The competition between dimensionality and ordering in multiferroic materials is of great interest for both fundamental physics and potential applications. Combining first-principles calculations with micromagnetic si...The competition between dimensionality and ordering in multiferroic materials is of great interest for both fundamental physics and potential applications. Combining first-principles calculations with micromagnetic simulations, we investigate recently synthesized ultrathin perovskite bismuth ferrite(BFO) films. Our numerical results reveal that, at the monolayer limit, the ferroelectricity of BFO is missing because the octahedral distortions are constrained. However, the monolayer bismuth ferrite is a topological antiferromagnetic metal with tunable bimeron magnetic structure. The dual topologically non-trivial characteristics make monolayer bismuth ferrite a multifunctional building block in future spintronic devices.展开更多
Magnetic nanostructures with nonhomogeneous magnetic properties exhibit distinct magnon modes,and their interactions are crucial for understanding magnetization dynamics.In this work,we numerically investigate the mag...Magnetic nanostructures with nonhomogeneous magnetic properties exhibit distinct magnon modes,and their interactions are crucial for understanding magnetization dynamics.In this work,we numerically investigate the magnon-magnon coupling in a nanodisk with radially varying magnetic anisotropy by using micromagnetic simulations.By introducing perpendicular magnetic anisotropy into the inner region of the nanodisk,a radially chiral spin texture is observed.The presence of the chiral spin texture results in coupling between the ferromagnetic resonance mode of the whole disk and the higher-order confined modes in the outer region.Moreover,we find that the coupling strength is highly sensitive to the perpendicular magnetic anisotropy,the saturation magnetization,and the interfacial Dzyaloshinskii-Moriya interaction.Our findings could enrich the understanding of the dynamic characteristics of chiral nanomagnets and suggest a possible route to harnessing tunable magnon-magnon coupling for spin-based quantum information processing.展开更多
Advances in information processing technologies rely fundamentally on the ability to manipulate,convey,and discern the information carriers[1].Topological spin textures,prized for robustness,tunability,and low energy ...Advances in information processing technologies rely fundamentally on the ability to manipulate,convey,and discern the information carriers[1].Topological spin textures,prized for robustness,tunability,and low energy consumption,are promising information carriers for next-generation spintronic technologies.Current research,like racetrack memories and logic gates[2,3],focused on manipulating spin textures via electrons/photons,while leveraging spin textures to control electrons/photons in semiconductors remains scarce.展开更多
The dynamic recrystallization(DRX)behavior and texture formation mechanism in an AZ31 magnesium alloy wheel hub during the spinning process were investigated.Analysis using optical microscopy,electron backscatter diff...The dynamic recrystallization(DRX)behavior and texture formation mechanism in an AZ31 magnesium alloy wheel hub during the spinning process were investigated.Analysis using optical microscopy,electron backscatter diffraction,transmission electron microscopy,and finite element simulation revealed that continuous dynamic recrystallization(CDRX)and grain boundary bulging occurred simultaneously throughout the spinning process,leading to an increased proportion of DRXed grain areas.The newly formed DRXed grains largely retained the orientations of their deformed parent grains.The spinning process had two stages:initially,deformation was driven by basalslip as the roller contacted the alloy and descended to its lowest point.In the later stage,pyramidal<c+a>slips became predominant as additional force was applied along the spinning direction(SD),forming a final texture with the c-axis tilting±15°towards the SD.This texture development led to discernible anisotropy in tensile properties along the SD and the tangential direction(TD).展开更多
In this study, we investigate theoretically the effect of spin-orbit coupling on the energy level spectrum and spin texturing of a quantum wire with a parabolic confining potential subjected to the perpendicular magne...In this study, we investigate theoretically the effect of spin-orbit coupling on the energy level spectrum and spin texturing of a quantum wire with a parabolic confining potential subjected to the perpendicular magnetic field. Highly accurate numerical calculations have been carried out using a finite element method. Our results reveal that the interplay between the spin-orbit interaction and the effective magnetic field significantly modifies the band structure, producing additional subband extrema and energy gaps. Competing effects between external field and spin-orbit interactions introduce comp｜ex features in spin texturing owing to the couplings in energy subbands. We obtain that spatia~ modulation of the spin density along the wire width can be considerably modified by the spin-orbit coupling strength, magnetic field and charge carrier concentration.展开更多
In this work, we investigate the effects of interplay of spin-orbit interaction and in-plane magnetic fields on the electronic structure and spin texturing of parabolically confined quantum wire. Numerical results rev...In this work, we investigate the effects of interplay of spin-orbit interaction and in-plane magnetic fields on the electronic structure and spin texturing of parabolically confined quantum wire. Numerical results reveal that the competing effects between Rashba and Dresselhaus spin--orbit interactions and the external magnetic field lead to a complicated energy spectrum. We find that the spin texturing owing to the coupling between subbands can be modified by the strength of spin- orbit couplings as well as the magnitude and the orientation angle of the external magnetic field.展开更多
Recently,the altermagnets,a new kind of collinear antiferromagnet with nearly zero net magnetization and momentumdependent spin-splitting of bands,have sparked great interest.Despite simple magnetic structures,these a...Recently,the altermagnets,a new kind of collinear antiferromagnet with nearly zero net magnetization and momentumdependent spin-splitting of bands,have sparked great interest.Despite simple magnetic structures,these altermagnets exhibit intriguing and intricate dependence of anomalous Hall effect(AHE)on the Néel vector,in contrast to the conventional perpendicular configuration of Hall current with magnetization in ferromagnets.However,the fundamental relationship between the AHE and the Néel vector remains largely elusive.Here,we reveal all the unconventional anomalous Hall textures in the Néel vector space,dubbed anomalous-Hall Néel textures(AHNTs)for altermagnets.Specifically,we identify 10 types across four categories of AHNTs for all altermagnets.Notably,we find that AHNTs resemble the known spin textures in momentum space and further reveal their symmetry origin.Meanwhile,we examine our key discoveries in prototypical altermagnets.Our work offers a thorough understanding of AHE in altermagnets and a complete and pictorial classification of altermagnets based on the geometry of response functions.展开更多
Skyrmions—topological spin/pseudospin textures—are natural charge excitations of quantum Hall(QH)ferromagnets.In a WSe_(2)-encapsulated bilayer graphene(BLG)heterostructure,we tune the valley-only Landau level(LL)cr...Skyrmions—topological spin/pseudospin textures—are natural charge excitations of quantum Hall(QH)ferromagnets.In a WSe_(2)-encapsulated bilayer graphene(BLG)heterostructure,we tune the valley-only Landau level(LL)crossings atν=±3 with an out-of-plane displacement field(D field)and use them as a platform to probe valley excitations.Activation gap measurements reveal a finite gap at degeneracy that rises sharply with D field near the crossing and exceeds the single-particle valley susceptibility,suggesting valley-skyrmion charge excitations.We quantify the skyrmion size and elucidate the mechanism governing its magnetic-field dependence.Similar behavior appears at valley-orbital and valley-spin entangled crossings(ν=±2 andν=±1,respectively).These results suggest controlled valley-skyrmion formation in BLG and open a route to engineering interacting multicomponent QH ferromagnets with tunable spin/pseudospin textures.展开更多
Chiral magnetic skyrmions are topological swirling spin textures that hold promise for future information technology. The electrical nucleation and motion of skyrmions have been experimentally demonstrated in the last...Chiral magnetic skyrmions are topological swirling spin textures that hold promise for future information technology. The electrical nucleation and motion of skyrmions have been experimentally demonstrated in the last decade, while electrical detection compatible with semiconductor processes has not been achieved, and this is considered one of the most crucial gaps regarding the use of skyrmions in real applications. Here, we report the direct observation of nanoscale skyrmions in Co Fe B/Mg O-based magnetic tunnel junction devices at room temperature. High-resolution magnetic force microscopy imaging and tunneling magnetoresistance measurements are used to illustrate the electrical detection of skyrmions,which are stabilized under the cooperation of interfacial Dzyaloshinskii–Moriya interaction, perpendicular magnetic anisotropy, and dipolar stray field. This skyrmionic magnetic tunnel junction shows a stable nonlinear multilevel resistance thanks to its topological nature and tunable density of skyrmions under current pulse excitation. These features provide important perspectives for spintronics to realize highdensity memory and neuromorphic computing.展开更多
The aggregation of topological spin textures at nano and micro scales has prac-tical applications in spintronic technologies.Here,the authors report the in-plane current-induced proliferation and aggregation of bimero...The aggregation of topological spin textures at nano and micro scales has prac-tical applications in spintronic technologies.Here,the authors report the in-plane current-induced proliferation and aggregation of bimerons in a bulk chiral magnet.It is found that the spin-transfer torques can induce the proliferation and aggrega-tion of bimerons only in the presence of an appropriate out-of-plane magneticfield.It is also found that a relatively small damping and a relatively large non-adiabatic spin-transfer torque could lead to more pronounced bimeron proliferation and aggre-gation.Particularly,the current density should be larger than a certain threshold in order to trigger the proliferation;namely,the bimerons may only be driven into translational motion under weak current injection.Besides,the authorsfind that the aggregate bimerons could relax into a deformed honeycomb bimeron lattice with a few lattice structure defects after the current injection.The results are promising for the development of bio-inspired spintronic devices that use a large number of aggregate bimerons.Thefindings also provide a platform for studying aggregation-induced effects in spintronic systems,such as the aggregation-induced lattice phase transitions.展开更多
The topological Hall effect(THE) as a powerful probe for the experimental observation of topological spin textures, such as magnetic skyrmions, has been observed in a wide variety of distinct material systems. However...The topological Hall effect(THE) as a powerful probe for the experimental observation of topological spin textures, such as magnetic skyrmions, has been observed in a wide variety of distinct material systems. However, limited experimental observations have been reported for antiferromagnetic(AFM) materials. Here, the THE signals in the AFM state were observed in compensated ferrimagnetic thin films interfaced with heavy metals at the magnetization compensation temperature(TM).Ferrimagnetic CoTb thin films grown on Pt thin films were used in the experiments. The Co Tb films exhibited a magnetization compensation point at which the moments of Co and Tb sublattices canceled each other, giving rise to the AFM state. The temperature(T)-dependent Hall measurements showed anomalous Hall effect(AHE) and THE responses at T≠T_(M) but pure THE responses at T=T_(M). Control measurements and analyses suggest that the THE responses are associated with interfacial Dzyaloshinskii-Moriya interaction(DMI) rather than the overlapping of different AHE signals in the structure. This work presents the first-ever observation of interfacial DMI-induced THE in AFM metal trilayered systems and demonstrates a new approach for electrical reading of chiral spin textures in AFM thin film-based heterostructures.展开更多
Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium.Recent experimental progress is much from optical,cold-atomic,and classical platforms due to the vast tunability and c...Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium.Recent experimental progress is much from optical,cold-atomic,and classical platforms due to the vast tunability and clear identification of observables.However,their counterpart in solid-state electronic systems in equilibrium remains unmasked although highly desired,where a variety of materials are available,calculations are solidly founded,and accurate spectroscopic techniques can be applied.We demonstrate that,in the surface state of a topological insulator with spin-dependent relaxation due to magnetic impurities,highly nontrivial topological soliton spin textures appear in momentum space.Such spin-channel phenomena are delicately related to the type of non-Hermiticity and correctly reveal the most robust non-Hermitian features detectable spectroscopically.Moreover,the distinct topological soliton objects can be deformed to each other,mediated by topological transitions driven by tuning across a critical direction of doped magnetism.These results not only open a solid-state avenue to exotic spin patterns via spin-and angle-resolved photoemission spectroscopy,but also inspire non-Hermitian dissipation engineering of spins in solids.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 12174382)the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB0460000 and XDB28000000)the Innovation Program for Quantum Science and Technology (Grant Nos. 2024ZD0300104 and 2021ZD0302600)。
文摘The competition between dimensionality and ordering in multiferroic materials is of great interest for both fundamental physics and potential applications. Combining first-principles calculations with micromagnetic simulations, we investigate recently synthesized ultrathin perovskite bismuth ferrite(BFO) films. Our numerical results reveal that, at the monolayer limit, the ferroelectricity of BFO is missing because the octahedral distortions are constrained. However, the monolayer bismuth ferrite is a topological antiferromagnetic metal with tunable bimeron magnetic structure. The dual topologically non-trivial characteristics make monolayer bismuth ferrite a multifunctional building block in future spintronic devices.
基金supported by the National Key Research and Development Program of China(Grant No.2023YFF0718400)the National Natural Science Foundation of China(Grant Nos.12474119 and 12074189)。
文摘Magnetic nanostructures with nonhomogeneous magnetic properties exhibit distinct magnon modes,and their interactions are crucial for understanding magnetization dynamics.In this work,we numerically investigate the magnon-magnon coupling in a nanodisk with radially varying magnetic anisotropy by using micromagnetic simulations.By introducing perpendicular magnetic anisotropy into the inner region of the nanodisk,a radially chiral spin texture is observed.The presence of the chiral spin texture results in coupling between the ferromagnetic resonance mode of the whole disk and the higher-order confined modes in the outer region.Moreover,we find that the coupling strength is highly sensitive to the perpendicular magnetic anisotropy,the saturation magnetization,and the interfacial Dzyaloshinskii-Moriya interaction.Our findings could enrich the understanding of the dynamic characteristics of chiral nanomagnets and suggest a possible route to harnessing tunable magnon-magnon coupling for spin-based quantum information processing.
基金supported by the National Key Research and Development Program of China(2022YFB3605604)the National Natural Science Foundation of China(62274139,61974123,62304188,62374143,and 62374144)+2 种基金the Natural Science Foundation of Fujian Province(2025J011001)the Basic Research Funds for Central Universities(20720220025)the Grants-in-Aid for Scientific Research from JSPS KAKENHI(JP25K17939 and JP20F20363).
文摘Advances in information processing technologies rely fundamentally on the ability to manipulate,convey,and discern the information carriers[1].Topological spin textures,prized for robustness,tunability,and low energy consumption,are promising information carriers for next-generation spintronic technologies.Current research,like racetrack memories and logic gates[2,3],focused on manipulating spin textures via electrons/photons,while leveraging spin textures to control electrons/photons in semiconductors remains scarce.
基金funded by the National Natural Science Foundation of China(No.52204407)the Natural Science Foundation of Jiangsu Province,China(No.BK20220595)the China Postdoctoral Science Foundation(No.2022M723689)。
文摘The dynamic recrystallization(DRX)behavior and texture formation mechanism in an AZ31 magnesium alloy wheel hub during the spinning process were investigated.Analysis using optical microscopy,electron backscatter diffraction,transmission electron microscopy,and finite element simulation revealed that continuous dynamic recrystallization(CDRX)and grain boundary bulging occurred simultaneously throughout the spinning process,leading to an increased proportion of DRXed grain areas.The newly formed DRXed grains largely retained the orientations of their deformed parent grains.The spinning process had two stages:initially,deformation was driven by basalslip as the roller contacted the alloy and descended to its lowest point.In the later stage,pyramidal<c+a>slips became predominant as additional force was applied along the spinning direction(SD),forming a final texture with the c-axis tilting±15°towards the SD.This texture development led to discernible anisotropy in tensile properties along the SD and the tangential direction(TD).
基金Project supported by Research Grants DEU-BAP：2009183 and DEU-BAP：2009184 from Scientific Research Fund of Dokuz EyliJl University.
文摘In this study, we investigate theoretically the effect of spin-orbit coupling on the energy level spectrum and spin texturing of a quantum wire with a parabolic confining potential subjected to the perpendicular magnetic field. Highly accurate numerical calculations have been carried out using a finite element method. Our results reveal that the interplay between the spin-orbit interaction and the effective magnetic field significantly modifies the band structure, producing additional subband extrema and energy gaps. Competing effects between external field and spin-orbit interactions introduce comp｜ex features in spin texturing owing to the couplings in energy subbands. We obtain that spatia~ modulation of the spin density along the wire width can be considerably modified by the spin-orbit coupling strength, magnetic field and charge carrier concentration.
文摘In this work, we investigate the effects of interplay of spin-orbit interaction and in-plane magnetic fields on the electronic structure and spin texturing of parabolically confined quantum wire. Numerical results reveal that the competing effects between Rashba and Dresselhaus spin--orbit interactions and the external magnetic field lead to a complicated energy spectrum. We find that the spin texturing owing to the coupling between subbands can be modified by the strength of spin- orbit couplings as well as the magnitude and the orientation angle of the external magnetic field.
基金supported by the National Key Research and Development Program of China(Grant Nos.2024YFA1611300,and 2023YFA1406500)the National Natural Science Foundation of China(Grant Nos.12474100,12204009,12204003,and 12174394)+4 种基金the Natural Science Foundation of Anhui Province(Grant No.2208085QA08)the HFIPS Director's Fund(Grant Nos.YZJJQY202304,and BJPY2023B05)the Anhui Provincial Major S&T Project(Grant No.s202305a12020005)the High Magnetic Field Laboratory of Anhui Province(Grant No.AHHMFX-2020-02)the Basic Research Program of the Chinese Academy of Sciences Based on Major Scientific Infrastructures(Grant No.JZHKYPT-2021-08)。
文摘Recently,the altermagnets,a new kind of collinear antiferromagnet with nearly zero net magnetization and momentumdependent spin-splitting of bands,have sparked great interest.Despite simple magnetic structures,these altermagnets exhibit intriguing and intricate dependence of anomalous Hall effect(AHE)on the Néel vector,in contrast to the conventional perpendicular configuration of Hall current with magnetization in ferromagnets.However,the fundamental relationship between the AHE and the Néel vector remains largely elusive.Here,we reveal all the unconventional anomalous Hall textures in the Néel vector space,dubbed anomalous-Hall Néel textures(AHNTs)for altermagnets.Specifically,we identify 10 types across four categories of AHNTs for all altermagnets.Notably,we find that AHNTs resemble the known spin textures in momentum space and further reveal their symmetry origin.Meanwhile,we examine our key discoveries in prototypical altermagnets.Our work offers a thorough understanding of AHE in altermagnets and a complete and pictorial classification of altermagnets based on the geometry of response functions.
基金Peking University was supported by the National Key Research and Development Program of China(Grant No.2021YFA1401900)the National Natural Science Foundation of China(NSFC)(Grant No.12141001)+2 种基金Zhejiang University was supported by the NSFC(Grant Nos.12374047 and U23A2076)the Fundamental Research Funds for the Central Universities(Grant No.226-2025-00118)the National Key Research and Development Program of China(Grant No.2021YFA1401902 for Z.L.)。
文摘Skyrmions—topological spin/pseudospin textures—are natural charge excitations of quantum Hall(QH)ferromagnets.In a WSe_(2)-encapsulated bilayer graphene(BLG)heterostructure,we tune the valley-only Landau level(LL)crossings atν=±3 with an out-of-plane displacement field(D field)and use them as a platform to probe valley excitations.Activation gap measurements reveal a finite gap at degeneracy that rises sharply with D field near the crossing and exceeds the single-particle valley susceptibility,suggesting valley-skyrmion charge excitations.We quantify the skyrmion size and elucidate the mechanism governing its magnetic-field dependence.Similar behavior appears at valley-orbital and valley-spin entangled crossings(ν=±2 andν=±1,respectively).These results suggest controlled valley-skyrmion formation in BLG and open a route to engineering interacting multicomponent QH ferromagnets with tunable spin/pseudospin textures.
基金financial support from the National Key R&D Program of China(2018YFB0407602,and 2020YFA0309300)National Natural Science Foundation of China(61627813,61871008,62001019,12004024,and 51901081)+5 种基金Beijing Natural Science Foundation(4202043)Beijing Nova Program from Beijing Municipal Science and Technology Commission(Z201100006820042)National Natural Science Foundation of China-German Research Foundation(52061135105)Outstanding Research Project of Shen Yuan Honors College,BUAA(230121102)the Science and Technology Program of Guangzhou(202002030052)Joint Research Key Fund for Guangzhou and Shen Zhen(2021B1515120047)。
文摘Chiral magnetic skyrmions are topological swirling spin textures that hold promise for future information technology. The electrical nucleation and motion of skyrmions have been experimentally demonstrated in the last decade, while electrical detection compatible with semiconductor processes has not been achieved, and this is considered one of the most crucial gaps regarding the use of skyrmions in real applications. Here, we report the direct observation of nanoscale skyrmions in Co Fe B/Mg O-based magnetic tunnel junction devices at room temperature. High-resolution magnetic force microscopy imaging and tunneling magnetoresistance measurements are used to illustrate the electrical detection of skyrmions,which are stabilized under the cooperation of interfacial Dzyaloshinskii–Moriya interaction, perpendicular magnetic anisotropy, and dipolar stray field. This skyrmionic magnetic tunnel junction shows a stable nonlinear multilevel resistance thanks to its topological nature and tunable density of skyrmions under current pulse excitation. These features provide important perspectives for spintronics to realize highdensity memory and neuromorphic computing.
基金Waseda University,Grant/Award Number:2024C-153Shenzhen Peacock Group Plan,Grant/Award Number:KQTD20180413181702403+4 种基金National Natural Science Foundation of China,Grant/Award Number:12374123Shenzhen Fundamental Research Program,Grant/Award Number:JCYJ20210324120213037Basic and Applied Basic Research Foundation of Guangdong Province,Grant/Award Number:2021B1515120047Japan Science and Technology Agency,Grant/Award Number:JPMJCR20T1Japan Society for the Promotion of Science,Grant/Award Numbers:JP20H00337,JP23H04522,JP24H02231。
文摘The aggregation of topological spin textures at nano and micro scales has prac-tical applications in spintronic technologies.Here,the authors report the in-plane current-induced proliferation and aggregation of bimerons in a bulk chiral magnet.It is found that the spin-transfer torques can induce the proliferation and aggrega-tion of bimerons only in the presence of an appropriate out-of-plane magneticfield.It is also found that a relatively small damping and a relatively large non-adiabatic spin-transfer torque could lead to more pronounced bimeron proliferation and aggre-gation.Particularly,the current density should be larger than a certain threshold in order to trigger the proliferation;namely,the bimerons may only be driven into translational motion under weak current injection.Besides,the authorsfind that the aggregate bimerons could relax into a deformed honeycomb bimeron lattice with a few lattice structure defects after the current injection.The results are promising for the development of bio-inspired spintronic devices that use a large number of aggregate bimerons.Thefindings also provide a platform for studying aggregation-induced effects in spintronic systems,such as the aggregation-induced lattice phase transitions.
基金supported by the National Key R&D Program of China(Grant No.2017YFB0405703)the National Natural Science Foundation of China(Grant Nos.51571136,61434002,51871137,and 51901118)the Graduate Student Innovation Project in Shanxi Province(Grant No.2020BY082)。
文摘The topological Hall effect(THE) as a powerful probe for the experimental observation of topological spin textures, such as magnetic skyrmions, has been observed in a wide variety of distinct material systems. However, limited experimental observations have been reported for antiferromagnetic(AFM) materials. Here, the THE signals in the AFM state were observed in compensated ferrimagnetic thin films interfaced with heavy metals at the magnetization compensation temperature(TM).Ferrimagnetic CoTb thin films grown on Pt thin films were used in the experiments. The Co Tb films exhibited a magnetization compensation point at which the moments of Co and Tb sublattices canceled each other, giving rise to the AFM state. The temperature(T)-dependent Hall measurements showed anomalous Hall effect(AHE) and THE responses at T≠T_(M) but pure THE responses at T=T_(M). Control measurements and analyses suggest that the THE responses are associated with interfacial Dzyaloshinskii-Moriya interaction(DMI) rather than the overlapping of different AHE signals in the structure. This work presents the first-ever observation of interfacial DMI-induced THE in AFM metal trilayered systems and demonstrates a new approach for electrical reading of chiral spin textures in AFM thin film-based heterostructures.
基金supported by JSPS KAKENHI(18H03676)JST CREST(JPMJCR1874)supported by RIKEN Special Postdoctoral Researcher Program。
文摘Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium.Recent experimental progress is much from optical,cold-atomic,and classical platforms due to the vast tunability and clear identification of observables.However,their counterpart in solid-state electronic systems in equilibrium remains unmasked although highly desired,where a variety of materials are available,calculations are solidly founded,and accurate spectroscopic techniques can be applied.We demonstrate that,in the surface state of a topological insulator with spin-dependent relaxation due to magnetic impurities,highly nontrivial topological soliton spin textures appear in momentum space.Such spin-channel phenomena are delicately related to the type of non-Hermiticity and correctly reveal the most robust non-Hermitian features detectable spectroscopically.Moreover,the distinct topological soliton objects can be deformed to each other,mediated by topological transitions driven by tuning across a critical direction of doped magnetism.These results not only open a solid-state avenue to exotic spin patterns via spin-and angle-resolved photoemission spectroscopy,but also inspire non-Hermitian dissipation engineering of spins in solids.
