Title: AC driven magnetic domain quantification with 5 nm
resolution
Authors: Zhenghua Li1, Xiang Li2, Dapeng Dong1, Dongping Liu1*, H.
Saito3 and S Ishio3
Author affiliations: 1Liaoning Key Lab of Optoelectronic Films &
Materials, School of Physics and Materials Engineering, Dalian
Nationalities University, Dalian, 116600, China; 2School of Materials
Science and Engineering, University of Shanghai for Science and
Technology, Shanghai, 200093, China; 3Venture Business Laboratory,
Akita University, Gakuen Machi 1-1, Tegata, Akita, 010-8502, Japan
Corresponding person: Dongping Liu (phone: +86-411-87508902, fax:
+86-411-87508902, email: dongping.liu@dlnu.edu.cn )
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SECTION 1: The 3-Dimensional schematic structure of trailing-edge shielded
single-pole-type head (Fujitsu SPT head)
Figure S1 (a) shows the 3-Dimensional schematic structure of the trailing shield
perpendicular write head. The main pole, the gap between main pole and trailing
shield, and the Air Bearing Surface (ABS, in X-Y plane, the AFM scanning plane)
can be clearly seen. Figure S1 (b) shows the schematic figure of ABS plane relating to
Figure S1 (a). The main pole, return pole, and a nonmagnetic layer connected with
main pole can be easily identified. In the side-band MFM, we can detect the signal
information from the ABS surface. When we capture the main pole area, we can get
strong MFM contrast near the pole position. The length and width of the pole tip are
140 and 100 nm (estimated from the SEM observation), respectively. The width of the
gap is estimated as 50 nm.
Figure S1 (a) The 3-Dimensional schematic structure of a trailing shield perpendicular
write head, (b) the schematic figure of the Air Bearing Surface (ABS) relating to (a).
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SECTION 2: The side-band MFM imaging of another write head (Hitachi SPT
head)
Figure S2 shows the side-band MFM images of another SPT head (Hitachi SPT
head). The head is driven by a sinusoidal AC current with a zero-to-peak amplitude of
20 mA and a frequency of 100 kHz. Figure S2 (a) shows a topographic image of the
shielded SPT head, where the main pole and side shields can be clearly observed.
Figure S2 (b) shows the corresponding amplitude image of the SPT head, where the
strong magnetic signal is formed at the main pole area. Figure S2 (c) shows the
relating MFM phase image. The bright and dark contrasts indicate that the magnetic
field direction at the main pole is opposite to the one at the side shields.
Figure S2 (a) Topographic image, (b) amplitude image, (c) phase image of the Hitachi
SPT head measured by the side-band MFM.
SECTION 3: Stroboscopic imaging of the time-variable AC magnetic field
In side-band MFM system, the alternating magnetic field from a write head has a
phase delay with respect to the driving head voltage due to the phase shift arising
from electronics (including the resistor-inductor circuit) and magnetics. Given the
total phase shift of alternating magnetic field with respect to the head voltage, we
have changed the phase delay using the lock-in amplifier by adding an extra phase (or
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time evolution operator ei m t ) to the original phase image. The theories relating to the
lock-in technique are described in the manuscript (METHODS: Theory for imaging
the rotation of magnetization). Figure S3 shows the stroboscopic analysis of AC
magnetic field for the Hitachi SPT head. The head is driven by a sinusoidal AC
current with a zero-to-peak amplitude of 20 mA and a frequency of 100 kHz. From
the figure, we can observe that the MFM contrast varies periodically at the pole area
(the MFM contrast changes from bright to dark, and then bright). The estimated
magnetization at the main pole region is thought to rotate periodically with the
modulation frequency.
Figure S3 The stroboscopic imaging of the time-variable AC magnetic domains for
the Hitachi SPT head.
Figure S4 shows the stroboscopic imaging of the time-variable AC magnetic
domains of the Fujitsu SPT write head studied in the main text. The head is driven by
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a sinusoidal AC current with a zero-to-peak amplitude of 20 mA and a frequency of
200 kHz. The relating domain wall motions are quantified via micromagnetics, as
discussed in the main text (Figure 4).
Figure S4 The stroboscopic imaging of the time-variable AC magnetic domains for
the Fujitsu SPT head.
SECTION 4: Other possible dynamics starting from different remanent states
In the manuscript, based on a deconvolution technique, the magnetic charge
distribution is obtained, combined with micromagnetics, and the possible magnetic
domain states with minimum energy can be determined. Based on micromagnetics,
only two remanent states with minimum energy are possible, as seen in Figure S5 (a)
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and (b) (the same as Figure 4 (d) and (i) in main text). The initial magnetization
configurations of the remanent states (Figure S5 (a) and (b)) are set parallel to the
head surface (yellow and green arrows). Assuming other initial states, such as the
magnetic moment perpendicular to head surface, or the magnetization randomly
distributed, the final stable remanent states also show two possibilities (Figure S5 (a)
and (b)). Figure S5 (c) and (f) are the detailed magnetization dynamics starting from
each remanent state. The maximum magnetic pole density  max  1.55 T. Figure S5
(d) and (e) show calculated MFM images relating to Figure S5 (c) and (f). Although
the magnetic dynamic states are different, the calculated MFM images are almost
identical.
Figure S5 (a) and (b) The possible remanent states, (c) and (f) the possible dynamic
states, (d) and (e) the calculated MFM images.
SECTION 5: Quantification of the magnetic point monopole within the MFM tip
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In this work, the MFM tip is a high-coercivity tip (SI-MF40-Hc, Nitto Optical
Co., Ltd, coercivity more than 10 kOe) coated with 20 nm FePt film. Before the
measurement, the MFM tip is magnetized perpendicular to the sample surface. Figure
S6 (a) is the likely configuration of the tip magnetization. The sample is an assumed
SPT head, and the tip-to-sample distance is 1 nm. The magnetic force distribution
within the tip is shown in Figure S6 (b). It is seen that the magnetic charge near the tip
end is highly sensitive to the sample field, therefore, at an operating distance very
close to the sample surface, the MFM signal is dominated by the monopoles near the
tip end.
Figure S6 (a) The magnetic configuration of the MFM tip, (b) the magnetic force
distribution within the tip.
To further quantify the monopole approximation, we performed a deconvolution
procedure on an assumed MFM, as shown in Figure S7. The assumed MFM is
considered as the convolution of the magnetized surface and the sensitivity field of
the calibrated FePt tip. From Figure S7 (a), it can be observed that the maximum and
minimum intensities appeared around the pole edge (see the normalized signal profile
along the blue line). Figure S7 (b) shows the distribution of the calculated magnetic
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charge obtained by performing a deconvolution process on the assumed MFM at the
tip-to-sample distance of 8 nm. The simulated magnetic charge is consistent with the
assumed one. For comparison, when the tip-to-sample distance increases to 10 nm,
there is a small transition area between the positive and negative charges (see the line
profile of Figure S7 (c)). Therefore, the quantified tip-to-sample distance is 8 nm.
Figure S7 Calculation of magnetic charge by performing a deconvolution process.
Another quantified parameter is the effective monopole value. Based on the
measured MFM phase image (Figure 3 (c) in main text), and the calibrated SPT head
field in the center of main pole (Figure S8), we can obtain the effective monopole
qm  8.2  10 -9 (Am). Here, the MFM phase signal is
   0
H z
180Q
(q m
k
z
z 8 nm
)
where Q is the quality factor of the tip, k the spring constant of the tip,  the
phase shift at the main pole center.
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Figure S8 Calibrated SPT head field in the center of main pole.
SECTION 6: Example of the recording process along a single track
Figure S9 (a) and (b) show the Hz profiles in the down-track and cross-track
directions (obtained from Figure 4(a) and (b) in the main text). We can evaluate the
z-component of magnetic field (maximum Hz of 8000 Oe at pole center and minimum
Hz of -1800 Oe around trailing shield), and Hz gradients (maximum value of 64
Oe/nm at head gap) in both down-track and cross-track directions. Figure S9 (c)
shows the micromagnetic simulation of the recording process along a single track.
The quantitative results (Figure 4(a) and (b) in the main text) of SPT head are used to
record the bit patterns. The head-medium speed is 35m/s, the head-medium distance is
8 nm, the track width is 125 nm，and the bit-aspect radio is 4.2. Therefore, by
optimizing the parameters of the system, the recording performance can be easily
evaluated.
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Figure S9 (a) The magnetic field Hz in the down-track and (b) cross-track directions,
(c) the micromagnetic simulation of the recording process along a single track.
SECTION 7: The determination of spatial resolution
The spatial resolution is determined by a Fourier-based analysis of the MFM
signals [35], as shown in Figure S10. The figure gives the response of the MFM
signal (force derivative) as a function of spatial frequency ( k x ). In the Fourier
spectrum, the maximum detectable spatial frequency introduced in Reference [36] is
used to evaluate the spatial resolution. Therefore, the MFM resolution is determined
by the maximum detectable frequency ( kc ), where the intensity of MFM signal
spectrum reduces to the white background level (thermodynamic noise of cantilever)
[35, 37, 38]. The thermodynamic noise, which is also considered as the minimum
detectable force gradient, is given by [28]:
( Fz) min  4ck BTB /(0QA2 )
where A is the oscillation amplitude,
c
the spring constant of the tip, k B the
Boltzmann constant, T the temperature, B the measurement bandwidth, and Q the
quality factor of the cantilever resonance. Therefore, the estimated thermodynamic
noise is about 0.55 N / m , as shown in Figure S10 (horizontal red line). The MFM
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resolution is estimated as half of the critical wavelength c 
1
. In Figure S10, the
2kc
critical frequency kc  91 （1/μm）, therefore, the estimated resolution is 5.5 nm.
Figure S10 The MFM spectrum of the write head.
SECTION 8：The imaging of nanoscale domain structures in a perpendicular
magnetic recording media based on the side-band MFM
Figure S11 shows the schematic diagram of the static magnetic field imaging by
the side-band MFM with an AC magnetic field driven soft MFM tip. The system was
based on a conventional JSPM-5400 (JEOL Ltd.) scanning probe microscope. A
perpendicular magnetic recording medium (coercivity larger than 4 kOe) is put on a
soft ferrite core, resulting in a homogeneous AC magnetic field up to 350 Oe
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(zero-peak). The MFM scans are carried out using a low coercivity (10 Oe) MFM tip
coated with 30 nm NiFe film. The AC magnetic field from the soft ferrite core
periodically rotates the magnetic moment of the NiFe tip, causing an alternating force
between the MFM tip and sample. Amplitude and phase information of the alternating
force between the sample and MFM tip can be extracted by a lock-in amplifier.
Figure S11 Schematic diagram of static magnetic field imaging by the side-band
MFM with an AC magnetic field driven soft MFM tip.
Figure S12 shows the side-band MFM amplitude, phase images and conventional
MFM images of the perpendicular magnetic recording medium. The MFM tip is close
to the sample surface (operating distance of 10 nm). Based on Figure S12, we can get
high quality side-band MFM amplitude and phase images with a high spatial
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resolution. However, at the same tip-to-sample distance, the conventional
phase-detection MFM cannot produce a clear image of the recording bits, because the
magnetic force is weaker than the short-range forces arising from the surface.
Figure S12 (a) side-band MFM amplitude image, (b) side-band MFM phase image,
and (c) conventional MFM phase image of a perpendicular magnetic recording
medium.
Here, we demonstrate the way to accurately control the real tip-to-sample
distance. Figure S13 shows measured side-band MFM phase images with the lift
height D ranging from -40 nm to -69 nm. When D reduces from -40 nm to -65 nm, the
two-valued phase images can be clearly observed with high quality. However, when
D=-69 nm, the phase signal deteriorates seriously with random noise. In this case, it is
considered that the MFM tip just contacts the sample surface. Here, the MFM tip may
get close to a sample surface (a few nanometers) by adjusting the amplitude of the tip
oscillation. Since the alternating force only causes the frequency modulation of the
cantilever, there is no effect on the amplitude. Therefore, we can precisely control the
operating distance down to 1 nm and obtain the actual tip-to-sample distance by
varying the lift height D.
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Figure S13 Measured side-band MFM phase images with the lift height ranging from
-40 nm to -69 nm.
SECTION 9：The comparison between conventional MFM and side-band MFM
images
Figure S14 shows the (a) topographic image, (b) side-band MFM phase image, (c)
conventional MFM phase image of the Hitachi SPT head. Figure S14 (b) is the
side-band MFM image of a Hitachi SPT head driven by a low AC current with a
zero-to-peak amplitude of 5 mA. The MFM tip is far from a sample surface (operating
distance of 80 nm), the estimated spatial resolution is about 30 nm. Figure S14 (c)
shows the conventional MFM image taken with the same spatial resolution. It is found
that the magnetic field around main pole can be clearly observed in the side-band
MFM image, while the magnetic signals cannot be resolved in the case of
conventional MFM.
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Figure S14 (a) Topographic image, (b) side-band MFM phase image, and (c)
conventional MFM phase image of the Hitachi SPT head.
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