The ability to characterize three-dimensional(3D)magnetization distributions in nanoscale magnetic materials and devices is essential to fully understand their static and dynamic magnetic properties.Phase contrast tec...The ability to characterize three-dimensional(3D)magnetization distributions in nanoscale magnetic materials and devices is essential to fully understand their static and dynamic magnetic properties.Phase contrast techniques in the transmission electron microscope(TEM),such as electron holography and electron ptychography,can be used to record two-dimensional(2D)projections of the in-plane magnetic induction of 3D nanoscale objects.Although the 3D magnetic induction can in principle be reconstructed from one or more tilt series of such 2D projections,conventional tomographic reconstruction algorithms do not recover the 3D magnetization within a sample directly.Here,we use simulations to describe the basis of an improved model-based algorithm for the tomographic reconstruction of a 3D magnetization distribution from one or more tilt series of electron optical phase images recorded in the TEM.The algorithm allows a wide range of physical constraints,including a priori information about the sample geometry and magnetic parameters,to be specified.It also makes use of minimization of the micromagnetic energy in the loss function.We demonstrate the reconstruction of the 3D magnetization of a localized magnetic soliton—a hopfion ring—and discuss the influence of noise,choice of magnetic constants,maximum tilt angle and number of tilt axes on the result.The algorithm can in principle be adapted for other magnetic contrast imaging techniques in the TEM,as well as for other magnetic characterization techniques,such as those based on X-rays or neutrons.展开更多
基金supported by the National Key R&D Program of China(Grant No.2022YFA1403603)the National Natural Science Funds for Distinguished Young Scholars(Grant No.52325105)+9 种基金the National Natural Science Foundation of China(Grant Nos.12241406,52173215,and 12374098)the CAS Project for Young Scientists in Basic Research(Grant No.YSBR-084)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB33030100)the Chinese Academy of Sciences(Grant No.JZHKYPT-2021-08)supported by the Office of Basic Energy Sciences,Division of Materials Sciences and Engineering,U.S.Department of Energy(Grant No.DESC0020221)financial support from Fundamental Research Funds for the Central Universitiesthe National Natural Science Fund for Excellent Young Scientists Fund Program(Overseas)and the General Program(Grant No.52373226)the Xiaomi Young Talents Programfunding from the European Research Council under the European Union’s Horizon 2020 Research and Innovation Programme(Grant No.856538)the Deutsche Forschungsgemeinschaft(Grant Nos.405553726,and 403502830)。
文摘The ability to characterize three-dimensional(3D)magnetization distributions in nanoscale magnetic materials and devices is essential to fully understand their static and dynamic magnetic properties.Phase contrast techniques in the transmission electron microscope(TEM),such as electron holography and electron ptychography,can be used to record two-dimensional(2D)projections of the in-plane magnetic induction of 3D nanoscale objects.Although the 3D magnetic induction can in principle be reconstructed from one or more tilt series of such 2D projections,conventional tomographic reconstruction algorithms do not recover the 3D magnetization within a sample directly.Here,we use simulations to describe the basis of an improved model-based algorithm for the tomographic reconstruction of a 3D magnetization distribution from one or more tilt series of electron optical phase images recorded in the TEM.The algorithm allows a wide range of physical constraints,including a priori information about the sample geometry and magnetic parameters,to be specified.It also makes use of minimization of the micromagnetic energy in the loss function.We demonstrate the reconstruction of the 3D magnetization of a localized magnetic soliton—a hopfion ring—and discuss the influence of noise,choice of magnetic constants,maximum tilt angle and number of tilt axes on the result.The algorithm can in principle be adapted for other magnetic contrast imaging techniques in the TEM,as well as for other magnetic characterization techniques,such as those based on X-rays or neutrons.
基金the National Key Research and Development Program of China(2017YFA0303100 and 2022YFA1403901)the National Natural Science Foundation of China(12174428,11888101,11920101005,and 11674278)+1 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(XDB28000000 and XDB33000000)U.S.Department of Energy,Basic Energy Science(DESC0020221)。
