Vol. 39 No. 5 2015 年 9 月 1 日発行 頒価 ¥2,000 （税込）送料実費

ISSN 2432-0250

Vol.43 No.1
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2019

Spin Electronics

Magnetoresistance in Bilayers of Heavy Metal and Non-collinear Antiferromagnet
発行（公社）日本磁気学会 〠101‒0052 東京都千代田区神田小川町2丁目8番地
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印刷（株）国 際 文 献 社 〠169‒0075 東京都新宿区高田馬場3の8の8☎(03)3362-9741

K. Oda, T. Moriyama, and T. Ono…01

Measurement Technique, High-Frequency Devices
High Coercivity and Resolution FePt•MgO-coated Tip for Imaging the Magnetic Field of Perpendicular
Magnetic Write Head by Alternating Magnetic Force Microscopy (A-MFM)
F. Zheng, S. Yoshimura, S. Yasui, G. Egawa, and H. Saito…06

Power Magnetics

Evaluation on Edge-supported Magnetic Levitation Apparatus for Thin Steel Plates

広告◇東英工業株式会社Y. Oda, Y. Ito, K. Okuno, M. Kida, T. Suzuki, A. Endo, T. Narita, H. Kato and H. Moriyama◇計測エンジニアリングシステム株式会社

…11

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HP: http://www.magnetics.jp/ e-mail: msj@bj.wakwak.com
Electronic Journal: http://www.jstage.jst.go.jp/browse/msjmag

1

2019

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Journal of the Magnetics Society of Japan
Vol. 43, No. 1
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Spin Electronics
Magnetoresistance in Bilayers of Heavy Metal and Non-collinear Antiferromagnet……………………………………………………………………………………K. Oda, T. Moriyama, and T. Ono

1

Measurement Technique, High-Frequency Devices
High Coercivity and Resolution FePt•MgO-coated Tip for Imaging the Magnetic Field of Perpendicular
Magnetic Write Head by Alternating Magnetic Force Microscopy (A-MFM)………………………………………………………F. Zheng, S. Yoshimura, S. Yasui, G. Egawa, and H. Saito

6

Power Magnetics
Evaluation on Edge-supported Magnetic Levitation Apparatus for Thin Steel Plates…………… Y. Oda, Y. Ito, K. Okuno, M. Kida, T. Suzuki, A. Endo, T. Narita, H. Kato and H. Moriyama

Board of Directors of The Magnetics Society of Japan
President:

K. Takanashi

Vice Presidents:

K. Nakagawa, S. Nakamura

Directors, General Affairs:

Y. Miyamoto, K. Niiduma

Directors, Treasurer:

K. Aoshima, K. Ishiyama

Directors, Planning:

Y. Saito, S. Nakagawa

Directors, Editorial:

K. Kobayashi, T. Ono

Directors, Public Relations:

H. Itoh, S. Greaves

Directors, International Affairs: Y. Takemura, M. Nakano
Auditors:

Y. Suzuki, R. Nakatani

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J. Magn. Soc. Jpn., 43, 1-5 (2019)<Paper>Magnetoresistance in bilayers of heavy metal and non-collinear antiferromagnet
K. Oda, T. Moriyamaa), and T. Ono
Institute for Chemical Research, Kyoto University, Uji, Kyoto, 611-0011, Japan

We report on magnetoresistance measurements in a heavy metal/ Mn3Ir multilayers. After a post
annealing process, we observed the magnetoresistance associated with the ordered crystalline structure of the Mn 3Ir.
The resistance change as a function of the strength as well as the direction of the applied field suggests that themagnetoresistance is partially related to a modification of the Néel order by the magnetic field. Our further detailed
investigation revealed that there is an additional component of the resistance change, perhaps due to the non-collinear
magnetic structure associated with the L12-ordered Mn3Ir, which cannot be accounted for by any conventional
magnetoresistance effects.
a)mtaka@scl.kyoto-u.ac.jp

Key words: antiferromagnetic spintronics, anisotropic magnetoresistance, spin Hall magnetoresistance, Mn3Ir, chiralmagnetic structure
1. Introduction
Antiferromagnetic
spintronics
isanemerging field which utilizes antiferromagnets (AFMs)
as active components in spintronic applications 1),2).
Compared to ferromagnets (FMs), AFMs have several
appealing properties, e. g., zero stray field, robustness
against magnetic field perturbations, and ultrafast
dynamics, leading to an ultrahigh density memory andultrafast information processing. However, in otherwords, the insensitivity to an external magnetic field
makes electrical manipulation and detection of the Néelorder in AFMs quite challenging. Especially, thedifficulty of the electrical detection obstructs
experimental advances of antiferromagnetic spintronics
as opposed to the ferromagnetic spintronics.
Nevertheless,recentstudieshavedemonstrated the electrical detection of the Néel orderin some of the antiferromagnetic materials by the same
principle having been used for ferromagnetic materials:
i.e. anisotropic magnetoresistance (AMR) 3) and the spin
Hall magnetoresistance (SMR) 4),5). AMR and SMR
depend on the square of the spontaneous magnetization,these magnetoresistances in principle appear not only in
FMs but also in the AFMs 6). These magnetoresistances
have been reported in some of the particular collinear
AFMs, such as FeRh 7),8), NiO 9)-12), CuMnAs 13), and
Mn2Au 14)-16), etc. in which the Néel order control isevidently possible.
More intriguing magnetoresistive effect in
AFMs is the giant anomalous Hall effect (AHE) not due
to the magnetic moments themselves but due to thechiral magnetic structure 17). Chen et al. theoretically
predicted that such an AHE can be observed in L12ordered Mn3Ir in which the magnetic moments make a

triangle lattice. Later, the giant anomalous Hall effect(AHE) was experimentally reported for a similarmaterial system, i.e. Mn3Sn 18).
As the electrical detection of the magnetic
state in AFMs is one of the indispensable ingredients foradvancing the antiferromagnetic spintronics, it isimportant to further investigate the magnetoresistive
effect in various antiferromagnetic multilayer systems.
In this work, we examined the magnetoresistance in
Pt/Mn3Ir and W/Mn3Ir bilayers. MnIr alloys are one of
the most commonly used metallic AFMs in spintronic
devices for creating exchange bias 19),20). Among various
intermetallic alloys of Mn and Ir, L12-ordered Mn3Ir is ofgreat interest for the abovementioned novel
magnetoresistive behavior owing to the non-collinear
chiral magnetic structure 21).
2. Experimental Procedure
We formed W 6 nm/Mn75Ir25 10 nm/MgO 2nm/W 2 nm
and Pt 6 nm/Mn75Ir25 10 nm/MgO 2 nm/W 2 nm on athermally oxidized Si substrate by magnetron sputtering.
The MgO 2 nm/W 2 nm capping layers in both samples
are to avoid the sample from oxidation and degradation.
The films annealing was performed at 220℃ for 30 min.
We separately confirmed that the Mn3Ir 10 nm layer inboth samples possesses an antiferromagnetic order 22).
Fig. 1 shows the X-ray diffraction (XRD) of the films
before and after the annealing. A distinct difference

between the W/Mn3Ir and the Pt/Mn3Ir multilayers can befound in the evolution of the (110) superlattice peak of L12
Mn3Ir 23) while (220) peak was buried in the intense (400)peak of Si substrate. The L12 order is developed in
W/Mn3Irafter

annealing

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while

the

annealing1

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Fig. 1 XRD patterns for (a)W 6 nm/Mn3Ir 30 nm/MgO 2 nm/W 2 nm and (b)Pt 6 nm/Mn3Ir 30 nm/MgO 2 nm/W 2
nm. The black line shows the result of the as deposited film and the red line is the result of the annealed film.

Fig. 2 (a-c) Experimental setup of the electrical transport property measurement and the definition of thecoordinate system. H denotes the magnetic field. (d,e) Angular dependence of Rxx and Rxy under the 9 T field
at T = 300 K for the as-deposited (gray data points) and annealed W 6 nm/Mn3Ir 10 nm/MgO 2 nm/W 6 nm(f,g) and for the as-deposited (gray dots) and annealed Pt 6 nm/Mn3Ir 10 nm/MgO 2 nm/W 6 nm.
annihilates the L12 order in the Pt/Mn3Ir case, indicatingthat the crystalline symmetry of the underlayer (α (b.c.c.)or β structure for W and f.c.c. for Pt) is important forcrystallinity of the Mn3Ir. For electrical measurements,
the films were patterned into a 120-μm-long and 30-μm-

2wide Hall bar structure by a conventional
photolithography and Ar ion milling process. The
electrical measurements were performed using thePhysical Property Measurement System (PPMS-9T,
Quantum Design). The longitudinal Rxx and transverse

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Fig. 3 Field dependence of the magnetoresistive signals in the annealed W/Mn3Ir(a) and Pt/Mn3Ir(b) samples.
(c)These magnetoresistance ratios are summarized as a function of magnetic field in red dots(Pt/Mn3Ir) andblue dots(W/Mn3Ir).

Rxy resistances were measured with the excitation
current of 1 mA (J ~ 2.1 x 105 A/cm2) in a rotating
magnetic field with a fixed magnitude (H = 0 ~ 9 T). The
excitation current flows along x-axis. The definition of
the rotating angles: α, β, and γ are indicated in Figs. 2(a-c).

3. Results
Figures 2 (d-g) show the magnetoresistanceratio ΔRxx/Rxx and ΔRxy/Rxx as functions of α, β, and γ with
H = 9 T before and after annealing. Both W/Mn3Ir and
Pt/Mn3Ir samples did not show any α dependent
magnetoresistive behaviors before annealing (asindicated in gray data points in Figs. 2 (d-g)).
Measurements in other angles β and γ are omitted. On
the other hand, after annealing, appreciablemagnetoresistances were observed but the behaviors
with respect to the rotating angles differ for the two
samples. The most intriguing and distinct differences
can be seen in the resistance variation with respect tothe rotating angle α which are shifted by π/2 between theW/Mn3Ir and Pt/Mn3Ir samples. Figure 3 shows the fielddependence of ΔRxx/Rxx in the annealed W/Mn3Ir(a) and
Pt/Mn3Ir(b) samples. Figure 3 shows the fielddependence of ΔRxx/Rxx in the annealed W/Mn3Ir(a) and
Pt/Mn3Ir(b) samples. These ΔRxx/Rxx are summarized in
Fig.3(c). The π/2 phase shift is denoted as a different
sign of ΔRxx/Rxx between the W/Mn3Ir and Pt/Mn3Ir
samples. When H = 0 T, only the noise level of the
ΔRxx/Rxx was obtained. ΔRxx/Rxx became larger withincreasing the magnitude of H. Although the resistancedifference between Rxx(α = 0 degree) and Rxx(α = 180
degree) is unclear, we can conclude that the saturation
magnetic field to manipulate the magnetic moments isover 9 T.

4. Discussion
In order to step into a quantitative argumenton these intriguing magnetoresistance behaviors, wefirstly consider the change in the longitudinal resistance
ΔRxx in these multilayer systems. The derivation of the
𝑅𝑅𝑥𝑥𝑥𝑥 change due to the SMR and the AMR can start from4),24),𝑛𝑛

𝑅𝑅𝑥𝑥𝑥𝑥 = ∑ (𝑅𝑅0 + ∆𝑅𝑅𝐴𝐴𝐴𝐴𝐴𝐴 𝑚𝑚𝑛𝑛,𝑥𝑥 2(1)+ ∆𝑅𝑅𝑆𝑆𝑆𝑆𝑆𝑆 (1 − 𝑚𝑚𝑛𝑛,𝑦𝑦 2 ))where 𝑅𝑅0 is the field independent resistance, and∆𝑅𝑅𝐴𝐴𝐴𝐴𝐴𝐴 and ∆𝑅𝑅𝑆𝑆𝑆𝑆𝑆𝑆 are the resistance change due to
AMR and SMR, respectively. 𝑚𝑚𝑛𝑛,𝑥𝑥 and 𝑚𝑚𝑛𝑛,𝑦𝑦 are

respectively a unit vector along x- and y-axis of the nthmagnetic sublattice. Here, we left aside a possible
magnetoresistance due to the chiral magnetic structure
in absence of a detailed quantitative model but will comeback to the point in the later argument. Assuming thatthe external field is large enough to induce the spinflopping of the AFM and the magnetic anisotropy energy
is negligibly small compared to the exchange energy,
Equation (1) leads to ΔRxx depending on the net
magnetization vector 𝑴𝑴∥ parallel to the external fieldand 𝑴𝑴⊥ perpendicular to the external field, where 𝑴𝑴∥
is regarded as the ferromagnetic order parameter and𝑴𝑴⊥ maybe regarded as the antiferromagnetic orderparameter, or the Néel vector. Table 1 shows themagnetoresistance ratio ∆𝑅𝑅𝑥𝑥𝑥𝑥 ⁄𝑅𝑅 considering SMR and
AMR for 𝑴𝑴∥ and 𝑴𝑴⊥ . One can notice from the list of themagnetoresistances in Table 1 that the contribution of
AMR and SMR can be separated out by having thecomplete data set for α, β, and γ rotations. Here, theamplitude of the trigonometric functions, AFS, AAS, AFA,
and AAA considers the resistance change due to SMR for𝑴𝑴∥ , SMR for 𝑴𝑴⊥ , AMR for 𝑴𝑴∥ , AMR for 𝑴𝑴⊥ ,respectively.  We also derive the change in the

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Table 1 Longitudinal resistance change due to SMR and AMR

Table 2 Transverse resistance change due to SMR and AMR

transverse magnetoresistances ΔRxy in a similar mannerstarting from the equation 4),24),𝑛𝑛

𝑅𝑅𝑥𝑥𝑥𝑥 = ∑(∆𝑅𝑅𝐴𝐴𝐴𝐴𝐴𝐴 𝑚𝑚𝑛𝑛,𝑥𝑥 𝑚𝑚𝑛𝑛,𝑦𝑦 + ∆𝑅𝑅𝑆𝑆𝑆𝑆𝑆𝑆 𝑚𝑚𝑛𝑛,𝑥𝑥 𝑚𝑚𝑛𝑛,𝑦𝑦+ ∆𝑅𝑅𝑂𝑂𝑂𝑂𝑂𝑂 𝑚𝑚𝑛𝑛,𝑧𝑧 )(2)where ∆𝑅𝑅𝑂𝑂𝑂𝑂𝑂𝑂 is the coefficient for the ordinary Hall
effect. The contributions to ΔRxy/Rxx by AMR, or planar
Hall effect, and SMR are summarized in Table 2 in termsof α, β, and γ rotations. Since the transverse resistancechange contains significant amount of the ordinary Hall
effect from the Pt layer, which makes the quantitativeargument difficult when using ΔRxy/Rxx in the following
discussion, we will focus on ΔRxx/Rxx for a quantitativeargument.
According to Table 1, considering both SMR
and AMR, the amplitude for the rotation α is representedas (𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 ) − (𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 ) , the amplitude for therotation β is represented as 𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 and that for therotation γ is represented as 𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 . For the W/Mn3Ircase, we find (𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 ) − (𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 ) = -6.4 x 10-5,
𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 = 8.4 x 10-5 and 𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 = -15.4 x 10-5 (seeFigs. 2 (d)), which are not self-consistent indicate that
there are additional magnetoresistances we are missingin our consideration in addition to antiferromagnetic
order dominant magnetoresistance. On the other hands,
for the Pt/Mn3Ir case, we find (𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 ) − (𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 )= 4.5 x 10-5, 𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 = 4.3 x 10-5 and 𝐴𝐴𝐹𝐹𝐹𝐹 − 𝐴𝐴𝐴𝐴𝐴𝐴 = -0.9
x 10-5 (see Figs. 2 (e), which are relatively self-consistent
within the error factor of ~ 7 x10-6. The results of thePt/Mn3Ir case is indeed very similar to the previous
report which is explained by an uncompensatedmagnetic moment is induced at Pt/FeMn interface25). In
other words, a ferromagnetic order parameter isdominant in this case.
Although Mn3Ir itself is generally robust
against 9 T of magnetic field, it is likely that themagnetic moments of Mn3Ir with the Pt and W
underlayer can become manipulated by magnetic field
after the annealing. In the case of W/Mn3Ir, the4emergences of the magnetoresistance as well as the
additional unknown magnetoresistance seem to be
associated with the formation of L12 ordered structure.
5. Conclusion
In summary, the magnetoresistance in theheavy metal/AFM metal multilayers has been studied.
Both Pt/Mn3Ir and W/Mn3Ir exhibit appreciablemagnetoresistance in a rotating magnetic field with ~ 9
T. Assuming that the AMR and SMR are the relevant
magnetoresistive effects in these systems, we found that
there
is
an
additional
unconventional
magnetoresistance contribution in the W/Mn3Ir. As thisadditional magnetoresistance is associated with theformation of L12- Mn3Ir structure, we speculate that it
could be related to the non-collinear antiferromagnetic
order.
Acknowledgements We thank Prof. Daisuke Kan for
helping us with performing the X-ray diffraction
measurements. This work was supported by JSPS
KAKENHI. Grant Numbers JP17J07666, JP17H04924,
JP15H05702, JP26870300, JP17H05181, JP16H04487.
We also acknowledge The Cooperative Research Project
Program of the Research Institute of ElectricalCommunication, Tohoku University.
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Received Aug. 13, 2018; Accepted Nov. 19, 2018

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J. Magn. Soc. Jpn., 43, 6-10 (2019)<Paper>High coercivity and resolution FePt•MgO-coated tip for imaging themagnetic field of perpendicular magnetic write headby alternating magnetic force microscopy (A-MFM)
F. Zheng1,2, S. Yoshimura3, S. Yasui3, G. Egawa3, and H. Saito3

Venture Business Laboratory, Akita University, Tegata Gakuen-machi 1-1, Akita 010–8502, Japan

1

School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, China

2

Research Center for Engineering Science, Graduate School of Engineering Science, Akita University,

3

Tegata Gakuen-machi 1-1, Akita 010–8502, Japan

High coercivity FePt•MgO films were successfully synthetized on cone-shape Si tips in a very high frequency(VHF) plasma irradiation-assisted magnetron sputtering system to prepare the MFM tips for evaluation of the AC
magnetic field of perpendicular magnetic write head at high write current. Alloying with MgO significantly enhanced
the coercivity of the magnetic coating due to the isolation of FePt grains by MgO. As a result, a high coercivity close to
20 kOe was achieved. The AC magnetic field images of the perpendicular magnetic write head at high write current
were taken on alternating MFM (A-MFM) by this tip. A clear amplitude image with a strong signal at the main poleposition was observe compared to the pure FePt layer-coated tip, which gave a blurry image and very small amplitude.
Fourier analysis of the images obtained by this kind of FePt•MgO tip gives a spatial resolution of about 15 nm in air
atmosphere. It is clear that the cone-shape FePt•MgO-coated MFM tip with a coercivity higher than the magnetic
field to be measured is effective and capable for measuring the high AC magnetic field for an HD perpendicularmagnetic write head at a very high write current.
Key words: high-coercivity and high-resolution FePt•MgO-coated tip, very high frequency (VHF) plasma irradiation,
perpendicular magnetic write head, alternating magnetic force microscopy (A-MFM)

1. Introduction
Magnetic force microscopy (MFM) is an effective
scanning probe for investigation of the magnetic domain
structures of magnetic materials in nanoscale such as
magnetic recording media because of its high spatial
resolution of the static magnetic field1). The MFM tip isthe most important key element to detect and image thesurficial magnetic signal of an object. A high coercivity
magnetic tip is one of the essential parameters for MFM
imaging. Commercially-available MFM tip is usually an
atomic force microscopy (AFM) tip coated with a thin
CoCrPt film. There have been many efforts to prepare
MFM tips such as synthetic antiferromagnetic coatingwith sandwich structures2),3), focused ion beam (FIB)
trimming4)-6), carbon nanotubes coated with magnetic
films7),8). Hard magnetic coatings of Fe-Pt9)-13), Fe-Pd13),14),
Co-Pt15)-18), Sm-Co19) were used for the preparation of
MFM tips to image large magnetic field. In addition to
the MFM tip, the methodology of MFM itself is also
critical. We have developed a new MFM imaging method
for characterization of AC magnetic field. We named it asalternating MFM (A-MFM)20). The A-MFM uses afrequency modulation (FM) of the cantilever oscillation
by applying an AC magnetic field on a mechanicallyoscillated tip. This can allow us to measure theperpendicular component of the AC magnetic field withrespect to the sample surface. Previously, we used inhouse-coated FePt tips with high-coercivity to image the6AC magnetic field of a perpendicular magnetic write
head having a one-sided trailing shield on our A-MFM setup21),22),23). The spatial resolution was estimated to be 15
nm (a lift height of 1 nm and AC current with a zero-topeak amplitude of 20 mA). However, this tip failed tocharacterize the AC magnetic field of the head having
three surrounding shields when a large write current
which generates a large magnetic field bigger than thecoercivity of the FePt coating on the tip. To estimate the
distribution of magnetic field from the head having threesurrounding shields, MFM tip with symmetry shape forthe magnetic charge and with high coercivity magnetic
film is effective. We had reported the cone-shaped MFM
tip with symmetry for the magnetic charge to get a MFM
image without distortion24). We also had reported thatcoercivity of the FePt coated MFM tip is lower than themagnetic field generated by the head having threesurrounding shields with large head current24).
We deposited FePt•MgO films on the tip by VHF
plasma irradiation-assisted magnetron sputtering inorder to increase the coercivity of magnetic FePt film.
The MgO25) was used for isolation of FePt grains. The
VHF plasma irradiation enhanced the L10 FePt phaseduring sputtering26). The new FePt•MgO MFM tip withvery high coercivity was used for observation of AC
magnetic image of perpendicular magnetic write head in
this work.

Journal of the Magnetics Society of Japan Vol.43, No.1, 2019

INDEX

Target10rpm

HeaterSubstrate
Plasma~~Sub.

HeaterSputtered Ar+
atoms

120mm

PlasmaTarget13.56 MHz

Fig. 1 Schematic image of VHF irradiation assisted
ultra-high vacuum sputtering system.
2. Experimental Procedure
FePt•MgO films with the total thickness of 20 nm wereprepared onto Si substrates which had thermallyoxidized surface for the purpose to check their structure
and magnetic properties. The FePt•MgO films were
deposited in two different paths: one path was to sputter
a composite target where many pieces of thin MgO plates
were placed on the top of a Fe50Pt50 target; another path
was to co-sputter both Fe50Pt50 and MgO targets. The
volume fraction (Vol.%) of MgO in the final film wasadjusted by changing the numbers of MgO thin plates on
the Fe50Pt50 target, the sputtering power, and/or thetarget-to-substrate (T-S) distance. During the sputtering,
the VHF plasma irradiation26) was fixed at 40.68 MHz
with the electric power (PVHF) of 5 ~ 20 W as shown in Fig.
1. After sputtering, the FePt•MgO films were annealed
at 750 ℃ in a rapid thermal annealing (RTA) system for
10 minute. The crystalline characteristics of the films
were analyzed by x-ray diffraction (XRD). The magnetic
properties were measured by a vibrating sample
magnetometer (VSM). The made-in-house MFM tips
with a cone-shaped Si tip (SSISC, Team Nanotec Co.
Ltd.) consisted of a very thin SiO2 layer formed by plasma
oxidation and a layer of the magnetic FePt•MgO (20 - 40nm) film which were prepared under the same sputteringand post-annealing conditions. SiO2 layer was used toFig. 2 Schematic of A-MFM system.

prevent interdiffusion between the magnetic film and Si
tip. Before measurement, the MFM tips were magnetized
to saturation along the tips axis, which means that themagnetization direction of the tips was vertical to thesample surface.
The A-MFM runs were carried out based on aconventional scanning probe microscope (JSPM-5400(JEOL Ltd.)) in an air atmosphere. Figure 2 shows ascheme of the A-MFM. A lock-in amplifier and a phaselocked loop (PLL) circuit were used for the AC magnetic
field measurement in the A-MFM21),22),23). The cantilever
was oscillated by using a piezoelectric element. The
resonant frequency of the cantilever with the MFM tip
was approximately 256 kHz. The oscillation frequency (fc)of the piezoelectric element was about 250 kHz which is
close to the resonant frequency of the tip, and the valueof Q was around 500. The AC magnetic field wasmeasured on the lift mode after topographic
characterization. The lift height was 8 nm or 1 nm. The
good spatial resolution was obtained at the lift height of
1 nm.
An advanced perpendicular magnetic write head
having three surrounding shields was used for evaluation.
In comparison with the magnetic write head having a
one-sided trailing shield21),22),23), this kind of write headcan generate focused magnetic field for high recording
density. The write head was run by a sinusoidal AC
current with a zero-to-peak amplitude of 20 - 40 mA anda frequency (fm) of 100 Hz.
3. Results and Discussions
Figure 3 shows θ-2θ XRD patterns of FePt, andFePt•MgO (16 Vol.% MgO) films without/with VHF
plasma irradiation power of 15 W. All of the films show
strong FePt(111) peak, which means the deposited FePtbased films have preferred (111)-texture. Due to thelowest interfacial energy of FePt(111) plane, the FePt
film deposited on amorphous SiO2 substrate can have a
Si sub.

40.68 MHz

Fig. 3 θ-2θ XRD patterns of FePt and FePt•MgOfilms.

Journal of the Magnetics Society of Japan Vol.43, No.1, 20197

INDEX(111)-favor texture growth. In Fig.3 you cannot see aclear (001) peak, but the sputtering film with VHF
plasma irradiation shows an enhanced (111) peakintensity, compared to the films without VHF plasma
irradiation. The integral intensity of FePt(111) was 4853,
5155, and 6763, for the films of FePt, FePt•MgO, andFePt•MgO with VHF plasma, respectively. In ourprevious study26), a VHF plasma irradiation during
sputtering deposition can effectively acceleratecrystallization and atom ordering. It is believed that the
VHF plasma irradiation can also accelerate thecrystallization and ordering of L10 FePt phase. As weknow, the high magnetic anisotropy of FePt films can beobtained in the chemically ordering state, which can leadto high coercivity.
An in-plane easy axis of magnetization of the magnetic
coating on is preferred for MFM tip preparation. Figure
4 shows the dependence of the in-plane coercivity of
FePt•MgO films on the volume fraction of MgO. The
inset
shows
hysteresis
loops
of
FePt
and
(FePt)84•(MgO)16 film (in Vol.%), respectively. The
coercivity rises from 9.2 kOe to 17.0 kOe when MgO’svolume percentage in FePt•MgO film increases from 0 to
35 Vol.%. It is obvious that MgO addition to the FePt film
significantly enhance the coercivity of the film. This isbelieved that the MgO’s effect of isolation of FePt grains
attributes to increased coercivity like the other kinds ofelement additives such as SiO227), C28), TiO229),30) added to
FePt-base films.
Figure 5 shows the in-plane coercivity of FePt•MgOfilms versus the VHF plasma irradiation power. The
inset shows hysteresis loops of (FePt)84•(MgO)16 filmwith VHF plasma irradiation power of 15 W. As shown in
the figure, the coercivity gradually increases from 14.5
kOe to 15.9 kOe when VHF power changes from 5 W to
15 W. And then coercivity drops to 15.2 kOe as VHF
power goes up to 20 W. The VHF bias is considered tohave two effects: 1) the enhancement of atoms/ molecules’

Fig. 4 The in-plane coercivity versus MgO volume
fraction in FePt•MgO films. The inset shows
hysteresis loops of FePt and (FePt)84•(MgO)16
film.

8

Fig. 5 Dependence of the in-plane coercivity of
FePt•MgO films on the VHF plasma irradiation
power. The inset is hysteresis loop of(FePt)84•(MgO)16 with VHF plasma irradiation
power of 15 W.
mobility for ordering and 2) the ion bombardment on film
during sputtering. The effect 1) of VHF bias is taking
place to increase coercivity when the VHF power is low.
This is supported by XRD measurement shown in Figure
3. The effect 2) of VHF bias becomes dominant andenhances disordering atoms/ molecules of FePt in thefilm so to reduce in-plane coercivity when VHF power ishigh. The highest in-plane coercivity achieved at thecomposition of 16 Vol.% MgO under a proper VHF plasma
irradiation during sputtering suggests the importance ofboth FePt atoms ordering and MgO molecules’ isolation
effects for making high coercivity films. This is also
supported by the (FePt)65•(MgO)35 film’s behavior as
shown in Figure 5. It is clearer that an optimized VHF
bias power (enhancement of FePt ordering) and more
MgO concentration (more isolations of FePt grains) cangive higher in-plane coercivity (more than 20 kOe) to
FePt films.
The two kinds of MFM tips with FePt and(FePt)84•(MgO)16 coatings were fabricated for evaluationof the AC magnetic field of a write head having threesurrounding shields. The (FePt)84•(MgO)16 film wasformed under a VHF plasma irradiation power of 15 W.
The nominal thickness of both FePt-base coatings was 40
nm. Here, we discussed the evaluation of magnetic
properties of MFM tips by using pulsed magnetic fieldmagnetic force microscope31), and also estimated thecoercivity of MFM tips32). The measured coercivity of
FePt•MgO MFM tips was closed to the values of
FePt•MgO films. The A-MFM measurement was taken
at a lift height of 8 nm. The head write current was 40
mA. Figs.6 (a) shows the topographic image of the write
head around the main pole area.
The amplitude images of AC magnetic field generated
from the write head measured by the FePt-coated tip and(FePt)84•(MgO)16-coated tip having an coercivity of 15.9
kOe is clear and has high amplitude signal at the mainpole position. In contrast, the amplitude image measured

Journal of the Magnetics Society of Japan Vol.43, No.1, 2019

INDEX

Fig. 6 (a) is a topographic image, (b) and (c) are
amplitude images of the AC magnetic field forthe magnetic write head, and (d) is down trackline profiles of amplitude signal of the white linein (b) and (c). The images in (b) and (c) are
obtained using the FePt- and FePt•MgO-coatedtips, respectively.
by FePt-coated tip having a coercivity of 9.2 kOe isunclear and has very low amplitude signal at the mainpole position. In contrast, the amplitude image measured
by FePt-coated tip having a coercivity of 9.2 kOe isunclear and has very low amplitude signal at the mainpole position. These results indicate that the FePt•MgOcoated tip with a coercivity higher than the field
generated from the write head can effectively image theAC magnetic field without signal decay because the highcoercivity can suppress the tip’s magnetization rotation.
In one word, the clear amplitude image is obtained by the
FePt•MgO-coated tip with a high coercivity in this case.
In order to clarify and enhance the spatial resolution of
our High coercivity MFM tips, a 20 nm-thick(FePt)84•(MgO)16-coated tip was fabricated under thesame conditions as above. Figs.7 (a) and (b) are
amplitude and phase images of the AC magnetic field fora magnetic write head measured by this tip. The lift
height was fixed at 1 nm. The head write current was also
40 mA. Figs.7 (c) and (d) are down track line profiles ofamplitude and phase signal over the white line locationsin Figs.7 (a) and (b), respectively. The clear amplitude
image and high amplitude signal at the main poleposition are achieved again. This further indicates that
the MFM tip with a coercivity higher than the AC
magnetic field to be measured can effectively image theAC magnetic field without signal decay. The phase image
near the main pole region was measured in the same scan.
The phase difference between the bright and dark area
was about 180o as shown in the line profile of Figs.7 (d).
When the direction of the perpendicular AC magnetic

Fig. 7 (a) amplitude and (b) phase images of the AC
magnetic field for the magnetic write headmeasured by 20 nm (FePt)84•(MgO)16 -coated tip.
(c) and (d) are down track line profiles ofamplitude and phase signal of the white line in(a) and (b), respectively. (e) is the spatial
resolution result of the amplitude image.
field is reversed from Hzac to -Hzac, the input signal of alock-in amplifier changes in the following way.
(1)
ｰHzac cos(m t) = Hzac cos(m t+ )Therefore, the areas with bright and dark colors in thephase image correspond to the opposite directions of
perpendicular magnetic field. In another words, thephase image gives the polarity of the AC magnetic fieldvertical to the surface measured.
Figs.7 (e) shows the spatial resolution of the amplitude
imaging. The resolution is obtained from Fouriertransformation of the amplitude scan line around mainpole. The details of this calculation were described inreference papers21). The spatial resolution of amplitude
imaging is 15.5 nm in this case. This value is very close
to the result of our previous study. Here, the coercivity of
FePt•MgO films maintains more than 15 kOe, even if its
film thickness is reduced to 10 nm. Therefore, the
FePt•MgO MFM tip with the thin FePt•MgO film is
expected to be useful for improvement of the spatial
resolution owing to the reduction of diameter of end pointof the tip. In consideration of that the head structure
having three surrounding shields and a high write
current of 40 mA, the high coercivity FePt•MgO-coated
MFM tip is so successful in imaging such high magnetic
field from the head.
4. Conclusion
In-plane (111)-textured FePt and FePt•MgO films
were deposited on pre-oxidized Si substrates and Si tips
for the study of the effect of coercivity of magnetic
coatings on MFM tips. The coercivity of FePt•MgO
coatings rises when increasing the MgO’s concertation in
FePt•MgO alloys under an optimized VHF plasma

Journal of the Magnetics Society of Japan Vol.43, No.1, 20199

INDEX

irradiation power. The high coercivity of FePt•MgO films
is believed due to the isolation of FePt grains by MgO andenhancement of atomic ordering of FePt by a VHF bias.
A clear amplitude image and high amplitude signal at
the main pole position were observed by using this High
coercivity FePt•MgO tip. The spatial resolution of thistype of MFM tip is around 15 nm. As simply speaking,the cone-shape FePt•MgO-coated MFM tip with acoercivity higher than the magnetic field to be measured
is effective and capable to measure the high AC magnetic
field for a perpendicular magnetic write head at a very
high write current.
Acknowledgements
JST/SENTAN.

This work was supported by
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Received Nov. 23, 2016; Revised Aug. 28, 2018; Accepted Nov.
05, 2018

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J. Magn. Soc. Jpn., 43, 11-16 (2019)<Paper>

Evaluation on Edge-supported Magnetic Levitation
Apparatus for Thin Steel Plates
Y. Oda, Y. Ito, K. Okuno, M. Kida, T. Suzuki,
A. Endo, T. Narita*, H. Kato* and H. Moriyama*

Course of Mechanical Engineering, Graduate School of Tokai Univ., 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan* Department of Prime Mover Engineering, Tokai Univ.

Grasping and conveying an object, by utilizing the frictional force generated by contact is performed in various
processes in the manufacturing line for an industrial product. The deterioration of the surface quality due to thesecontacts is a problem. As a solution to this problem, a noncontact transport of steel plates, using electro-magnetic force,has been proposed. However, in these systems, electromagnets are installed vertically. In this method, if the steel plateis thin and does not have sufficient flexural rigidity, it is difficult to add a suspension force for levitation over the entire
steel plate. In order to solve this problem, we proposed an edge supported electromagnetic levitation system for flexible
steel plates using electromagnets installed horizontally. In order to verify the effectiveness of the proposed system weconstructed a prototype of an edge-supported type magnetic levitation system, which applied electromagnetic force
only from the horizontal direction of the steel plate. Consequently, we carried out levitation experiment and discussed
characteristics of horizontal positioning and levitation suspension.
Key words: electromagnetic levitation, thin steel plate, vibration control, magnetic field
1. Introduction
Thin steel plates are used in many industrial products
and their transportation take place by contact with alarge number of rollers in the manufacturing process.
Recently, the demand of high quality steel is increasing.
Therefore, the deterioration of the surface quality is aproblem for this type of contact transportation. To solve
this problem, the application of a magnetic levitation
technology to a non-contact transport system is actively
being studied1)-5). The authors' research group had
installed electromagnets not only vertically but also
horizontally. Vertical electromagnets’ levitation isapplying tension to the steel plate edges. We haveconfirmed that horizontal electromagnets improve
levitation stability in thin steel plates with extremely low
flexural rigidity6)-7). Furthermore, they help realize
advanced levitation control systems considering the steel
plate deflection as well as the vibration characteristics.
Levitation control using only electromagnets from theedge direction is important. Hitherto, we have confirmed
the characteristics of the suspension force of the edge
direction electromagnet acts on the steel plate byexperiment and analysis8). In this study, we made a
prototype edge supported electromagnetic levitation
system based on these characteristics and we discuss thelevitation characteristics.
2. Edge Supported Electromagnetic Levitation System
Figure 1 shows a schematic illustration of the newly
made edge supported electromagnetic levitation system.
Figure 2 shows the placement of the electromagnet andthe sensor view from the top. As Fig. 2 shown, the verticaldirection is defined as Z direction, the longitudinal

Electromagnet for levitation and horizontal positioning control
Steel plate( 400 mm × 100 mm × 0.24 mm)

Laser type sensor
Eddy current type sensor

x1 x2 x3

x4

i1 i2

A/D converter

DSP
iBIS 7101A 1.6GHzi 3 i 4 z1 z2
D/A
converter

Levitation and horizontal
positioning controller

AMP4
AMP3
AMP2
AMP1

AmplifierResistanceFig. 1 Edge supported levitation system for steel plateusing only electromagnets installed horizontally.
direction of steel plate is defined as Y direction and thetransverse direction is defined as X direction. Figure 3
shows a photograph of the electromagnetic levitation
system during the levitation of a steel plate. The
levitating object is a rectangular galvanized steel plate(material SS400) whose length is 400 mm, width is 100
mm, and thickness is 0.24 mm. In the electromagnetic
levitation system, as shown in Fig. 4, two electromagnets
facing each other are installed in the longitudinal
direction near the edge of the thin steel plate. The
attractive force of the electromagnets installed in the X
direction, near the edge of the steel plate, perform noncontact positioning control. In a previous study7), we
calculated the deflection shape using magnetic field
analysis and the finite difference method. The
electromagnets are installed at such position to minimize

Journal of the Magnetics Society of Japan Vol.43, No.1, 201911

INDEXZ

100 mmEddy current typenoncontact
displacement sensor

Y

X

Electromagnetic forlevitation and horizontal
positing control

Schematic illustration of the edge supported
levitation system.

Laser typesensorY

Laser type sensor

Electromagnet for levitationand horizontal positioning
control
Steel plate

X
Fig. 4

Placement of electromagnet and displacement
field sensor.
Coil ( 1005 turns )36
28

Fig. 2220 mm

400 mmSteel plate

8

14

16
60

8

16

Ferrite core[mm]Fig. 5

Configuration of the electromagnet.

Eddy current type noncontact
displacement sensor

Fig. 3

Photograph of the electromagnetic levitation
system.

deflection and to expect stability on the steel plate. A
laser-type sensor, which measure the displacement by
the cut-off amount of a belt-like laser beam
manufactured by KEYENCE was used to measure thehorizontal displacement in X direction of the edge of thesteel plate. Thereby, the steel plate is controlled by noncontact positioning by the electromagnets at a distanceof 5 mm from the edge of the steel plate. Furthermore,
the control law is calculated by detecting the current ineach electromagnet from the measured externalr e s i s t a n c e a n d , s u b se qu e n t l y , i n p u t t i n g e i g h t
measurement values into a digital signal processor of an
A/D converter. The core, shown in Fig. 5, is an E-type
electromagnet, and the material is ferrite. The
electromagnet’s core is an enamel wire of 0.5 mm
diameter wound around it 1005 times. For evaluating the

12

Electromagnetz
Displacement z
Z0=0 mm

8 mm

x

0

Steel plate

Fig. 6

Position of eddy current type noncontact
displacement sensor.

levitating state of the steel plate, a vertical direction
displacement sensor was installed as shown in Fig. 4 andFig. 6. An eddy current non-contact displacement sensor
manufactured by SENTEC was used. To consider thecharacteristic of suspension force generated byelectromagnet, electromagnetic analysis was carried out.
The analytical model is consisting of one electromagnet
and steel plate (400 mm × 100 mm). The suspension force

Journal of the Magnetics Society of Japan Vol.43, No.1, 2019

INDEX

Suspension Force fz [N]

0.6-10 mm

-8 mm

0.5

-6 mm

0.4

-5 mm

0.3

-4 mm
-3 mm

Weight of steel plate

0.2

Z0 = -2 mm

0.1
0.0
0

0.2

Fig. 7

0.4

0.6

0.8

1

1.2

1.4

Steady current Ix [A]

1.6

1.8

2

Relationship between the vertical attractive
force fz for each displacement Z0.

Electromagnet

x

Steel plate

Fig. 8

Z0

Γ0

z
0

Coordinate of static levitating steel plate.

f1Fig. 9Steel plate

F =



Schematic illustration of attractive force ofelectromagnets.

was analyzed in the case that the steady current andvertical displacement of the steel plate is changed. Figure
7 shows the relationship between the vertical directionsuspension force and the steady current in theelectromagnet, which is obtained from the magnetic
analysis. Each data shows the suspension force that wasapplied on the steel plate in the z direction from thecenter of the electromagnet core. The dashed line (0.18
N) in the figure means the quarter weight of the steel
plate, which is equal to suspension force for levitation
generated by one electromagnet in this system. It is
possible to levitate the steel plate at a steady current
value that corresponds to the steel plate’s weight.

Leff i 2
2  sp 2(1)

Where iem is coil current [A], sp is distance from center ofelectromagnet to edge of the steel plate [mm], Leff /  sp is
a constant corresponding to the effective magnetic flux ofthe electromagnet. It is also,(2)=
x 2+z 2sp

sp

sp

In equilibrium levitating state, X0 is static displacementin x axis direction [mm], Z0 is static displacement in z
axis direction [mm] and I0 is steady current ofelectromagnet [A]. The eq. (1) is linearized by performing
Taylor expansion.
FX
FZF
F ( X + x, Z + z, I + i=) F − 2 0 0 x − 2 0 0 z + 2 0 i (3)
0

X0

f2

attractive force generated on the steel plate by theelectromagnet is generated toward the tip of center
convex part of the electromagnet core. Attractive force F
generated on the steel plate is shown by the following
equation.

0

0

0

Γ02

Γ02

I0

Where F0 is static attractive force of equilibrium
levitating state [N], 0 is distance from center ofelectromagnet to edge of steel plate in equilibrium
levitating state [mm], x is steel plate displacement inhorizontal direction on equilibrium levitating state [m], z
is steel plate displacement in vertical direction onequilibrium levitating state [m], i is current fluctuation
value of coil [A]. In the proposed system installed so thatthe electromagnets are opposed to each other across thesteel plate, attractive force f1, f2 that generated by eachelectromagnet suppose that occurs from the steel plateedge towards the center of each electromagnet core asshown in Fig. 9. When on the f1 side steel plate isdisplaced by Δx, on the f2 side steel plate is displaced by-Δx. Also, to perform positioning control, when on the f1
side the current changes Δi, on the f2 side the current
changes - Δ i. Also, when steel plate is displaced in z
direction, both electromagnets are Δ z displaced.
Attractive force f1, f2 near the equilibrium levitating state,
are as follow.
(4)=
f1 F ( X 0 + x, Z0 + z, I 0 + i )=f2

F ( X 0 − x, Z0 + z, I 0 − i )(5)

When attractive forces from both electromagnets andthe angle formed by the x axis defined as ，, the x
direction component in attractive force ,are as follow.

f1 cos 1 + f 2 cos  2

3. Control Model of Edge Supported Electromagnetic
X0X=
F ( X 0 + x, Z0 + z, I 0 + i ) + 0 F ( X 0 − x, Z0 + z, I 0 − i )Levitation System
0
0

FX
(6)
x + 4 0 0 i
I 0 0 03
3.1 Equation of motion for levitated thin steel plate
The z direction component in attractive force, are as
As shown in Fig. 8, edge of the steel plate is displacedfollow.
from electromagnet surface in the x direction xsp [mm]and from center of electromagnet in the z direction zsp
f1 sin 1 + f 2 sin  2[mm], when the steel plate is levitate horizontally in
Z0Z=
F ( X 0 + x, Z0 + z, I 0 + i ) − 0 F ( X 0 − x, Z0 + z, I 0 − i )equilibrium state. Attractive force by magnetic field from0
0installed electromagnet is generated near edge of the
F Z2
Z
(7)
=−4 0 30 z + 2 F0 08)00steel plate . From the previous study, in theelectromagnet core and the steel plate size used in thisThe weight of the steel plate to be supported by a pairstudy, the suction force is regarded generated in oneof electromagnets is m. As, Δ x = -x, Δ z = -z, Δ i = ipoint in the edge of steel plate. We confirmed that theestablishing the equation of motion shows it, as follows.
=−4

F0 X 02

Journal of the Magnetics Society of Japan Vol.43, No.1, 201913

INDEX

m

F X2
FX
d 2x
+ 4 0 30 x − 4 0 0 i =02dt
I 0 00(8)

Table 1 Coefficient of the control model.

(9)
F Z2
Z
d 2z
+ 4 0 30 z =2 F0 0 − mg
2
dt
0
0
At this time, taking the values of 0，Z0，F0 which satisfy

SymbolValue

X0

5×10-3 m

Lxeff

1.25×10-5 H

Lxlea

1.89×10-1 H

Lx

1.92×10-1 H

Rx

10 Ω

mx

3.74×10-2 kgm

the following equation, steel plate can be magneticallylevitated.
Z0− mg =
0(10)
0
As described above, we obtained the motion of x direction
by attractive force from facing electromagnet is dependon amount of change from stationary value of pairelectromagnets, the motion of z direction is depending on
stationary value of electromagnet. Therefore, in thispaper, focusing only on the horizontal direction, a
position control model is constructed with Z0 = z = 0，0
= X0.
2 F0

3.2 Horizontal positioning control model
Although the flexible thin steel plate exhibits elastic
vibration in the vertical direction, it can be regarded as arigid body in the X direction. The proposed system
virtually divides the steel plate into two parts as shownin Fig. 10. We modeled the motion of the steel plate in
the X direction using a 1-DOF model that actively
controls each part. The same static attractive force isapplied by the two installed electromagnets in order tosandwich the steel plate and, the equilibrium position of
the steel plate is at the same distance from eachelectromagnet. The displacement of the steel plate fromthe equilibrium position is defined as x and the motion
and circuit equations are as follows. Furthermore, theattractive force of the electromagnets at the equilibrium
point was linearized.

mx = f1 − f 2 = f x
4 Fx
4F
=
fx
x + x ix
X0
Ix
Lxeff I x
R
d
1
ix =
−
 2 x − x ix +
vx
2Lx
2Lx
dt
Lx X 0
Lxeff=
Lx+ Lxlea
X0

(1)
(2)
(3)
(4)

Using the state vector, Eqs. (1)-(4) can be rewritten as
follow.
(5)=x Ax x + Bx vx

x = x
 0
 4 FxAx = 
 mx X 0

 0

14

x ix 

T

1
0−

Lxeff I xLx X 020 

4 Fx  ,mx I x R − x 
2 Lx 

Table 2 Feedback gain of Fx.

fx

fv

fi

1.04×103

3.66×102

4.2×101㻌 㻌

I x + ix

㻌Steel plate (rigid body)

㻌

x

f1

㻌 m㻌

f2

x

mx

㻌

㻌 㻌

I x + ix

Electromagnet for levitation andhorizontal positioning control

㻌Fig. 10㻌㻌

Laser type sensor

㻌Experimental model of electromagnetic
suspension
T force.


1 
Bx = 0 0

2Lx 


where Fx is the magnetic force of the coupled magnets inthe equilibrium state [N], X0 is the gap between the steel
plate and the electromagnet in the equilibrium state [m],Ix is the current of the coupled magnets in theequilibrium state [A], ix is the dynamic current of thecoupled magnets [A], Lx is the inductance of the magnet
coil in the equilibrium state [H], Rx is the resistance ofthe coupled magnet coils [Ω], vx is the dynamic voltage ofthe coupled magnets [V], Lxeff/X0 is the effective
inductance of the one magnet coil [H], and Lxlea is theinductance leakage of the magnet. Furthermore, vx is the
feedback x, the state variable x and is expressed in thefollowing equation.

vx = −Fx x

Fx =  f x

(6)

fv

fi 

4. Levitation Experiment of Steel Plate by Edge
Supported Electromagnetic Levitation System
4.1 Experimental conditions
The steady current Ix of the electromagnet was varied.
In order to evaluate the levitating characteristics of thesteel plate at that time, we carried out a magnetic steel
plate experiment. The steel plate is supported by jack,and levitated by lowering the jack. The parameter thatwas used to design the control system is shown Table 1.

Journal of the Magnetics Society of Japan Vol.43, No.1, 2019

0

-1
1
Time [s]

-2
0

2

2
1
0
-1
-2
0

0.5

1
Time [s]

1.5

0.5

1
Time [s]1.52(a) Ix = 0.9 A

2
1
0

-1
-2
0

0.5

1
Time [s]

1.5

-2
0

0.5

1
Time [s]

1.5

2

1

0
-1
-2
0

2

2

0.5

1
Time [s]

1.5

2

1
0
-1
-2
0

0.5

1
Time [s]

1.5

2

2
1
0
-1
-2
0

(c) Ix = 1.1 A

0.5

1Time [s]1.52(d) Ix = 1.2 A

Time histories of the vertical displacement z of the steel plate.

0.5

0.5

Standard deviation ofvertical displacement z [mm]Standard deviation ofhorizontal displacement x [mm]-1(b) Ix = 1.0 A
Fig. 12

0.4

0.4
0.3

0.3

0.2

0.2

0.1

0.1
0

2

0

2

(b) Ix = 1.0 A(c) Ix = 1.1 A(d) Ix = 1.2 A
Time histories of the horizontal displacement x of the steel plate.

Fig. 11

Displacement [mm]Displacement [mm](a) Ix = 0.9 A

1.5

-1

1

Displacement [mm]0.50Displacement [mm]

-2
0

1

2

Displacement [mm]12Displacement [mm]2Displacement [mm]Displacement [mm]

INDEX

0.9

1

1.1

Steady current Ix [A]

1.2

Fig. 13 Relationship between the steady current Ix
and the standard deviation of the horizontal
displacement x.
Furthermore, we searched for the feedback gain Fx ofequation (6), which was determined by trial and error
and is shown in Table 2. For the experimental conditions,the range of steady current was changed to Ix = 0.9 ～1.2A.
At each steady current, there is a position where thesteel plate could levitate. We searched the position where
the steel plate could levitate at each steady current value
by trial and error. The standard deviation of
displacement was calculated in order to evaluate thedisplacement amplitude in the x and z directions of thesteel plate. The experiment was conducted five times foreach condition and for the evaluation the average of theresults was used.
4.2 Experimental results
Figure 11 shows the time history of the displacementof the steel plate in the x direction. Figure 12 shows thetime history of the displacement of the steel plate in the

0

0.9

1

1.1

1.2

Steady current Ix [A]Fig. 14 Relationship between the steady current Ix
and the standard deviation of the verticaldisplacement z.

z direction. Figure 11 and Fig. 12 both show the resultsof each steady current of (a) 0.9 A, (b) 1.0 A, (c) 1.1 A, and(d) 1.2 A. Figure 13 summarizes the relationship between
the steady current and the standard deviation of the x
direction in each steady current. The standard deviationof displacement in the x direction was suppressed to 0.1
mm or less in all steady currents. Even in the proposedmagnetic levitation system, the sufficiently positioned
control in the x direction. Figure 14 summarizes therelationship between the steady current and thestandard deviation of the z direction in each steadycurrent. Comparing the results in Fig. 14 for each steadycurrent value, by increasing the steady current value asuppression in vibration of the z direction was confirmed.
In the case of the minimum steady current, Ix = 0.9 A, thestandard deviation of the z direction is 0.474 mm. In thecase of the maximum steady current, Ix = 1.2 A, thestandard deviation of the z direction is 0.179 mm. Whenthe steady currents 0.9A and 1.2A were compared, thevibration in the z direction could be suppressed by 62%.

Journal of the Magnetics Society of Japan Vol.43, No.1, 201915

INDEX

6. Conclusion

Levitation position Z0 [mm]

-2
-3

-4
-5

-6

Analysis result-7

Experimental result

-8

0.8

Fig. 15

0.9

1

1.1

Steady current Ix [A]

1.2

1.3

Relationship between steady current Ix andlevitation position Z0.

As the steady current Ix of the electromagnet increased,
the tension applied to the steel plate in the x direction
increased. As a result, it is considered that the restoring
force in the z direction increased and the vibration of thesteel plate in the z direction could be suppressed.
5. Levitation Position Measurement Experiment of Steel
Plate of Vertical Displacement
For the experimental conditions similar to chapter 4,
the range of steady current was changed to Ix = 0.9 ～1.2
A. The levitation position in the z direction was measured
five times for each condition. The average of those results
is the experimental value. Figure 15 shows the levitatedposition of the steel plate in each measured steadycurrent. The dashed line in Fig. 15 which is extracted
from the analysis results in Fig. 7 shows the relationshipbetween the levitation position Z0 and the steady current
Ix at which the steel plate levitates. Plots in Fig.15 areaveraged experimental results. As a result, when thesteady current is the minimum, Ix = 0.9 A, the levitation
position of the vertical direction was 0.474 mm. In
contrast when the steady current is the maximum, Ix =1.2 A, the levitation position of the vertical direction was
0.402 mm. The levitated position of the steel plateincrease by 0.7 mm. Furthermore, the trend of theexperimental values agreed with the analysis result. We
confirmed the effectiveness of the electromagnetic field
analysis. As a result, using electromagnetic field analysis,
even for steel plates of different thickness and material,
we confirmed that we could establish such a system’s
design guidelines.

16

In this study, we constructed a prototype of an edge
supported type magnetic levitation system applying
electromagnetic force only from the X direction of a steel
plate. We verified the levitating characteristics of the
proposed control system. We carried out levitation
experiments using an ultra-thin steel plate of 0.24 mm.
We confirmed the achieved stable levitation.
Furthermore, we carried out levitation experiments bychanging the steady current value of the electromagnet.
The experimental and analytic results of the calculated
vertical levitating position agree with each other. The
results showed that it is, possible to experimentally
construct a control system for the steel plate stationary
vertical direction displacement. In this study, we
confirmed the effectiveness of the proposed magnetic
levitation system. However, under transient conditions
there were instance when it became practically an
unstable system. In order to solve the problem, it isnecessary to construct a control system that changes
steady-state current by feedback of vertical displacementin addition to the proposed control system in this paper.
For the future, we will consider in detail a more effective
sensing method and modeling for the stability of thismethod. Furthermore, the shape of the electromagnet togenerate more effective attractive force to flexible steel
plate would be considered.
References
1) O. Suzuki, T. Nakagawa: J. Jpn. Soc. App. Elec. Mech., 25,
118 (2017), [in Japanese].
2) K. Matsushima, F. Kato, T. Ohji, K. Amei, M. Sakui: J. Jpn.
Soc. App. Elec. Mech., 21, 296 (2013), [in Japanese].
3) M. Morishita, M. Akashi: Workshop of The Institute ofElectrical Engineers of Japan, LD-98-36, (1998), [inJapanese].
4) K. Sato, S. Torii: Trans. IEEJ, 128, 267 (2008), [in Japanese].
5) T. Mizuno, D. Sekine, M. Takasaki, Y. Ishino: Trans. Jpn. Soc.
Mech. Eng., 80, DR0163 (2014), [in Japanese].
6) T. Narita, T. Kurihara, H. Kato, Y. Oshinoya: Mech. Eng.
Jour., 3, 15-00376 (2016).
7) T. Kurihara, T. Narita, H. Kato: Int. J. App. Elec. Mech., 52,1495(2016).
8) T. Narita, M. Kida, T. Suzuki, H. Kato: J. Magn. Soc. Jpn., 41,
14(2017).
Received May 17, 2018; Revised Jul. 06, 2018; Accepted Aug. 30,
2018

Journal of the Magnetics Society of Japan Vol.43, No.1, 2019

INDEX

Editorial Committee Members・Paper Committee Members
K. Kobayashi and T. Ono (Director), T. Kato, K. Koike and T. Taniyama (Secretary)
A. Fujita
H. GotoH. Hashino
S. Honda
S. Inui
S. Kasai
A. Kikitsu
H. Kikuchi
T. Kimura
T. Kubota
T. Nagahama
H. Naganuma
M. Naoe
M. Ohtake
N. PhamT. SatoT. SatoK. Sekiguchi
M. Sekino
T. Shima
M. Sonehara
T. Tanaka
S. YamadaK. Yamamoto
H. Yuasa
N. Adachi
S. Isogami
Y. Kota
T. Narita
M. Takezawa
S. Yoshimura

K. Bessho
K. KamataT. MakiD. Oyama
T. Takura

M. DoiH. KatoE. Miyashita
J. Ozeki
M. Tsunoda

T. DoiK. KatoT. Morita
T. Saito
S. Yabukami

Y. Kanai
K. Miura
T. Sasayama
Y. Shiratsuchi

T. Hasegawa
T. KodaS. Muroga
S. Seino
T. Yamamoto

N. Inaba
S. Kokado
H. Nakayama
K. Tajima
K. Yamazaki

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編 集 委 員・論 文 委 員
小林宏一郎（理事） 小 野 輝 男 （理事）加 藤 剛 志 （幹事）小 池 邦 博 （幹事）谷 山 智 康 （幹事）
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崇
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佐藤
拓
佐藤
岳
嶋
敏之
白土
優
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直江正幸
永沼
博
長浜太郎
橋野早人
PHAM NAMHAI
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山田晋也
山本健一
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安達信泰
古門聡士
土井正晶
薮上
信

磯上慎二
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中山英俊
山崎慶太

稲葉信幸
齊藤敏明
成田正敬
山本崇史

小瀬木淳一
清野智史
長谷川崇
吉村
哲

小山大介
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別所和宏

加藤宏朗
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槙
智仁

加藤和夫
田島克文
宮下英一

窪田崇秀
曽根原誠
本多周太

後藤博樹
田中哲郎
三浦健司

鎌田清孝
角田匡清
室賀
翔

神田哲典
土井達也
森田
孝

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