The Topological Hall Effect in CoGd Films Controlled by Hydrogen Migration under Gate Voltage

The topological Hall effect (THE) presents hump signals in the Hall resistance versus magnetic field hysteresis loop, showing promise for future spintronics due to its robust chiral magnetic textures. Here, it is shown that solid‐state protonic gating can control possible topological magnetic structures in CoGd thin films. Injecting H+ leads to sizable hump signals in the film. Magneto‐optical Kerr microscopy shows that induced hump signals in transporting measurements do not scale with magnetization, supporting topological magnetism. Successive hydrogen ion extraction completely erases the effect. Thus, topological magnetism manipulations are reversible, nonvolatile, and effective. Ab inito calculations and effective chiral spin models demonstrate that hydrogen injection remarkably enhances the Dzyaloshinskii–Moriya interaction over fourfold, stabilizing chiral structures contributing to the large THE. These findings reveal the vital role of hydrogen ions in topological magnetism and suggest that amorphous ferrimagnetic CoGd thin films are outstanding platforms for realizing controllable topological spintronics at room temperature.


Introduction
[3][4][5] Due to compensated magnetization, conventional detection struggles to read out information in topological magnetic structures.Alternatively, the topological Hall effect (THE), a chiral magnetism-DOI: 10.1002/aelm.202300752[8][9] Under finite external magnetic field (H), the total Hall resistance (R xy ) can be separated into three parts: R xy = R xy N + R xy A + R xy T .The normal Hall resistance (R xy N ) arises from the Lorentz force acting on transporting charges, proportional to the external field: R xy N = R 0 μ 0 H z , where R 0 is the normal Hall coefficient.The anomalous Hall resistance (R xy A ) can be induced by extrinsic parts, for example, the skewscattering and the side-jump effects in magnet.For a crystal in which the translation symmetry is well-defined, the R xy A has an intrinsic part that is caused by Berry curvature.[18][19][20] In a system with considerable spin-orbital couplings (SOC), the phase of transporting charges is modulated by the orientations of local magnetic moments.So, the chiral magnetization texture can generate real-space Berry curvature, leading to a nonvanishing geometry phase for the transporting states.The whole effects of chiral magnetization texture can be effectively approached by an emergent magnetic field H eff T , yielding extra scattering tunnels called THE. [21,22] For discrete magnetic lattice, H eff T is proportional to the triple product of three neighbored magnetizations, leading to R xy T = k T M 1 × (M 2 × M 3 ).In the continuum limit, R xy T (r) = k T M(r)×(∂M/∂x × ∂M/∂y)/4.For a region with several Skyrmions with the same chirality, the whole R xy T is proportional to the number of Skyrmions.Other chiral magnetic textures, such as the chiral domain walls, can also generate nonzero R xy T , providing the extra Hall responses in the R xy -H hysteretic loops featured by the hump signals near the coercive fieldH C .With the aid of bias-field, field-free R xy T can also be exhibited.Therefore, THE is one of the most promising routes to approach the applications of topological spintronics.
Controlling the THE efficiently, nonvolatilely, and reversibly thus becomes key for logic and memory applications of chiral magnetism.Recent studies on iontronics, the ion migrationinduced modulation of nano-device electronic structures, show potential for nonvolatile, programable devices essential for low-power electronics, neuromorphic computing, etc. [14,[23][24][25][26][27] Using ion migration to modulate room temperature chiral magnetic structures and THE is a promising route for next-generation spintronics. [2]However, combining the emerging fields of iontronics and topological spintronics is challenging due to the scarcity of suitable platforms.Ferrimagnet (FiM) can exhibit long-range magnetic order above room temperature.[40][41][42] Hydrogen gas-induced modulations of FiM THE were also achieved. [43]However, gas-based devices are incompatible with current electronics.Modulable topological FiM devices with all-solid designs are urgently needed for future low-power topological spintronics applications and studies.
In this work, we achieved effective, reversible, nonvolatile modulations of the topological magnetic phase in a FiM Co 61.1 Gd 38.9 thin film using gate voltages (V G s) applied through a solid proton electrolyte.

Hydrogen-Injection-Induced Topological Hall Effect
Figure 1a,b illustrates the structures of the sample and the Hall device for transport measurements.The ferrimagnetic sample is a heterostructure thin film consisting of Pt (5 nm)/Co 61.1 Gd 38.9 (6 nm)/Pt (0.5 nm)/TaN (1 nm).The TaN layer is to protect the underlying layers from oxidation.The Pt layers are to induce the perpendicular magnetic anisotropy (PMA) in the CoGd layer.Pt/CoGd interface can produce substantial DMI, leading to the possibly sturdy THE that are hard to control.Thus, a relatively symmetric sandwich structure Pt(thick)/CoGd/Pt(thin) is employed here.Since the interfacial DMI should be dominated by the interfacial layers between Pt and CoGd, the Pt layers away from the interface are less important for the interfacial-DMI. [44,45]Therefore, the Pt(thick)/CoGd/Pt(thin) stack is expected to produce minor net interfacial-DMI since the contributions from the upper and lower interfaces counteract each other.
The directions are defined as follows.The dc-current (I C ) is applied along the long channel in the x-direction.The magnetic fields (H) are swept in the out-of-plane z-direction, and the Hall voltage (V xy ) is measured along the short channel in the y-direction.A solid proton electrolyte source (blue square in Figure 1b) is placed on the device, simultaneously covering both the long channel and the gate electrodes.Thus, the positive V G can inject H + into the Co 61.1 Gd 38.9 thin film, while negative V G extracts H + .Figure 1c shows the magnetic field-dependent Hall resistance (R xy = V xy /I C ) for devices processed with different V G s at 300 K.The leftmost one in Figure 1c corresponds to the R xy -H loop of the virgin device, displaying an ideal rectangular shape with negligible slopes.Hence, the device displays significant PMA, and the whole R xy is contributed by the anomalous Hall effects in the initial device.Given the fact that the f-shells of Gd ions are localized and exhibit vanishingly small density of states (DOS) on the Fermi level (see Section S4, Supporting Information), the R xy A is dominated by the magnetizations of Co. [12,14,15,46] By checking the temperature-dependent polarity of R xy A -H loops, the compensation temperature (T M ) of the virgin device is determined as T M ≈ 345 K and the ordering temperature is T C > 380 K, both higher than the room temperature (see Section S1, Supporting Information, for more details).
The other four R xy -H loops in Figure 1c display the magnetotransport properties controlled by V G s. To focus on the nonvolatile modulations, the protocol of applying V G s and detecting modulations is as below: first switch on V G (value of V G is marked in Figure 1c), wait for 1.5 min for sufficient reaction.Then, switch off V G and wait for another 1.5 min for the equilibration of possible slow reactions.Afterward, conduct the transporting measurements to obtain R xy -H loops.
sparking intense interests and debates.Using solid-state protonic V G s to trigger large hump signals and completely erase them in a CoGd system, that initially displays no humps, distinguishes our findings and reveals the programable nature of these exotic responses.
To further examine the possible origin of the Hall signals, Figure 2 shows the M z -H loops measured by in situ MOKE in the device at initial states and in the device processed by several V G s. Since the Kerr rotations arise from the Co-sublattice, the hysteresis loops in Figure 2 display the behavior of Co magnetization under the sweeping of the field. [12,15,49]Clearly, all M z -H loops are rectangular without humps, contrasting to the R xy -H loops (Figure 1c) in transporting measurements.Considering the tree parts of which the Hall signals consist, the R xy N is proportional to the field H, contributing to the slope of R xy -H loops; the R xy A approximately scales with magnetizations of Co, contributing to a loop with a rectangular shape similar to the MOKE in Figure 2; the R xy T generated by the extra scattering tunnels in chiral magnetic textures can be the possible sources for the observed hump signals.
Moreover, the center panel in Figure 1c (for the device processed by V G = +1.5 V) displays that the hump signals can establish ahead of the field change sign, even when one accounts for the bias field.(see Section S2, Supporting Information, for more details).The picture in which the hump signals are attributed to an extra small hysteretic loop with reversed polarity is hard to describe the R xy evolution ahead of the field in the hysteresis loops.Nevertheless, THE can indeed occur before the reversion of the external field, since the formation of a chiral magnetic structure is principally independent of the field.Once the chiral magnetic structure possesses lower free energy than homogenous states, the energy barrier can be overcome via, for example, thermal activation.So, the nonzero R xy T can establish ahead the field changes sign, breaking the hysteresis in R xy -H hysteretic loop, in line with the observations in Figure 1c.All these further substantiate the existence of THE in the device.In the following, the hump signals are marked by the R xy T .The dependence of R xy A on temperature and V G aligns with previous studies, [14,15] and can be understood by V G -induced modulations on the T M .The Co 61.1 Gd 38.9 sample presented here exhibits T M ≈ 345 K.At T M , the sample shows minimal R xy A due to enhanced fluctuations of Co magnetization.Therefore, as temperature increases from 280 to 320 K, the device approaches T M and R xy A reduces.Meanwhile, positive V G s inject H + into the sample, lowering T M through H + -induced modulations on colinear exchange couplings. [14,15]Thus, positive (negative) V G s also push the system toward (away from) T M , reducing (enhancing) R xy A .More importantly, the THE sensitively depends on both temperature and the applied V G s (Figure 3a).At 280 K, R xy T increases from zero to its maximum value of 20 mΩ after applying V G = +1.5 V and is erased by the V G = −1.5 V.At 300 K, R xy T increases to 25 mΩ at V G = +1.5 V and vanishes at V G = −1.5 V.At 320 K, R xy T increases to 39 mΩ at V G = +1.5 V and disappears at V G = −1.5 V. Thus, THE can be generated and eliminated via different V G s. Additionally, R xy T gradually grows with increasing temperature.
The temperature effects in R xy T (Figure 3a) can be understood as the result of approaching T M .In more detail, as the system gets close to T M , the magnetizations of Co and Gd are comparable.Both Co and Gd magnetizations have trends to align with the external field.Besides, the anti-ferromagnetic exchange couplings favor the anti-parallelization between Co and Gd magnetizations.These two competing effects can lead to the possible noncolinear magnetic configuration in the two sublattices, [50] which can further help the emergence of noncolinear chiral magnetic texture (with the help of DMI, of course).The temperature-dependent THE displayed here agrees with previous observations in amorphous ferrimagnet CoTb. [47]

Characterizations of the Hydrogen-Migration under Protonic Gate Voltage
Figure 4a shows the migrations of H + under V G , as indicated by secondary ion mass spectroscopy (SIMS).To focus on the RE-TM thin film, the thick solid proton electrolyte source is removed before the SIMS measurements.For the as-prepared sample, hydrogen intensity is very low with a peak value of ≈10 occurring at the alloy surface (purple line Figure 3a).H + in the solid proton electrolyte source can diffuse into the surface region, contributing to the peak signals.Notably, in the sample gated by V G = +1.5 V, the hydrogen intensity increases by one order of magnitude (red line in Figure 3a).The peak value is ≈400 at the surface, with intensity gradually decaying with depth.Thus, the Co 61.1 Gd 38.9 sample with solid proton electrolyte realizes the H + migration, with V G = +1.5 V effectively injecting enormous H + into the system.
Such a large H + intensity from V G = +1.5 V leads to significant modulations of the CoGd electronic states.Figure 4b,c displays the X-ray photoelectron spectroscopy (XPS) of the Pt/CoGd/Pt heterostructures, including the virgin one, the one processed by V G = +1 V for 1.5 min, the one processed by further V G = +1.5 V for 1.5 min, the one processed by further V G = −1 V for 1.5 min and the one processed by further V G = −1.5 V for 1.5 min.At the initial state, the peak positions are Co:2p 3/2 at 777.8 eV (Co 0 metal peak) and Gd:4d 5/2 at 141.5 eV (Gd 0 metal peak).After the applying of positive V G s = +1 and +1.5 V, the valence states of both Co and Gd shift to higher levels (Co:2p 3/2 at 777.9 eV, Gd:4d 5/2 at 141.7 eV for V G = +1 V and Co:2p 3/2 at 778.3 eV, Gd:4d 5/2 at 141.8 eV for V G = +1.5 V), displaying the H + -injection induced modulations on the electronic configurations of alloy.After the modulations by V G s = −1 and −1.5 V, the valence states of both Co and Gd partially recover to the lower levels (Co:2p 3/2 at 778.1 eV, Gd:4d 5/2 at 141.8 eV for V G = −1 V and Co:2p 3/2 777.8 eV, Gd:4d 5/2 at 141.7 eV for V G = −1.5 V) but cannot fully restore the initial states.So, the electronic configurations of the Co 61.1 Gd 38.9 can be controlled by applying the V G s, but the initial states cannot be fully restored by only applying the negative V G s = −1 and −1.5 V for 1.5 min, in line with the irreversible changes in some of the magnetic properties such as the saturated R xy A (Figure 1c).

Theory on the Hydrogen-Migrations-Induced Modulations on Topological Magnetism
To further study the H + -induced modulations of CoGd electronic and magnetic structures, theoretical investigations based on DFT are performed.Previous studies show the C15 Laves phase of Co 2 Gd alloy effectively captures the bulk property of the CoGd sample. [14,15]Hence, a thin film model derived from the C15 Laves used here as displayed in Figure 5a.Several possible H + occupation sites are considered, with the most favored site shown by red balls in Figure 5a (see Figures S2 and S3, Supporting Information, for other possible sites).The free energy cost for H + -injection is ΔG = −0.62 eV, indicating the thermal stability of the H + -inserted Co 2 Gd thin film, consistent with the abundant H + -intensity observed in Figure 4a.To directly see the structure of exchange interactions especially the DMI, an effective Heisenberg spin Hamiltonian is established where i, j label the periodic cells and ,  label the magnetic ions.S i denotes the spin of th ion in the ith cell.Up to the semiclassical approximation, the ionic are treated as SO(3) unit vectors.J i,j are the colinear exchange couplings and D i,j are the DMI couplings.K  are the single-ion magnetic anisotropies.
All the interaction parameters are computed by DFT and perturbation theory.
Figure 5b shows the DMI energies between Co-Co, Co-Gd, and Gd-Gd pairs.With H + insertion, the Co-Co DMI enhances from −9.6 to −11.4 meV.The Co-Gd DMI enhances from −1.9 to −40.7 meV.The Gd-Gd pairs show distinct chirality, with DMI also enhanced from 0.3 to 0.6 meV.The total DMI per cell remarkably increases over fourfold, indicating the H + -inserted system readily presents noncollinear magnetic structures like chiral domain walls and topological spin vortexes.
Since the DMI are ultimately the results of SOC, the magnitude of the DMI is closely related to the band filling and hybridization between 5d and 3d orbitals near the Fermi level. [45,51]igure S10, Supporting Information, displays the projective density of states (PDOS) in pristine CoGd alloy and the H + -injected CoGd alloy, which is calculated by relativistic DFT on the same model in the main text.At the Fermi level, the pristine system exhibits the PDOS of Co:3d is 10.8.The H + -injected system shows the PDOS of Co:3d is 7.7.Hence, the filling in Co:3d at the Fermi level is significantly lowered after the H + -injections, providing one of the possible sources for the H + -injection-induced modulations on DMI.Besides, both the XPS spectra (Figure 3) and DFT calculations (see Figure S9, Supporting Information) show that the inserted hydrogen can capture electrons of the CoGd alloy.Thus, the observed enhancements on DMI may be also explained by the charge asymmetry resulting from the charge transfer. [52]o link the DMI and chiral magnetic textures, the chiral domain wall model is employed.Up to the continuous media approximation, the magnetic domain wall energy is [53] here, J, D, and K are the colinear exchange coupling energy, DMI energy, and magneto anisotropic energy, corresponding to the three terms in Equation (1).The sign before the DMI term corresponds to chirality.Hence, once the DMI energy D is negative and the magnitude is large enough to cover the first kinetical term, the system may undergo the topological phase transition from a homogenous magnetic state to the chiral stripe state (labyrinth state).Under proper external fields, the skyrmions birth from the chiral stripes and contribute to the THE.So, the stability of topological domain walls can be inferred by the following dimensionless parameter The topological magnetic phase is stable for  > 1.According to DFT calculations, the pristine system shows J = 499.8meV for the colinear coupling per cell, and K = 3.2 meV for the PMA.The DMI magnitude is |D| = 11.2 meV.Thus, the pristine CoGd film has  = 0.22, indicating the absence of THE.After H + -injection, the colinear coupling reduces to J = 334.2meV per cell, consistent with the H-induced lowering of T M . [14,15]The PMA increases to K = 4.2 meV.Remarkably, the DMI is promoted to |D| = 51.5 meV.These changes give  = 1.08, revealing the chiral phase is energetically favored.The alignment between the experiments in Figure 1 and theoretical calculations suggests hydrogen injection may lead to a topological magnetic phase transition in the CoGd system.
To further study the several relevant magnetic structures and understand why the THE always emergent near H C , the kinetical stability of the topological magnetic phase is examined via the chiral spin waves theory.Since the characteristic lengths of possible topological spin textures are sufficiently longer than the lattice constant, the interactions between magnetic ions in Equation ( 1) can be renormalized to the averaged interactions between cells, and the Hamiltonian in Equation ( 1) is re-expressed with spinwave coordinates here J d and D d are the colinear and DMI coupling energy between cells with a distance of d.K is the magnetic anisotropy energy per cell.S k is the coordinate of the semiclassical spin wave, denoting a spin wave propagating with wave vector k and the spins are rotating in the plane k-z (see the insets in Figure 5b).Figure 5c shows the spin wave spectra of the pristine CoGd film, where all spin waves have energy beyond zero.Thus, the pristine CoGd film presents homogeneous magnetic ground states, corresponding to the dark dot in the symmetric free energy profile on the left in Figure 5e.Applying an external field can distort the free energy profile.Once the field reaches critical H C , the free energy changes to shape on the right side of Figure 5e, and the pristine CoGd film undergoes conventional magnetic reversal.
Figure 5d shows the spectra of the H + -injected CoGd film.Notably, two regions with negative spin wave energies are found near the Γ point (circled with label zero), indicating chiral spin wave states are energetically favored over homogenous states.Figure 4f shows the evolution of free energies for the two possible topological magnetic structures under external fields.Initially, the H + -injected CoGd film exhibits the +m homogenous state, protected by an energy barrier.When the applied field reaches the first critical value H p , the system drops into the topological magnetic phase, exhibiting large THE (center of Figure 5f).Finally, at H C the system evolves to the −m state with homogenous and reversed magnetization.All these align excellently with former experimental observations (Figure 1c,d), revealing the relevance of the proposed mechanism.
The theoretical model presented here is not to fit the experiments but to provide some insights into the possible mechanism.The well-ordered phase, the C15 Lave phase of the Co 66.7 Gd 33.3 model utilized above displays composition close to the Co 61.1 Gd 38.9 in the device.Thus, it is hopeful that the model can describe the properties that are not strictly relevant to the exact atomic positions but the compositions.In previous studies, [14,15] the ordered model of CoGd alloy successfully captured the H + -insertions induced modulations on T M , the H + -insertions induced charge transferring, the evolutions of XAS, etc., proving its ability to approach some of the properties of the amorphous CoGd.THE considered in this study is one of the resultants of DMI.A recent study reported that the DMI in ferrimagnetic amorphous GdFeCo alloy can be qualitatively captured by even a 1D tight-binding model with random ordering, [54] revealing that the averaged net effects of bulk DMI are barely decided by the exact atomic position but the composition.Furthermore, the electrically modulable THEs are observed in the device composed of amorphous CoGd alloy, and the phenomena are found to be highly repeatable.Hence, the THE and the origins of the THE (the net effects of DMI) in the device should have weak dependences on the exact ordering of the atomic structure of CoGd.
Besides, the DMI and the DMI-controlled macro quantity (such as THE, the spectra of the chiral spin wave) drastically depend on the existence of the interstitial H + .However, this does not imply that the exact position of H + plays a drastic role.Given the fact that the 1s-shell of hydrogen ions/atoms cannot host stable local magnetic moment, H + can only contribute to the exchange couplings in an indirect way, for example, the modulations on the charges of the CoGd, the modulations on the position of Fermi level, the modulations on the fillings in the 3d-shells (see the Section S4, Supporting Information, for more details).All these should present less dependence on the exact ordering of the medium.So, the ordered theory model utilized here is expected to shed some insights into the possible reasons beneath the observed THE and the modulations with H + .

Conclusion
In conclusion, we observed H + -injection-induced THEs in an allsolid device composed of FiM amorphous Co 61.1 Gd 38.9 thin layer at room temperature.The as-prepared device shows a rectangular R xy -H loop, but positive V G s produce significant humps via H + injection.Direct magnetization characterization by MOKE displays rectangular M z -H loops without humps, supporting the hump signals possibly arising from topological Hall resistance R xy T due to chiral magnetic textures.R xy T , signaling THE, strengthens with increasing positive V G s and temperature.The maximal R xy T occurs at 320 K and V G = +1.5 V with a value of 39 mΩ.Applying negative V G = −1.5 V completely erases the R xy T .Thus, hydrogen-induced THE modulations in CoGd film are reversible, nonvolatile, and effective.SIMS and XPS show that the CoGd device realized efficient iontronics.Applying V G = +1.5 V enhances hydrogen intensity in the CoGd film over tenfold, significantly changing electronic states.Moreover, DFT calculations show H + -injection promotes CoGd DMI over fourfold.Domain wall and chiral spin wave theory show that H + -injected CoGd film favors topological magnetic structures, likely the sources of the observed THE.These results demonstrate the essential role of H + in FiM amorphous THE, shedding light on the FiM-based topological spintronics.

Experimental Section
Sample Preparation: A series of thin films consisting of Pt (5 nm)/Co 61.1 Gd 38.9 (6 nm)/Pt (0.5 nm)/TaN (1 nm) were deposited on Si (100) substrates with thermal oxidation at room temperature using magnetron sputtering.The Pt layers at the bottom (5 nm) and the Pt (0.5 nm)/TaN (1 nm) layers on top were used as buffer and capping layers, respectively.The deposition process was carried out under a vacuum level better than 1 × 10 −4 Pa, with an Ar pressure of 0.2 Pa during sputtering.The Co 61.1 Gd 38.9 alloys with a thickness of 6 nm were prepared by combining a Co target (diameter: 50 mm) with Gd-strips.The composition of the CoGd layer was adjusted by varying the area of the Gd-strips, resulting in Co 61.1 Gd 38.9 compositions.
Device Fabrication and Transport Measurement: The film stacks were processed into Hall bar devices with a width of 200 μm and a length of 1800 μm through the utilization of photolithography and Ar ion milling techniques.A bilayer electrode consisting of Ti (6 nm)/Pt (30 nm) was deposited using magnetron sputtering.Transport measurements were conducted using a Versalab system (Quantum Design) equipped with a Keithley 6221 for current sourcing, a Keithley 2182 for voltage measurement, and a Keithley 2400 for applying gate voltage.The protocol for applying V G s and detecting modulations are as below: first switch on V G (the source and drain are in ground voltage in this step), and wait for 1.5 min for sufficient reaction.Then, switch off V G and wait for another 1.5 min for the equilibration of possible slow reactions.Afterward, conduct the further transporting measurements.
The concentration of the CoGd films was analyzed and determined using an electron probe micro-analyzer (EPMA-1720H, Shimadzu Corporation).Porous silica exhibited great potential as a highly efficient proton exchange membrane in energy systems. [55]To initiate the synthesis, tetraethyl orthosilicate (purchased from Alfa Aesar), phosphoric acid (as a proton source, 85% wt% obtained from Alfa Aesar), ethanol, and deionized water were combined in a molar ratio of 1:18:6:0.03.Subsequently, the mixture was stirred for 2 h and then annealed at 50 °C in a sealed container for an additional 2 h.This process resulted in the formation of polymerized Si─O─Si chains. [56]IMS Characterization: Before SIMS measurements, the solid proton electrolyte source layers on the device were removed.The instrument utilized for SIMS detection was the SIMS 5 time-of-flight (TOF) secondary ion mass spectrometer manufactured by IONTOF.Oxygen was used to etch the samples gradually, with an energy of 0.25 keV and an etching area of ≈300 μm × 300 μm.Bismuth ions were employed as the analysis source, with an energy of 30 keV.
XPS Characterization: The solid-state protonic layers were removed before the XPS detections.The XPS detections employed the aluminum X-ray source (K: 1486.6 eV) operating at 150 W power (ESCALAB 250Xi, Thermo Fisher Scientific).All binding energy calibrations were based on the C 1s peak (C 1s: 284.8 eV).
MOKE Measurements: The magnetic hysteresis loops were measured with polar MOKE (Evico, em-Kerr-highres, Germany).The MOKE device offered an optical resolution of up to 500 nm and can generate an out-ofplane magnetic field of up to 100 mT.
Ab Initio Calculation: The ab intio calculations based on DFT were done with the projector augmented plane-wave basis, which was implemented in the Vienna ab initio simulation package. [57,58]The plane waves were cut-off at 550 eV.The exchange-correlations of electrons were described by the generalized gradient approximations with the form proposed by Perdew, Burke, and Ernzerhof. [59]The energy converge criterion for solving self-consistent Kohn-Sham equations was 10 −6 eV.The Brillouin zone was sampled with resolutions better than 0.02 Å −1 , using the scheme of Monkhorst-Pack. [60]All the structures in this study were fully relaxed until the Hellman-Feynman was smaller than 0.01 eV Å −1 .The effective Hamiltonian in the coordinates of the local atomic orbital basis was extracted from the DFT with the Wannierization scheme as implemented in the WANNIER90 package. [61,62]o obtain the interaction parameters in Equation ( 1), the perturbation theory was employed.Up to the independent particle approximation, the free energy relevant to the magnetic couplings between two magnetic ions was a bubble diagram with two vertexes ) G ji (i) (5)   in which B i is the magnetic field acting on ith magnetic ion.G  (i) is the finite temperature Green's function, which is determined by the Wannier Hamiltonian.The summation on Matsubara frequencies  is done by conventional Dirac function with the electron temperature of 300 K.The exchange coupling tensor is the 2nd derivate of free energy where the  and  can be x, y, and z, labeling the spatial direction.The isotropic exchange coupling in Equation ( 1) is the average of diagonal elements, and the DMI coupling is the anti-symmetric part of off-diagonal elements.

Figure 1 .
Figure 1.Topological Hall effect observed in Pt/Co 61.1 Gd 38.9 /Pt heterostructures under different V G s. a) Sample structure.b) Device geometry.The small blue square denotes the solid proton electrolyte.c) The magnetic field-dependent Hall resistance (R xy ) at different gate voltages for Pt/Co 61.1 Gd 38.9 /Pt device at 300 K. Topological Hall resistance (R xy T ) is shadowed by gray color.d) V G s-dependent R xy T .
The virgin Co 61.1 Gd 38.9 device shows rectangular R xy -H hysteresis loops.After H + -injection with V G = +1 V, clear hump signals emerge in the R xy -H loop.In situ polar magneto-optical Kerr microscopy (MOKE) shows the M z -H hysteresis in H + -injected device is rectangular without humps, revealing the abnormal hump signals possibly arise from the R xy T of THE not scaling with magnetization.Further, H + -injection at V G = +1.5 V largely enhances R xy T to 24 mΩ, ≈14.6% of the saturated R xy A = 164 mΩ.Subsequently, the R xy T is completely erased at V G = −1.5 V due to H + -extraction.Ab initio calculations show that H + -injection remarkably promotes the non-collinear Dzyaloshinskii-Moriya interaction (DMI) over fourfold and suppresses colinear interactions.Hydrogen-induced chiral magnetic structures are further corroborated by chiral spin wave theory.These findings reveal exotic H + migration-induced nontrivial topological magnetic structures in amorphous CoGd films, paving the way for future topological FiM spintronics at room temperature.

Figure 2 .
Figure 2. In situ polar MOKE hysteresis loops measured with sweeping external field H along the out-of-plane direction, including the measurements in the virgin Pt/Co 61.1 Gd 38.9 /Pt heterostructure thin film, the film processed by V G = +1 V, the film processed by another V G = +1.5 V, the film processed by further V G = −1 V and the film further processed by V G = −1.5 V.All polar MOKE hysteresis loops are obtained in 300 K.

5 ,
and −1 V in Figure 1c show additional hump features near the H C .To extract these hump signals, a linear fit is performed on the high-field Hall resistance to subtract R xy N .By further subtracting the high-field R xy A beyond the H C , the remaining hump structures are separated.Figure 1d shows the hump evolutions with the modulations of V G s at 300 K. Initially, the virgin device shows no humps.Applying positive V G = +1 V induces nonzero humps.Successive application of V G = +1.5 V further increases hump to 25 mΩ.Then, hump signals decrease to 21 mΩ under V G = −1 V. Finally, humps are completely erased under V G = −1.5 V. Therefore, posi-tive V G s can induce hump signals in the Co 61.1 Gd 38.9 sample, with modulations reversibly recovered by negative V G s. Recently, similar hump signals are reported in SrRuO 3 , FeTaS 2 , CoTb, pristine CoGd alloy, CoFeGe alloy, etc.,

Figure 3 .
Figure 3. Temperature-gate voltage (T-V G ) phase diagrams with different resistances as a function of T and V G s.The T-V G phase diagrams of a) R xy T , b) R xy A of the Co 61.1 Gd 38.9 devices.

Figure 3
Figure3shows the R xy T and R xy A of the device measured at several temperatures and processed by a series of V G s.They are extracted from the R xy -H loops (see FigureS1, Supporting Information).Clearly, R xy A is sensitive to both the temperature and the modulations via V G s. Positive and negative V G s can generally weaken and strengthen the R xy A , respectively.At 300 K, the initial R xy A is 210 mΩ, decreasing to 160 m Ω at V G = +1.5 V, then recovering to 180 mΩ at V G = −1.5 V.At 320K, the initial R xy A is 210 mΩ, dropping to 130 mΩ at V G = +1.5 V, then recovers to 150 mΩ at V G = −1.5 V.The dependence of R xy A on temperature and V G aligns with previous studies,[14,15] and can be understood by V G -induced modulations on the T M .The Co 61.1 Gd 38.9 sample presented here exhibits T M ≈ 345 K.At T M , the sample shows minimal R xy A due to enhanced fluctuations of Co magnetization.Therefore, as temperature increases from 280 to 320 K, the device approaches T M and R xy A reduces.Meanwhile, positive V G s inject H + into the sample, lowering T M through H + -induced modulations on colinear exchange couplings.[14,15]Thus, positive (negative) V G s also push the system toward (away from) T M , reducing (enhancing) R xy A .More importantly, the THE sensitively depends on both temperature and the applied V G s (Figure3a).At 280 K, R xy T increases from zero to its maximum value of 20 mΩ after applying V G = +1.5 V and is erased by the V G = −1.5 V.At 300 K, R xy T increases to 25 mΩ at V G = +1.5 V and vanishes at V G = −1.5 V.At 320 K, R xy T increases to 39 mΩ at V G = +1.5 V and disappears at V G = −1.5 V. Thus, THE can be generated and eliminated via different V G s. Additionally, R xy T gradually grows with increasing temperature.The temperature effects in R xy T (Figure3a) can be understood as the result of approaching T M .In more detail, as the system gets close to T M , the magnetizations of Co and Gd are comparable.Both Co and Gd magnetizations have trends to align with the external field.Besides, the anti-ferromagnetic exchange couplings favor the anti-parallelization between Co and Gd magnetizations.These two competing effects can lead to the possible noncolinear magnetic configuration in the two sublattices,[50] which can further help the emergence of noncolinear chiral magnetic texture (with the help of DMI, of course).The temperature-dependent THE displayed here

Figure 4 .
Figure 4. Characterizations on the H + migrations and H + -insertion-induced electronic changes.a) The etching-time-dependent hydrogen intensity for TaN/Pt/Co 61.1 Gd 38.9 /Pt sample in initial state and sample processed by V G = +1.5 V. Longer etching time corresponds to the deeper region of the device.The solid proton electrolyte layer is removed before the detection.b) XPS measured at the 2p peaks of the Co atom.c) XPS on the 4d peaks of the Gd atom.Color corresponds to the V G sequence utilized to process the sample.

Figure 5 .
Figure 5. DFT calculations on the electronic and magnetic structures of CoGd thin film modulated by the H + -injection.a) Atomic structure of the H +inserted CoGd thin film (derived from C15 Laves phase).The purple, blue, and red balls denote Gd, Co, and H ions. b) The calculated DMI couplings contributed by Co-Co, Co-Gd, and Gd-Gd pairs in the systems with and without H + -injection.The small blue arrows show the arrangement of noncollinear magnetic moments along the propagation direction (black arrow) due to the positive and negative DMI. c) The chiral spin wave spectra of pure film.d) The chiral spin wave spectra of H + -inserted film.e) The evolution of the free energy profile relevant to the magnetization reversion in the pristine CoGd film under a coercive field.The system evolves from the state marked by a light dot into a dark dot.f) The evolution of the free energy profile relevant to the emergent topological magnetic structures in the H-inserted CoGd film under two critical fields.