3D magnetic configuration of ferrimagnetic multilayers with competing interactions visualized by soft X-ray vector tomography

Hermosa, Javier; Hierro-Rodríguez, A.; Sorrentino, Andrea; Martín, José Ignacio; Álvarez-Prado, L. M.; Rehbein, Stefan; Pereiro, Eva; Quirós, C.; Vélez, María; Ferrer, S.

doi:10.1038/s42005-021-00800-3

Cited by 10 publications

(7 citation statements)

References 47 publications

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“…In particular, the observed contrast changes as a function of θ and ϕ from the two tilt-series of MTXM projections (85 images) can be used to obtain a quantitative characterization of the magnetic configuration of the sample with the help of a vector magnetic tomography algorithm 41 . The resulting tomogram is a reconstruction without any a priori assumptions of the magnetization vector mðrÞ at each point of the microstructure that corresponds most closely with the experimental MTXM images 26,41,42 .…”

Section: Resultsmentioning

confidence: 99%

“…In a first step, a standard scalar tomography of the microstructure 3D shape is performed using TXM images in a volume of 8000 × 4000 × 1000 nm 3 with pixel size 10 nm. This is used to define the region of interest in which the reconstruction of the magnetic signals is performed (see Supplementary Note 1), taking also into account the planes defined by gold fiducials on top of the microstructure and on the bare membrane 42 . The result is a 3D vector map of the magnetization convoluted with the lateral resolution function of the microscope (~30 nm) and an axial resolution of 70 nm estimated as reported in refs.…”

Section: Methodsmentioning

confidence: 99%

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Bloch points and topological dipoles observed by X-ray vector magnetic tomography in a ferromagnetic microstructure

et al. 2023

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Bloch points are small 3D magnetic textures with unit topological charge that require the use of advanced vector imaging techniques for their direct experimental characterization. Here we show results from the reconstruction of the magnetization field $${{{{{\bf{m}}}}}}\left({{{{{\bf{r}}}}}}\right)$$ m r of an elongated permalloy microstructure by X-ray vector magnetic tomography. A central asymmetric Bloch domain wall is observed, decorated by Bloch points arranged in several dipoles and a triplet. The analysis of the $${{{{{\bf{m}}}}}}\left({{{{{\bf{r}}}}}}\right)$$ m r map in terms of topological concepts provides a quantitative description of the Bloch points as topological monopoles connected by bundles of emergent magnetic field lines carrying a fractional topological flux. It also reveals the topological constraints that determine chirality transitions of the central domain wall in the vicinity of Bloch points, independent of specific material properties. This approach could be readily extended to the study of magnetic microstructures in arbitrary remanent configurations.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Bloch points and topological dipoles observed by X-ray vector magnetic tomography in a ferromagnetic microstructure

et al. 2023

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“…X-rays can also be used to access the magnetization configuration at the nanoscale with element specificity. The exploitation of X-ray Magnetic Circular Dichroism (XMCD) in hard and soft X-ray regimes has shown the extreme potential of vector tomography for the observation of magnetic textures and singularities in magnetic microstructures 11 , 12 , nanostructures 13 and continuous films 14 – 16 . This new paradigm of experimental three-dimensional characterization of the magnetization is not restricted to the study of static configurations but permits analyzing the magnetization dynamics in three-dimensions 17 .…”

Section: Introductionmentioning

confidence: 99%

A fast magnetic vector characterization method for quasi two-dimensional systems and heterostructures

Herguedas-Alonso,

Aballe,

Fullerton

et al. 2023

Sci Rep

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The use of magnetic vector tomography/laminography has opened a 3D experimental window to access the magnetization at the nanoscale. These methods exploit the dependence of the magnetic contrast in transmission to recover its 3D configuration. However, hundreds of different angular projections are required leading to large measurement times. Here we present a fast method to dramatically reduce the experiment time specific for quasi two-dimensional magnetic systems. The algorithm uses the Beer-Lambert equation in the framework of X-ray transmission microscopy to obtain the 3D magnetic configuration of the sample. It has been demonstrated in permalloy microstructures, reconstructing the magnetization vector field with a reduced number of angular projections obtaining quantitative results. The throughput of the methodology is × 10–× 100 times faster than conventional magnetic vector tomography, making this characterization method of general interest for the community.

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“…However, in some important applications, vector tomography is required, where each voxel has a magnitude and a direction such as the electric and magnetic field. Over the years, several vector tomography reconstruction methods have been developed, including vector electron tomography with Lorentz transmission electron microscopy and holography [18][19][20][21][22][23][24][25] , soft and hard x-ray vector tomography [26][27][28][29][30][31][32][33][34][35] . In particular, the combination of ptychography, a powerful coherent diffractive imaging method 36,37 , and vector tomography can in principle achieve the highest spatial resolution, which is only limited by the wavelength and the diffraction signal 27,31,34 .…”

Section: Introductionmentioning

confidence: 99%

Real space iterative reconstruction for vector tomography (RESIRE-V)

Pham,

Osher,

Miao

et al. 2023

Preprint

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Tomography has had an important impact on the physical, biological, and medical sciences. To date, most tomographic applications have been focused on 3D scalar reconstructions. However, in some crucial applications, vector tomography is required to reconstruct 3D vector fields such as the electric and magnetic fields. Over the years, several vector tomography methods have been developed. Here, we present the mathematical foundation and algorithmic implementation of REal Space Iterative REconstruction for Vector tomography, termed RESIRE-V. RESIRE-V uses multiple tilt series of projections and iterates between the projections and a 3D reconstruction. Each iteration consists of a forward step using the Radon transform and a backward step using its transpose, then updates the object via gradient descent. Incorporating with a 3D support constraint, the algorithm iteratively minimizes an error metric, defined as the difference between the measured and calculated projections. The algorithm can also be used to refine the tilt angles and further improve the 3D reconstruction. To validate RESIRE-V, we first apply it to a simulated data set of the 3D magnetization vector field, consisting of two orthogonal tilt series, each with a missing wedge. Our quantitative analysis shows that the three components of the reconstructed magnetization vector field agree well with the ground-truth counterparts. We then use RESIRE-V to reconstruct the 3D magnetization vector field of a ferromagnetic meta-lattice consisting of three tilt series. Our 3D vector reconstruction reveals the existence of topological magnetic defects with positive and negative charges. We expect that RESIRE-V can be incorporated into different imaging modalities as a general vector tomography method.To make the algorithm accessible to a broad user community,, we have made our RESIRE-V MATLAB source codes and the data freely available at https://github.com/minhpham0309/RESIRE-V.

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3D magnetic configuration of ferrimagnetic multilayers with competing interactions visualized by soft X-ray vector tomography

Cited by 10 publications

References 47 publications

Bloch points and topological dipoles observed by X-ray vector magnetic tomography in a ferromagnetic microstructure

Bloch points and topological dipoles observed by X-ray vector magnetic tomography in a ferromagnetic microstructure

A fast magnetic vector characterization method for quasi two-dimensional systems and heterostructures

Real space iterative reconstruction for vector tomography (RESIRE-V)

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