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

2022

Magnetic Recording
Negative Spin-Polarization Tri-Layer STO for MAMR
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
三井住友海上小川町ビル5階☎(03)5281-0106
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

I. Tagawa…1

Magnetization Analysis of Magnetic Nanowire Memory Utilizing Two Recording Metal Wires for Low Current
Recording

K. Ogura, M. Takahashi, N. Nakatani, N. Ishii, and Y. Miyamoto…6

Information Degradation during Archiving in Heat-Assisted Magnetic Recording
T. Kobayashi, Y. Nakatani, and Y. Fujiwara…10Power Magnetics

A Consideration of Eﬃciency and Power Factor of IPM-type Magnetic-Geared Motor
K. Ito, K. Nakamura

…16

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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

2022

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Journal of the Magnetics Society of Japan
Vol. 46, No. 1
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Magnetic Recording
Negative Spin-Polarization Tri-Layer STO for MAMR……………………………………………… I. Tagawa

1Magnetization Analysis of Magnetic Nanowire Memory Utilizing Two Recording Metal Wires for Low
Current Recording…………………………………………K. Ogura, M. Takahashi, N. Nakatani, N. Ishii, and Y. Miyamoto

6

Information Degradation during Archiving in Heat-Assisted Magnetic Recording………………………………………………………………… T. Kobayashi, Y. Nakatani, and Y. Fujiwara

10Power Magnetics
A Consideration of Efficiency and Power Factor of IPM-type Magnetic-Geared Motor……………………………………………………………………………………………… K. Ito, K. Nakamura

Board of Directors of The Magnetics Society of Japan
President:
S. Sugimoto
Vice Presidents:
Y. Takemura, J. Hayakawa
Directors, General Affairs:
H. Saito, H. Yuasa
Directors, Treasurer:
H. Takahashi, A. Yamaguchi
Directors, Planning:
T. Kondo, M. Mizuguchi
Directors, Editorial:
T. Kato, S. Yabukami
Directors, Public Relations:S. Sakurada, K. Kakizaki
Directors, International Affairs:
H. Yanagihara, H. Kikuchi
Specially Appointed Director, Gender Equality:
F. Akagi
Specially Appointed Director, Societies Collaborations: K. Fujisaki
Specially Appointed Director, International Conferences: Y. Miyamoto
Auditors:
Y. Takano, K. Kobayashi

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J. Magn. Soc. Jpn., 46, 1-5 (2022)<Paper>

Negative Spin-Polarization Tri-Layer STO for MAMR
Ikuya Tagawa

Electrical and Electronic Engineering, Tohoku Institute of Technology, 35-1 Yagiyama-Kasumicho, Sendai 982-8577, Japan

In microwave-assisted magnetic recording (MAMR), it is still a challenge to obtain a large microwave-assist field(MA field). It is also not easy to enhance the static head field gain (DC gain) brought by the effect of recording flux
control. In this paper, we propose a tri-layer spin-torque-oscillator (STO) made of negative spin-polarization material,
and we compare the MA field and the DC gain with a conventional dual-layer STO. With this new design, a field
generation layer (FGL) can easily obtain stronger spin-transfer torque to overcome the magneto-static interaction withhead poles. It works well to increase the DC gain without losing the MA field at lower injection currents. A remaining
problem is a significant reduction in the MA field when the injection current becomes too large.
Key words: microwave-assisted magnetic recording, MAMR, spin-torque-oscillator, STO, tri-layer, spin-polarization,negative polarization
1.

Introduction

Microwave-assisted magnetic recording (MAMR) is
one of the promising technologies for next-generation
hard disk drives (HDD) 1-3). Western Digital and Toshiba
have made announcements on their introduction plans of
MAMR into production-level HDD 4). Moreover, Toshiba
has announced that they have actually shipped MAMR
HDD samples to specific customers 5).
In MAMR, uniform and stable oscillation of themagnetization in a spin-torque-oscillator (STO) is one of
the most important factors. We have pointed out that one
possible problem in a practical MAMR head is oscillation
disturbance by transmitted electron spins from headpoles, i.e., a main pole (MP) and a trailing shield (TS).
Therefore, we proposed to use negative spin-polarizationmaterial in one of head poles 6).
As Toshiba has explained a new concept of MAMR, i.e.,
FC-MAMR (flux control-microwave-assisted magnetic
recording) 7), there is a possibility to obtain static head
field gain even without magnetization oscillation in STO.
However, if the DC magnetization component of the STO
is not oriented to the opposite direction to magnetizationof the head poles, this gain can be negative, or loss. In
this paper, we show difficulty of avoiding such static field
loss in the conventional STO design, and we propose a
new design, i.e., a tri-layer STO consisting of threemagnetic layers with negative spin-polarization.
2.

Modeling

Fig. 1 Pole tip area views of MAMR head model for(a) down-track section, (b) air-bearing surface, (c)cross-track section.
Fig. 1 shows the dimensions of MAMR head model usedin analysis. A main pole (MP) and a trailing shield (TS)are divided into hexahedron meshes due to software
requirements for calculation of spin-transfer torquebetween MP and STO, or TS and STO. The STO consistsof a spin injection layer (SIL) and a field generation layer(FGL). The SIL is located on the MP side of the FGL. The
microwave-assist field (MA field) is evaluated 5 nm below
the trailing edge of the MP.
Table 1 Material parameters used in simulation.

2.1 Head model
A commercial micromagnetics software (Fujitsu
Examag v2.1) is used, in which the Landau-LifshitzGilbert (LLG) equation with the spin-transfer torqueterm is solved 8).
Corresponding author: I. Tagawa (e-mail: i-tagawa@
tohtech.ac.jp)

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INDEXOther magnetic and geometric properties are
summarized in Table 1. Here, α, A, P, and t are thedamping constant, magnetic exchange constant, spinpolarization factor, and layer thickness, respectively.
Even in a tri-layer STO design discussed later, thethickness of two SILs is set at 2 nm and that of the FGL
is 8 nm. A rectangular wave current of 100 mA at 1 Gbps
frequency is applied to a single-turn head coil.
2.2 Figures of merit
Fig. 2(a) shows a typical example of time-response
waveforms of the writing field including the microwave
field generated by STO, observed under the main poleedge by 5 nm from the air bearing surface. The downtrack field (Hx) shows strong microwave oscillation
superposing on the low frequency “quasi-static” field. The
cross-track field (Hy) also shows some oscillation,
however, there is no clear oscillation in the perpendicularfield (Hz), which indicates the microwave field is
elliptically rotational in the media plane. Fig. 2(b) shows
the Fourier amplitude spectra obtained with FFT. The
spectra show clear peaks at about 25 GHz, which areabout 1.7 kOe in the down-track field (Hx) and 0.6 kOe
in the cross-track field (Hy), respectively. Here, the MA(microwave assist) field amplitude is defined as anaveraged value of these two peaks.
As Toshiba has explained in the report 7), the MAMR
head has the effect of recording flux control. For
quantitative analysis of this effect, the time-averaged
writing field profile is calculated as shown in Fig. 2(c),and the quasi-static head field (DC field) magnitude isdefined under the main pole inner by 5 nm from the mainpole edge. In addition, we have defined the DC field gain
which is an increment on the DC field by the flux control
effect of STO compared with that of a conventional noSTO head. Note that “conventional head” does not mean“no oscillation of STO” but means “no existence of STO”.
So, two DC field profiles are calculated and subtraction
is made to get the DC field gain.
Static Field Gain

Fig. 2 (a) Time-response waveforms of writing field
including STO oscillation field and (b) Fourier
amplitude spectra and (c) down track profile of timeaveraged perpendicular field.

3.1 Conventional dual-layer STO
Fig. 3 illustrates design structures near the head pole
tip including STO (= FGL + SIL), (a) when STO isconnected to TS and MP, and both TS and MP havepositive spin-polarizations, (b) when STO is connected tonegative polarization TS and positive polarization MP,
and (c) when STO is not connected to TS and MP. In theoriginal idea of MAMR 1-2), separate electrodes areconnected to STO directly as shown in (c). In contrast, themain pole and the trailing shield are used as electrodes
in practical MAMR heads, as shown in (a) and (b),because the write gap is too narrow to fabricate
additional electrodes inside. In this situation, electron
spins transmitted from the MP to the SIL disturb the

STO oscillation if they worked to align the SIL
magnetization with the MP magnetization.
Fig. 4(a) shows the injection current dependence of theMA field amplitude, for the STO connected to positive
polarization TS and MP (▲), for the STO connected tonegative polarization TS and positive polarization MP (■),
and for the unconnected STO (○), respectively. As wediscussed in the previous work 6), no oscillation isobserved when electrons flow into the STO from thepositive spin-polarization MP (▲). On the other hand, alarge MA field is obtained when electrons flow from thenegative polarization TS (■). The MA field is even larger
than that of the unconnected STO at a lower injection

3.

2

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Fig. 3 Head designs of dual-layer STO connected (a)to positive polarization TS and MP, (b) to negative
polarization TS and positive polarization MP, and (c)STO not connected to TS and MP.
current region. This result clearly shows an advantage ofthe negative polarization TS design.
However, if we look at the DC field gain in Fig. 4(b), we
can see that the gain is always negative in the negative
polarization TS design. Even in the case of theunconnected STO, the DC field gain is very small, and it
becomes slightly positive only at very high injection
currents.
3.2 Magnetization distribution
Fig. 5 shows magnetization distributions near the headpole tip looked from the media side in the case of (a) theSTO connected to negative polarization TS and positive
polarization MP and (b) the unconnected STO,
respectively, at the injection current of 4×108 A/cm2. The
FGL magnetizations tilt towards the cross-track
direction but it is not completely in the film plane in bothcases of (a) and (b). Therefore, a static component of thedown-track FGL magnetization causes the DC field loss,
even with good magnetization precession. This indicatesthat the effect of magneto-static interaction between FGL
and TS is still stronger than that of the spin-transfer
torque delivered by electrons from TS and SIL. On theother hand, the SIL magnetization is almost opposite to
the MP magnetization in the unconnected STO as shownin (b). This means that the magneto-static coupling
between SIL and MP could be weak because the SIL
thickness is very thin and the total magnetic moment ismuch smaller than that of the FGL.
4.

Tri-layer STO

4.1 Negative polarization tri-layer STO
Based upon the discussion above, another thin SIL
between the TS and the FGL looks to be desirable toenjoy larger spin-transfer torque. Actually, a tri-layer

Fig. 4 Injection current dependencies of (a) MA field
amplitude and (b) DC field gain in three dual-layer
STO designs defined in Fig. 3.

Fig. 5 Magnetization distributions near head pole
tip in case of (a) negative polarization TS andpositive polarization MP and (b) unconnected STO,
respectively.

STO design in which a FGL is sandwiched by two SILs
has been proposed by Kanai 9), however, this design
didn’t work well. The reason is that the spin directions oftransmitted electrons from the two adjacent layers areopposite each other as shown in Fig. 6(a). For instance,in the FGL, the spin direction delivered from SIL1 on theleft side of MP is opposite to that from SIL2 on the left
side of TS. That is why the spin-torque effect is canceledout.

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Fig. 6 Head designs of tri-layer STO made of (a)positive and (b) negative polarization materials.

To avoid this problem, we propose the tri-layer STO
made of negative spin-polarization materials as shown in
Fig. 6(b). In this design, first, the magnetization directionof the SIL1 is flipped by spin torque of both transmitted
electrons through the negative polarization FGL andreflected electrons from the MP. Then, the spin directionof reflected electrons from the SIL1 becomes opposite to
the magnetization direction of the MP. The spin directionof transmitted electrons through SIL2 is also opposite to
the TS magnetization because of negative polarization.
Therefore, it is expected that the FGL can obtain large
spin-transfer torque even at lower injection currents.
Negative polarization materials are not well known atpresent, but there are several academic reports fromTohoku University 10) and Toshiba 11), and Fe4N, Co3FeN,
and Ni3FeN materials are referenced in those reports.
However, the spin-polarization values of these materials
are not clear, so further study is expected.
4.2 Effect in the DC field gain
Fig. 7 shows the injection current dependence of (a) theMA field amplitude and (b) the DC field gain, in the caseof the negative polarization tri-layer STO (○), the positive
polarization tri-layer STO (▲), and the dual-layer STO
with negative polarization TS (■). When all layers havepositive polarization in the tri-layer STO (▲), not only nooscillation is observed but also the large DC field loss isshown, even at larger injection currents. On the other
hand, in the case of the tri-layer STO with negative
polarization (○), the MA field amplitude increases rapidly
according to the injection current, though it gets worse
when the injection current becomes larger than about
4×108 A/cm2. Moreover, there is a big advantage on the
DC field gain. The gain is much larger than that of thedual-layer STO, and it increases up to about 0.5 kOe
according to the injection current.
Fig. 8 shows magnetization distributions near the headpole tip looked from the media side in the negative
polarization tri-layer STO at the injection current of (a)4×108 A/cm2 and (b) 6×108 A/cm2, respectively. When theinjection current is 4×108 A/cm2, the magnetization in the
SIL1 under MP is the opposite of that in the MP. The
magnetization in the SIL2 on TS is in the same direction
as that in the TS, and the magnetization in the FGL is

4

Fig. 7 Injection current dependencies of (a) MA field
amplitude and (b) DC field gain, in case of negativeand positive polarization tri-layer STOs and duallayer STO with negative polarization TS.

Fig. 8 Magnetization distributions near head pole
tip in negative polarization tri-layer STO at injection
currents of (a) J=4×108, and (b) J= 6×108 A/cm2.

in-plane. In this situation, good magnetization precession
occurs in the FGL, therefore, the MA field amplitude
becomes maximum as shown in Fig. 7(a).
However, when the injection current increases over
4×108 A/cm2, the MA field decreases suddenly. If welooked at the magnetization distribution at 6×108 A/cm2,
as shown in (b), we can see that the magnetization in boththe SIL1 and the SIL2 are almost in-plane, though anti-

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parallel each other. And the FGL magnetization directionis almost opposite to that of the MP. Even themagnetization in the TS is tilted toward the cross-track
direction by spin torque of reflected electrons from theSIL2. All these suggest that the spin-transfer torque is
too strong for good rotation of the FGL magnetization.
Instead, the FGL magnetization easily flips against themagnetizations of the MP and the TS, therefore, we canget the large DC field gain, as shown in Fig. 7(b).
4.3 STO Bs dependence
As discussed above, there is a clear peak on theinjection current dependence of the MA field, and at thissingular current-point, the DC field gain turns positivefrom negative. It is supposed that the effect of the spintransfer torque in the FGL has a good balance with thatof the magneto-static interaction between the FGL andthe head poles at this singularity. If this is correct, thesingular current-point should be changed by themagnetic interaction which is changed by the magnetic
moments of the FGL and the SILs.
We have investigated the MA field and the DC field bychanging the saturation magnetization (Bs) of STO. Fig.
9 shows injection current dependence of (a) the MA fieldand (b) the DC field gain when Bs of the FGL and the two
SILs are set at 1.0 T, 1.6 T, and 2.4 T, respectively, forthe negative polarization tri-layer STO. In the MA fieldcharacteristics, the singular current-point giving thepeak moves from 2×108 A/cm2 to 6×108 A/cm2 according
to the increase of the Bs. And the peak value of the MA
field also changes from 0.7 kOe to 1.4 kOe. If we look at
the DC field gain characteristics, we can see that the zerocross current-point of the gain also moves from 2×108
A/cm2 to 6×108 A/cm2 consistently with that in the MA
field characteristics. From these results, it can be
possible to conclude that the lower Bs is preferable toreduce the injection current, but it has a disadvantage ofreducing both the MA field amplitude and the DC field
gains.
5.

Conclusion

We discussed the DC field gain brought by the effect ofrecording flux control of STO as well as the microwave
assist (MA) field generated by the STO oscillation. It was
shown that in the conventional dual-layer STO, it isdifficult to get the DC field gain even if negative spinpolarization was assumed in the trailing shield (TS),though the reasonably large MA field is obtained. This isbecause, in the field generation layer (FGL), the effect ofthe magneto-static interaction with TS is stronger thanthat of the spin-transfer torque of transmitted electrons.
To solve this problem, we proposed the tri-layer STO
made of negative polarization material. The new design
has worked well to increase the DC field gain without
losing the MA field amplitude at lower injection currents.
However, a significant decrement of the MA field wasshown when the injection current was too large. Further
study is needed to achieve the large MF field amplitude
and the large DC field gain at the same time.
References
1).

J.-G. Zhu, X. Zhu, and Y. Tang: IEEE Trans. Magn., 44, 125 (2008)

2).

Y. Tang and J. G. Zhu: IEEE Trans. Magn., 44, 3376 (2008)

3).

I. Tagawa, M. Shiimoto, M. Matsubara, S. Nosaki, Y. Urakami and
J. Aoyama: IEEE Trans. Magn., 52, 3101104, (2016)4).

http://innovation.wdc.com/game-changers/why-mamr.html (2017)5).

https://toshiba.semicon-storage.com/jp/company/news/news-topics/2021/02/storage-20210218-1.html (2021)

6).

I. Tagawa, J. Magn. Soc. Jpn., 44, 5 (2020)

7).

A. Takeo, The 31st Magnetic Recording Conference, C1 (2020)8).

Fig. 9 Injection current dependencies of (a) MA field
amplitude and (b) DC field gain, in negative
polarization tri-layer STO when Bs was 1.0 T, 1.6 T,
and 2.4 T.

http://www.fujitsu.com/global/about/resources/news/press-releases/2015/0324-01.html (2015)
9). Y. Kanai, R. Itagaki, S. Greaves, H. Muraoka, MSJ 40th annual
conference, 7pB-4 (2016)10). M. Tsunoda, Y. Komasaki, S. Kokado, S. Isogami, C. Chen and M.
Takahashi.: Appl. Phys. Express 2, 083001 (2009)11). M. Shimizu, K. Koi, S. Murakami, N. Fujita, K. Yamada, and A.
Takeo: MSJ 39th annual conference, 10pE-3 (2015)

Received Aug. 31, 2021; Accepted Oct. 12, 2021

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J. Magn. Soc. Jpn., 46, 6-9 (2022)<Paper>Magnetization Analysis of Magnetic Nanowire Memory
Utilizing Two Recording Metal Wires for Low Current Recording
K. Ogura, M. Takahashi, N. Nakatani, N. Ishii, and Y. Miyamoto

Science & Technology Research Laboratories, NHK (Japan Broadcasting Corporation)
1-10-11 Kinuta, Setagaya-ku, Tokyo 157-8510, Japan

We have developed magnetic nanowire memories with no mechanical moving parts in order to achieve thelarge-capacity and ultra-high data transfer rates required for spatial imaging three-dimensional television (3D-TV).
In a magnetic nanowire, binary information is recorded by means of a magnetic field induced by two recording wires
that are orthogonally fabricated above the nanowire. We simulated the magnetic domain formation process andfound that it was formed stably in a magnetic nanowire when we utilized two recording wires. In addition, by adding
a certain time difference to the current, the magnetic domains were formed with low current density. We analyzed
the behavior inside the magnetic nanowire and found that magnetization reversal can be achieved at low current
density when torque is applied at the appropriate time during the precession of the magnetic moment.
Key words: magnetic nanowire memory, magnetization reversal, magnetic domains, current-driven domain wallmotion1. Introduction
We have been developing magnetic storage devices
that work with huge amounts of data at ultra-highspeed to be utilized for future 3D-TV storage. Since thedata transfer rate required for storage devices in spatial
imaging 3D-TVs 1) (light field spatial imaging) is expected
to exceed at 1 Tbps, which is far faster than that of
uncompressed ultra-high definition TV (144 Gbps), it isextremely difficult to utilize existing memories, such as
HDDs or SSDs. There is therefore a need to develop a
new one that has both a large capacity and a hightransfer rate, and that can hold data for a long time.
Many researches on utilizing a magnetic nanowire as amemory have been reported 2)–4) in recent years andthey are also promising candidates for future 3D-TV
storage devices. Unlike HDDs, which have a magnetic
head and a disk drive mechanism, magnetic nanowire
memories contain no mechanically moving parts anddomain walls are driven at high speed by spin transfer
torque 5). Also, by synchronizing the parallel operationof many nanowires, they have the advantage of further
high data transfer rate 6)–8).

We have already succeeded in driving multiple
magnetic domains along magnetic nanowire 9-12) andforming magnetic domains in nanowire by magnetic
recording head used in HDD 13). However, in order to use
it as a real device, it is necessary to form magnetic
domains at a lower recording current and all thecomponents, i.e. magnetic nanowire media, insulator,
writer and readers, should be integrated onto silicon wafer
substrates. For the racetrack memory, writing data is
accomplished by a current magnetic field induced by asingle metal wire 14). We consequently developed arecording method utilizing two metal wires for stable andCorresponding author: K. Ogura mail:ogura.k-ja@nhk.or.jp

6

low current domain formation 15). In this study, we
propose a method for adding a time difference to thecurrent applied to the two metal wires and managed torecord binary information at a lower current. The purposeof this work is to analyze the behavior of the magnetic
moment and to determine the mechanism underlying thelower current recording.
2. Magnetic nanowire memory
As shown in Fig. 1, the memory consists of a large
number of magnetic nanowires, which are fabricated to
be a couple of hundred nanometers wide and tworecording metal wires. The recording wires are
orthogonally arranged above the magnetic nanowires.
The flow of the memory operation is as follows: First, weapply a magnetic field induced from each recording wire
to the magnetic nanowires by sending a pulse current toeach recording wire in the opposite direction. Magnetic
domains are then formed directly below the gap
between the two recording wires using the synthesizedmagnetic field to record information. Next, a driving
pulse current is applied to the left side of the magnetic
nanowire to shift the magnetic domains at high speed.
By repeating these recording and driving operation, themagnetic nanowire accumulates the magnetic domains.
Finally, these stored magnetic domains are detected andreproduced with a tunnel magnetoresistance (TMR)
head.

Fig. 1 Magnetic nanowire memory.

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3. Micromagnetic simulation
3.1 Simulation model
We analyzed the behavior of the magnetic moment
during the magnetic domain formation process by
micromagnetic simulation using the Landau-Lifshitz-Gi
lbert (LLG) equation. The nanowire model used in thecalculation is shown in Fig. 2. The magnetic nanowire isrectangular and measures 1.6 µm long, 120 nm wide(Wm), and 12 nm thick (Hm). The recording wire is 2 µm
in length (Lr) and has a 120-nm square on each side incross section (Wr, Hr). The gap between the tworecording wires is 100 nm (Sp), and an air gap between
the recording wires and the magnetic nanowires as an
insulating layer is 10 nm. The magnetic nanowire wasdivided into 4nm cube meshes for calculation from theperspective of calculation accuracy.
3.2 Simulation conditions
The recording currents IA and IB (current density: j )shown in Fig. 3 were respectively applied to recording
wires A and B in the opposite direction with a timedifference T. We calculated the magnetic domain
formation below the gap after 2 ns of applying thecurrent. The parameters of the recording current andthe magnetic properties of the magnetic nanowire arelisted in Table 1. The initial magnetization direction
was set to the +z direction.

Fig. 2 Simulation model of magnetic nanowire memory.

Fig. 3 Pulse diagrams of recording current applied to
two metal recording wires. The current density of IA and
IB is set so that magnetization reversal cannot occur
when IA and IB are applied simultaneously without timedifference.
3.3 Simulation results
Fig. 4 shows the analysis results of the magnetization
after 2 ns of the current applied to two recording wires.
For (a) a single recording wire, the left end of themagnetic wall was stable and formed a straight line.
However, the right edge of the domain wall was swaying
throughout the calculation and was not stable at theTable 1 Magnetic properties and recording current
parameters of magnetic nanowire.
Magnetic nanowire
Anisotropic magnetic
field:
Hk (kOe)
Exchange coupling
constant:
A (J/m)Saturation
magnetization:
4πMs (T)

Recording current
5

1.2×10-11
0.15

Pulse width:(ns)

Current
density:jw (A/cm2)

IA: 2
IB: 2-T

3.3×108

end, indicating that more time was required for themagnetic domain to stabilize. In this case, the recording
currents of 110 mA which is the minimum value tosuccessfully form the magnetic domain was applied. In
contrast, for (b), when recording currents IA and IB wereapplied to the recording wires in the opposite direction
with no time difference, the minimum recording current
was around 60 mA which is lower than the current
needed for a single recording wire. Moreover, whenrecording currents were applied with a time differenceof T = 0.15 ns the minimum recording current wasaround 50 mA, which means we succeeded in reducing
the recording current by 10 mA. This was because themagnetic field induced by the current was generated
symmetrically from each recording wire, and the z
component of the synthetic magnetic field was
uniformly distributed around the gap between the tworecording wires.
Next, to examine the tolerance, we calculated themagnetic domain formation in the case when the pulse
currents IA and IB, shown in Fig. 3, were applied to therecording wires A and B in the opposite directions witha time difference of T = 0–0.25 ns (0.01 ns step). We
found that the magnetic domain was specifically formedat around T = 0.05 ns and T = 0.15 ns. Fig. 5 shows themagnetic domain formation after 2 ns of the current
applied to the recording wires. These results
demonstrate that it is possible to reverse themagnetization in the magnetic nanowires just below therecording gap in the range of time differences T =0.03–0.08 ns and T = 0.15–0.18 ns, and that there was adifference in each magnetic domain formation process.
In this paper, we focus on the typical behavior of themagnetic moment at T = 0.15 ns, as the clearest
simulation results of magnetization reversals including
nucleation and domain wall propagation were obtained
for this timing.

Fig. 4 Spatial distributions of magnetizations at elapsed
time of 2 ns.

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4. Analysis of magnetization reversals
Fig. 6 shows the spatial distribution of themagnetizations after 0.1 ns in the process of magnetic
domain formation when the time difference of T = 0.15
ns was provided. We can see that the magnetization
reversal at the  point (50 nm, –58 nm, 6 nm), which isthe core of the magnetic domain formation, was induced
at first, and then a reversed magnetic domain was
spread and formed in the entire gap between therecording wires by diffusion propagation of the magnetic
wall 16). We therefore focused our analysis on thetemporal changes of the magnetic moment at  point
and at  point (2 nm, 2 nm, 6 nm), which is near theorigin, as the representative points of the propagation.

Fig. 5 Spatial distributions of magnetization at eachtime difference.

Fig. 6 Nucleation and magnetic wall propagation byrecording current with the time difference T = 0.15 ns.

8

The magnetization trajectory at the time ofmagnetization reversal at  and  points is shown in Fig.
7. At  point (red line), precession was induced in themagnetic moment after the current was applied torecording nanowires, and the magnetic moment
reversed after passing through a complicated pathseveral times while pointing in the +z direction. Since point was the core of the magnetization reversal (asdescribed above), whether or not magnetic domains
were formed in the gap depended on the feasibility ofthe magnetization reversal at  point. On the other
hand, at  point (blue line), the magnetic wall
propagated due to the interaction of the magnetic
moments between the neighboring meshes and themagnetic reversals occurred in a short time.
Fig. 8 shows the time variation of the z-component of
the magnetic moment after the recording current IA wasapplied. Here, the magnetization trajectory that
occurred when recording current IA was applied at t = 0
and IB was applied with a time difference of T =0.14–0.19 ns is also shown. For the time differences of T
= 0.14 ns and T = 0.19 ns (dotted lines), the magnetic
moment failed to reverse even after the torque wasapplied by the recording current IB. In contrast, in therange of T = 0.15–0.18 ns (solid line), the magnetic
moment succeeded in reversing, which indicates thatthe magnetization reversed while oscillating in the z
direction. When we examined the first time at which the
z-component of the magnetic moment turned negative,i.e., below zero, we found that magnetization reversal in
the case of T = 0.16 ns and 0.17 ns commenced in a
relatively short time (t = 0.25 ns).
In the range of T = 0.15–0.18 ns, where magnetization
reversal occurred, there was a slight difference in theprocess of reversal depending on the time difference T.
This indicates that the feasibility of the magnetization
reversal is related to the position at which the recording
current IB applied the torque to the precession of themagnetic moment at  point. Therefore, we next
investigatedtherelationshipbetweenthemagnetization trajectory and the time when the torquesuperposition commenced.
The magnetization trajectory at  point, the core of
the magnetic domain formation, is shown on the x-yplane in Fig. 9. First, the magnetic moment started its
precession from the origin, and after drawing a larger
circle counterclockwise for 0.11 ns, it entered the second
track. Here, we overlay the magnetization trajectorywhen the recording current IB was applied with the timedifference T = 0.14–0.19 ns. We found that when atorque was applied to the precession of the magnetic
moment, the subsequent magnetization trajectorychanged in accordance with the time difference T. At thetime difference T indicated by the red dotted line,
magnetization reversed in a relatively wider range on
the left side of the larger magnetization trajectory(second and third quadrants) and in a narrow range on
the left side of the second track of the precession.

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Our future work will involve investigating thephysical significance of the optimal torque position (inthe range of 150–225°) for the precession.

Fig. 7 Magnetization trajectory at analysis points.

showed that magnetic domains were successfully
formed by low current density in a magnetic nanowire
when a current in the opposite direction with anappropriate time difference was applied to the recording
wires. We analyzed the behavior of the magnetization todetermine the appropriate range of the time difference
and found that there was a close relationship between
the precession and the position where the torque wasapplied by the current IB, and that the magnetization
reversed in a specific range on the magnetization
trajectory.
Overall, we demonstrated that our method of forming
magnetic domains by controlling the time difference
between the currents applied to the two recording wires
is very useful. In a real device, it is possible to adjust
the time difference between the two recording currents
with an ultrashort pulse generator, or to determine theextra length of the U-shaped recording wire to create
the appropriate time difference.
In future work, we will conduct a more detailed
analysis and verify the range of the time difference inthe case of multiple interacting magnetic nanowires.
References

Fig. 8 Time variation of z component of magnetic
moment at  point.

Fig. 9 In-plane magnetization trajectory at  point.
4. Conclusion
We have proposed a magnetic nanowire memory with
two recording wires and analyzed the magnetic domain
formation process by micromagnetic simulation. Results

1) R. Higashida, N. Funabashi, K. Aoshima, and K. Machida:
IEEE Trans. Magn., 4, 1 (2021).
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Yamanouchi, H. Ohno, Soong-Geun Je, Sug-Bong Choe, andT. Ono: Appl. Phys. Lett. 101, 022407 (2012).
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Fukami, T. Suzuki, N. Ohshima, N. Ishiwata, Y. Nakatani:Appl. Phys. Express, 2, 053002 (2009).
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Ono: J. Magn. Soc. Jpn. 45, 6 (2021).
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Shinjo: Phys. Rev. Lett., 92, 077205 (2004).
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and S. S. P. Parkin: Phys. Rev. Lett., 98, 037204 (2007).
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S. Auffret, B. Rodmacq, S. Pizzini, J. Vogel, M. Bonfim, A.
Schuhl, and G. Gaudin: Nat. Mater., 10, 419 (2011).
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9) M. Okuda, Y. Miyamoto, M. Kishida, and N. Hayashi: IEEE
Trans. Magn., 47, 2525 (2011).
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Appl. Phys., 115, 17D113 (2014).
11) M. Okuda, Y. Miyamoto, E. Miyashita, and N. Hayashi: J.
Jpn. Soc. Powder Powder Metall., 61, S37 (2014).
12) M. Okuda, Y. Miyamoto, E. Miyashita, N. Saito, N.
Hayashi, and S. Nakagawa: J. Appl. Phys., 117, 17D516(2015).
13) M. Okuda, Y. Miyamoto, M. Kawana, E. Miyashita, N.
Saito, and S. Nakagawa: IEEE Trans. Magn., 52, 3401204(2016).
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190 (2008).
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JP 2020-027805 (2020).
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Zhukov: J. Appl. Phys. 111, 07E311 (2012).
Received Aug. 13, 2021; Revised Sep. 22, 2021; Accepted Oct.
18, 2021

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J. Magn. Soc. Jpn., 46, 10-15 (2022)<Paper>I n fo r m a t io n D e g r a d a t io n d u r in g A r c h iv in g
in H e a t - A s s is t e d M a g n e t ic R e c o r d in g
T. Kobayashi, Y. Nakatani*, and Y. Fujiwara

Graduate School of Engineering, Mie Univ., 1577 Kurimamachiya-cho, Tsu 514-8507, Japan*Graduate School of Informatics and Engineering, Univ. of Electro-Communications,

1-5-1 Chofugaoka, Chofu 182-8585, Japan

We examine the dependence of information stability on certain medium parameters, namely mean Curie
temperature, grain height, and anisotropy constant ratio in 4 Tbpsi heat-assisted magnetic recording, for 10 years ofarchiving. We introduce a minimum normalized readout field H0 after 10 years of archiving and an information
degradation rate R0 during 10 years of archiving. To interpret the results, we investigate whether there is a correlation
between H0 or R0 and an effective thermal stability factor for 9 and 6 grains/bit. We find that there is a strong
correlation since the anisotropy constant is much larger than the shape anisotropy. The H0 and R0 values are functionsof the effective thermal stability factor and grain number, and are independent of grain number per bit. The effective
thermal stability factor necessary for no information degradation is more than about 120. Furthermore, there is aweak correlation between the initial readout field or minimum readout field after 10 years of archiving and the effective
thermal stability factor.
Key words: HAMR, bit error rate, degradation rate, thermal stability factor, grain number
1. Introduction

The long-term stability of archived information is oneof the most important properties of magnetic recording
media. This stability has been widely discussed using
the thermal stability factor 𝐾𝐾! 𝑉𝑉/(𝑘𝑘𝑘𝑘), where 𝐾𝐾! , 𝑉𝑉, 𝑘𝑘,
and 𝑇𝑇 are the grain anisotropy constant, grain volume,
Boltzmann constant, and temperature, respectively1).
Heat-assisted magnetic recording (HAMR) is apromising candidate as a next generation magnetic
recording method that can operate beyond the trilemma
limit1). HAMR is a recording method in which themedium is heated to reduce coercivity during the writing
period. We have introduced an HAMR medium
parameter, namely, the medium anisotropy constantratio 𝐾𝐾! /𝐾𝐾"!#$ 2) in place of the medium anisotropy
constant 𝐾𝐾! since the 𝐾𝐾! value at the storage
temperature is a function of the medium Curie
temperature 𝑇𝑇% , which is strongly related to the writing
property. 𝐾𝐾! /𝐾𝐾"!#$ is the intrinsic ratio of the medium
𝐾𝐾! to bulk FePt 𝐾𝐾! regardless of 𝑇𝑇% where FePt is acandidate HAMR medium material thanks to its large
𝐾𝐾! and relatively low 𝑇𝑇% .
We have already calculated the numerical values of
𝐾𝐾! 𝑉𝑉/(𝑘𝑘𝑘𝑘) and 𝐾𝐾! /𝐾𝐾"!#$ necessary for 10 years ofarchiving in 2 Tbpsi HAMR by employing a bit error rate
calculation using the grain error probability3). We used
an error (signal) threshold of 0.5 as a calculation
condition.
In this paper, we estimate the minimum normalized
readout field related to the minimum error threshold,that must be readable without error after 10 years ofarchiving in 4 Tbpsi HAMR. Furthermore, we also
Corresponding author: T. Kobayashi (e-mail: kobayasi@phen.mie-u.ac.jp).

10examine the information degradation rate during 10
years of archiving. The mean Curie temperature 𝑇𝑇%&
affects various properties in HAMR. The larger grain
aspect ratio ℎ/𝐷𝐷& of the grain height (medium layer
thickness) ℎ to the mean grain size 𝐷𝐷& appears tomake it too difficult to manufacture the medium.
Furthermore, there is a concern that 𝐾𝐾! , namely,
𝐾𝐾! /𝐾𝐾"!#$ decreases as 𝐷𝐷& decreases. Thus, we examine
the dependence of information stability on the medium
parameters 𝑇𝑇%& , ℎ, and 𝐾𝐾! /𝐾𝐾"!#$ .
2. Calculation Method and Conditions

2.1 Magnetic properties
The temperature dependence of the magnetization 𝑀𝑀'
was calculated by employing a mean field analysis4), andthat of the anisotropy constant 𝐾𝐾! was assumed to be
proportional to 𝑀𝑀'( 5). 𝑀𝑀' (𝑇𝑇% , 𝑇𝑇) is a function of 𝑇𝑇% and
𝑇𝑇. And 𝑀𝑀' (𝑇𝑇% = 770 K, 𝑇𝑇 = 300 K) = 1000 emu/cm3 wasassumed for FePt. With this assumption, the 𝑀𝑀' value
can be calculated for all 𝑇𝑇% and 𝑇𝑇 values.
The anisotropy constant 𝐾𝐾! (𝑇𝑇% , 𝐾𝐾! /𝐾𝐾"!#$ , 𝑇𝑇) is afunction of 𝑇𝑇% , 𝐾𝐾! /𝐾𝐾"!#$ , and 𝑇𝑇. And 𝐾𝐾! (𝑇𝑇% = 770 K, 𝐾𝐾! /𝐾𝐾"!#$ = 1, 𝑇𝑇 = 300 K) = 70 Merg/cm3 was assumed forbulk FePt. With this assumption, the 𝐾𝐾! value can becalculated for all 𝑇𝑇% , 𝐾𝐾! /𝐾𝐾"!#$ , and 𝑇𝑇 values. No
intrinsic distribution of 𝐾𝐾! was assumed. However,there was a fluctuation in 𝐾𝐾! caused by 𝑇𝑇% variation.
The 𝑇𝑇% value can be adjusted by changing the Cu
composition 𝑧𝑧 for (Fe).+ Pt ).+ ),-. Cu. .
2.2 Field strength
The recording density is 4 Tbpsi, and the bit area 𝑆𝑆 is
161 nm2. We assumed the medium to be granular. One
bit has 𝑚𝑚 grains in the cross-track direction and 𝑛𝑛
grains in the down-track direction, namely, there are
𝑚𝑚 × 𝑛𝑛 grains/bit. The mean grain size 𝐷𝐷& was

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determined by
𝐷𝐷& = !

!

"×$− Δ/ ,(1)

where Δ/ is the intergrain spacing. The bit aspect ratio
is 𝐷𝐷0 /𝐷𝐷1 = 𝑚𝑚/𝑛𝑛 where 𝐷𝐷0 = 𝑚𝑚(𝐷𝐷& + Δ/ ) and 𝐷𝐷1 =𝑛𝑛(𝐷𝐷& + Δ/ ) are the track width and bit pitch,
respectively. The flying height ℎ2#3 = 4.0 nm is the
distance between the magnetic head reader and therecording layer surface.
The magnetic field strength from the medium at thecenter of 𝑚𝑚 grains and the reader position was
calculated using 𝑚𝑚 × 30 grains with no grain size
distribution when calculating the field strength.
2.3 Bit error rate
The bit error rate bER was calculated by employing
each grain error probability 𝑃𝑃4 ,
5

6

(2)

IJ,
𝑃𝑃4 = 1 − exp E−𝑓𝑓) 𝑡𝑡 exp H− !"##
78

taking account of the shape anisotropy 𝑀𝑀' 𝐻𝐻9 /2 using aself-demagnetizing field 𝐻𝐻9 where 𝑓𝑓) , 𝑡𝑡 = 10 years,
and 𝐾𝐾!:22 are the attempt frequency6), time, andeffective anisotropy constant, respectively. And 𝐾𝐾!:22 =𝐾𝐾! − 𝑀𝑀' 𝐻𝐻9 /2 , 𝐻𝐻9 = 8𝑀𝑀' arctan (𝐷𝐷( /(ℎ√2𝐷𝐷( + ℎ( )) , 𝑉𝑉 =𝐷𝐷 × 𝐷𝐷 × ℎ where 𝐷𝐷 is the grain size. Since 𝐻𝐻9 does notaffect the results as mentioned below, the magnetostatic
field from surrounding grains can also be ignored. It was
assumed that there is no exchange coupling between
grains. For example, for 4 grains/bit, the 1 grain-error
bit error rate 4bER1 is expressed as
4bER1 =

𝐸𝐸𝐸𝐸, 𝑃𝑃, (1 − 𝑃𝑃( )(1 − 𝑃𝑃; )(1 − 𝑃𝑃< ) + ∙ ∙ ∙+𝐸𝐸𝐸𝐸< (1 − 𝑃𝑃, )(1 − 𝑃𝑃( )(1 − 𝑃𝑃; )𝑃𝑃< ,(3)

the 2 grain-error bit error rate 4bER2 as
4bER2 =

𝐸𝐸𝐸𝐸,( 𝑃𝑃, 𝑃𝑃( (1 − 𝑃𝑃; )(1 − 𝑃𝑃< ) + ∙ ∙ ∙+𝐸𝐸𝐸𝐸;< (1 − 𝑃𝑃, )(1 − 𝑃𝑃( )𝑃𝑃; 𝑃𝑃< ,(4)

the 3 grain-error bit error rate 4bER3 as
4bER3 =

𝐸𝐸𝐸𝐸,(; 𝑃𝑃, 𝑃𝑃( 𝑃𝑃; (1 − 𝑃𝑃< ) + ∙ ∙ ∙+𝐸𝐸𝐸𝐸(;< (1 − 𝑃𝑃, )𝑃𝑃( 𝑃𝑃; 𝑃𝑃< ,(5)∑4,? 𝑀𝑀'4? (𝑇𝑇%4? , 330 K)𝐷𝐷4?(to(𝑚𝑚 ×
the ratio of(𝑛𝑛)𝑀𝑀' (𝑇𝑇%& , 330 K)𝐷𝐷& in Eqs. (7) and (8) is more than theerror threshold 𝐸𝐸=> , the bit is error-free after 10 years ofarchiving where the numerator ∑4,? 𝑀𝑀'4? (𝑇𝑇%4? , 330 K)𝐷𝐷4?(is the surface magnetic charge of the grains for which themagnetization turns in the recording direction, and the(is the total
denominator (𝑚𝑚 × 𝑛𝑛)𝑀𝑀' (𝑇𝑇%& , 330 K)𝐷𝐷&
surface magnetic charge at the readout temperature of
330 K. 𝑀𝑀'4? , 𝑇𝑇%4? , and 𝐷𝐷4? are the magnetization, theCurie temperature, and the grain size of the 𝑖𝑖𝑖𝑖-th grain,
respectively. The total bit error rate 4bER is thesummation of each bit error rate 4bERk as follows
4bER =

Σ7 4bERk.

(9)

The calculation bit number was 1E+7. The criterion
determining whether or not information is stable wasassumed to be a bER of 1E−3.
The minimum normalized readout field 𝐻𝐻) after 10
years of archiving can roughly be represented by 𝐸𝐸=> as(10)𝐻𝐻) = 2𝐸𝐸=> − 1.

We defined the information degradation rate 𝑅𝑅)
during 10 years of archiving as𝑅𝑅) =012(3,., 567)8012(,.,,3 567)
012(,.,,3 567)

.

(11)

For example, the 𝑅𝑅) values are 99, 9.0, and 0.25 when
the bER(0.001 yrs) values are 1E−5, 1E−4, and 8E−4,
respectively, since the bER(10.0 yrs) value is 1E−3. The
𝑅𝑅) value for no information degradation is less thanabout 0.25.
The conditions used when calculating the bER aresummarized in Table 1. We assumed that the intergrain
spacing Δ/ was 1.0 nm. The grain size distribution was
log-normal with a standard deviation 𝜎𝜎 A /𝐷𝐷& of 15 %,and the 𝑇𝑇% distribution was normal with a standard
deviation 𝜎𝜎0% /𝑇𝑇%& of 2 %. The attempt frequency 𝑓𝑓) is afunction of the Gilbert damping constant 𝛼𝛼 6), and weused an 𝛼𝛼 value of 0.1. The storage temperature 𝑇𝑇'=B
was 350 K since we take a certain margin fortemperature into account.
Table 1 Conditions for bit error rate calculation.

and the 4 grain-error bit error rate 4bER4 as
4bER4 =

where

𝑃𝑃, 𝑃𝑃( 𝑃𝑃; 𝑃𝑃< ,𝐸𝐸𝐸𝐸7 = 1, if

and𝐸𝐸𝐸𝐸7 = 0, if(6)%∑",# &!"# (($"# , ++, -)/"#%("×$)&! (($' , ++, -)/'%∑",# &!"# (($"# , ++, -)/"#%("×$)&! (($' , ++, -)/'

≤ 𝐸𝐸=> , (7)> 𝐸𝐸=> . (8)Errors occur in some grains of a bit. We assumed that if

3. Calculation Results
3.1 Various medium parameters
The bER value as a function 𝐸𝐸=> and 𝐻𝐻) after 10
years of archiving for various 𝑇𝑇%& values in 𝑚𝑚 × 𝑛𝑛 =3 × 3 = 9 grains/bit is shown in Fig. 1 (a) where ℎ = 10.5
nm and 𝐾𝐾! /𝐾𝐾"!#$ = 0.8. The bER value increases as the

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11

INDEX

𝑇𝑇%& value decreases. There is no 𝐸𝐸=> more than 0.5,
namely, no 𝐻𝐻) more than 0 that satisfies bER = 1E−3
for 𝑇𝑇%& = 600 K. The time dependence of the bER isshown in Fig. 1 (b) where 0.001 years corresponds toabout 9 hours. Errors increase over time for 𝑇𝑇%& = 650
K, therefore the initial bER before archiving must be low,for example, 1E−4. On the other hand, the error scarcely
increases for 𝑇𝑇%& = 750 K.

Fig. 1 (b), the 𝐻𝐻) × 𝐻𝐻. value becomes small as shown in
Fig. 2 (b).

(a)

(a)

(b)
Fig. 2 (a) Initial readout field 𝐻𝐻. and (b) minimum
readout field 𝐻𝐻) × 𝐻𝐻. after 10 years of archiving forvarious mean Curie temperatures 𝑇𝑇%& (ℎ = 10.5 nm and
𝐾𝐾! /𝐾𝐾"!#$ = 0.8).

(b)Fig. 1 (a) Bit error rate as a function of error thresholdand normalized field amplitude after 10 years ofarchiving and (b) time dependence of bit error rateduring 10 years of archiving for various mean Curie
temperatures 𝑇𝑇%& (ℎ = 10.5 nm and 𝐾𝐾! /𝐾𝐾"!#$ = 0.8).

Figure 2 shows (a) the 𝑧𝑧 component 𝐻𝐻. of the initial
readout field for the down-track direction and (b) the
minimum readout field 𝐻𝐻) × 𝐻𝐻. that must be readable
without error after 10 years of archiving. Although theerror scarcely increases for 𝑇𝑇%& = 750 K as shown in Fig.
1 (b), the 𝐻𝐻) × 𝐻𝐻. value is small as shown in Fig. 2 (b).
This means that the error is caused by the cluster ofsmall grains. The grain number per bit may increase atthat time, and the 𝐻𝐻) × 𝐻𝐻. value may be larger. This
problem is a future subject for study. In contrast, sinceerrors increase over time for 𝑇𝑇%& = 650 K as shown in
12

If 𝑇𝑇%& = 750 K, ℎ = 6.5 nm, and 𝐾𝐾! /𝐾𝐾"!#$ = 0.8, or if
𝑇𝑇%& = 750 K, ℎ = 10.5 nm, and 𝐾𝐾! /𝐾𝐾"!#$ = 0.5, there is
no 𝐸𝐸=> more than 0.5, or no 𝐻𝐻) more than 0 thatsatisfies bER = 1E−3.
The results for various medium parameters, namely
𝑇𝑇%& , ℎ, and 𝐾𝐾! /𝐾𝐾"!#$ , are summarized in Tables 2 and 3
for 𝑚𝑚 × 𝑛𝑛 = 3 × 3 = 9 grains/bit and 𝑚𝑚 × 𝑛𝑛 = 3 × 2 = 6
grains/bit, respectively. 𝐻𝐻.C:D$ is the peak 𝑧𝑧
component 𝐻𝐻. of the initial readout field, and 𝐻𝐻) ×
𝐻𝐻.C:D$ is the minimum peak readout field that must be
readable without error after 10 years of archiving. Whenadjacent track interference is considered, some grains
are used as a guard band. Therefore, we also examined
𝐻𝐻) , 𝑅𝑅) , 𝐻𝐻.C:D$ , and 𝐻𝐻) × 𝐻𝐻.C:D$ for 𝑚𝑚 × 𝑛𝑛 = 2 × 3 = 6
grains in 9 grains/bit and 𝑚𝑚 × 𝑛𝑛 = 2 × 2 = 4 grains in 6
grains/bit.
The information during 10 years of archiving is stablefor 9 grains/bit media with 𝑇𝑇%& = 750 K, ℎ = 10.5 nm,
and 𝐾𝐾! /𝐾𝐾"!#$ = 0.8 as shown in Table 2.

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Table 2 Minimum normalized readout field 𝐻𝐻) ,information degradation rate 𝑅𝑅) , initial readout field
𝐻𝐻.C:D$ , and minimum readout field 𝐻𝐻) × 𝐻𝐻.C:D$ after 10
years of archiving for 9 and 6 grains in 9 grains/bit.

depending on the difficulty of manufacturing the
medium.
Since the mean grain size 𝐷𝐷& for 6 grains/bit
increases to 4.2 nm from 3.2 nm in 9 grains/bit as shownin Table 3, the degree of freedom in design increases. The(
ratio is 1.68 and more than 9 / 6 = 1.5
grain area 𝐷𝐷&
between 6 and 9 grains/bit since the Δ/ value isindependent of the grain number per bit.
3.2 Effective thermal stability factor
To enable us to interpret the above calculated results,
we plot the 𝐻𝐻) and 𝑅𝑅) values against
𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) = (𝐾𝐾! − 𝑀𝑀' 𝐻𝐻9 /2)(𝐷𝐷& × 𝐷𝐷& × ℎ)/(𝑘𝑘𝑘𝑘)
at 350 K in Figs. 3 and 4 for 9 and 6 grains/bit,
respectively. All the calculated data for 9 and 6 grains in
9 grains/bit and for 6 and 4 grains in 6 grains/bit are on
their lines. Furthermore, the 𝐻𝐻) and 𝑅𝑅) values for 6
grains in 9 and 6 grains/bit are the same as shown in
Figs. 4 (a) and (b), respectively. 𝐻𝐻) and 𝑅𝑅) are
functions of 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) and grain number, and are
independent of grain number per bit since 𝐾𝐾! ≫ 𝑀𝑀' 𝐻𝐻9 /2
in 𝐾𝐾!:22 .

Table 3 Minimum normalized readout field 𝐻𝐻) ,information degradation rate 𝑅𝑅) , initial readout field
𝐻𝐻.C:D$ , and minimum readout field 𝐻𝐻) × 𝐻𝐻.C:D$ after 10
years of archiving for 6 and 4 grains in 6 grains/bit.

(a)

Although the 𝑇𝑇%& , ℎ , and 𝐾𝐾! /𝐾𝐾"!#$ values can be
reduced to 700 K, 8.5 nm, and 0.6, respectively,
simultaneous reduction cannot be realized. The ℎ/𝐷𝐷&
value necessary for information stability is especiallylarge due to the small grain size 𝐷𝐷& of 3.2 nm. The
medium parameters to be reduced must be selected(b)Fig. 3 (a) Minimum normalized readout field 𝐻𝐻) and (b)information degradation rate 𝑅𝑅) against effective
thermal stability factor 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) for 9 and 6 grains in
9 grains/bit.

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INDEX

grains/bit, it is easy to increase the 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) value
for 6 grains/bit since the one grain area is 1.68 times
larger. However, there is a concern that the readout SNRfor 6 grains/bit is smaller than that for 9 grains/bit due
to the small grain number.
A linear relationship was found between logarithmic𝑅𝑅) and 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘), and the 𝑅𝑅) value decreases slightly
in the order of 4, 6, and 9 grains as shown in Figs. 3 (b)and 4 (b). The 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) value necessary for no
information degradation is more than about 120.
The 𝐻𝐻.C:D$ and 𝐻𝐻) × 𝐻𝐻.C:D$ values are plottedagainst 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) in Figs. 5 and 6 for 9 and 6
grains/bit, respectively. The lines in the figures are
guides for the eye. The cause of data scattering is that𝐻𝐻) is a function of 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘), and 𝐻𝐻.C:D$ is a functionof 𝑀𝑀' , 𝐷𝐷& , and ℎ . And although the 𝑀𝑀' value is afunction of 𝑇𝑇% , it is independent of 𝐾𝐾! /𝐾𝐾"!#$ . Roughly, allcalculation data for 9 and 6 grains in 9 grains/bit and for
6 and 4 grains in 6 grains/bit are on their lines as shownin Figs. 5 and 6, respectively.

(a)

(b)
Fig. 4 (a) Minimum normalized readout field 𝐻𝐻) and (b)information degradation rate 𝑅𝑅) against effective
thermal stability factor 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) for 6 and 4 grains in
6 grains/bit.

(a)

The 𝐻𝐻) value for 9 grains is larger than that for 6
grains in 9 grains/bit as shown in Fig. 3 (a) due to astatistical factor. The statistical factor can be explainedusing the following example. If one bit contains manygrains, the bER becomes low since the probability of asimultaneous error is very low for more than half of thegrains in one bit. For example, when all the grains are
assumed to be homogeneous, and 𝑃𝑃 and 𝐸𝐸=> are 0.1 and
0.5, respectively, the bER calculated for 5 grains/bit isbER = ∑+7E;e7+ f𝑃𝑃7 (1 − 𝑃𝑃)+-7 ≈ 0.009.

(12)

bER = ∑F7E+e7F f𝑃𝑃7 (1 − 𝑃𝑃)F-7 ≈ 0.0009,(13)

On the other hand, the bER for 9 grains/bit iswhich is much lower than that for 5 grains/bit. Therefore,
to obtain the same bER , 𝑃𝑃 must be reduced for 5
grains/bit, and a larger 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) value is necessary.
And the 𝐻𝐻) value for 6 grains in 9 grains/bit is larger
than that for 4 grains in 6 grains/bit as shown in Fig. 4(a). Although it is necessary to increase the 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘)
value for 6 grains/bit to obtain the same 𝐻𝐻) value for 9
14(b)Fig. 5 (a) Initial readout field 𝐻𝐻.C:D$ and (b) minimum
readout field 𝐻𝐻) × 𝐻𝐻.C:D$ against effective thermal
stability factor 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) for 9 and 6 grains in 9
grains/bit.

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INDEX

We must comprehensively examine all the factors if weare to determine the medium parameters. Since thesefactors are currently being experimentally investigatedby many researchers, it is currently impossible todetermine the medium parameters. However, the above
calculations will be useful for determining them in the
future.
4. Conclusions

(a)

(b)
Fig. 6 (a) Initial readout field 𝐻𝐻.C:D$ and (b) minimum
readout field 𝐻𝐻) × 𝐻𝐻.C:D$ against effective thermal
stability factor 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) for 6 and 4 grains in 6
grains/bit.
The 𝐻𝐻) × 𝐻𝐻.C:D$ value for 9 grains is larger than thatfor 6 grains in 9 grains/bit as shown in Fig. 5 (b) sinceboth 𝐻𝐻) and 𝐻𝐻.C:D$ for 9 grains are larger than thosefor 6 grains as shown in Figs. 3 (a) and 5 (a).
Furthermore, the 𝐻𝐻) × 𝐻𝐻.C:D$ values for 6 grains in 9
and 6 grains/bit are roughly the same as shown in Fig. 6(b).
There are many factors to be considered when
designing the medium. A high 𝑇𝑇%& is disadvantageous
in terms of the heat resistance of the writing head and/or
the surface lubricant. On the other hand, a low 𝑇𝑇%& isdisadvantageous in terms of information stability for 10
years of archiving since 𝐾𝐾! at the storage temperature
becomes small3). A low 𝑇𝑇%& is also disadvantageous
since the thermal gradient becomes small7). A largerℎ/𝐷𝐷& seems to make it too difficult to manufacture themedium. There is a concern that 𝐾𝐾! decreases as 𝐷𝐷&
decreases.

We examined the dependence of information stability
for 10 years of archiving on various medium parameters,
namely 𝑇𝑇%& , ℎ, and 𝐾𝐾! /𝐾𝐾"!#$ , in 4 Tbpsi HAMR. As aresult, we found that the minimum normalized readoutfield 𝐻𝐻) and information degradation rate 𝑅𝑅) are
functions of the effective thermal stability factor
𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) and grain number, and are independent ofgrain number per bit since 𝐾𝐾! ≫ 𝑀𝑀' 𝐻𝐻9 /2 in 𝐾𝐾!:22 . The
𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) value necessary for no information
degradation is more than about 120. Furthermore, there
is a weak correlation between the initial readout field
𝐻𝐻.C:D$ or the minimum readout field 𝐻𝐻) × 𝐻𝐻.C:D$ and
𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘).
Although the 𝑇𝑇%& , ℎ , and 𝐾𝐾! /𝐾𝐾"!#$ values can be
reduced to 700 K, 8.5 nm, and 0.6, respectively, for 9
grains/bit, a simultaneous reduction cannot be realized.
The ℎ/𝐷𝐷& value necessary for information stability is
especially large due to the small grain size 𝐷𝐷& of 3.2 nm.
Depending on the difficulty involved in manufacturing a
medium, we must select the medium parameters to be
reduced.
It is easy to increase the 𝐾𝐾!:22 𝑉𝑉/(𝑘𝑘𝑘𝑘) value for 6
grains/bit since the one grain area is 1.68 times larger.
Acknowledgement We acknowledge the support of theAdvanced Storage Research Consortium (ASRC), Japan.
References
1) S. H. Charap, P. -L. Lu, and Y. He: IEEE Trans. Magn., 33,
978 (1997).
2) T. Kobayashi, Y. Isowaki, and Y. Fujiwara: J. Magn. Soc. Jpn.,
39, 8 (2015).
3) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 43, 114 (2019).
4) M. Mansuripur and M. F. Ruane: IEEE Trans. Magn., MAG22, 33 (1986).
5) J. -U. Thiele, K. R. Coffey, M. F. Toney, J. A. Hedstrom, andA. J. Kellock: J. Appl. Phys., 91, 6595 (2002).
6) E. D. Boerner and H. N. Bertram: IEEE Trans. Magn., 34,
1678 (1998).
7) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 44, 122 (2020).
R eceiv ed O c t. 8 , 2 0 2 1 ; A ccep ted O c t. 2 6 , 2 0 2 1

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INDEX
J. Magn. Soc. Jpn., 46, 16-21 (2022)<Paper>A Consideration of Efficiency and Power Factor of
IPM-type Magnetic-Geared Motor
K. Ito, K. Nakamura

Graduate School of Engineering, Tohoku University, 6-6-11 Aoba Aramaki Aoba-ku, Sendai, Miyagi 980-8579, Japan

Magnetic-geared motors (MGMs) have attracted attention since their torque density is superior to conventional
electric motors. Among the types of MGMs, an interior permanent magnet (IPM) type has a feature of high efficiency
because the IPM-type can reduce the eddy current loss in magnets. On the other hand, in the IPM-type MGM, the PM
motor part and the MG part magnetically interact with each other, which is called the magnetic interaction. In aprevious paper, the influence of the magnetic interaction on the output torque was investigated. However, theinfluence on the power factor and the efficiency has not been clarified yet. This paper studies the influence of themagnetic interaction on the power factor and the efficiency of the IPM-type MGM. The influence of the magnetic
interaction on the power factor is discussed by deriving a voltage equation of IPM-type MGM. Moreover, the power
factor and the efficiency are calculated and measured to clarify a suitable current phase from the viewpoint of ahigh-power-factor and high-efficiency drive.
Key words: Magnetic-geared motor (MGM), Magnetic interaction, Efficiency, Power factor

1. Introduction
 The electrification of vehicles and ships has been required toreduce the carbon dioxide emissions on the global environment.
In many cases, a general drive system of electric vehicles andships consists of an electric motor and a mechanical gearbox toobtain the desired speed and torque in terms of reducing size
and weight. However, the mechanical gearbox has inherent
problems due to mechanical contacts, e.g., acoustic noise, wear
and tear, vibration, and periodical maintenance.
To solve the above problems, a magnetic-geared motor(MGM) has attracted attention 1) - 3). An MGM consists of apermanent magnet (PM) motor and a flux-modulated typemagnetic gear (MG). It can transmit the torque without any
mechanical contacts by using an electromagnetic force. In
addition, the MGM has the structure that a PM motor and an
MG are magnetically integrated as a single electric machine sothat it can offer a higher torque density than the conventional
drive system. Hence, the MGM is expected to be put into
practical use.
Fig. 1 shows a basic configuration of MGMs, which consist ofa PM motor part and an MG part, and they share a single
high-speed-rotor (HSR). The PM motor part consists of thearmature and the shared HSR, while the MG part consists ofthe shared HSR, a magnetic modulator called pole-pieces (PP),and the low-speed-rotor (LSR). As shown in the figure, they can
be classified roughly into two types in terms of the HSR
structure. One is a surface permanent magnet (SPM) type, andthe other is an interior permanent magnet (IPM) type 4) - 6).
Fig. 1 (a) shows the SPM-type MGM. It has permanent
magnets on the surface of the HSR yoke. Thus, the PM motor
part and the MG part are magnetically decoupled by the HSR
yoke, so that magnetic fluxes from both parts do not influenceeach other. However, the SPM-type MGM causes a large eddy
current loss in magnets of the HSR due to asynchronous
harmonic fluxes 6).
Corresponding author: K. Ito (e-mail: kouki.ito.t4@dc.toh
oku.ac.jp).

16

Low-speed-rotor (LSR)

Pole pieces (PP)Armature(a) SPM

Shared high-speed-rotor(HSR)(b) IPM

Fig. 1 Basic configuration of magnetic-geared motors (MGMs).
Fig. 1 (b) shows the IPM-type MGM that permanent
magnets are embedded in the HSR yoke. The efficiency of theIPM-type is higher than the SPM-type because the eddy
current loss in magnets can be reduced by the embedding
structure 6). However, the PM motor part and the MG partmagnetically interact with each other 7). This interaction iscalled the magnetic interaction.
In previous studies, Refs. 7) and 8) have reported themagnetic interaction. However, these studies only discussed therelationship between the magnetic interaction and the output
torque of the IPM-type MGM. It is concerned that the magnetic
interaction influences not only the output torque but also thepower factor and the efficiency. Thus, if the magnetic interaction
is utilized effectively, the power factor and the efficiency of theIPM-type MGM will be further improved. However, theinfluence of the magnetic interaction on the power factor andthe efficiency has not been clarified.
This paper investigates the influence of the magnetic
interaction on the power factor and the efficiency of theIPM-type MGM. First, a voltage equation of the IPM-type
MGM considering the magnetic interaction is derived to clarify
the influence of the magnetic interaction on the power factor.
Next, to verify the derived voltage equation, the power factor
and the efficiency are calculated by a three-dimensional finite
element method (3D-FEM). Finally, the experimental
verification is carried out by using a prototype IPM-type MGM.

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2. Derivation of Voltage Equation of
IPM-type MGM Considering Magnetic Interaction
2.1 Conventional voltage equation
If the magnetic interaction does not occur, then the voltage
equation of the MGM is the same as that of a conventional PM
motor, which can be represented in the d-q axis coordinate
system by

R+pLd
vd(v ) = (ωeh Ldq

ωeh LqR+pLq

id0) (i ) +ωeh (ψ ) ,
q

h

(1)

where the d- and q-axis components of currents and voltages
are id, iq, vd, vq, respectively. The phase resistance is R, and theamplitude of the flux linkage from the HSR magnet is ψh. The
electric angular velocity of the HSR is ωeh. The d- and q- axis
inductances are Ld and Lq. A differential operator is p (= d/dt). In
general, the MGM is driven by the id = 0 control because theelectrical property is similar to that of a conventional SPM-type
PM motor 8).
In case of the PP are stationary, the gear ratio Gr isrepresented by using the pole-pairs of HSR ph and LSR pl, andthe number of poles of PP npp as follows 9):

Gr =

ph

npp -ph

=

ph
pl

.

(2)

When a three-phase ac current flows the armature windings,
the rotating magnetic field is generated and the HSR is
synchronously rotated. Then, the magnetic flux of the HSR ismodulated by PP, and the LSR is rotated at a speed according to(2).
2.2 Derivation of voltage equation of IPM-type MGM
Fig. 2 denotes the schematic diagram of the IPM-type
MGM. From the top, it shows LSR, PP, HSR, and thearmature, respectively. Table 1 shows the parameters
shown in Fig. 2. The solid line arrows indicate themagnetic flux of each rotor magnet. On the other hand,the dashed line arrows express the modulated magnetic
flux by the PP. In the IPM-type MGM, as shown in the
figure, the modulated magnetic flux of the LSR magnet
ψml reaches the armature due to the magnetic interaction.
Hence, in addition to the armature fluxes Ldid, Lqiq, andthe magnetic flux of the HSR magnet ψh, the modulated
magnetic flux of the LSR magnet ψml also links with thearmature winding. Accordingly, in order to derive thevoltage equation of the IPM-type MGM, these four
magnetic fluxes should be considered.
Fig. 3 indicates the vector diagram of the IPM-type
MGM in the d-q axis coordinate system which rotatessynchronously with the HSR. As described above, since
the modulated magnetic flux of the LSR magnet reaches
the armature, its magnetic flux is taken into
consideration as the vector ψml in the figure. The phasedifference between ψml and ψh is equal to the load angle δ.
As shown in the figure, the linkage flux of thearmature winding ψo is determined by the sum of four
magnetic fluxes Ldid, Lqiq, ψh, and ψml. Here, the phase of
ψml changes with the load angle δ, i.e. the load torque,and thereby the phase of ψo changes too. As a result, thephase of the armature voltage va is varied since thephase difference between va and ψo is always 90 degrees.
Consequently, it is found that the power factor angle Φdepends on the modulated magnetic flux ψml.
Based on the above discussion, it can be concluded
that the modulated magnetic flux ψml influences thepower factor due to the magnetic interaction. Moreover,the current phase angle β should be actively controlled
so that the power factor is kept high, namely, the id = 0
control is not the most suitable way for the IPM-type
MGM. It is understood from Fig. 3 that the d- and qcomponents of the modulated magnetic flux of the LSR
magnet ψmld and ψmlq are given byψmld−ψ sin δ(ψ ) = ( ml) .
ψ cos δ
mlq

(3)

ml

LSR

ψl

PP
q

d

HSR

ψh

Modulatedmagnetic flux

ψmlArmaturerqFig. 2

Schematic diagram of the IPM-type MGM.

Ta b l e 1

ψl
ψh
ψml
ψo
va
ia
β
Φ
δ

Parameters shown in Figs 2 and 3.

magnetic flux of the LSR magnet
magnetic flux of the HSR magnet
modulated ψllinkage flux of the armature winding(Ldid + Lqiq + ψh + ψml)
armature voltage
armature current
current phase angle
power factor angle
load angle of magnetic gear parts

q

va ia
Φ

β

Ld id
ψo

δ
ψml
Fig. 3

Lq iq
ψh

d

Vector diagram of the IPM-type MGM.

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17

INDEXhml

It is also understood from (4) that the armature voltages
vd, vq depend on the modulated magnetic flux ψml.
3. Investigation of Influence of Magnetic Interaction on
Basic Characteristics of IPM-type MGM

3 .1

SpecificationsofI P M - ty p e

MGM

used

for

sinusoidal wave, namely, harmonic components are notconsidered due to the switching of the converter.
Fig. 5 indicates the calculated torque at various
current phases and load angles. It is understood that thetorque increases when the current phase is lagging,while decreases when it is leading. The reason is thatthe magnetic flux is strengthened in the lagging current
phase while weakened in the leading current phase due
to aTable 2 Specifications of the IPM-type MGM used for
examinations.

examinations
Table 2 shows the specifications of the IPM-type
MGM shown in Fig. 1(b). The diameter is 140 mm, theaxial length including the coil end is 36 mm, and thethree air gap lengths are 1 mm each, respectively. The
PM motor part is composed of the 9-slots armature withthree-phase concentrated windings and the shared
4-pole-pairs HSR. The MG part is composed of theshared 4-pole-pairs HSR, the 23-pole-pairs LSR, and the
27-poles PP. Therefore, the gear ratio is 5.75 from (2).
The material of each rotor magnets is sintered Nd-Fe-B.
The material of the armature core, the HSR yoke, andthe LSR yoke is 6.5%Si-Fe steel. The material of PP is a
soft magnetic composite.

3.3 Influence on the efficiency and the power factor
The power factor and the efficiency are calculated by
3D-FEM in various current phases and load angles. In
the calculation of the efficiency, the copper loss, the ironloss, and the eddy current loss in magnets are
considered, while the mechanical loss is neglected. Thus,
the efficiency η is calculated by the following equation:
ωl T lη=× 100 (%),
Wc +Wi +Wem +ωl Tl(5)where the mechanical angular velocity of the LSR is ωl,the torque of the LSR is Tl, the copper loss is Wc, the ironloss is Wi, and the eddy current loss in magnets is Wem,
respectively. In 3D-FEM, the input current is an ideal

18

140 mm
36 mm
101 mm59 turns/pole
1.2 mm
46.1%

HSR magnet pole pairs

4

LSR magnet pole pairs

23

PP number of poles

27

Radial length of HSR magnets

4 mm

Radial length of LSR magnets

4 mm

Radial length of PP

2.5 mmGear ratio
Gap length
Material of magnet
Material of iron core
Material of PP
HSR rotational speed
LSR rotational speed

5.75
1.0 mm × 3
Sintered Nd-Fe-B
6.5%Si-Fe steel
Soft magnetic composite
3000 rpm-521.7 rpm

80
Fundemental component ofarmature voltage (V)

40
20
0

-20

2

NoloadLoad ang. = 90°
Load ang. = 45°
Load ang. = 30°
Input current

60

Full load

10

No load

-40

-1

-60
-80

0 30 60 90 120 150 180 210 240 270 300 330 360
Rotational ang. (elec deg.)-2

Fig. 4 Calculated waveforms of the armature voltage atvarious load angles.
20
18
Torque (N‧m)

3.2 Influence on the phase of armature voltage
The phase of the armature voltage is calculated by
3D-FEM in various load angles, namely, in various load
torques, to clarify the influence of the magnetic
interaction
onthearmature
voltage.
The
JMAG-Designer software ver. 19.0 is used for
calculation by FEM. In 3D-FEM, the rotational speed
and the current phase are kept constant (= 0 deg.).
Fig. 4 indicates the calculated fundamental
component waveform of the armature voltage at various
load angles of 0 (no-load), 30, 45, and 90 (full-load)
degrees. An input current is also indicated in the figure
as a reference of the phase. It is understood that thephase of the armature voltage is gradually shifted byincreasing the load angles, i.e. the load torque. Thus, thevalidity of the discussion in Section 2.2 is proved.

Outer diameter of LSR
Axial length
Outer diameter of stator
Number of turns/poleWinding diameter
Winding space factor

Input current (p. u.)

Finally, the voltage equation of the IPM-type MGM canbe derived based on (1) and (3) as follows:
R+pLd ωeh Lq id
vd−ψml sin δ(v ) = () (i ) +ωeh () .
(4)
ωeh Ld R+pLqqψ + ψ cos δq16

δ = 90°14

δ = 60°12

δ = 45°10δ = 30°8
6-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
Current phase (deg.)

Fig. 5 Calculated torque at various current phases andload angles.

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INDEX

60

Copper loss (W)50δ = 90°40

δ = 60°30

Eddy curr. loss in magnets (W)δ = 30°10-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
Current phase (deg.)

Fig. 6 Calculated copper loss at various current phases
and load angles.

1211

δ = 90°10

δ = 60°δ = 45°98

δ = 30°-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
Current phase (deg.)

94
93.8
93.6
93.4
93.2
93
92.8
92.6
92.4
92.2
92

δ = 45°
δ = 60°δ = 30°δ = 90°-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
Current phase (deg.)

115

δ = 6.13°

0.95

14.5
14

δ = 30°13.5

Power factor

Iron loss (W)13

Fig. 9 Calculated efficiency at various current phases
and load angles.

15.5

12.5

δ = 60°0.8

δ = 90°0.75-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
Current phase (deg.)

Fig. 7 Calculated iron loss at various current phases
and load angles.

δ = 30°δ = 45°0.85

δ = 45°12δ = 15°

0.9

13

11.5

14

Fig. 8 Calculated eddy current loss in magnets at
various current phases and load angles.

δ = 45°20

0that the eddy current loss in magnets increases when
the current phase decreases, while decreases when thecurrent phase increases in the same way described in
the torque and the iron loss shown in Figs. 5 and 7. It
can be considered that the armature flux influences theasynchronous harmonic flux which causes the eddy
current loss in magnets. Accordingly, the asynchronous
harmonic flux is increased at a lagging current phase,
while decreased at a leading current phase.
Furthermore, it is understood that the eddy current loss
in magnets changes with the load angle when thecurrent phase is constant. The reason is that thearmature flux affects the asynchronous harmonic flux as
described above, so that the eddy current loss inmagnets is larger at a heavy load of a large load angle.

Efficiency (%)

to the magnetic interaction7). As shown in the figure, themaximum torque calculated by 3D-FEM is about 17 N‧
m.
Fig. 6 shows the calculated copper loss at various
current phases and load angles. The figure reveals thatthe copper loss becomes minimum at the current phaseof around zero since the PM motor part of the IPM-type
MGM has almost the same structure as the conventional
SPM-type PM motor. In addition, the copper loss at theleading current phase is smaller than the one at thelagging current phase due to reluctance torque. As
shown in Fig. 1(b), the iron yoke of HSR is thin andsaturated by HSR magnets. Therefore, HSR has amagnetic saliency, by which the leading current cangenerate larger reluctance torque than the lagging
current, which results in reducing the input current
when it is leading.
Fig. 7 indicates the iron loss at various current phases
and load angles. It is understood that iron loss increases
when the current phase decreases, while decreases when
the current phase increases. The reason is that themagnetic flux is strengthened in the lagging current
phase while weakened in the leading current phase in
the same way as the torque shown in Fig. 5. In addition,
the iron loss is decreased by increasing the load angle
when the current phase is constant. This is because thephase difference of fluxes between HSR and LSR
magnets increases when the load angle increases, which
results in decreasing the combined flux.
Fig. 8 shows the eddy current loss in magnets at
various current phases and load angles. It can be foundthaδ = 60°δ = 90°-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
Current phase (deg.)

Fig. 10Calculated displacement power factor atvarious current phases and load angles.

Journal of the Magnetics Society of Japan Vol.46, No.1, 2022

19

INDEX

Fig. 9 indicates the calculated efficiency at various
current phases and load angles obtained from Eq. (5).
The figure reveals that the efficiency is high when thecurrent phase is zero, and that it is also the same or
higher when the current phase is leading. On thecontrary, the efficiency is low in the lagging current
phase. That is because the torque and the iron and eddy
current losses increase when the current is lagging as
shown in Figs. 5, 7, and 8, however, the increasing rateof losses is higher than that of torque. Moreover, it canbe seen that the highest point of efficiency gets close to a
current phase of zero as the load angle increases. The
reason is that the copper loss remarkably increases
when the load angle increases as shown in Fig. 6. Thus,
the copper loss becomes major, and the efficiency ismaximized around a current phase of zero. From theabove discussion, it is revealed that the zero or leading
current phase is more suitable for the high efficiency
drive of the IPM-type MGM.
Fig. 10 shows the displacement power factor atvarious current phases and load angles. The figure
reveals that the power factor becomes maximum at thecurrent phase of around zero when the load angle, i.e.
the load torque is small, while when the load angle isincreasing, the maximum point of the power factor is
gradually shifted to the leading current phase region.
Hence, in the IPM-type MGM, it can be concluded thatthe leading current phase control is better than the id = 0
control from the viewpoint of the power factor and theefficiency.

housing, and the harmonic iron loss caused by PWM
switching are included in the experiment. Accordingly,
the measured efficiency is the highest at the leading
current phase. However, it can be seen that the overall
trend of the measured efficiency is in good agreementwith the calculated one.
Fig. 13 indicates the displacement power factor atvarious current phases and load torques. It is
understood from the figure that the power factor
decreases when the load torque, i.e., the load angle
increases, and that the power factor reaches almost 1.0
when the current phase is leading. The figure revealstaata
DC supplyPC
Three-phaseconverter

Torque detector

20

Hysteresis brake

Hall sensor
signalsFig. 11

Effficiency (%)

4. Experimental Verification

Prototype
IPM-type MGM

Configuration of the experimental setup.

90
89.5
89
88.5
88
87.5
87
86.5
86
85.5
85

10 N·m8 N·m
6 N·m-30-25-20-15-10 -5 0 5 10 15 20 25 30
Current phase (deg.)

Fig. 12 Measured efficiency at various current phases
and load torques.
1
0.95Power factor

In this chapter, to prove the validity of the calculation
results, the power factor and the efficiency are measured
by using the prototype IPM-type MGM.
Fig. 11 indicates the configuration of the experimental
setup. It consists of the prototype IPM-type MGM, thetorque detector, the hysteresis brake, the dc supply, thethree-phase converter, and the power meter, respectively.
The prototype IPM-type MGM is controlled by the vector
control, and the position of the HSR is detected by a hallsensor. In the experiment, the rotational speed of the
HSR is controlled to be 3000 rpm, and the load torque isset to be 2, 4, 6, 8, and 10 N‧m.
Fig. 12 shows the measured efficiency at various
current phases and load torques. The measured results,
which have over 85% efficiency, are plotted. The figure
reveals that the measured efficiency is lower than thecalculated one because the mechanical loss, the eddy
current loss in the housing, and the harmonic iron loss
caused by PWM switching are ignored in 3D-FEM. In
addition, it is understood that the measured efficiency at
the leading current phase is higher, which is slightly
different from the calculated one shown in Fig. 9. This isbecause the calculated copper loss is obviously larger
than the calculated iron loss in 3D-FEM. On the other
hand, the difference between the measured copper andiron losses is small since the eddy current loss in thePower meter

0.9

10 N·m
8 N·m
6 N·m

0.85

4 N·m

0.8

2 N·m

0.75

-30-25-20-15-10 -5 0 5 10 15 20 25 30
Current phase (deg.)
Fig. 13 Measured displacement power factor at various
current phases and load torques.

Journal of the Magnetics Society of Japan Vol.46, No.1, 2022

INDEX

that the trend of the measured power factor is in good
agreement with the calculated one shown in Fig. 10.
Hence, it is proved in the experiment that the leading
current phase control is more suitable than the id = 0
control from the viewpoint of the power factor and theefficiency.
5. Conclusion
This paper presented the influence of the magnetic
interaction on the power factor and the efficiency of theIPM-type MGM.
Based on the conventional voltage equation, thevoltage equation of the IPM-type MGM was derived
considering the modulated magnetic flux of the LSR
magnet. In addition, the vector diagram of the IPM-type
MGM was described based on the proposed equation. As
a result, it was clear that the power factor changes withthe load angle due to the magnetic interaction.
Next, the power factor was calculated by 3D-FEM toprove the validity of the proposed equation. Moreover,the efficiency was calculated to clarify the suitablecurrent phase for a high-efficiency drive. As a result, thevalidity of the proposed equation was proved, and it wasclarified that the leading current phase control is better
than the conventional id = 0 control from the viewpoint of
the power factor and the efficiency.
Finally, the validity of the calculated results wasproved by the experiment of the prototype IPM-type
MGM.

Acknowledgements
This work was supported in partby the WISE Program for AI Electronics, Tohoku
University and JSPS KAKENHI Grant Number
21J10759 and 21H01302.
References
1) K. T. Chau, Z. Dong, J. Z. Jiang, L. Chunhua, and Z. Yuejin: IEEE
Trans. Magn., 43, 2504-2506 (2007).
2) K. Atallah, J. Rens, S. Mezani, and D. Howe: IEEE Trans. Magn.,
44, 4349-4352 (2008).
3) K. Ito, T. Kadomatsu, K. Obana, and K. Nakamura: International
Journal of Applied Electromagnetics and Mechanics, 64, 157-163(2020).
4) T. V. Frandsen, L. Mathe, N. I. Berg, R. K. Holm, T. N. Matzen, P.
O. Rasmussen, and K. K. Jensen: IEEE Trans. Ind. Appl., 51,
1516-1525 (2015).
5) S. Gerber and R.-J. Wang: IEEE Trans. Magn., 51, Art. no. 8107010(2015).
6) K. Ito, T. Kadomatsu, and K. Nakamura: J. Magn. Soc. Jpn. (Special
Issues), 3, 69-73 (2019) (in Japanese).
7) K. Ito and K. Nakamura: IEEE Trans. Magn., 57, Art. no. 8202005(2020).
8) E. Morimoto, N. Niguchi, and K. Hirata: J. JSAEM, 26, 15-21(2018) (in Japanese).
9) K. Atallah and D. Howe: IEEE Trans. Magn., 37, 2844-2846 (2001).
Received Sep. 22, 2021; Accepted Oct. 28, 2021

Journal of the Magnetics Society of Japan Vol.46, No.1, 2022

21

INDEX

Editorial Committee Members・Paper Committee Members
T. Kato and S. Yabukami (Chairperson), K. Koike, K. Kobayashi and Pham NamHai (Secretary)
T. Hasegawa
K. Hioki
S, Inui
K. ItoK. KamataH. Kikuchi
S. Kokado
Y. Kota
T. Kouda
A. Kuwahata
S. Muroga
Y. Nakamura
H. Nakayama
T. Narita
K. Nishijima
D. Oyama
T. SatoT. Suetsuna
T. Takura
K. ThamN. Wakiya
T. Yamamoto
K. Yamazaki

Y. Kamihara
K. Masuda
T. Nozaki
T. Tanaka

N. Adachi
T. GotoH. KuraE. Shikoh
M. Toko

M. GotoT. Kojima
M. Sekino
K. Tajima
S. Yoshimura

H. AokiS. Honda
T. MakiK. Suzuki
S. YakataK. Bessho
S. Isogami
M. NaoeI. TagawaS. Yamada

M. DoiM. Iwai
M. OhtakeY. Takamura
A. YaoT. DoiY. Kanai
S. Seino
M. Takezawa
M. Yoshida

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加 藤 剛 志 （理事） 薮 上
伊藤啓太
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Journal of the Magnetics Society of Japan
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