By combining the scanning transmission electron microscopy with the ultrafast optical pump–probe technique, we improved the time resolution by a factor of ∼1012 for the differential phase contrast and convergent-beam electron diffraction imaging. These methods provide ultrafast nanoscale movies of physical quantities in nano-materials, such as crystal lattice deformation, magnetization vector, and electric field. We demonstrate the observations of the photo-induced acoustic phonon propagation with an accuracy of 4 ps and 8 nm and the ultrafast demagnetization under zero magnetic field with 10 ns and 400 nm resolution, by utilizing these methods.

Material properties and applications are determined by internal processes and interactions on a wide range of length and time scales. Microscopic systems are generally associated with intrinsic time scales ranging from femtosecond to microsecond.1–4 For example, once the ultrashort pulsed light is irradiated to the solids, the electrons are non-thermally excited to higher energy levels. These electrons normally relax and obey the Fermi Dirac distribution around the Fermi level, thus defining a “temperature (i.e., electron temperature)” in the electronic system (<100 fs).5 According to the two-temperature model,6 the excess energy of electrons is transferred to the lattice system through the electron–phonon coupling, resulting in the quasi-thermal-equilibrium state with nearly equivalent electron and lattice temperatures (∼ps).7,8 Finally, after the thermal diffusion to the whole sample and to out of the system, the initial state is recovered (ns ∼ μs). In parallel with these processes, the crystal lattice, magnetic and electric properties are expected to exhibit multi-scale dynamics in space and time as shown in Fig. 1.

FIG. 1.

Examples of the non-equilibrium phenomena in solids. The phenomena highlighted by green, red, and light blue represent those detectable by mapping the internal magnetic field, crystal lattice, and electric field, respectively.

FIG. 1.

Examples of the non-equilibrium phenomena in solids. The phenomena highlighted by green, red, and light blue represent those detectable by mapping the internal magnetic field, crystal lattice, and electric field, respectively.

Close modal

A transmission electron microscope (TEM) is a powerful technique to characterize the local structure of solids. Great efforts have been made for capturing the dynamics of the nanoscale objects under the stimuli of current,9 light,10 and mechanical stress.11 However, most of the phenomena in Fig. 1 have been difficult to be tracked by TEM because of the time resolution (ms) limited by the camera speed. Improving the time resolution of TEM enables the discovery of as-yet-unknown local phenomena and the understanding of complex physical and chemical properties.

A promising way to improve the time resolution is the application of the ultrafast optical pump–probe technique. Previous pump–probe TEM12–20 and scanning TEM (STEM)21 studies reported the morphological changes in the nanostructures in the fs–ns regime, being independent of the camera response time. The convergent beam electron diffraction (CBED) with a CCD camera has been conducted to investigate the transient lattice temperature at a fixed sample position after the femtosecond laser irradiation.22 For accessing a wide range of dynamics in Fig. 1, it is necessary to realize the nanoscale mapping of the physical quantities by pump–probe TEM/STEM. One of the applications will be the ultrafast magnetic-field mapping, which clarifies the mobility of the nanoscale magnetic objects as a non-volatile information carrier.23 For example, it is an important issue to visualize how the magnetic skyrmion is created and stabilized in the ps regime under the application of light24 and current.25 In other cases, the phase-change materials exhibit the amorphous-to-crystalline structural transition whose switching speed can be faster than ns depending on the nanostructure.26,27 The ultrafast crystal-structure mapping provides important information on the limiting factor of the switching speed. Tracking the transient physical quantity will deepen our understanding of the functional properties in nano-materials and devices acting in a short time, such as magnetic/ferroelectric memories,23,28,29 switching devices,30 and phonon engineering.31 

Here, we focus on the differential phase contrast (DPC) and CBED imaging with STEM, which are well-established methods for nanoscale visualization of the electromagnetic field and crystal lattice, respectively.32–43 In the former, when the diameter of the converged electron beam has a comparable size to the length scale of the variations in the field, it will be forward scattered at the sample. The detector image obtained at each probe position is transformed into the vector representing the change in the momentum of the deflected electrons. The DPC imaging has been developed owing to the advancement of the detector technology. Segmented detectors with 4–16 concentric channels have been developed, and the atomic resolution has recently been achieved in the electric field mapping.37,39,43 The accuracy of the direction and amplitude of the deflection can be increased by measuring the momentum change of the electron probe from its center of mass by using a pixelated detector.44 This technique, the so-called four-dimensional (4D) STEM, records 2D images by scanning the converged electron beam over a 2D sample position [Fig. 2(a)], thus obtaining the 4D dataset.44 The use of the pixelated detector further enables the CBED imaging. The electron diffraction pattern at each probe position can be used to extract the quantitative information of the crystal lattice [Fig. 2(b)]. For the 4D STEM, the hybrid pixel array detectors have been developed by employing high-gain integration and counting circuits in each pixel, realizing a high dynamic range, fast readout, and high detection sensitivity.43 Since the time resolution of the 4D STEM is limited by the scanning speed of the electron probe, which generally ranges from seconds to minutes, this technique has not been advantageous for dynamic observations.

FIG. 2.

Schematics of the experimental geometry of STEM with a pixelated detector for (a) DPC and (b) CBED. The yellow cones represent the focused electron beam and scattered electrons passing through the sample.

FIG. 2.

Schematics of the experimental geometry of STEM with a pixelated detector for (a) DPC and (b) CBED. The yellow cones represent the focused electron beam and scattered electrons passing through the sample.

Close modal

In this work, we apply the optical pump–probe technique to the 4D STEM to improve the time resolution by a factor of ∼1012. We propose a new technique—5D STEM—which generates a 5D dataset including an ultrafast time axis. We demonstrate the CBED observation on the acoustic wave propagation and the DPC observation on the magnetic domain dynamics. The former maps the photo-induced strain of the thin film with 4 ps and 8 nm resolution, and the latter maps the magnetization vector with 10 ns and 400 nm resolution. This method will widen the potential of the pump–probe TEM/STEM as a probe of the ultrafast change in the physical quantities of nanoscale objects.

Figure 3 shows the schematics of the 5D STEM system at RIKEN, consisting of a TEM (Tecnai Femto, Thermo Fisher), a pixelated detector (Merlin, Quantum Detectors), and a femtosecond laser (PHAROS, Light Conversion). The repetition rate of the femtosecond laser ranges from 1 kHz to 1 MHz. The fundamental laser beam (1030 nm, 290 fs) is split into two branches, the pump and the probe, by a polarized beam splitter. The probe line passes through two β-Ba2B2O4 crystals for fourth-harmonic generation. The frequency-quadrupled 257-nm laser pulse is focused on a LaB6 photocathode in TEM. The electron packet for the probe is then generated by the photoelectric effect. The electron packets are accelerated to 200 keV and converged to the sample. The rest of the laser beam is used to excite the sample with a controlled time delay relative to the electron packet. The diameter of the pump laser spot size is set to 100 µm at the sample, which ensures the homogeneous photoexcitation in the probing area. A two-dimensional image of the scattered electrons passing through the sample is obtained at the pixelated detector. By scanning the focused pulsed electron beam, we can obtain a 4D dataset at a fixed delay time t. The best spatial resolution was estimated to be 8 nm [Fig. 4(a)] and 400 nm [Fig. 4(b)] in a magnetic field of 2 and 0 T, respectively. The former is mainly limited by the drift motion of the sample, while the latter is determined by the spot size of the pulsed electrons at the sample position. The magnetic field of 2 T was applied by the objective lens, while the zero magnetic field condition was set by turning it off. Note that the electron spot size is relatively large since the present 5D STEM system has not been optimized for the use of few electrons under zero magnetic field. By further sweeping the optical delay stage, we finally obtain a 5D dataset. We confirmed that the temporal resolution of the 5D STEM system is 4 ps when we set the number of electrons per pulse to ∼1000 [Fig. 4(c)]. We can also choose the time resolution of 10 ns by using nanosecond lasers (Wedge-HF, Bright Solutions) and an electrical delay generator [Fig. 4(d)].20 The diagram for the 5D-data acquisition is shown in Fig. 5(a).

FIG. 3.

Schematics of the 5D STEM system at RIKEN.

FIG. 3.

Schematics of the 5D STEM system at RIKEN.

Close modal
FIG. 4.

(a) and (b) Estimation of the spatial resolution of the 5D STEM in magnetic fields of 2 and 0 T, respectively. The former was conducted on the real-space mapping of the intensity at the direct beam spot in the CBED pattern, crossing the heterostructure interface of GaP/Si having a width of 1–2 nm grown by the metal–organic vapor phase epitaxy,45–48 and the latter was the sample edge of the thin film of yttrium iron garnet. (c) and (d) Estimation of the temporal resolution of the 5D STEM in a magnetic field of 2 T for the cases with femtosecond laser and nanosecond laser, respectively. The black markers represent the intensity of the electron diffraction for a 1T′-MoTe2 thin film showing the rapid suppression around t = 0 due to the Debye–Waller effect. The red curves indicate the step functions convoluted by the Gaussian with the full width at half maximum of 8 nm in (a), 400 nm in (b), 4 ps in (c), and 10 ns in (d).

FIG. 4.

(a) and (b) Estimation of the spatial resolution of the 5D STEM in magnetic fields of 2 and 0 T, respectively. The former was conducted on the real-space mapping of the intensity at the direct beam spot in the CBED pattern, crossing the heterostructure interface of GaP/Si having a width of 1–2 nm grown by the metal–organic vapor phase epitaxy,45–48 and the latter was the sample edge of the thin film of yttrium iron garnet. (c) and (d) Estimation of the temporal resolution of the 5D STEM in a magnetic field of 2 T for the cases with femtosecond laser and nanosecond laser, respectively. The black markers represent the intensity of the electron diffraction for a 1T′-MoTe2 thin film showing the rapid suppression around t = 0 due to the Debye–Waller effect. The red curves indicate the step functions convoluted by the Gaussian with the full width at half maximum of 8 nm in (a), 400 nm in (b), 4 ps in (c), and 10 ns in (d).

Close modal
FIG. 5.

(a) 5D-data acquisition diagram. We use the electron pulses converged at the xy plane of the sample. First, we obtain the 2D image of the electrons passing through the mounted sample at a sample coordinate (x, y) by using the pixelated detector. Then, we repeat the measurement at the next coordinate. If the 2D images are obtained at all sample coordinates, we complete the 4D data at a certain time delay t. Similarly, we continue the 4D-data acquisition at other delay points. If all the delay points are scanned, we finally obtain the 5D dataset. (b) Schematics of the measurement procedure of the 5D STEM.

FIG. 5.

(a) 5D-data acquisition diagram. We use the electron pulses converged at the xy plane of the sample. First, we obtain the 2D image of the electrons passing through the mounted sample at a sample coordinate (x, y) by using the pixelated detector. Then, we repeat the measurement at the next coordinate. If the 2D images are obtained at all sample coordinates, we complete the 4D data at a certain time delay t. Similarly, we continue the 4D-data acquisition at other delay points. If all the delay points are scanned, we finally obtain the 5D dataset. (b) Schematics of the measurement procedure of the 5D STEM.

Close modal

Figure 5(b) explains the detailed procedures to obtain the 5D data. First, at a delay time t = t0, the train of converged electron pulses probes the sample at the coordinate (x0, y0). Deflected or diffracted electrons are imaged at the pixelated detector and integrated for many pump–probe cycles depending on the repetition rate of the laser and the dwell time of the electron beam scanning [e.g., the combination of 5 ms dwell time at each coordinate (x, y) and 20 kHz laser repetition rate results in the integration of 100 electron pulses at the pixelated detector]. After the integration, the obtained image is transferred to the data storage as the 2D data at t = t0. The same procedure is repeated at the adjacent coordinates (x0, y1), (x0, y2),…, (xn, ym) through the 2D scanning of the convergent electron beam on the sample. Then, we obtain a 4D dataset at t = t0. By further sweeping the delay, we obtain the 5D data from t = t0 to tN. The acquisition time for the 5D data with a 5 ms dwell time, 1002 sample coordinates, and 100 delay points will be ∼1.4 h. The size of the 5D data will be ∼260 GB for a 32-bit image with 2562 pixels, 1002 sample coordinates, and 100 delay points. The 5D data are postprocessed to generate a movie of the photo-induced ultrafast phenomena. In the case of the DPC, the center of mass of the deflected electrons is obtained from the 2D image at each sample coordinate, which can be mapped as a local magnetic or electric field. For the CBED, the electron diffraction pattern is analyzed by measuring the radial shifts or integrating the intensity of the Bragg lines. The former extracts the sample deformation via the crystal lattice parameters, while the latter is used to investigate the changes of the internal crystal structure of the unit cell (structural factor).

Here, we demonstrate the picosecond CBED imaging on a Si thin film in a magnetic field of 2 T. We evaporated the W island (a diameter of 700 nm and a thickness of 100 nm) onto the Si thin film [Fig. 6(a)]. When the femtosecond laser is irradiated to the sample, only the W island absorbs the photons since Si has a bandgap slightly higher than the energy of the pump laser. Then, the photothermalization of the W island acts as a source of the acoustic phonons at the Si interface.49 Here, we map the photo-induced displacement gradient of the thin film converted from the shift of the 8̄00 excess Bragg line in the CBED pattern at each sample coordinate. As a function of time, we observed the evolution of the concentric circles in the displacement gradient mapping, indicating the acoustic phonon propagation [Figs. 6(b)6(e)].

FIG. 6.

(a) Bright-field STEM imaging of the Si thin film. The black circle indicates the W-deposited area with a diameter of 700 nm, which acts as a source of the acoustic phonons. (b)–(e) Snapshots of the coherent acoustic phonons propagating on a Si thin film at −120, 200, 700, and 1700 ps, respectively, obtained by the CBED. Color represents the displacement gradient of the sample. The scale bar indicates 500 nm.

FIG. 6.

(a) Bright-field STEM imaging of the Si thin film. The black circle indicates the W-deposited area with a diameter of 700 nm, which acts as a source of the acoustic phonons. (b)–(e) Snapshots of the coherent acoustic phonons propagating on a Si thin film at −120, 200, 700, and 1700 ps, respectively, obtained by the CBED. Color represents the displacement gradient of the sample. The scale bar indicates 500 nm.

Close modal

We visualize the photothermal demagnetization by employing the nanosecond DPC imaging at the zero magnetic field. We prepared the 100-nm-thick Fe1.9Ni0.9Pd0.2P thin film with square holes (500 × 500 nm2).50Figure 7(a) shows the magnetization vector mapping at 370 K, which is slightly below the ferromagnetic transition temperature of 380 K, obtained at t = −320 ns. The white dotted lines represent the magnetic domain walls that separate the 180° magnetic domains indicated by the white arrows. The photothermalization by nanosecond optical pulse irradiation induces demagnetization, resulting in the disappearance of the magnetic domain walls. This event was confirmed by the rapid suppression of the amplitude of the magnetization vector at t = 20 ns [Fig. 7(b)]. In the line profile of the DPC image along the white line in Fig. 6(b), the positive and negative signs represent the magnetization vector pointing to the left and right, respectively [Fig. 7(c)]. It is clearly shown that the intensity along the cut reaches nearly zero within 20 ns, suggesting the demagnetization. At t = 20 µs, the magnetic domains are almost recovered in a repeatable way (not shown). Note that the magnetic domain wall tends to be pinned between the square holes and the sample edge, which realizes the repeatable annihilation and nucleation in the stroboscopic pump–probe measurements.

FIG. 7.

(a) and (b) Snapshots of the photothermal demagnetization in a Fe1.9Ni0.9Pd0.2P thin film of the (1 1 0) plane at −320 and 20 ns, respectively, obtained by the CBED with a time resolution of 10 ns. The magnetic domain walls (white dotted lines) are pinned between the holes (left white squares) and the sample edge (right white area). The white arrows indicate the in-plane magnetization vectors in the magnetic domains. The color scale shows the amplitude and direction of the in-plane magnetization vector. (c) Line profiles of the DPC images at −320 and 20 ns along the cut in (b). The scale bar indicates 500 nm.

FIG. 7.

(a) and (b) Snapshots of the photothermal demagnetization in a Fe1.9Ni0.9Pd0.2P thin film of the (1 1 0) plane at −320 and 20 ns, respectively, obtained by the CBED with a time resolution of 10 ns. The magnetic domain walls (white dotted lines) are pinned between the holes (left white squares) and the sample edge (right white area). The white arrows indicate the in-plane magnetization vectors in the magnetic domains. The color scale shows the amplitude and direction of the in-plane magnetization vector. (c) Line profiles of the DPC images at −320 and 20 ns along the cut in (b). The scale bar indicates 500 nm.

Close modal

We proposed a new experimental method—5D STEM—by combining the DPC and CBED employing a pixelated detector with the ultrafast optical pump–probe technique, which provides the ultrafast movie of the crystal lattice and electromagnetic field in nano-materials. This method can be further combined with the in situ TEM holder, which introduces the pulsed current, magnetic/electric field, and mechanical pressure to excite the nano-materials. The ultrafast and nanoscale mapping of the physical quantities will progress the understanding of the functional nano-materials and devices in various application fields, such as magnetic/ferroelectric memories,23,28,29 switching devices,30 and phonon engineering.31 

We thank J. Belz, K. Volz, and U. Höfer for providing the heterostructure sample of GaP/Si; K. Karube and Y. Taguchi for providing Fe1.9Ni0.9Pd0.2P single crystals; and Y. Togawa for valuable discussions on the pixelated detector. This work was supported by JSPS KAKENHI (Grant Nos. 18H01818 and 19K22120).

The authors have no conflicts to disclose.

T.S. and A.N. contributed equally to this work.

T. Shimojima: Conceptualization (lead); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Writing – original draft (lead). A. Nakamura: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (lead); Writing – review & editing (equal). K. Ishizaka: Funding acquisition (equal); Project administration (lead); Resources (lead); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
S.
Mathias
,
C.
La-O-Vorakiat
,
P.
Grychtol
,
P.
Granitzka
,
E.
Turgut
,
J. M.
Shaw
,
R.
Adam
,
H. T.
Nembach
,
M. E.
Siemens
,
S.
Eich
,
C. M.
Schneider
,
T. J.
Silva
,
M.
Aeschlimann
,
M. M.
Murnane
, and
H. C.
Kapteyn
,
Proc. Natl. Acad. Sci. U. S. A.
109
,
4792
(
2012
).
2.
A.
Barman
and
A.
Haldar
,
Solid State Phys.
65
,
1
108
(
2014
).
3.
Y.
Zhang
,
J.
Dai
,
X.
Zhong
,
D.
Zhang
,
G.
Zhong
, and
J.
Li
,
Adv. Sci.
8
,
2102488
(
2021
).
4.
J.
Lloyd-Hughes
,
P. M.
Oppeneer
,
T.
Pereira dos Santos
,
A.
Schleife
,
S.
Meng
,
M. A.
Sentef
,
M.
Ruggenthaler
,
A.
Rubio
,
I.
Radu
,
M.
Murnane
,
X.
Shi
,
H.
Kapteyn
,
B.
Stadtmüller
,
K. M.
Dani
,
F. H.
da Jornada
,
E.
Prinz
,
M.
Aeschlimann
,
R. L.
Milot
,
M.
Burdanova
,
J.
Boland
,
T.
Cocker
, and
F.
Hegmann
,
J. Phys.: Condens. Matter
33
,
353001
(
2021
).
5.
W. S.
Fann
,
R.
Storz
,
H. W. K.
Tom
, and
J.
Bokor
,
Phys. Rev. B
46
,
13592
(
1992
).
6.
S. I.
Anisimov
,
B. L.
Kapeliovich
, and
T. L.
Perel’man
,
Sov. Phys. JETP
39
,
375
(
1974
).
7.
H. E.
Elsayed-Ali
,
T. B.
Norris
,
M. A.
Pessot
, and
G. A.
Mourou
,
Phys. Rev. Lett.
58
,
1212
(
1987
).
8.
R. W.
Schoenlein
,
W. Z.
Lin
,
J. G.
Fujimoto
, and
G. L.
Eesley
,
Phys. Rev. Lett.
58
,
1680
(
1987
).
9.
X. Z.
Yu
,
D.
Morikawa
,
K.
Nakajima
,
K.
Shibata
,
N.
Kanazawa
,
T.
Arima
,
N.
Nagaosa
, and
Y.
Tokura
,
Sci. Adv.
6
,
eaaz9744
(
2020
).
10.
R.
Senga
,
Y.-C.
Lin
,
S.
Sinha
,
T.
Kaneko
,
N.
Okoshi
,
T.
Sasaki
,
S.
Morishita
,
H.
Sawada
,
S. T.
Park
, and
K.
Suenaga
,
Microsc. Microanal.
27
(
Suppl. S1
),
2344
(
2021
).
11.
X.
Han
,
L.
Wang
,
Y.
Yue
, and
Z.
Zhang
,
Ultramicroscopy
151
,
94
(
2015
).
12.
B.
Barwick
,
H. S.
Park
,
O.-H.
Kwon
,
J. S.
Baskin
, and
A. H.
Zewail
,
Science
322
,
1227
(
2008
).
13.
U. J.
Lorenz
and
A. H.
Zewail
,
Science
344
,
1496
(
2014
).
14.
D. R.
Cremons
,
D. A.
Plemmons
, and
D. J.
Flannigan
,
Nat. Commun.
7
,
11230
(
2016
).
15.
G.
Berruto
,
I.
Madan
,
Y.
Murooka
,
G. M.
Vanacore
,
E.
Pomarico
,
J.
Rajeswari
,
R.
Lamb
,
P.
Huang
,
A. J.
Kruchkov
,
Y.
Togawa
,
T.
LaGrange
,
D.
McGrouther
,
H. M.
Rønnow
, and
F.
Carbone
,
Phys. Rev. Lett.
120
,
117201
(
2018
).
16.
N. R.
Silva
,
M.
Möller
,
A.
Feist
,
H.
Ulrichs
,
C.
Ropers
, and
S.
Schäfer
,
Phys. Rev. X
8
,
031052
(
2018
).
17.
M.
Zhang
,
Z.-A.
Li
,
H.
Tian
,
H.
Yang
, and
J.
Li
,
Appl. Phys. Lett.
113
,
133103
(
2018
).
18.
Y.-J.
Kim
,
H.
Jung
,
S. W.
Han
, and
O.-H.
Kwon
,
Matter
1
,
481
495
(
2019
).
19.
A.
Nakamura
,
T.
Shimojima
,
Y.
Chiashi
,
M.
Kamitani
,
H.
Sakai
,
S.
Ishiwata
,
H.
Li
, and
K.
Ishizaka
,
Nano Lett.
20
,
4932
(
2020
).
20.
T.
Shimojima
,
A.
Nakamura
,
X. Z.
Yu
,
K.
Karube
,
Y.
Taguchi
,
Y.
Tokura
, and
K.
Ishizaka
,
Sci. Adv.
7
,
eabg1322
(
2021
).
21.
V.
Ortalan
and
A. H.
Zewail
,
J. Am. Chem. Soc.
133
,
10732
(
2011
).
22.
A.
Yurtsever
and
A. H.
Zewail
,
Science
326
,
708
(
2009
).
23.
N.
Nagaosa
and
Y.
Tokura
,
Nat. Nanotechnol.
8
,
899
911
(
2013
).
24.
W.
Koshibae
and
N.
Nagaosa
,
Nat. Commun.
5
,
5148
(
2014
).
25.
J.
Iwasaki
,
M.
Mochizuki
, and
N.
Nagaosa
,
Nat. Nanotechnol.
8
,
742
(
2013
).
26.
W. J.
Wang
,
L. P.
Shi
,
R.
Zhao
,
K. G.
Lim
,
H. K.
Lee
,
T. C.
Chong
, and
Y. H.
Wu
,
Appl. Phys. Lett.
93
,
043121
(
2008
).
27.
D.
Loke
,
T. H.
Lee
,
W. J.
Wang
,
L. P.
Shi
,
R.
Zhao
,
Y. C.
Yeo
,
T. C.
Chong
, and
S. R.
Elliott
,
Science
336
,
1566
(
2012
).
28.
S. S. P.
Parkin
,
M.
Hayashi
, and
L.
Thomas
,
Science
320
,
190
(
2008
).
29.
J. F.
Scorr
and
C. A.
Paz de Araujo
,
Science
246
,
1400
(
1989
).
30.
F.
Xiong
,
A. D.
Liao
,
D.
Estrada
, and
E.
Pop
,
Science
332
,
568
(
2011
).
31.
M.
Nomura
,
J.
Shiomi
,
T.
Shiga
, and
R.
Anufriev
,
Jpn. J. Appl. Phys.
57
,
080101
(
2018
).
32.
N. H.
Dekkers
and
H.
Lang
,
Optik
41
,
452
456
(
1974
).
33.
J. N.
Chapman
,
P. E.
Batson
,
E. M.
Waddell
, and
R. P.
Ferrier
,
Ultramicroscopy
3
,
203
(
1978
).
34.
J. N.
Chapman
,
J. Phys. D: Appl. Phys.
17
,
623
(
1984
).
35.
J. N.
Chapman
,
I. R.
McFadyen
, and
S.
McVitie
,
IEEE Trans. Magn.
26
,
1506
(
1990
).
36.
C. W.
Sandweg
,
N.
Wiese
,
D.
McGrouther
,
S. J.
Hermsdoerfer
,
H.
Schultheiss
,
B.
Leven
,
S.
McVitie
,
B.
Hillebrands
, and
J. N.
Chapman
,
J. Appl. Phys.
103
,
093906
(
2008
).
37.
N.
Shibata
,
S. D.
Findlay
,
Y.
Kohno
,
H.
Sawada
,
Y.
Kondo
, and
Y.
Ikuhara
,
Nat. Phys.
8
,
611
(
2012
).
38.
D.
McGrouther
,
R. J.
Lamb
,
M.
Krajnak
,
S.
McFadzean
,
S.
McVitie
,
R. L.
Stamps
,
A. O.
Leonov
,
A. N.
Bogdanov
, and
Y.
Togawa
,
New J. Phys.
18
,
095004
(
2016
).
39.
N.
Shibata
,
S. D.
Findlay
,
T.
Matsumoto
,
Y.
Kohno
,
T.
Seki
,
G.
Sánchez-Santolino
, and
Y.
Ikuhara
,
Acc. Chem. Res.
50
,
1502
(
2017
).
40.
T.
Matsumoto
,
Y.-G.
So
,
Y.
Kohno
,
Y.
Ikuhara
, and
N.
Shibata
,
Nano Lett.
18
,
754
(
2018
).
41.
S.
Pöllath
,
T.
Lin
,
N.
Lei
,
W.
Zhao
,
J.
Zweck
, and
C. H.
Back
,
Ultramicroscopy
212
,
112973
(
2020
).
42.
F. S.
Yasin
,
L.
Peng
,
R.
Takagi
,
N.
Kanazawa
,
S.
Seki
,
Y.
Tokura
, and
X. Z.
Yu
,
Adv. Mater.
32
,
2004206
(
2020
).
43.
44.
M.
Krajnak
,
D.
McGrouther
,
D.
Maneuski
,
V. O.
Shea
, and
S.
McVitie
,
Ultramicroscopy
165
,
42
(
2016
).
45.
K.
Volz
,
A.
Beyer
,
W.
Witte
,
J.
Ohlmann
,
I.
Németh
,
B.
Kunert
, and
W.
Stolz
,
J. Cryst. Growth
315
,
37
(
2011
).
46.
A.
Beyer
,
A.
Stegmüller
,
J. O.
Oelerich
,
K.
Jandieri
,
K.
Werner
,
G.
Mette
,
W.
Stolz
,
S. D.
Baranovskii
,
R.
Tonner
, and
K.
Volz
,
Chem. Mater.
28
,
3265
(
2016
).
47.
A.
Beyer
and
K.
Volz
,
Adv. Mater. Interfaces
6
,
1801951
(
2019
).
48.
G.
Mette
,
J. E.
Zimmermann
,
A.
Lerch
,
K.
Brixius
,
J.
Güdde
,
A.
Beyer
,
M.
Dürr
,
K.
Volz
,
W.
Stolz
, and
U.
Höfer
,
Appl. Phys. Lett.
117
,
081602
(
2020
).
49.
A.
Nakamura
,
T.
Shimojima
, and
K.
Ishizaka
,
Struct. Dyn.
8
,
024103
(
2021
).
50.
K.
Karube
,
L.
Peng
,
J.
Masell
,
X. Z.
Yu
,
F.
Kagawa
,
Y.
Tokura
, and
Y.
Taguchi
,
Nat. Mater.
20
,
335
(
2021
).