into bimeron assemblies with the use of current stimulations.These significant findings provide a fundamental basis for designing topological states and enabling the emergence of respective unique phenomena within the identical material, tailored to specific cases.

Experimental Section
Sample Synthesis: Polycrystals of Fe 0.5 Co 0.5 Ge were synthesized using a high-pressure synthesis technique.First, a homogenously stoichiometric mixture of Fe, Co, and Ge was prepared by arc melting in an argon atmosphere; subsequently, the mixed materials were poured into a cubic anvil and heat-treated at 1073 K under a high pressure of 5.0 GPa for 1 h.Powder X-ray diffraction analyses confirmed that the crystal structure of single-phase Fe 0.5 Co 0.5 Ge was cubic with a P2 1 3 symmetry.
Preparation of Thin Plates and Microdevices: The plates of Fe 0.5 Co 0.5 Ge with different thicknesses were obtained by thinning bulky samples using a dual-beam system (Helios 5UX, Thermal Fisher Scientific), which provided focused ion and scanning electron beams for fabricating and imaging the samples, respectively.The thin-sample extraction process was conducted at 30 kV using a Ga-ion beam.The thin plates were then gently polished using a Ga-ion beam at 1 kV to remove the damaged surface layer.To allow the current pulse to flow through the thin sample, an easy-lift probe was used for transferring the thin plate onto a homemade Si membrane with two electrical terminals.Next, Pt was deposited to connect the plate on the Si membrane to the electric terminals.
Tomographic Lorentz TEM: The Lorentz force which was perpendicular to both the beam direction and magnetic moment in the magnetic sample, deflects the electron beam, thereby leading to a convergent or divergent beam at the imaging plane.Consequently, bright or dark contrasts corresponding to a magnetic structure in the sample could be discerned in the defocused (underfocused or overfocused) Lorentz TEM images.The B field (magnetic induction) map in the sample could be extracted from the intensity changes in a series of defocused Lorentz TEM images, which were obtained by tuning the defocus distance. [27]Tomographic Lorentz TEM was performed using a transmission electron microscope (JEM-2800, JEOL) in the field-free mode.The dual-axis tilt series of the Lorentz TEM images were acquired with a sample-plate tilt ranging from −50°to +50°i n increments of 2°.Subsequently, the tilt series of the magnetic induc-tions B x and B y derived from the corresponding Lorentz TEM images was obtained according to the transport-of-intensity equation, [27] and B z was calculated by assuming The 3D vector field map was constructed using homemade scripts based on digital micrography (Gatan) and TomoPy and visualized using ParaView and MuView.The observed 3D vector-field distributions in a meron and an antimerion are shown in Figure 2f and Figure S3 (Supporting Information), respectively.The former was coded by MuView while the latter was viewed by ParaView.
In Situ Lorentz TEM under Tunable Temperature, Magnetic Field, and Current Pulse: The Lorentz TEM micrographs were acquired with transmission electron microscopes (JEM-2800 (JEOL) and Talos F200X (Thermo Fisher Scientific), equipped with a liquid nitrogen holder (Gatan 636) and an electric feedthrough holder (HC3500, Gatan)) allowing cryogenic Lorentz TEM imaging under external magnetic fields and electric currents.By controlling the lens current of the objective lens in the microscope, a tunable external magnetic field was generated and applied to the TEM sample.The current pulses flowing through the sample were supplied using a function generator (Tektronix).A current of 1 mA corresponded to a current density of 8 × 10 8 A m −2 in the present experimental setup.

Figure 1 .
Figure 1.Schematics of magnetization textures (a-e) and simulated bimeron texture (f) and corresponding Lorentz transmission TEM image (g) in a chiral-lattice magnet Fe 0.5 Co 0.5 Ge. a) Domain wall.Colors indicated by a color bar show the magnitude of in-plane magnetizations.b) Magnetic skyrmion.c,d) (Anti)merons with a vorticity w = ±1.The N = ±1/2 indicates the topological charge for meron and antimeron, respectively.e) A schematic illustration showing a bimeron as a bundle of two merons with opposite signs of vorticity.f,g) Simulated magnetization textures of f) a bimeron and g) the corresponding Lorentz TEM configuration.

Figure 2 .
Figure 2. Various spin textures emerging spontaneously in thin Fe 0.5 Co 0.5 Ge samples were observed by the cryogenic Lorentz TEM.a) Schematic of the cubic structure of Fe 0.5 Co 0.5 Ge with a space symmetry of P2 1 3. b) An overfocused Lorentz TEM micrograph of DWs with in-plane-oriented magnetizations (indicated by dark and orange arrows) that appear between FM domains with antiparallel magnetizations (indicated by red and blue arrows) observed in a 20-nm-thick plate-shaped Fe 0.5 Co 0.5 Ge.Alternate dark and bright DW lines indicate a staggered alignment of DW helicities.c-e) A c) overfocusedLorentz TEM micrograph of a meron (dark circular domain on the left side) and an antimeron (bright elliptic domain on the right side) observed in a 40-nm-thick Fe 0.5 Co 0.5 Ge; the helicity is CW for the meron, and CCW for the antimeron, as indicated by the corresponding in-plane field (magnetic induction) maps (d,e).f) 3D vector field map for the meron texture visualized using tomographic Lorentz TEM.The colored arrows show the vector field at every point.g-i) Bimerons observed in a 60-nm-thick Fe 0.5 Co 0.5 Ge plate under a zero field and at 100 K: g) overfocused Lorentz TEM image, and (h,i) the corresponding magnetic induction maps for the squared bimerons in (g).

Figure 3 .
Figure 3.On-demand topological states by tuning the external magnetic field in an 80-nm-thick Fe 0.5 Co 0.5 Ge sample.a-h) Normal magnetic field drives transformations between skyrmions and bimerons: the transformation from a) a skyrmion to b) a bimeron and c,d) in-plane helices in a decreasing of the magnitude of normal fields applied along the −z direction, and the reversible transformation from e) bimerons to h) skyrmions via f,g) (anti)merons in an increasing of the magnitude of normal field applied along the +z direction.Insets show magnetic induction maps for the squared areas.Both Lorentz TEM images shown in Figure3were obtained in the underfocused mode.i-n) Micromagnetic simulations of the field-induced transformation between skyrmions and bimeron strings in an 80-nm-thick Fe 0.5 Co 0.5 Ge plate with a square-shaped sample geometry of 1000 × 1000 nm 2 .The snapshots in (i-n) showing the state transformation between skyrmions and bimerons at selected normal magnetic fields during the decreasing and increasing runs.The blue-white-red color scale represents the out-of-plane magnetization component, as indicated by a color bar, while the in-plane magnetization component is indicated by dark arrows.The out-of-plane magnetic field first decreases from 400 to 100 mT, and then reaches to zero field, which is maintained for a long period, and then increases from 0 to 400 mT.The area surrounded by dark dashed rectangular marks skyrmions (i,n) and the area surrounded by yellow dashed rectangular outlines bimeron strings (j,m) whose 3D spin textures are represented in FigureS8(Supporting Information).

Figure 4 .
Figure 4. Transformation of topological spin textures with electric-current stimulations.a,b) The bimerons observed under a 15-mT normal field using Lorentz TEM: a) an overfocused image and b) the corresponding magnetic induction map.c,d) Bimeron assemblies after a current-pulse excitation (pulse width, 10 μs; pulse height, 7 mA): c) an overfocused Lorentz TEM image and d) the corresponding field map.e-g) Various states of e) individual bimerons without current flow, f) bimeron and g) a skyrmion lattice were observed after current-pulse stimulations by varying the amplitude from f) 7 mA to g) 12 mA, respectively, while maintaining the pulse interval at 10 μs.The current pulse flows in the x-direction.