Field-free topological behavior in the magnetic domain wall of ferrimagnetic GdFeCo

Exploring and controlling topological textures such as merons and skyrmions has attracted enormous interests from the perspective of fundamental research and spintronic applications. It has been predicted theoretically and proved experimentally that the lattice form of topological meron-skyrmion transformation can be realized with the requirement of external magnetic fields in chiral ferromagnets. However, such topological transition behavior has yet to be verified in other materials. Here, we report real-space observation of magnetic topology transformation between meron pairs and skyrmions in the localized domain wall of ferrimagnetic GdFeCo films without the need of magnetic fields. The topological transformation in the domain wall of ferrimagnet is introduced by temperature-induced spin reorientation transition (SRT) and the underlying mechanism is revealed by micromagnetic simulations. The convenient electric-controlling topology transformation and driving motion along the confined domain wall is further anticipated, which will enable advanced application in magnetic devices.

T opological magnetic textures including (anti)meron 1-3 , (anti)skyrmions 4-10 , biskyrmions 6,11 , and bobbers 12 in the form of vortex 13,14 spin configurations represent a promising direction for fundamental research and future spintronics. Their nanometer size and electric-current detection/manipulation/generation behavior endow them as competitive candidates for encoding the information bits with dense integration and energy efficiency in the next generation spintronic devices. By exploring and tuning the dedicated interplay among spin-orbit coupling and the competition of magnetic interactions, the materials hosting these topologically nontrivial magnetic textures have been extended from initial chiral magnets with Dzyaloshinskii-Moriya interaction (DMI) to diversified ferromagnets with different stabilization mechanisms [15][16][17] . Currently, the transverse motion of skyrmions in response to external electric current drive in ferromagnets, known as skyrmion Hall effect 9,18-20 is regarded as a hurdle in promoting skyrmion applications in racetrack memories, where it is preferable for skyrmions to move along the racetrack. Theoretically, compensated antiferromagnets with two equivalent but antiparallel magnetic subsystems can perfectly cancel the transverse motion and allow skyrmions to move along the electric current direction [21][22][23] . However, it is hard to experimentally visualize and study intrinsic antiferromagnetic (AFM) skyrmions by using the standard imaging methods because of their net-zero magnetization. Therefore, it is of great importance to figure out distinctive features and properties of the topological textures in ferrimagnetic materials with partially compensated magnetic moments 24,25 .
Due to the compatibility with standard spintronic devices, magnetic thin films or multilayers present good application possibilities, where magnetic bubbles, skyrmions, vortices, and together with magnetic domain walls can be easily tuned by balancing the ferromagnetic exchange, spin anisotropy, and dipolar energy through layer thickness and deposition conditions [26][27][28] . Recently the topologically nontrivial meron 29 and skyrmions [30][31][32][33] localized in magnetic domain walls have attracted considerable interest. The intrinsic canted spin configuration and the confining potential in the domain wall might advance the specialties of these magnetic textures and restrict them to move only within the domain wall. In this way, the detrimental skyrmion Hall effect can be avoided. The amorphous ferrimagnetic GdFeCo films 34-36 regain the focus in skyrmion generation and manipulation due to the antiferromagnetically coupled sublattices 37 and possible DMI 35 . In this work, we demonstrate the topological transformation between meron pairs and skyrmions in the domain wall via the temperature-induced spin reorientation transition (SRT) and their electric control capability, which does not require any external magnetic field unlike that in chiral lattices 1,2,38 .

Results
The temperature-induced Meron-Skyrmion transformation in the domain wall without external magnetic fields. The ferrimagnetic amorphous Gd 15+x (Fe 94 Co 6 ) 85−x (x = 0.7, 0.4, 0.2, 0) films with thickness about 40 nm are prepared with different REto-TM ratios in composition to tune its perpendicular magnetic anisotropy (PMA) (Supplementary Figs. 1 and 2). The SRT temperature increases with x in Gd 15+x (Fe 94 Co 6 ) 85−x and the topological transformation can be adjusted to near room temperature for convenient applications (Supplementary Figs. 3 and 4). Figure 1a shows the schematic layer structure with different orientations of TM and RE magnetic moments. The SRT is introduced by the magnetic competition between PMA and shape anisotropy 39 while changing the temperature. The SRT manifests abrupt spin anisotropy change near 290 K as shown in the reduced remanence magnetization (Fig. 1b), which is extracted from the M-H curve of Gd 15+x (Fe 94 Co 6 ) 85−x (x = 0.2). It has been known that the topological nature of the magnetic texture is intimately related to the spin anisotropy with (anti)merons [1][2][3] usually in the magnets with easy plane anisotropy and skyrmions/ bubbles in magnets with easy axis anisotropy 8,17,18 . The internal magnetic structure evolution inside the domain wall due to the SRT is unraveled by in-situ L-TEM images ( Fig. 1d-h). The inplane magnetization distribution on both sides of the selected domain wall is reconstructed from the transport-of-intensity equation (TIE) analysis (details in the "Methods" section) and is displayed in Fig. 1c and i, respectively. Here, the white arrows aligning antiparallel on the sides of the domain wall demonstrate the local opposite in-plane magnetization component distribution. Since TIE analysis are performed at the same condition, the smaller arrows in Fig. 1i than those in Fig. 1c indicates the inplane magnetization component tends to point to out-of-plane, which corresponds well with the SRT (Fig. 1b). The significant feature along the domain wall is the disappearance of the white contrast while increasing the temperature.
We then focus on the dedicated spin textures in the domain wall in Fig. 2. The magnetic textures with dark/white contrast at the temperature of 243 K correspond to meron pairs (Fig. 2a). With the diminishing of the white contrast in the domain wall, the well-separated dark dot domains at 300 K are identified as skyrmions (Fig. 2c). It should be noted that the domain walls with opposite contrast have the equivalent topological transformation as shown in Supplementary Fig. 3. The size of the topological textures is about 200 nm, which is comparable to the size of the domain wall. Pictorially, a meron can be regarded as a half skyrmion (Schematics in Fig. 2j). A meron has two internal degrees of freedom 3,40 : the polarity, p, which is defined as the direction of the spins at the core of the meron, and the standard vorticity, w. The topological charge of a meron is given by N = pw/2, where p = +1 for up and p = −1 for the down polarity of the cores and w = ±1. To determine the topology of the spin texture in Fig. 2a, it is important to identify the spin direction at the core of these magnetic textures, which is unfortunately not accessible by L-TEM. The core polarities of meron pairs have four possibilities which are clarified into two categories (up/up or down/down, up/down, or down/up). If the core polarities of meron pairs are the same (up/up or down/down), their core spin polarization simultaneously tends to either parallel or antiparallel to the out-of-plane spin component in the wall when the out-ofplane easy-axis anisotropy increases across the SRT. That means the pairs will stay or disappear simultaneously when increasing the temperature in contrast to the disappearance of white contrast and the preservation of black contrast in our experiment. Combining with the fact that the final state ends up with magnetic nontrivial textures in our experiment, we propose the opposite core polarity for these spin textures and the same topological charge N = −1/2 (meron pair) or N = 1/2 (antimeron pair) 3,40,41 . Here, we only demonstrate the spin configuration of the meron pair to present an equal possibility of antimeron pair. When the spin anisotropy is flipped from in-plane to out-ofplane near the SRT, the meron with core polarity antiparallel to the out-of-plane spins remain stable and evolve into skyrmions with topological charge −1, which is well corroborated in the following simulations ( Fig. 2e-h). We confirm the reversible transformation between meron pairs and skyrmions in the domain wall while changing the temperature in several heating/ cooling cycles. Different from the reported Néel-type skyrmions in sandwiched GdFeCo thin film (5 nm) with interfacial DMI 42 , the skyrmions here are identified as Bloch-type (Fig. 2c)   Simulations for the topological transformation in the domain wall. The numerical simulations are conducted by using the object-oriented micromagnetic framework (OOMMF) software. The in-plane easy axis anisotropy at 243 K can be inferred from the ripple domain and the elongated meron or skyrmion configurations, where the region with spins aligning along the easy axis direction is longer compared to that perpendicular to the easy axis. Also note that domain walls become unstable without the in-plane easy axis anisotropy, because of the in-plane spin rotation symmetry. Across the SRT, an extra out-of-plane easyaxis anisotropy develops and increases with temperature. The above consideration motivates us to introduce the following spin anisotropies H A ¼ ÀA y S 2 y À A z S 2 z . The spin anisotropy in H A supports four degenerate domains which we denote by (±, ±). The first/second sign represents the y/z component of the spin in the domain. Domain walls can be generated between any pair of these four degenerate states. The antiparallel in-plane magnetization component near each side of the domain wall (Fig. 1c)  These periodic Bloch lines generated in the in-plane Bloch domain walls are different from those in a perpendicular bubble or stripe domains [43][44][45][46] . The skyrmion number (N s ) integrated over the x-direction and the top half part along y-direction of the simulation images in Fig. 2e-h (marked out by the dotted rectangle) is defined as 7 where n is the direction vector of magnetization. The N s of a meron is −1/2 despite that the spins away from the meron core are parallel to the domain wall. When the out-of-plane easy axis anisotropy increases across the SRT, the meron with core spin polarization in the same direction (red +m z ) as the out-of-plane spin component becomes unstable and shrinks, because there is no energy barrier separating this type of meron and the fully polarized state. At a stronger out-of-plane easy-axis anisotropy, this type of meron disappears completely. For the core spin polarization in the opposite direction (blue −m z ) in the wall, the meron remains stable and evolves into a full skyrmion through continuous growth of the topological charge from −1/2 to −1 (Fig. 2e-h), as illustrated by schematics (Fig. 2j-l). The simulated images with decreasing M s and increasing K u values ( Fig. 2e-h) and the corresponding domain wall contrast simulation ( Fig. 2d and i) agree well with the experimental domain wall evolution of Gd 15+x (Fe 94 Co 6 ) 85−x (x = 0.2) at different temperatures (Fig. 2b). For other possibilities with both opposite in-plane and out-of-plane magnetization moments on each side of the domain wall ( Supplementary  Fig. 11), the spin configuration on the edge of a continuous domain wall presents significant differences. Accordingly, the simulated domain wall contrast does not agree with the contrast evolution in L-TEM images (Fig. 1).
The simulation parameters are based on the experimental results of Gd 15+x (Fe 94 Co 6 ) 85−x (x = 0.2) (Fig. 3a). The overall domain wall structures in the K u −M s phase diagram are summarized in Fig. 3b with the data points at different temperatures marked out as red rhombic points. Considering the effects of the added uniaxial in-plane anisotropy in our simulation, the out-of-plane anisotropy is slightly larger than in experiments. The transformation between meron and skyrmions is expected near Q = K u /2πM s 2 = 1 due to the easily tuned magnetization moments in the canted state, which agrees well with the skyrmion generation condition reported in the previous studies [4][5][6][7][8][9] . Merons and skyrmions exist in a proper range of K u and M s with a narrow transition region between them, corresponding to the SRT in our experiments. When K u is increased, the skyrmion number gradually changes from meron with N s = − 0.5 to skyrmion with N s = −1 and then abruptly jump to stripe domain state with N s = 0. Figure 3c shows the detailed simulated magnetization states for different magnetic parameters. To focus on the evolution of the meron pair located in the domain wall, we only present the central part of these simulation images and leave the complete parts listed in Supplementary Note 5. The highlighted images correspond to the experimental transformation at different temperatures. The Néel-type cross tie domain wall remains in the bottom of the phase diagram (Fig. 3b) where the in-plane anisotropy is dominant. It should be noted that no DMI and external magnetic fields are added in the simulations. The intrinsic noncollinear spin textures in the confined domain wall and the spin anisotropy change due to SRT are responsible for the topology transformation between meron pairs and skyrmions, which could be understood better by domain wall topology theory 30,31 .
Electric control of domain wall topology without magnetic field. The significant transverse deflection of electric-driven skyrmions even within a patterned narrow path 19 is known as the skyrmion Hall effect in a ferromagnet. The ferrimagnetic materials might offer platforms to minimize the skyrmion Hall effect due to the partially compensated magnetization 35,42,46 . Because of the confining effects for domain wall skyrmions, the only movement along the wall is allowed, thereby, avoiding the detrimental skyrmion Hall effect. Theoretically, the skyrmion motion guided by the domain wall is verified in the simulation (Supplementary Video 1). In experiments, pinning of skyrmions due to the defects in materials can be significant, which requires a more systematic study in preferable nano-fabricated films. Here, the preliminary experiments with electric control behavior in the uniform large sample have promisingly shown that the electric current not only can initiate the SRT and the transformation from merons to skyrmions (Fig. 4) but also can induce the skyrmion motion in the domain wall ( Fig. 5 and Supplementary Video 2). The less significant skyrmion movements along the domain wall in experiments than simulations may be attributed to the disorder and pinning effects which are not included in our simulation. It has been verified that electric manipulation can increase the perpendicular anisotropy 47 , switch the magnetization, drive skyrmion movements via spin-transfer 5 or spin-orbit torque (SOT) 6 . Here, we leave the underlying mechanism of the current induced SRT and skyrmion motion in nano-fabricated films for future study.

Discussion
We have observed the direct topological transformation between meron pair and skyrmion in the domain wall of amorphous ferrimagnetic GdFeCo, which is enabled by spin anisotropy change across the SRT. The critical role of domain walls in generating topological textures and transformation without the requirement of external magnetic fields is revealed through experiments and micromagnetic simulation and agrees with the recently proposed theory about domain wall skyrmion [30][31][32][33] . Our results, therefore, point to a promising direction of controlling the spin topology by simply varying temperatures or electric current at zero field. The guided motion of skyrmions inside the domain wall and the contribution of partially compensated magnetization in the ferrimagnetic film will open great opportunities for a deep understanding of topological Hall effects and their application in electronics, spintronics storage. Given that domain walls are ubiquitous magnetic structures with potential fast DW dynamics, our findings provide critical insights in discovering, yet hitherto unknown, topological spin textures and magnetic phase transition in the domain wall.  L-TEM observation. The magnetic domain structures were studied by using a JEOL-dedicated Lorentz TEM (JEOL2100F) equipped with a liquid-nitrogen or high-temperature TEM holder for temperature manipulation. No magnetic field is applied during the L-TEM observation due to the special design of the objective lens. There is about a 10 K temperature difference between L-TEM observation and the magnetic properties measurement in Gd 15+x (Fe 94 Co 6 ) 85−x (x = 0.7, 0.4) because the sample cannot be cooled first before heating up by using a hightemperature TEM holder. The magnetic domain wall contrast is imaged under the convergent or divergent electron beam due to the interaction of the electron beam with the in-plane magnetization. The under-and over-focal images were recorded by a charge-coupled device (CCD) camera to work out phase images and then the quantitative in-plane magnetization component on the basis of the TIE equation using commercial software QPt. The colors and arrows depict the magnitude and orientation of the in-plane magnetization according to the color wheel. The skyrmion manipulation behavior by an electric current is conducted using a double-tilt electrical TEM holder with two electrical conducting blocks at two sides of the TEM sample. The dc current was supplied using a source-measure unit instrument (Keithley 2601B).

Methods
The first equation reveals the relationship between intensity I(x,y,z) and phase Ф(x,y,z). λ is the spectrally weighted mean wavelength of illumination. In our experiment, we put the under-focused and over-focused pictures in software QPt to find the value of ∂Iðx;y;zÞ ∂z to obtain the phase information. Then by using the second equation, the in-plane magnetization components (M n) can be accordingly found. n is the unit vector along the beam direction, M is the magnetization vector and t is the local sample thickness.
Micromagnetic simulation. Micromagnetic simulations are performed using the OOMMF 49 to investigate the dependence of magnetic structures on parameters, such as PMA (K u ) and saturated magnetization (M s ) for a fixed exchange stiffness (A = 7 × 10 −12 J/m). To aim at the magnetization evolution towards energy minimum for the given conditions, the ferrimagnetic sample is simplified as a ferromagnetic system with reduced saturation magnetization and uniform exchange term. The size of the thin plate GdFeCo film for simulation is about 1400 × 500 × 40 nm 3 (the experimental thickness) with periodic boundary conditions in the y-direction and open boundary conditions in the x-direction. According to the simulation, the distance between each Bloch line at steady-state scales around 250 nm based on the experiment parameters ( Supplementary Fig. 7), the y range used in our simulation is set as 500 nm which is enough for the stabilization of one meron pair. The mesh size is 2 × 2 × 5 nm 3 , which is much smaller than the typical exchange length and the skyrmion size, to ensure a balance between numerical accuracy and computational efficiency. In-plane spin anisotropy value of 2 × 10 3 J/m 3 along (100) direction is added to stabilize the domain wall during simulation. We then change the out-ofplane anisotropy and study the evolution of the magnetization configuration. We used an exchange stiffness parameter of about 7 pJ/m to make the domain width wider and simultaneously varied M s , K u to study the domain evolution. The corresponding L-TEM image simulation is carried by the software called micromagnetic analysis to Lorentz TEM simulation (MALTS) 50 .

Data availability
All the data that support the findings of this study are present in the paper and are available from the corresponding author upon reasonable request.

Materials availability
Supplementary materials are available from the corresponding author upon reasonable request.
Received: 29 January 2021; Accepted: 9 September 2021; Fig. 5 The skyrmion motion in the domain wall driven by an electric current at room temperature in Gd 15+x (Fe 94 Co 6 ) 85−x (x = 0.7). L-TEM images showing the skyrmion motion after turning on the electric current of 32 mA for the different time periods, respectively. The blue circle for the fixed defect is marked out to identify the relative movement of the skyrmions on the domain wall. The relative movement of the three skyrmions is demonstrated with different colors, respectively.