Supplemental material
Mapping the Magnetic and Crystal Structure in
Cobalt Nanowires
Jesus Cantu-Valle1, Israel Betancourt11, John E. Sanchez1, Francisco Ruiz-Zepeda1, Mazin M.
Maqableh2, Fernando Mendoza-Santoyo12, Bethanie J.H. Stadler2and Arturo Ponce1*
1
Department of Physics and Astronomy, University of Texas at San Antonio. One UTSA Circle,
San Antonio, TX 78249, USA.
2
Electrical and Computer Engineering, University of Minnesota, 4-174 EE/CSci Bldg., 200
Union St. SE, Minneapolis, Minnesota 55455, USA.
*Corresponding author:
University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249
Office: 210-458-8267
E-mail: arturo.ponce@utsa.edu
1
2
On Sabbatical leave from Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, C.P., D.F 04510 México.
On Sabbatical leave from Centro de Investigaciones en Optica, A.C., León, Guanajuato, México.
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I.
Electron holography
An additional hologram for a different Co nanowire (respect to Figure 1, main text) is shown in
Figure S1a. The corresponding unwrapped phase is displayed in Figure S1b, from which is
possible to distinguish the magnetic contours following a predominant axial direction as a
consequence of the prevailing influence of the shape anisotropy over the magnetocrystalline
contribution. As in the original sample of Figure 1, no extra nanowires are nearby and thus, no
inter-wire interaction of magnetostatic nature is present. The magnetic contours of Figure S1b
amplified by three times the cosine of the magnetic phase image is shown in Figure S1c. For this
nanowire, the stray field arising around the tip as leaking magnetic flux clearly suggest the
formation of an uncompensated vortex structure, which causes the asymmetric flux lines observed
in Figure S1.
In order to calibrate the magnetic contribution inside the TEM due to the main objective lens, an
analytical commercial holder was modified by adapting a Hall effect sensor (Figure S2). The
holder outputs were connected directly to the Gaussmeter (model GM-700) to register the field
measurements. The Hall effect sensor is a transducer that varies its output voltage in reponse to a
magnetic field. As a transducer the sensor converts the magnetic energy to a voltage. The output
is then sent to a Gaussmeter that reads out the magnetic field measured.
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Figure S1. a) Electron hologram for an additional Co nanowire b) Unwrapped phase image,
displaying the phase variations associated to magnetic contours c) magnetic contours amplified by
three times the cosine of the magnetic phase image, showing the asymmetric flux arising around
the tip.
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Figure S2. (a) Hall effect sensor welded to the commercial sensor. (b) Chip mounted in the holder,
the cap of the holder provides the electrical contacts. (c) Wiring the holder outputs through the
Gaussmeter. (d) Picture of the mounted experimental setup in the microscope.
After inserting The Hall efffect sensor into the JEOL ARM 200F, the objective lens voltage was
varied, and a measured with a Gaussmeter to see how the magnetic field changed. Before inserting
the probe into the microscope we zeroed it measuring at -14.3 Gauss (G). Magnetization reversal
in single nanowires was experimentally induced by the manipulation of the TEM objective lens as
external field source. The magnetic field at the sample position was measured as the excitation
voltage of the objective lens was swept from zero to the maximum value (10V), Figure S3. The
field had a remnant value of 45 Oe, and it appeared to saturate as it approached 18 kOe.
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Figure S3. Calibration of the lens magnetic contribution versus the excitation voltage of the
objective lens.
The configuration of the off-axis electron holography in the microscope is shown in Figure S4. In
this diagram a magnetic sample is placed in a position that covers the wavefront interfering with
the sample (object hologram) and the vacuum. In addition a reference hologram (no sample) is
recorded separately for a precise phase reconstruction. Both holograms, reference and object, are
combined and the modulated phase shift caused by electric and magnetic fields into the sample
can be recovered.
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Figure S4. Schematic illustration of the off-axis electron holography setup using a Lorentz lens
for a magnetic sample.
This microscope is equipped with a pole piece model UHR22, which possesses a remanent field
of 45 Oe. The magnetic contribution of the objective lens excitation was quantified by adapting a
Hall effect sensor into a commercial holder. Electron holograms were recorded with Gatan’s
Digital Micrograph (DM) software and reconstructed by HoloWorks 5.0.7. The nanowire had been
oriented longitudinally in a parallel direction of the interference fringes. The holograms shown in
this work, were numerically reconstructed using a reference hologram and the object hologram to
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remove the influence of the perturbed reference wave and using an average fringe spacing, σ = 5
nm and a fringe contrast of µ = 18%. For the recovered phase maps, a series of 10 holograms was
averaged to enhance the phase resolution, which was measured in reference phase regions as the
standard deviation of the phase image. Figure S5, the left column (Figures S5 a-b) represents the
unwrapped phase images and the phase contours of the initial state of the nanowire. It is important
to remark that this phase image has the complete information, electric and magnetic contribution
from the nanowire. However, it is possible to identify the magnetization direction (represented by
the solid arrow in Figure S5a) and the phase contours give us an insight of the magnetic behavior
since they are related to magnetic flux distribution. The column in the middle (Figures. S5 c-d),
represents the corresponding phase and contours of the nanowire after it was tilted +20° and a Hfield of 10.5 kOe was applied perpendicular to the specimen stage. The parallel component of H
is represented by the dashed arrow in the phase image. Finally, the last column shows the
magnetization reversal by tilting the sample by -20° and turning on OL in order to revert the
magnetization. From the phase contour images in Figure 4, it can be observed that parallel
component of H, aligned the leakage field in the tip of the nanowire. Usually we will hope the
nanowire to form a typical dipole shape, in where each tip of the nanowire will be a magnetic pole.
Nevertheless, the dipole seems not to be completely aligned along the nanowire, i.e., the flux
leakage is not symmetric. In the initial magnetic state (Figure 5b), it seems that there are 2 points
from where the field is leaking, one aside from the other. In Figure 5d, after being magnetized,
one of these points have disappear, and two more appear on the other side of the nanowire. In
Figure 5f, when reversing the magnetization, a closure appears resembling a vortex state at the tip
and the asymmetry of the flux leakage.
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Figure S5. (a) - (b) Unwrapped phase image of the Co nanowire in its remanent state, and its
phase contours by 1.5 x phase, respectively. (c) – (d) Unwrapped phase image of the Co nanowire
in its remanent state, and its phase contours by 1.5 x phase, respectively, after +20° tilt (e) – (f)
Unwrapped phase image of the Co nanowire in its remanent state, and its phase contours by 1.5 x
phase, respectively, after -20° tilt. Solid arrows represent the magnetization direction and dashed
arrows represent the direction of the applied magnetic field H.
II.
Precession electron diffraction and orientation mapping
In Figure S6 is depicted a diagram of the PED- assisted orientation mapping in TEM. The beam is
scanned along the sample while precessing at each step according to the selected frequency and
angle of precession.
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Figure S6. (a) Schematic representation of the precession geometry in a TEM. The incident
electron beam is tilted and rotated in a conical hollow surface around the optical axis using the
beam tilt coils. The diffracted intensities are then de-scanned in a complementary way, with the
image shift coils, so that the diffraction pattern appears as a stationary spot pattern. (b) Probe size
diameter around 2 nm as measured in the analysis.
The off-line data processing software uses template matching by calculating the correlation index
between the experimental and the calculated spot pattern. The template database considered for
the matching was generated from the hexagonal structure of Co with lattice parameters a = b =
2.507 and c = 4.096 with space group p63/mmc; 5151 templates were used for the matching with
angular resolution of around 1°. To estimate the confidence of the pattern matching, a reliability
map is generated from the two maximum values obtained from the correlation index. The lower
values in the reliability map appear as dark pixels due to poor quality of the recording intensity of
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the diffraction spots or due to multiple solutions of the matching due to different superimposed
diffraction spot patterns. In Figure 4 from the text some of the grains boundaries are denoted by
black pixels.
The studied Co nanowire shows an hcp structure with polycrystalline growth. This information is
extracted from the crystal orientation map obtained after indexing and matching the recorded
diffraction patterns with the calculated templates, confirming the hcp structure in the nanowire.
The step size and probe size used in this analysis was set to 2 nm and 1.1 nm, respectively (Figure
S6b). However due to beam broadening when precessing the beam the final measured spot size
was 2 nm. In addition, a representation of the geometry of the disorientations in the nanowire is
show in Figure S7. In the region near the tip, the grains were smaller than the nanowire diameter
such that the diffraction patterns show multiple orientations. It is important to note that the crystal
orientation map does not display a 3D orientation structure when two or more diffraction patterns
overlap, since the indexing algorithm can only display one of the possible solutions in the
orientation map. This makes the indexation of small grains difficult. To address this issue, a
reliability map can be obtained displaying areas where two or more solutions are almost equally
possible. Figure S8 shows measurements of grain disorientation in different areas of the nanowire.
A disorientation is the smallest possible rotation between two orientations taking the crystal
symmetry into account. In bigger grains the disorientation is of around 21.5° as shown in Figure
S8e. In Figure S8d the disorientation is around 70° which is the area where the small
polycrystalline grains begin to grow. The disorientation between the small grains ranges between
35° and 45° (Figures S8a, S8b and S8c).
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Figure S7. Pole figures representing the different orientation of crystal grains in the nanowire and
stereogram of poles for the hexagonal system.
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Figure S8. Disorientations measured across different grains in the Co nanowire indicated by the
arrows and the letters a, b, c, d, and e. The largest disorientation measured was around 70° in (d).
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