⇦Chinese Physics Letters, 2023, Vol. 40, No. 3, Article code 037502 Quantum Anomalous Hall Effects Controlled by Chiral Domain Walls Qirui Cui (崔琪睿)1,2, Jinghua Liang (梁敬华)2, Yingmei Zhu (朱英梅)2, Xiong Yao (姚雄)2, and Hongxin Yang (杨洪新)1,2* Affiliations 1National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China 2Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China Received 17 December 2022; accepted manuscript online 12 February 2023; published online 24 February 2023 *Corresponding author. Email: hongxin.yang@nju.edu.cn Citation Text: Cui Q R, Liang J H, Zhu Y M et al. 2023 Chin. Phys. Lett. 40 037502    Abstract We report the interplay between two different topological phases in condensed matter physics, the magnetic chiral domain wall (DW), and the quantum anomalous Hall (QAH) effect. It is shown that the chiral DW driven by Dzyaloshinskii–Moriya interaction can divide the uniform domain into several zones where the neighboring zone possesses opposite quantized Hall conductance. The separated domain with a chiral edge state (CES) can be continuously modified by external magnetic field-induced domain expansion and thermal fluctuation, which gives rise to the reconfigurable QAH effect. More interestingly, we show that the position of CES can be tuned by spin current driven chiral DW motion. Several two-dimensional magnets with high Curie temperature and large topological band gaps are proposed for realizing these phenomena. The present work thus reveals the possibility of chiral DW controllable QAH effects.
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 DOI:10.1088/0256-307X/40/3/037502 © 2023 Chinese Physics Society Article Text The magnetic chiral domain wall (DW) is a type of topological defect with discrete symmetry, which is the boundary between domains with opposite magnetization and could be excited from uniform domain ground states. The topological charge of chiral DW is defined as $Q_{\scriptscriptstyle{\rm DW}} =(1/\pi)\int_{-\infty }^\infty {\nabla \theta } dx$, where $\theta$ represents the polar angle of normalized spin vector ${\boldsymbol S}$. $Q_{\scriptscriptstyle{\rm DW}}$ equals 1 or $-1$ when ${\boldsymbol S}$ rotates from $+z$ to $-z$ or $-z$ to $+z$. Domains separated by the chiral DW with topological protection is widely used as the information bit in emergent spintronic memory and logic devices, and the current-driven chiral DW displacement via spin-transfer torque (STT) or SOT underpins the operations of these devices.[1-9] Notably, one key term for stabilizing the chiral DW is Dzyaloshinskii–Moriya interaction (DMI), which favors the formation of noncollinear spin configuration in magnets lacking inversion symmetry.[10-14] Quantum anomalous Hall (QAH) effect is another type of topological phases, which is characterized by the quantized Hall conductance ($Ce ^{2}$)/$h$ without external magnetic field (where $C$, $e$, and $h$ represent Chern number, elementary charge, and Planck constant, respectively). Due to its dissipationless chiral edge states (CESs), QAH effect shows promising applications in future electronic devices with ultralow-energy consumption[15-20] and provides an intriguing platform to investigate topological quantum physics, such as chiral topological superconductivity and Majorana fermions.[21-24] QAH effect is initially predicted by Haldane in 1988[25] and first observed in a magnetically doped topological insulator, i.e., Cr-doped (Bi,Sb)$_{2}$Te$_{3}$ thin films, by Chang et al. in 2013.[17] However, the extremely low full quantization temperature of 30 mK largely impedes its practical applications. Thus, tremendous efforts have been devoted to optimizing and designing material systems with high QAH effect temperature.[26-32] Besides high temperature, it is a long-sought goal for QAH effect that realizes effective manipulation of CESs, which probably leads to the artificial designing of quantum information transferring.[33,34] In Cr-doped (Bi,Sb)$_{2}$Te$_{3}$ thin films, Yasuda et al. demonstrated that two CESs would co-propagate along the DW[35-37] and first realized the reconfigurable CESs by using the tip of a magnetic force microscope to write domain.[33] However, the investigation of interaction between two topological phases, chiral DW and QAH effect, in realistic materials remains very limited as far as we know, and particularly, it is still interesting and challenging to utilize chiral DW to control the high-temperature QAH effects. As shown in Fig. 1, the coexistence of QAH effect and chiral DW could occur in materials combining nontrivial electronic states and sizable DMI. Importantly, the nontrivial topological gap should appear when magnetization is out-of-plane (OOP) and totally vanish when magnetization is in-plane (IP), thus resulting in chiral DW being an intrinsic boundary separating two parallel chiral states. Since CESs are intimately hinged with spin configurations, the approaches that are applied for controlling spin configurations will eventually lead to modification of the CESs. For example, the spin vector can be aligned by a uniform magnetic field, spin fluctuations can be induced by laser or thermal excitations, and spin vector orientation can be explicitly and energy-efficiently controlled by spin current-generated torque. In the following, based on the first-principles calculations, Wannier-based tight binding models, and atomic spin model simulations, we first take VSe$_{2}$ monolayer with $P\bar{4}m2$ layer group as a representative example to demonstrate the manipulation of QAH effect via chiral DW, and then extend the discussions to other thin films, i.e., Fe$_{2}X$I ($X$ = Cl, Br) Janus monolayers with $P4mm$ layer group. The detailed computational methods for elucidating structural, electronic and magnetic properties[14,38-47] are given in the Supplemental Information (SI).[48]
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Fig. 1. The schematic of manipulation of QAH effects via chiral DW. For achieving the coexistence of these two topological phases, materials are required to combine nontrivial electronic states and sizable DMI. Due to CESs closely depending on the morphology of spin configurations, traditional approaches for tuning spin configurations all could lead to modifications of the CESs.
The crystal structure of VSe$_{2}$ is shown in Figs. S1(a)–S1(c). Each V atom is tetrahedrally surrounded by four Se atoms, and a Se atom bonding with two V atoms along $x$ and $y$ directions locates at bottom and top layer, respectively. The calculations of phonon spectrum demonstrate the dynamic stability since there is no imaginary frequency in the whole Brillouin zone [Fig. S2(a)]. Using the standard Voigt notation, the elastic strain energy for VSe$_{2}$ per unit cell can be expressed as $E_{\rm s}=\frac{1}{2}C_{11}\varepsilon_{x}^{2}+\frac{1}{2}C_{22}\varepsilon_{y}^{2} +C_{12}\varepsilon_{x}\varepsilon_{y}+2C_{66}\varepsilon_{xy}^{2}$, where the coefficients $C_{11}$, $C_{22}$, $C_{12}$, and $C_{66}$ are components of the elastic tensor, $\varepsilon_{x}$ ($\varepsilon_{y}$) and $\varepsilon_{xy}$ represent the uniaxial strain in the $x$ ($y$) direction and shear strain, respectively. We find that these elastic constants satisfy $C_{11}C_{22}-C_{12}^{2}>0$ and $C_{66}>0$ [see specific values of coefficients in the SI], which demonstrates the mechanical stability. For investigating crucial magnetic properties, we adopt the following spin Hamiltonian: \begin{align} H=\,&-J_{1}\sum\limits_{\langle i,j \rangle } \boldsymbol{S}_{i} \boldsymbol{S}_{j}-J_{2}\sum\limits_{\langle i',j' \rangle } \boldsymbol{S}_{i'} \boldsymbol{S}_{j'}-A\sum\limits_i {{(S}_{i}^{z})}^{2} \notag\\ &-\sum\limits_{\langle i,j \rangle } \boldsymbol{D}_{ij} \cdot (\boldsymbol{S}_{i}\times \boldsymbol{S}_{j})-\mu B_{\rm ext}\sum\limits_i S_{i}^{z}, \tag {1} \end{align} where $J_{1}$ and $J_{2}$ represent the nearest-neighbor (NN) and next-nearest-neighbor (NNN) exchange couplings, respectively, $A$ refers to the single-ion magnetic anisotropy, and $\boldsymbol{D}_{ij}$ refers to the DMI between NN V pairs. For extracting magnetic parameters in spin Hamiltonian, we apply the energy mapping methods [detailed discussion given in the SI], and the results are shown in Table SI. $J_{1}$ in pristine VSe$_{2}$ reaches 39.44 meV, implying strong ferromagnetic exchange coupling between V atoms. Despite $J_{2} = -1.12$ meV favoring antiferromagnetic coupling, its magnitude is much smaller compared with $J_{1}$. VSe$_{2}$ possesses perpendicular magnetic anisotropy of 0.47 meV, which is an essential condition for achieving large size domain with OOP magnetization. Notably, due to the coexistence of $M_{x}$ and $M_{y}$ mirror symmetries, and $S_{4z}$ rotoreflection symmetry, the anisotropic DMI is allowed [orange arrows in Fig. S1(a)] according to the Moriya rules.[11,49] Specifically, IP components of DMI between V pairs in $x$ ($d_{\parallel }^{x}$) and $y$ ($d_{\parallel }^{y}$) directions satisfy the relationship $d_{\parallel }^{x}=-d_{\parallel }^{y} = 2.24$ meV, which is confirmed by the first-principles calculations [see Table SI].
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Fig. 2. (a) Normalized magnetization $m$ and heat capacity $C$ of pristine VSe$_{2}$ versus temperature. (b) Spin configurations of VSe$_{2}$ with 1% tensile strain. The simulated zone is chosen to be a $150{\,\rm nm} \times 150{\,\rm nm}$ square. [(c), (d)] Zoom of spin textures of chiral DW and antiskyrmion as indicated by the black dashed in (b).
We then perform atomic spin model simulations to investigate the spin textures since all magnetic parameters in spin Hamiltonian [Eq. (1)] are resolved. For describing the spin dynamics, the Landau–Lifshitz–Gilbert (LLG) equation is employed: \begin{align} \frac{\partial \boldsymbol{S}_{i}}{\partial t}=-\frac{\gamma }{(1+\alpha^{2})}[\boldsymbol{S}_{i}\times\boldsymbol{B}_{\rm eff}^{i}+\alpha \boldsymbol{S}_{i}\times(\boldsymbol{S}_{i}\times \boldsymbol{B}_{\rm eff}^{i})], \nonumber \end{align} where $\gamma$ and $\alpha$ represents the gyromagnetic ratio and damping constant, respectively. $\boldsymbol{B}_{\rm eff}^{i}$ indicates the effective field applied on each spin site and is defined as $\boldsymbol{B}_{\rm eff}^{i}=-\frac{1}{\mu_{\rm s}}\frac{\partial H}{\partial \boldsymbol{S}_{i}}$. For pristine VSe$_{2}$, only uniform ferromagnetic state emerges arising from the strong ferromagnetic exchange coupling and perpendicular magnetic anisotropy, and Monte Carlo simulations confirm that Curie temperature reaches 290 K [Fig. 2(a)]. For realizing noncollinear spin configurations, the amplitudes of $J$ and $A$ should be decreased while that of $d$ should be enhanced. These conditions are satisfied simultaneously by applying a slight tensile strain [Fig. S3]. Based on obtained elastic constants $\varepsilon$, we determine that the maximum Young moduli of VSe$_{2}$ reaches 48.48 N/m, which is obviously smaller than graphene (340 N/m), indicating the high flexibility. Interestingly, single chiral DW with width of 6 nm appears under 1% tensile strain [Figs. 2(b) and 2(c)]. We also find the appearance of antiskyrmion soliton with diameter of 10 nm in strained VSe$_{2}$ [Fig. 2(d)]. For chiral DW, $Q_{\scriptscriptstyle{\rm DW}}$ equals 1 as spin rotates from $+z$ to $-z$, and for the observed antiskyrmion, topological charge $Q_{\scriptscriptstyle{\rm SK}}$ is defined as $Q_{\scriptscriptstyle{\rm SK}}= \frac{1}{4\pi }\int \boldsymbol{S} \cdot (\partial_{x}\boldsymbol{S}\times \partial_{y}\boldsymbol{S})dxdy$ and equals 1. We now focus on the electronic states of the VSe$_{2}$ monolayer. Figure 3(a) shows the spin-polarized band structure. The spin-down channel exhibits a gap while spin-up channel is gapless at $\varGamma$ point. The projected band structures show that electronic states nearby the Fermi level are dominated by the $p_{x}$ and $p_{y}$ orbitals of Se, and except for $\varGamma$ point, these two orbitals do not degenerate along $-X\leftrightarrow \varGamma$ or $\varGamma \leftrightarrow X$ lines in reciprocal space [Fig. S4]. When the spin-orbit coupling (SOC) effects are considered, a band gap of 116 meV is achieved, accompanied with the $p_{x} - p_{y}$ orbitals reversion [Fig. 3(b)], implying the emergence of topological electronic phase. Notably, if we apply the HSE06 rather than the standard GGA+$U$ approach, the calculated band gap reaches 239 meV. For revealing topological properties, the Wannier-based tight binding model is constructed by the $p_{x}, p_{y}$ orbitals of Se and $d$ orbitals of V. By integrating the Berry curvatures over the Brillouin zone, we obtain the quantized anomalous Hall conductivity $\sigma_{xy}=e^{2}/h$ [Fig. 3(c)]. The edge state calculations show that a gapless chiral edge mode appears in the band gap [Fig. 3(d)]. We thus demonstrate that VSe$_{2}$ is a QAH insulator with high critical temperature of 290 K. Notably, this QAH effect is robust to the external strain ranging from $-5$% to 3% [Figs. 3(e) and 3(f)]. For directly elucidating the boundary feature of chiral DW, we calculate the spin configurations-dependent band structures. The SOC-induced band gap appears in VSe$_{2}$ with OOP magnetization and vanishes when the magnetization is tuned to be IP [Fig. 3(g)]; and in a $50 \times 1\times 1$ supercell, the system with uniform ferromagnetism as ($\overbrace{\uparrow\cdots\cdots\uparrow}^{50\uparrow}$) clearly exhibits insulating properties, and interestingly, four edge modes emerge in band gap when two chiral DWs are introduced into spin configuration as ($\overbrace{\uparrow\cdots\uparrow}^{24\uparrow}\rightarrow\overbrace{\downarrow\cdots\downarrow}^{24\downarrow}\leftarrow$) [Fig. 3(h)].
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Fig. 3. (a) Spin-polarized band structures of VSe$_{2}$. (b) Zoom of projected band structures around the Fermi level with considering the SOC effects. The inset shows band structures without considering SOC effects. (c) Anomalous Hall conductivity $\sigma_{xy}$ as a function of energy level. The inset shows the heat mapping of Berry curvature in Brillouin zone. [(d), (e)] Edge states of semi-infinite plane of VSe$_{2}$ monolayer under 0% and 1% tensile strain. (f) SOC-induced bandgap as a function of strain. (g) Magnetization orientation-dependent band structures. (h) Band structures of a $50 \times 1\times 1$ supercell without and with considering chiral DW in spin configurations.
Since chiral DW and QAH effect can coexist in VSe$_{2}$ under 1% tensile strain [Figs. 2(c) and 3(e)], we choose it as an example to reveal the chiral DW controllable QAH effects. As shown in the top panel in Fig. 4 ($B_{\rm ext} = 0$ T), chiral DWs connect two edges of a strip and divide the uniform domain into several separate domains. The neighboring domain possesses opposite magnetization that opens the topological band gap with opposite Chern number ($C=+$1 or $-1$). Therefore, when the electrical current is injected from left-side current contact to right-side current contact, the emerging edge states of neighboring domain will exhibit the opposite chirality in the stripe [see lines with arrows in Fig. 4]. It is also expected that topological Hall effects are observed in the same system via slight electron/hole doping due to the existence of topological quasiparticles, antiskyrmion.[50-53] Notably, the coexistence of QAH state and Néel-type skyrmion is very recently reported in Janus MnBi$_{2}$S(Se)$_{2}$Te$_{2}$ monolayer.[54,55] Via applying a nonzero $B_{\rm ext}$, the domain with OOP magnetization expands, accompanied with the chiral DW motion, and uniform ferromagnetic background is finally achieved as $B_{\rm ext} = 0.4$ T. These results indicate that the zone of QAH state with $C = 1$ or $-1$ can be artificially designed via changing the magnitude of magnetic field. We further consider the temperature effects by assuming that thermal fluctuations of each spin are represented by a Gaussian white noise term. The thermal field on spin site is written as $\boldsymbol{B}_{\rm th}^{i}=\mathrm{\boldsymbol{\mathit{\Gamma }}}(t)\sqrt \frac{2\alpha k_{\scriptscriptstyle{\rm B}}T}{\gamma \mu_{\rm s}\Delta t}$, where $\mathrm{\boldsymbol{\mathit{\Gamma }}}(t)$ and $T$ represent the Gaussian distribution and temperature, respectively, and the effective field is rewritten as $\boldsymbol{B}_{\rm eff}^{i}=-\frac{1}{\mu_{\rm s}}\frac{\partial H}{\partial \boldsymbol{S}_{i}}+\boldsymbol{B}_{\rm th}^{i}$. As shown in Fig. 4, the uniform ferromagnetic phase with single QAH state is destroyed by thermal fluctuation when temperature increases up to 350 K and recovers to the initial state with multiple QAH states by zero-field cooling. Thus, we achieve the reconfigurable QAH effects.
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Fig. 4. Reconfigurable QAH states controlled by external magnetic/temperature field. The top view of spin configurations of $300 \times 50$ nm VSe$_{2}$ stripe with open boundary. The black and white lines with arrows represent the quantized CESs in domain with up and down magnetization, respectively.
Chiral DW can also be driven by the spin current that is a lower-energy consumption and more convenient approach compared with external magnetic/temperature field. Usually, there are two distinct mechanisms to implement the spin current approach, i.e., STT and SOT. In STT, the spin-polarized current is injected into materials to transfer spin-angular momentum, which is impractical for the QAH insulator. In SOT, the spin accumulation at the interfaces exerts a torque on the magnetization of the adjacent magnet layer [see illustration of SOT in Fig. 1]. Interestingly, several vdW semiconductors, including MoTe$_{2}$, WSe$_{2}$, WTe$_{2}$, etc., have been demonstrated to be able to generate sizable spin current via spin Hall effects or interface Rashba–Edelstein effects, and SOT-induced magnetization switching has been observed in these vdW semiconductors/ferromagnets heterostructures.[56-60] We include the SOT term $\boldsymbol{T}_{\rm sot}^{i}$ in the LLG equation for describing the spin dynamics of VSe$_{2}$ monolayer as \begin{align} \frac{\partial \boldsymbol{S}_{i}}{\partial t}=-\frac{\gamma}{(1+\alpha^{2})}[\boldsymbol{S}_{i}\times \boldsymbol{B}_{\rm eff}^{i}+\alpha \boldsymbol{S}_{i}\times (\boldsymbol{S}_{i}\times \boldsymbol{B}_{\rm eff}^{i})+\boldsymbol{T}_{\rm sot}^{i}], \nonumber \end{align} with \begin{align}\boldsymbol{T}_{\rm sot}^{i}\boldsymbol{=}\frac{\hslash J_{\rm c}\theta_{\rm sh}}{2e}\frac{a^{2}}{\mu_{\rm s}}[\boldsymbol{S}_{i}\boldsymbol{\times}(\boldsymbol{S}_{i}\boldsymbol{\times p})\boldsymbol{-}\alpha (\boldsymbol{S}_{i}\boldsymbol{\times p})]. \nonumber \end{align} The first and second terms of $\boldsymbol{T}_{\rm sot}^{i}$ represent the damping-like and filed-like torques, respectively. In atomic spin model simulations, $J_{\rm c}$ is the current density; $\theta_{\rm sh}$ is the spin Hall angle and is set to 0.1; and $\boldsymbol{p}$ is the orientation of spin polarization and is set to be along +$x$. Figure 5(a) shows the initial spin configurations and fully relaxed spin configurations after injecting 0.1 ns current with $J_{\rm c} = 1\times 10^{12}$ A/m$^{2}$. The chiral DW is driven by the SOT at an estimated high velocity $v$ of 623 m/s. We also find that $v$ linearly depends on $J_{\rm c}$ and is enhanced to 805 m/s with $J_{\rm c} = 1.4\times 10^{12}$ A/m$^{2}$ [Figs. 5(b) and S5]. The motion of chiral DW naturally leads to the variation of CES positions, indicating that the accurate and fast controlling of a chosen zone of QAH state can be realized by adjusting the magnitude, polarization, or injecting time of spin current.
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Fig. 5. (a) Top view of VSe$_{2}$ stripe at initial state $t = 0$ ns and the later stage $t = 0.1$ ns, under the time-invariant current density $J_{\rm c}=10^{12}$ A/m$^{2}$. The orange arrow of down panel indicates the motion orientation of chiral DW. (b) Current density-dependent motion velocity of chiral DW.
Finally, we show that coexistence of large-size domain separated by chiral DWs and high-temperature QAH effect can also be achieved in 2D Janus magnets, Fe$_{2}X$I ($X$ = Cl, Br) monolayers, providing additional platforms for chiral DW controllable QAH effects. The dynamic and mechanical stability of Fe$_{2}X$I has also been demonstrated by phonon dispersions and elastic constants [see the SI]. Inversion symmetry breaking of $P4mm$ layer group allows the DMI between Fe pairs. For resolving potential spin configurations, we adopt the following spin Hamiltonian: \begin{align} H=\,&-J_{1}\sum\limits_{\langle i,j \rangle} \boldsymbol{S}_{i} \boldsymbol{S}_{j}-J_{2}\sum\limits_{\langle i',j' \rangle } \boldsymbol{S}_{i'} \boldsymbol{S}_{j'}-A\sum\limits_i {(S_{i}^{z})}^{2}\notag\\ &-\sum\limits_{\langle i,j \rangle} \boldsymbol{D}_{ij} \cdot (\boldsymbol{S}_{i}\times \boldsymbol{S}_{j})-\sum\limits_{\langle i',j' \rangle } \boldsymbol{D}_{i'j'}^{\scriptscriptstyle{\rm Cl/Br}} \cdot (\boldsymbol{S}_{i'}\times \boldsymbol{S}_{j'})\notag\\ &-\sum\limits_{\langle i',j' \rangle} \boldsymbol{D}_{i'j'}^{\scriptscriptstyle{\rm I}} \cdot (\boldsymbol{S}_{i'}\times \boldsymbol{S}_{j'}). \tag {2} \end{align} Besides the NN DMI $\boldsymbol{D}_{ij}$ [orange arrows of Fig. S6(a)], two additional terms $\boldsymbol{D}_{i'j'}^{\scriptscriptstyle{\rm Cl/Br}}$ and $\boldsymbol{D}_{i'j'}^{\scriptscriptstyle{\rm I}}$ are applied to describe the NNN DMIs between Fe pairs mediated by Cl/Br and I, respectively [blue arrows of Fig. S6(a)]. The magnitudes of IP components of the above-mentioned DMIs are labeled as $d_{\parallel}$, $d_{\parallel }^{\scriptscriptstyle{\rm Cl}}$, $d_{\parallel }^{\scriptscriptstyle{\rm Br}}$, and $d_{\parallel }^{\scriptscriptstyle{\rm I}}$. As shown in Table SII, sizeable DMI is achieved in both Fe$_{2}$ClI and Fe$_{2}$BrI, and notably, $d_{\parallel }^{\scriptscriptstyle{\rm I}}$ of Fe$_{2}$ClI reaches 2.79 meV. The magnitudes of $d_{\parallel}$ and $d_{\parallel }^{\scriptscriptstyle{\rm I}}$ are much larger than that of $d_{\parallel }^{\scriptscriptstyle{\rm Cl}}/d_{\parallel }^{\scriptscriptstyle{\rm Br}}$ due to the strong SOC scattering from I.[12] Atomic spin model simulation shows that uniform domain is divided into several regular zones by chiral DW [Figs. S6(b) and S6(c)]; and Monte Carlo simulations show that Curie temperature of Fe$_{2}X$I is around 400 K [Fig. S7]. We further discuss the electronic states of Fe$_{2}X$I. When magnetization axis is tuned from $x$ to $z$, the SOC-induced Dirac gaps of 211 and 253 meV are achieved for Fe$_{2}$ClI and Fe$_{2}$BrI, respectively [Figs. S8(a)–S8(d)], and there are two gapless chiral edge modes emerging in the band gap [Figs. S6(d) and S6(e)], confirming the emergence of QAH effects with high Chern number $C = 2$. It is thus expected that double CESs could be controlled simultaneously by chiral DWs in Fe$_{2}X$I, which is distinct from single CES in VSe$_{2}$ monolayer. We note that for Fe$_{2}X$I monolayers, coexistence of QAH effects and piezoelectricity has been demonstrated in Ref. [61], while the DMI and its favored topological spin configurations are revealed in the present work for the first time. Recently, multiple efforts have been taken to CES manipulation in real space. The numerical simulations show that CES can be spatially shifted in a disordered Chern insulator with multistep potential, by tuning the Fermi energy.[62] Interestingly, the chiral DW has been experimentally observed in antiferromagnetic topological insulators MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$, which could hold QAH or axion insulator state,[63,64] and the existence of CES along chiral DW associated with nontrivial transport phenomena is further theoretically proposed based on layered MnBi$_{2}$Te$_{4}$.[65,66] In summary, we have presented a general approach of manipulation QAH effects and revealed its possibility in 2D magnets, VSe$_{2}$ and Fe$_{2}X$I ($X$ = Cl, Br), with robust noncollinear magnetic order and high QAH temperatures. Specifically, the uniform domain in a strip is divided by DMI-favored chiral DWs into several domains, where the neighboring domains possess opposite quantized Hall conductances, and these separated domains with single/double CESs can be effectively tuned under the assistance of uniform magnetic and temperature fields, leading to the reconfigurable QAH effects. More interestingly, spin-orbit torque generated by spin current triggers translational motion of chiral DW at high velocity, which gives rise to the precise and fast manipulation of QAH effect. Our findings thus open a previously unknown pathway to control the quantum transport of spin, which could benefit to novel and practical quantum applications.[67] Acknowledgement. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11874059 and 12174405), the Key Research Program of Frontier Sciences, CAS (Grant No. ZDBS-LY-7021), the Ningbo Key Scientific and Technological Project (Grant No. 2021000215), “Pioneer” and “Leading Goose” R&D Program of Zhejiang Province (Grant No. 2022C01053), Zhejiang Provincial Natural Science Foundation (Grant No. LR19A040002), and Beijing National Laboratory for Condensed Matter Physics (Grant No. 2021000123). 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