Understanding and control of the dynamic response of magnetic materials with a three-dimensional magnetization distribution is important both fundamentally and for technological applications. From a fundamental point of view, the internal magnetic structure and dynamics in bulk materials still need to be mapped1, including the dynamic properties of topological structures such as vortices2, magnetic singularities3 or skyrmion lattices4. From a technological point of view, the response of inductive materials to magnetic fields and spin-polarized currents is essential for magnetic sensors and data storage devices5. Here, we demonstrate time-resolved magnetic laminography, a pump–probe technique, which offers access to the temporal evolution of a three-dimensional magnetic microdisc with nanoscale resolution, and with a synchrotron-limited temporal resolution of 70 ps. We image the dynamic response to a 500 MHz magnetic field of the complex three-dimensional magnetization in a two-phase bulk magnet with a lateral spatial resolution of 50 nm. This is achieved with a stroboscopic measurement consisting of eight time steps evenly spaced over 2 ns. These measurements map the spatial transition between domain wall motion and the dynamics of a uniform magnetic domain that is attributed to variations in the magnetization state across the phase boundary. Our technique, which probes three-dimensional magnetic structures with temporal resolution, enables the experimental investigation of functionalities arising from dynamic phenomena in bulk and three-dimensional patterned nanomagnets6.
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All data associated with this manuscript are available at https://doi.org/10.5281/zenodo.3660827.
All analysis code and reconstruction algorithms associated with the work of this manuscript are available at https://doi.org/10.5281/zenodo.3660827.
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We thank D. Marty for initial discussions about the sample fabrication and design, E. Müller for focused ion beam patterning of the sample. All data was measured at the cSAXS beamline, Swiss Light Source, Paul Scherrer Institute, Switzerland. C.D. acknowledges funding from the Leverhulme Trust (grant no. ECF-2018-016), the Isaac Newton Trust (grant no. 18-08) and the L’Oréal-UNESCO UK and Ireland Fellowship for Women In Science 2019. A.H. was funded by the European Union's Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement no. 794207 (ASIQS). S.M. acknowledges funding from the Swiss National Science Foundation under grant agreement no. 172517.
The authors declare no competing interests.
Peer review information Nature Nanotechnology thanks Salvador Ferrer and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Extended Data Fig. 1 The error in the direction of the reconstructed magnetization vector field(Δθm) for different laminography tilt angles is determined by numerical simulations of magnetic laminography.
The simulations show that there exists a range of angles (40°–80°) for which the 3D structure can be reconstructed with a high degree of accuracy. The accuracy of the reconstruction is determined by calculating the RMS error of the direction of the reconstructed magnetization with respect to the original structure (Δθm). The tilt angle used in the experiment presented in this manuscript is 61°, which lies comfortably within this range and is indicated with an arrow.
Extended Data Fig. 2 Determination of the spatial resolution of the reconstructed magnetization by calculating the edge sharpness across the core of a vortex domain wall.
Line profiles of (a) the mx and (b) the mz components of the magnetization across the vortex domain wall. The 25%-75% edge sharpness is found to be on average 50 nm, indicating a half-period spatial resolution of 50 nm. c, The line along which the profile is measured is drawn in blue.
Extended Data Fig. 3 Determination of the spatial resolution of the reconstructed magnetization by calculating the Fourier Shell Correlation.
Fourier Shell Correlation of (a) the mx, (b) the my and (c) the mz components of the magnetization. An estimate of the spatial resolution is obtained using the 1/2 bit threshold36 (red dashed line) and is found to be 184 nm, 360 nm and 180 nm for the mx, my and mz components of the magnetization, respectively.
Extended Data Fig. 5 Comparison of the divergence and angular direction of the magnetization within a single slice, that are used for alignment purposes.
Images of a, ∇sin(θm) and b, sin(θm) of the lowest slice of the magnetization. One can see that for ∇sin(θm) in a, the signal is limited to the domain walls, whereas for sin(θm) the signal is non-zero in the majority of the structure.
Displacement of the vortex domain walls with negative vorticity (a, blue in left-hand panel and Fig. 4) and positive vorticity (b, red in left-hand panel and Fig. 4) in the direction perpendicular to the long axis of the domain wall (indicated by grey arrows in the left-hand panel) as a function of time for different heights within the structure. The oscillatory behaviour is clearest for both vortices at a height of 46 nm and is less clear at the top. When comparing the motion of the two vortex domain walls, the oscillations appear to be consistently out of phase through the height of the sample. Scale bar is 1 μm.
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Donnelly, C., Finizio, S., Gliga, S. et al. Time-resolved imaging of three-dimensional nanoscale magnetization dynamics. Nat. Nanotechnol. 15, 356–360 (2020). https://doi.org/10.1038/s41565-020-0649-x
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