We have studied the magnetic and electrical transport properties of epitaxial NiAs-type CrTe thin films grown on SrTiO3(111) substrates. Unlike rectangle hysteresis loops obtained from magnetic measurements, we have...We have studied the magnetic and electrical transport properties of epitaxial NiAs-type CrTe thin films grown on SrTiO3(111) substrates. Unlike rectangle hysteresis loops obtained from magnetic measurements, we have identified intriguing extra bump/dip features from anomalous Hall experiments on the films with thicknesses less than 12 nm. This observed Hall anomaly is phenomenologically consistent with the occurrence of a topological Hall effect (THE) in chiral magnets with a skyrmion phase. Furthermore, the THE contribution can be tuned by the film thickness, showing the key contribution of asymmetric interfaces in stabilizing N6el-type skyrmions. Our work demonstrates that a CrTe thin film on SrTiO3(111) substrates is a good material candidate for studying real-space topological transport.展开更多
Mixed-valance manganites with strong electron correlation exhibit strong potential for spintronics,where emergent magnetic behaviors,such as propagation of high-frequency spin waves and giant topological Hall Effects ...Mixed-valance manganites with strong electron correlation exhibit strong potential for spintronics,where emergent magnetic behaviors,such as propagation of high-frequency spin waves and giant topological Hall Effects can be driven by their mesoscale spin textures.Here,we create magnetic vortex clusters with flux closure spin configurations in single-crystal La0.67Sr0.33MnO3 wire.A distinctive transformation from out-of-plane domains to a vortex state is directly visualized using magnetic force microscopy at 4 K in wires when the width is below 1.0μm.The phase-field modeling indicates that the inhomogeneous strain,accompanying with shape anisotropy,plays a key role for stabilizing the flux-closure spin structure.This work offers a new perspective for understanding and manipulating the non-trivial spin textures in strongly correlated systems.展开更多
Oxygen usually plays crucial roles in tuning the phase structures and functionalities of complex oxides such as high temperature superconductivity, colossal magnetoresistance, catalysis, etc. Effective and considerabl...Oxygen usually plays crucial roles in tuning the phase structures and functionalities of complex oxides such as high temperature superconductivity, colossal magnetoresistance, catalysis, etc. Effective and considerable control of the oxygen content in those functional oxides could be highly desired. Here, using perovskite manganite(La0.5Sr0.5)MnO3 as a paradigm, we develop a new pathway to synthesize the epitaxial thin films assisted by an in-situ chemical process, where the oxygen content can be precisely controlled by varying oxidative activity tuned by the atmospheric temperature(Tatm)during the growth. A hidden metal-insulator transition(MIT)emerges due to the phase competition, which is never shown in the phase diagram of this classic manganite. The oxygenmediated interaction between Mn ions together with the change of carrier density might be responsible for this emerging phase, which is compatible with the results of firstprinciple calculations. This work demonstrates that, apart from traditional cation doping, a precise modulation of anion(O2-, S2-, etc.) may provide a new strategy to control phase structures and functionalities of epitaxial compound thin films.展开更多
The ability to control magnetic vortex is critical for their potential applications in spintronic devices.Traditional methods including magnetic field,spin-polarized current etc.have been used to flip the core and/or ...The ability to control magnetic vortex is critical for their potential applications in spintronic devices.Traditional methods including magnetic field,spin-polarized current etc.have been used to flip the core and/or reverse circulation of vortex.However,it is challenging for deterministic electric-field control of the single magnetic vortex textures with time-reversal broken symmetry and no planar magnetic anisotropy.Here it is reported that a deterministic reversal of single magnetic vortex circulation can be driven back and forth by a space-varying strain in multiferroic heterostructures,which is controlled by using a bi-axial pulsed electric field.Phase-field simulation reveals the mechanism of the emerging magnetoelastic energy with the space variation and visualizes the reversal pathway of the vortex.This deterministic electric-field control of the single magnetic vortex textures demonstrates a new approach to integrate the low-dimensional spin texture into the magnetoelectric thin film devices with low energy consumption.展开更多
Solid state reaction is a conventional method to synthesize structurally stable inorganic solids by mixing powdered reactants together at high pressure (over 1 x 105 mbar (1 mbar = 100 Pa)) and high temperature (...Solid state reaction is a conventional method to synthesize structurally stable inorganic solids by mixing powdered reactants together at high pressure (over 1 x 105 mbar (1 mbar = 100 Pa)) and high temperature (over 1300 K) [1-4]. This method is effective and sophisticated to prepare solid mate- rials, especially the functional complex oxides such as high temperature superconductors, piezoelectrics, dielectrics, etc. However, the chemical reactions cannot be intrinsically con- trolled and integrated at an atomic level in order to achieve the applications of future thin film devices with reduced dimensions [5]. With the desire of designing high-quality products with the micro/nanoscale integration, many pow- erful physical techniques, such as, pulsed-laser deposition (PLD), molecular beam epitaxy (MBE), sputtering deposi- tion, etc., have experienced enormous development due to their ability of lattice and/or interfacial controls. Using these growth techniques, layer-by-layer deposition (multilayer and/or superlattice) can be achieved, providing us a platform to tune the crystal structures at an atomic level by controlling the interfacial terminations and epitaxial strain, which are absent in their bulk counterparts [6-8]. From this point of view, well-controlled interfacial structures may also provide the solid state reaction at an atomic level during the physical depositions, which provides us an effective way to design the desired products from the chemical bonding reconstruction.展开更多
Rare earth orthoferrites(RFeO3,R=Y,Gd,Sm,Nd)have recently attracted much attention due to their novel magnetic and electrical properties such as magneto-electrics,magneto-dielectrics.and magneto-optics[1-3].The comple...Rare earth orthoferrites(RFeO3,R=Y,Gd,Sm,Nd)have recently attracted much attention due to their novel magnetic and electrical properties such as magneto-electrics,magneto-dielectrics.and magneto-optics[1-3].The complex interactions between the two sublattices of R^3+and Fe^3+in RFeO3 provide the feasibility of control-ling spins in these solids,which makes them promising candidates for the spintronics[4].展开更多
In recent years,iridium oxides have attracted intensive research interests both in experiments and theories due to their comparable energy scales of the Coulomb repulsion and strong spin-orbit coupling(SOC)[1,2],where...In recent years,iridium oxides have attracted intensive research interests both in experiments and theories due to their comparable energy scales of the Coulomb repulsion and strong spin-orbit coupling(SOC)[1,2],where a plenty of novel quantum states such as Weyl semimetal,topological insulator and quantum spin liquid have been studied[3–7].Among the iridates,the layered-perovskite Sr2IrO4(SIO)is a Jeff=1/2 Mott insulating antiferromagnet caused by the interplay of the SOC and electronic correlations[8,9].展开更多
Control of magnetic anisotropy in low-dimensional systems is of paramount importance in terms of their fundamental and technological perspectives.La_(0.7)Sr_(0.3)MnO_(3)(LSMO)is a ferromagnetic half-metal with a high ...Control of magnetic anisotropy in low-dimensional systems is of paramount importance in terms of their fundamental and technological perspectives.La_(0.7)Sr_(0.3)MnO_(3)(LSMO)is a ferromagnetic half-metal with a high Curie temperature and many efforts have been made to control its magnetic anisotropy.However,the relationship between the evolution of the magnetic anisotropy orientation and the electronic structure of low-dimensional LSMO still remains poorly understood.Here,the high-quality superlattices comprised of LSMO and SrMnO_(3)(SMO)layers are synthesized with a compatible structure at the atomic scale.Their magnetic anisotropy is gradually varied from planar to perpendicular by increasing the SMO thickness,and the special fourfold magnetic anisotropy is also observed at the intermediate superlattice thickness.The evolution of the magnetic anisotropy in these systems is confirmed by the electronic transport and magnetic measurements.Moreover,X-ray linear dichroism measurements and first-principles calculations reveal the interfacial orbital reconstruction with the in-plane to out-ofplane magnetic reorientation transition.Therefore,a new microscopic method for magnetic anisotropy manipulation is developed in the present study,enabling discovery of novel phenomena as well as control of the magnetic properties.展开更多
With the ever-growing demand of clean water for the healthy world,water purification has become an urgent global issue.Singlet oxygen(^(1)O_(2))as unique non-radical derivative of oxygen,possessing unoccupiedπ*orbita...With the ever-growing demand of clean water for the healthy world,water purification has become an urgent global issue.Singlet oxygen(^(1)O_(2))as unique non-radical derivative of oxygen,possessing unoccupiedπ*orbital and exhibiting high selectivity towards electron-rich organic pollutants.Nevertheless,most of the approaches suffer from low-efficiency or biotoxicity,which severely restrict their potential applications.Therefore,in this work,we propose a general strategy via photoelectrocatalytic for selectively reducing oxygen to^(1)O_(2)with designed carbon bridged carbon nitride(CBCN).This work highlights the important role of synergistic photo-electro-catalytic effect for selectively generating the^(1)O_(2)via oxygen reduction pathway,which can be a promising way especially for degrading electron-rich pollutants.展开更多
Good dispersibility of graphene in a medium or matrix is a critical issue in practical applications.In this work,graphene was functionalized using N-(4-hydroxyl phenyl)maleimide(4-HPM)via the Diels—Alder(DA)reaction ...Good dispersibility of graphene in a medium or matrix is a critical issue in practical applications.In this work,graphene was functionalized using N-(4-hydroxyl phenyl)maleimide(4-HPM)via the Diels—Alder(DA)reaction by a one-step catalyst-free approach.The optimal reaction condition was found to be 90℃for 12 h using dimethytformamide(DMF)as the solvent.FTIR,Raman spectroscopy,XPS and EDS proved that 4-HPM moieties were successfully grafted onto the surface of graphene.UVvis and TGA confirmed that the grafting amount of 4-HPM was 3.75%-3.97%based on the mass of graphene.Functionalized graphene showed excellent dispersion stability when dispersed in common solvents such as ethanol,DMF,water,tetrahydrofuran and pxylene.Meanwhile,functionalized graphene also exhibited pH sensitivity in aqueous due to the phenolic hydroxyls from the 4-HPM moieties.As a result of good dispersion stability and pH sensitivity,compared with graphene,functionalized graphene had better adsorption capacity for methylene blue(MB)from aqueous solution.展开更多
Domain walls/boundaries in ferroic materials usuallyexhibit properties which do not exist in their bulks (e.g.,superconducting, piezoelectricity, etc.) [1,2]. Ferroelectricdomain walls with a size of several nanomet...Domain walls/boundaries in ferroic materials usuallyexhibit properties which do not exist in their bulks (e.g.,superconducting, piezoelectricity, etc.) [1,2]. Ferroelectricdomain walls with a size of several nanometers displayexotic conduction [3-5] among their insulating bulk. Dueto its electric-field controllable nature, ferroelectric/mul-tiferroic domain walls could be a promising candidate forhigh-density data storage or logic devices with ultralowenergy consumption.展开更多
Most economic and industrial processes are governed by inherently nonlinear dynamic system in which mathematical analysis (with few exceptions) is unable to provide general solutions; even the conditions to the exis...Most economic and industrial processes are governed by inherently nonlinear dynamic system in which mathematical analysis (with few exceptions) is unable to provide general solutions; even the conditions to the existence of equilibrium point for the nonlinear dynamic system are simply not established in some special cases. In this paper, based on numerical solution of a nonlinear multi-stage automatic control dynamic (NMACD) in fed-batch culture of glycerol bioconversion to 1,3-propanediol (1,3-PD) induced by KlebsieUa pneumoniae (K. pneumoniae), we consider an optimal design of the NMACD system. For convenience, the NMACD system is reconstructed together with the existence, uniqueness and continuity of solutions are discussed. Our goal is to prove the strong stability with respect to the perturbation of initial state for the solution to the NMACD system. To this end, we construct corresponding linear variational system for the solution to the NMACD system, and also prove the boundedness of fundamental matrix solutions to the linear variational system. On this basis, we prove the strong stability appearing above through the application of this boundedness.展开更多
文摘We have studied the magnetic and electrical transport properties of epitaxial NiAs-type CrTe thin films grown on SrTiO3(111) substrates. Unlike rectangle hysteresis loops obtained from magnetic measurements, we have identified intriguing extra bump/dip features from anomalous Hall experiments on the films with thicknesses less than 12 nm. This observed Hall anomaly is phenomenologically consistent with the occurrence of a topological Hall effect (THE) in chiral magnets with a skyrmion phase. Furthermore, the THE contribution can be tuned by the film thickness, showing the key contribution of asymmetric interfaces in stabilizing N6el-type skyrmions. Our work demonstrates that a CrTe thin film on SrTiO3(111) substrates is a good material candidate for studying real-space topological transport.
基金supported by the National Key Research and Development Program of China(2016YFA0302300)the Beijing Natural Science Foundation(Z190008)+9 种基金the National Natural Science Foundation of China(11974052 and 11474024)the Beamline 1W1A of the Beijing Synchrotron Radiation Facilitythe National Natural Science Foundation of China(11604011)Beijing Institute of Technology Research Fund Program for Young Scholarsthe National Natural Science Foundation of China(11672264 and 11621062)support by the German Research Foundation DFG SFB TRR173 Spin+X,project KL1811/18the Graduate School of Excellence Materials Science in Mainz(GSC266)Peking University was supported by the National Key R&D Program of China(2016YFA0300804)the National Natural Science Foundation of China(11974023 and 51672007)the Key R&D Program of Guangdong Province(2018B030327001 and 2018B010109009).
文摘Mixed-valance manganites with strong electron correlation exhibit strong potential for spintronics,where emergent magnetic behaviors,such as propagation of high-frequency spin waves and giant topological Hall Effects can be driven by their mesoscale spin textures.Here,we create magnetic vortex clusters with flux closure spin configurations in single-crystal La0.67Sr0.33MnO3 wire.A distinctive transformation from out-of-plane domains to a vortex state is directly visualized using magnetic force microscopy at 4 K in wires when the width is below 1.0μm.The phase-field modeling indicates that the inhomogeneous strain,accompanying with shape anisotropy,plays a key role for stabilizing the flux-closure spin structure.This work offers a new perspective for understanding and manipulating the non-trivial spin textures in strongly correlated systems.
基金financially supported by the National Key Research and Development Program of China (2016YFA0302300)the support from the National Natural Science Foundation of China (51332001)the Fundamental Research Funds for the Central Universities (2017EYT26)
文摘Oxygen usually plays crucial roles in tuning the phase structures and functionalities of complex oxides such as high temperature superconductivity, colossal magnetoresistance, catalysis, etc. Effective and considerable control of the oxygen content in those functional oxides could be highly desired. Here, using perovskite manganite(La0.5Sr0.5)MnO3 as a paradigm, we develop a new pathway to synthesize the epitaxial thin films assisted by an in-situ chemical process, where the oxygen content can be precisely controlled by varying oxidative activity tuned by the atmospheric temperature(Tatm)during the growth. A hidden metal-insulator transition(MIT)emerges due to the phase competition, which is never shown in the phase diagram of this classic manganite. The oxygenmediated interaction between Mn ions together with the change of carrier density might be responsible for this emerging phase, which is compatible with the results of firstprinciple calculations. This work demonstrates that, apart from traditional cation doping, a precise modulation of anion(O2-, S2-, etc.) may provide a new strategy to control phase structures and functionalities of epitaxial compound thin films.
基金supported by the National Key Research and Development Program of China(2016YFA0302300 and 2017YFA0206200)Basic Science Center Program of the National Natural Science Foundation of China(51788104)+5 种基金National Natural Science Foundation of China(11974052,51972028)Beijing Natural Science Foundation(Z190008)Chinese Academy of Sciences Interdisciplinary Innovation Teamfunded by the Director,Office of Science,Office of Basic Energy Sciences,Materials Science and Engineering Department of the US Department of Energy(DOE)in the Quantum Materials Program(KC2202)under Contract No.DEAC02-05CH11231the support by the Science Alliance Joint Directed Research&Development Programthe Transdisciplinary Academy Program at the University of Tennessee。
文摘The ability to control magnetic vortex is critical for their potential applications in spintronic devices.Traditional methods including magnetic field,spin-polarized current etc.have been used to flip the core and/or reverse circulation of vortex.However,it is challenging for deterministic electric-field control of the single magnetic vortex textures with time-reversal broken symmetry and no planar magnetic anisotropy.Here it is reported that a deterministic reversal of single magnetic vortex circulation can be driven back and forth by a space-varying strain in multiferroic heterostructures,which is controlled by using a bi-axial pulsed electric field.Phase-field simulation reveals the mechanism of the emerging magnetoelastic energy with the space variation and visualizes the reversal pathway of the vortex.This deterministic electric-field control of the single magnetic vortex textures demonstrates a new approach to integrate the low-dimensional spin texture into the magnetoelectric thin film devices with low energy consumption.
基金supported by the National Natural Science Foundation of China(Grant Nos.51332001,11604011,and 11404016)the National Basic Research Program of China(Grant No.2014CB920902)Open Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications)(Grand No.2016B002)
文摘Solid state reaction is a conventional method to synthesize structurally stable inorganic solids by mixing powdered reactants together at high pressure (over 1 x 105 mbar (1 mbar = 100 Pa)) and high temperature (over 1300 K) [1-4]. This method is effective and sophisticated to prepare solid mate- rials, especially the functional complex oxides such as high temperature superconductors, piezoelectrics, dielectrics, etc. However, the chemical reactions cannot be intrinsically con- trolled and integrated at an atomic level in order to achieve the applications of future thin film devices with reduced dimensions [5]. With the desire of designing high-quality products with the micro/nanoscale integration, many pow- erful physical techniques, such as, pulsed-laser deposition (PLD), molecular beam epitaxy (MBE), sputtering deposi- tion, etc., have experienced enormous development due to their ability of lattice and/or interfacial controls. Using these growth techniques, layer-by-layer deposition (multilayer and/or superlattice) can be achieved, providing us a platform to tune the crystal structures at an atomic level by controlling the interfacial terminations and epitaxial strain, which are absent in their bulk counterparts [6-8]. From this point of view, well-controlled interfacial structures may also provide the solid state reaction at an atomic level during the physical depositions, which provides us an effective way to design the desired products from the chemical bonding reconstruction.
基金the National Key Research and Development Program of China(2016YFB0700901,2017YFA0206303,2017YFA0206301 and 2017YFA0403701)the National Natural Science Foundation of China(51731001,11675006 and11805006)。
文摘Rare earth orthoferrites(RFeO3,R=Y,Gd,Sm,Nd)have recently attracted much attention due to their novel magnetic and electrical properties such as magneto-electrics,magneto-dielectrics.and magneto-optics[1-3].The complex interactions between the two sublattices of R^3+and Fe^3+in RFeO3 provide the feasibility of control-ling spins in these solids,which makes them promising candidates for the spintronics[4].
基金the support from the National Key Research and Development Program of China(2016YFA0302300)CAS Interdisciplinary Innovation Team+2 种基金the support from the National Natural Science Foundation of China(11974052)Beijing Natural Science Foundation(Z190008)the beamline 1W1A of Beijing Synchrotron Radiation Facility。
文摘In recent years,iridium oxides have attracted intensive research interests both in experiments and theories due to their comparable energy scales of the Coulomb repulsion and strong spin-orbit coupling(SOC)[1,2],where a plenty of novel quantum states such as Weyl semimetal,topological insulator and quantum spin liquid have been studied[3–7].Among the iridates,the layered-perovskite Sr2IrO4(SIO)is a Jeff=1/2 Mott insulating antiferromagnet caused by the interplay of the SOC and electronic correlations[8,9].
基金financially supported by the National Natural Science Foundation of China(51901118,51871137,12174237,and 52171183)the 1331 Engineering of Shanxi Province+1 种基金the Research Project Supported by Shanxi Scholarship Council of China(2021-093)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(2020L0237)。
文摘Control of magnetic anisotropy in low-dimensional systems is of paramount importance in terms of their fundamental and technological perspectives.La_(0.7)Sr_(0.3)MnO_(3)(LSMO)is a ferromagnetic half-metal with a high Curie temperature and many efforts have been made to control its magnetic anisotropy.However,the relationship between the evolution of the magnetic anisotropy orientation and the electronic structure of low-dimensional LSMO still remains poorly understood.Here,the high-quality superlattices comprised of LSMO and SrMnO_(3)(SMO)layers are synthesized with a compatible structure at the atomic scale.Their magnetic anisotropy is gradually varied from planar to perpendicular by increasing the SMO thickness,and the special fourfold magnetic anisotropy is also observed at the intermediate superlattice thickness.The evolution of the magnetic anisotropy in these systems is confirmed by the electronic transport and magnetic measurements.Moreover,X-ray linear dichroism measurements and first-principles calculations reveal the interfacial orbital reconstruction with the in-plane to out-ofplane magnetic reorientation transition.Therefore,a new microscopic method for magnetic anisotropy manipulation is developed in the present study,enabling discovery of novel phenomena as well as control of the magnetic properties.
基金funding from the National Natural Science Foundation of China(Nos.22076142,21677106,22076140)National Key Basic Research Program of China(No.2017YFA0403402)+2 种基金National Natural Science Foundation of China(No.U1932119)the Science&Technology Commission of Shanghai Municipality(No.14DZ2261100)the Fundamental Research Funds for the Central Universities.
文摘With the ever-growing demand of clean water for the healthy world,water purification has become an urgent global issue.Singlet oxygen(^(1)O_(2))as unique non-radical derivative of oxygen,possessing unoccupiedπ*orbital and exhibiting high selectivity towards electron-rich organic pollutants.Nevertheless,most of the approaches suffer from low-efficiency or biotoxicity,which severely restrict their potential applications.Therefore,in this work,we propose a general strategy via photoelectrocatalytic for selectively reducing oxygen to^(1)O_(2)with designed carbon bridged carbon nitride(CBCN).This work highlights the important role of synergistic photo-electro-catalytic effect for selectively generating the^(1)O_(2)via oxygen reduction pathway,which can be a promising way especially for degrading electron-rich pollutants.
基金the National Natural Science Foundation of China(Grant No.51573211)for financial support.
文摘Good dispersibility of graphene in a medium or matrix is a critical issue in practical applications.In this work,graphene was functionalized using N-(4-hydroxyl phenyl)maleimide(4-HPM)via the Diels—Alder(DA)reaction by a one-step catalyst-free approach.The optimal reaction condition was found to be 90℃for 12 h using dimethytformamide(DMF)as the solvent.FTIR,Raman spectroscopy,XPS and EDS proved that 4-HPM moieties were successfully grafted onto the surface of graphene.UVvis and TGA confirmed that the grafting amount of 4-HPM was 3.75%-3.97%based on the mass of graphene.Functionalized graphene showed excellent dispersion stability when dispersed in common solvents such as ethanol,DMF,water,tetrahydrofuran and pxylene.Meanwhile,functionalized graphene also exhibited pH sensitivity in aqueous due to the phenolic hydroxyls from the 4-HPM moieties.As a result of good dispersion stability and pH sensitivity,compared with graphene,functionalized graphene had better adsorption capacity for methylene blue(MB)from aqueous solution.
文摘Domain walls/boundaries in ferroic materials usuallyexhibit properties which do not exist in their bulks (e.g.,superconducting, piezoelectricity, etc.) [1,2]. Ferroelectricdomain walls with a size of several nanometers displayexotic conduction [3-5] among their insulating bulk. Dueto its electric-field controllable nature, ferroelectric/mul-tiferroic domain walls could be a promising candidate forhigh-density data storage or logic devices with ultralowenergy consumption.
基金This work was supported by the National (Grant Nos. 11171050 and 11371164), the Natural Science Foundation of China National Science Foundation for the Youth of China (Grant Nos. 11301051, 11301081, 11401073 and 11501574), the Provincial Natural Science Foundation of Fujian (Grant No. 2014J05001), the Fundamental Research Funds for Central Universities in China (Grant No. DUT15LK25), Natural Science Foundation of Shandong Province in China (Grant No. ZR2015AL010) and the China Scholarship Council (CSC, Grant No. 201506060121).
文摘Most economic and industrial processes are governed by inherently nonlinear dynamic system in which mathematical analysis (with few exceptions) is unable to provide general solutions; even the conditions to the existence of equilibrium point for the nonlinear dynamic system are simply not established in some special cases. In this paper, based on numerical solution of a nonlinear multi-stage automatic control dynamic (NMACD) in fed-batch culture of glycerol bioconversion to 1,3-propanediol (1,3-PD) induced by KlebsieUa pneumoniae (K. pneumoniae), we consider an optimal design of the NMACD system. For convenience, the NMACD system is reconstructed together with the existence, uniqueness and continuity of solutions are discussed. Our goal is to prove the strong stability with respect to the perturbation of initial state for the solution to the NMACD system. To this end, we construct corresponding linear variational system for the solution to the NMACD system, and also prove the boundedness of fundamental matrix solutions to the linear variational system. On this basis, we prove the strong stability appearing above through the application of this boundedness.