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.45 No.2
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2021

Hard and Soft Magnetic Materials
Miniaturized Permanent Magnets Applied to Extremely Small Stepping Motors
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

Masaki Nakano…12

T. Kobayashi, Y. Nakatani, and Y. Fujiwara…16

Magnetic Recording
Medium Layer Structure in Three-Dimensional Heat-Assisted Magnetic Recording

Magnetic Phenomena
Spin Wave Resonance in Perpendicularly Magnetized Synthetic Antiferromagnets
M. Ishibashi, Y. Shiota, S. Funada, T. Moriyama, and T. Ono…25

Thin Films, Fine Particles, Multilayers, Superlattices
Void-Defect Induced Magnetism and Structure Change of Carbon Materials- I : Graphene Nano Ribbon
Norio Ota and Laszlo Nemes…30

Hiroki Koizumi, Atsushi Hidaka, Takashi Komine, and Hideto Yanagihara…37

Spin Electronics
Anomalous Nernst and Seebeck eﬀects in NiCo2O4 ﬁlms

Thin Films, Fine Particles, Multilayers, Superlattices
Void-Defect Induced Magnetism and Structure Change of Carbon Material- II : Graphene Molecules
Norio Ota, Aigen Li, Laszlo Nemes, and Masaaki Otsuka

広告◇東英工業株式会社

…41

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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

2

2021

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Journal of the Magnetics Society of Japan
Vol. 45, No. 2
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Hard and Soft Magnetic Materials
Miniaturized Permanent Magnets Applied to Extremely Small Stepping Motors…………………………………………………………………………………………………… Masaki Nakano

12Magnetic Recording
Medium Layer Structure in Three-Dimensional Heat-Assisted Magnetic Recording…………………………………………………………………T. Kobayashi, Y. Nakatani, and Y. Fujiwara

16

Magnetic Phenomena
Spin Wave Resonance in Perpendicularly Magnetized Synthetic Antiferromagnets…………………………………………… M. Ishibashi, Y. Shiota, S. Funada, T. Moriyama, and T. Ono

25

Thin Films, Fine Particles, Multilayers, Superlattices
Void-Defect Induced Magnetism and Structure Change of Carbon Materials- I : Graphene Nano Ribbon…………………………………………………………………………………… Norio Ota and Laszlo Nemes

30

Spin Electronics
Anomalous Nernst and Seebeck effects in NiCo2O4 ﬁlms………………………… Hiroki Koizumi, Atsushi Hidaka, Takashi Komine, and Hideto Yanagihara

37

Thin Films, Fine Particles, Multilayers, Superlattices
Void-Defect Induced Magnetism and Structure Change of Carbon Material- II : Graphene Molecules…………………………………………………Norio Ota, Aigen Li, Laszlo Nemes, and Masaaki Otsuka

Board of Directors of The Magnetics Society of Japan
President:
K. Nakagawa
Vice Presidents:
S. Sugimoto, S. Matsunuma
Directors, General Affairs:
Y. Miyamoto, H. Saito, H. Yuasa
Directors, Treasurer:
K. Ishiyama, H. Takahashi
Directors, Planning:
S. Nakagawa, T. Kondo
Directors, Editorial:
T. Ono, T. Kato
Directors, Public Relations:S. Greaves, S. Sakurada
Directors, International Affairs:
M. Nakano, H. Yanagihara
Specially Appointed Director, Gender Equality:
F. Akagi
Specially Appointed Director, Societies Collaborations: K. Fujisaki
Specially Appointed Director, International Conferences: Y. Miyamoto
Auditors:
R. Nakatani, Y. Takano

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J. Magn. Soc. Jpn., 45, 12-15 (2021)<Review>

12

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Shaft

Hcj ≧1000 kA/m

Hcj

It was found that
controlling the Pr content is indispensable when trying toachieve not only high coercivity but also an increase inthickness without mechanical destruction such as peeling.

Journal of the Magnetics Society of Japan Vol.45, No.2, 2021

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INDEX○ : Before thermal exposure△ : After thermal exposure

14

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J. Magn. Soc. Jpn., 45, 16-24 (2021)<Paper>M e d iu m L a y e r S t r u c t u r e
in T h r e e - D im e n s io n a l 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 a medium layer structure in three-dimensional heat-assisted magnetic recording (3D HAMR) at 2 Tbpsi
per layer (total density of 4 Tbpsi) where the medium consists of a high Curie temperature (HC) layer and a low Curie
temperature (LC) layer. We perform a heat transfer simulation for 3D HAMR media including the isolation layer. To
evaluate the grain error distribution, the expected value of the magnetization is calculated using the grain error
probability. The error threshold and the time dependence of the bit error rate are discussed for 10 years of archiving.
The information stability in the HC layer while writing in the LC layer is estimated using the temperature profile
calculated by the heat transfer simulation. An LC (upper, namely, surface) / HC (lower) layer structure is comparedwith an HC (upper) / LC (lower) layer structure. The former is disadvantageous in relation to the medium surface
temperature as regards writing in the HC layer. The latter may be disadvantageous in relation to the difference
between the thermal gradients for HC and LC writing.
Key words: 3D HAMR, heat transfer simulation, temperature profile, information stability, error distribution
1. Introduction

Microwave-assisted magnetic recording (MAMR),
heat-assisted magnetic recording (HAMR), and threedimensional magnetic recording are candidates as next
generation magnetic recording methods for achieving ahigh recording capacity. HAMR is a recording technique
where the medium is heated to reduce coercivity during
the writing period.
Three-dimensional HAMR (3D HAMR) has been
proposed1) where the medium consists of a high Curie
temperature 𝑇𝑇!" (HC) layer and a low Curie
temperature 𝑇𝑇#" (LC) layer with an isolation layer
inserted between the two layers to suppress exchange
coupling between them. With 3D HAMR, once data havebeen written in the HC layer, other data can be written
in the LC layer by employing lower temperature heating.
We have previously discussed the information
stability in the HC and LC layers for 10 years ofarchiving, and the stability of the information in the HC
layer while writing is under way in the LC layer2). We
have also discussed 3D HAMR media design3). We used
these results to roughly determine the preferable layer
structure for 3D HAMR, namely an LC (upper, namely,
surface) / HC (lower) layer, where the LC layer has a 𝑇𝑇#"of 625 K and a layer thickness ℎ#" of 4.5 nm, and the
HC layer has a 𝑇𝑇!" of 750 K and an ℎ!" of 6.0 nm.
However, we analytically estimated the temperature
profile in it using previously published data where therecording layer thickness was 8.0 nm without theisolation layer.
In this paper, we carry out a heat transfer simulationfor 3D HAMR media where the recording layer thickness
is 11.5 nm including an isolation layer of 1.0 nm. To
evaluate the grain error distribution, the expected valueof the magnetization is calculated using the grain error
16

probability. We discuss both the error threshold and thetime dependence of the bit error rate for 10 years ofarchiving. We then estimate the information stability in
the HC layer while writing in the LC layer using atemperature profile calculated by using a heat transfer
simulation. Furthermore, we examine two layer
structures consisting of an LC / HC layer and an HC / LClayer.
2. Calculation Method
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 the Curie
temperature 𝑇𝑇' and temperature 𝑇𝑇 . And 𝑀𝑀$ (𝑇𝑇' =770 K, 𝑇𝑇 = 300 K) = 1000 emu/cm3 was assumed for FePt.
We introduced an HAMR design parameter, namely,
the medium anisotropy constant ratio 𝐾𝐾% /𝐾𝐾(%)* 6) since
the 𝐾𝐾% value is a function of 𝑇𝑇' . 𝐾𝐾% /𝐾𝐾(%)* is theintrinsic ratio of the medium 𝐾𝐾% to bulk FePt 𝐾𝐾%
regardless of 𝑇𝑇' . Although a low 𝑇𝑇' medium is easy towrite when employing HAMR, a high 𝐾𝐾% /𝐾𝐾(%)* isneeded for a low 𝑇𝑇' medium for 10 years of archiving7),
and a medium with a high 𝐾𝐾% /𝐾𝐾(%)* is difficult tomanufacture regardless of 𝑇𝑇' 8). Moreover, a high 𝐾𝐾% /𝐾𝐾(%)* must be achieved in 3D HAMR to realize
information stability in the LC layer for 10 years ofarchiving, and to realize information stability in the HC
layer while writing in the LC layer2). 𝐾𝐾% (𝑇𝑇' , 𝐾𝐾% /𝐾𝐾(%)* , 𝑇𝑇)
is a function of 𝑇𝑇' , 𝐾𝐾% /𝐾𝐾(%)* , and 𝑇𝑇 . And 𝐾𝐾% (𝑇𝑇' =770 K, 𝐾𝐾% /𝐾𝐾(%)* = 1, 𝑇𝑇 = 300 K) = 70 Merg/cm3 wasassumed for bulk FePt. We used 𝐾𝐾% /𝐾𝐾(%)* = 0.8 in thispaper.
The 𝑇𝑇' value can be adjusted by adjusting the Cu
composition 𝑧𝑧 for (Fe+.- Pt +.- )./0 Cu0 .

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2.2 Field strength
We assumed the medium to be granular and therecording density to be 2 Tbpsi per layer (total density of
4 Tbpsi). The magnetic field strength from the upper andlower layers, as shown in Fig. 1, was calculated using ananalytical equation. One bit has 𝑚𝑚 = 3 grains for the
cross-track direction and 𝑛𝑛 = 3 grains for the downtrack direction, namely, there are 𝑚𝑚 × 𝑛𝑛 = 9 grains/bit.
The bit aspect ratio is one. The grain size 𝐷𝐷1 and theintergrain spacing Δ2 are 5.0 nm and 1.0 nm,
respectively, with no grain size distribution. The grainheights (layer thicknesses) and the magnetizations forthe upper and lower layers are ℎ3 , ℎ# , 𝑀𝑀$3 , and 𝑀𝑀$# ,respectively. The flying height ℎ4)5 = 4.0 nm is the
distance between the magnetic head reader and theupper layer surface.
The isolation layer is used to suppress the exchange
coupling between the upper and lower layers. That layer
thickness ℎ6$7 must be thinner due to the higher fieldstrength from the lower layer at the reader since thefield strength decreases exponentially with an ℎ4)5 +ℎ3 + ℎ6$7 value of more than 3 nm3). On the assumptionthat we had selected an appropriate material for theisolation layer, we chose an ℎ6$7 value of 1.0 nm.

and 𝑧𝑧 axes are the down-track, cross-track, and film
normal directions, respectively, where 𝑦𝑦 = 0 at the trackcenter and 𝑧𝑧 = 0 at the RL surface. The writing
temperature of the grains at the track edges 𝑦𝑦 = ±6.0
nm was assumed to be 𝑇𝑇'1 + 2𝜎𝜎8' for the HC and LC
layers where 𝑇𝑇'1 and 𝜎𝜎8' are the mean Curie
temperature and the standard deviation of 𝑇𝑇'1 ,respectively, taking account of the Curie temperature
variation.

Fig. 2 Medium structure for heat transfer simulation.
Table 1 (a) Calculation conditions, (b) optical constants,and (c) thermal constants for heat transfer simulation.
(a)

(b)

Fig. 1 Grain arrangement for field calculation. (a) Top
and (b) side views.
2.3 Temperature profile
We needed to determine the temperature profiles of
the LC and HC layers at the time of writing for the 3D
HAMR design. A heat transfer simulation was carriedout using Poynting for Optics (Fujitsu Ltd.). Figure 2
shows a schematic illustration of the structure of a
medium that consists of four layers, namely, a recording
layer (RL) (FePt base, upper + isolation + lower layers =11.5 nm), interlayer 1 (IL1) (MgO base, 5 nm), interlayer
2 (IL2) (Cr base, 10 nm), and a heat-sink layer (Cu base,
30 nm). Since suitable intergrain and isolation layermaterials are currently unknown, we used the opticaland thermal constants of FePt for these materials. The
total layer thickness of the LC and HC layers was 11.5
− 1.0 = 10.5 nm. IL1 is a layer for the 𝑐𝑐-axis orientation
control of RL, and IL2 is a seed layer for IL1. The 𝑥𝑥, 𝑦𝑦,(c)Journal of the Magnetics Society of Japan Vol.45, No.2, 2021

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We focused on the medium surface temperature 𝑇𝑇$%94
while writing in the HC layer, the thermal gradients forthe down-track 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 and cross-track 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕
directions while writing in the LC and HC layers, andthe grain temperature difference Δ𝑇𝑇!# between the HC
and LC layers while writing in the LC layer at the trackedges 𝑦𝑦 = ±6.0 nm.
Table 1 summarizes (a) calculation conditions, (b)optical constants, and (c) thermal constants used in thesimulation. The light spot diameter (FWHM) is about 9.0
nm for the down-track and cross-track directions. The
linear velocity is 10 m/s. The ambient temperature is the
maximum working temperature of the hard disk drive,and is assumed to be 330 K.
2.4 Information stability
The information stability in 3D HAMR was estimatedusing the grain error probability 𝑃𝑃2), taking account of
the shape anisotropy 𝑀𝑀$ 𝐻𝐻: /2 using a selfdemagnetizing field 𝐻𝐻: 3). The conditions used whencalculating the information stability in the LC and HC
layers are summarized in Table 2.
We assumed that the grain size distribution was lognormal with a mean grain size 𝐷𝐷1 of 5.0 nm and astandard deviation 𝜎𝜎 ; /𝐷𝐷1 of 15 %. The 𝑇𝑇' distribution
was assumed to be normal with a mean Curie
temperature 𝑇𝑇'1 and a standard deviation 𝜎𝜎8' /𝑇𝑇'1 of
2 %. No intrinsic distribution of 𝐾𝐾% was assumed.
However, there was a fluctuation in 𝐾𝐾% caused by 𝜎𝜎8' .
The result calculated with a heat transfer simulationin 2.3 was used as the temperature profile for the crosstrack direction while writing in the LC layer.
To evaluate the grain error distribution, we calculated
the expected value of the magnetization 𝐸𝐸[𝑀𝑀$ ]𝐸𝐸[𝑀𝑀$ ] = (1 − 𝑃𝑃)𝑀𝑀$ + 𝑃𝑃(−𝑀𝑀$ ) = (1 − 2𝑃𝑃)𝑀𝑀$ . (1)The 𝐸𝐸[𝑀𝑀$ ] value was averaged over one-bit grains(𝑚𝑚 × 𝑛𝑛 = 9) to give the information stability during 10
years of archiving,𝐸𝐸[𝑀𝑀$ ] =%∑(!&' ∑"&'(#$%&!" )(#!" ()$!" , ,,- .)

/×1

, (2)

and was averaged over one-row grains (𝑛𝑛 = 3) for the
information stability in the HC layer while writing in the
LC layer,
𝐸𝐸[𝑀𝑀$< ] =∑%"&'(#$%&!" )(#!" ()$!" , ,,- .)
1

,

(3)

since there is a temperature distribution for the crosstrack direction.
Furthermore, we introduced an error threshold 𝐸𝐸=> toestimate the bit error rate (bER). Errors occur in somegrains of a bit. We assume that if the ratio of the surface
magnetic charge ∑<,? 𝑀𝑀$<? (𝑇𝑇'<? , 330 K)𝐷𝐷<?& of the grains
where the magnetization turns in the recording direction
to the total surface magnetic charge (𝑚𝑚 ×&in a bit is more than 𝐸𝐸=> , namely,𝑛𝑛)𝑀𝑀$ (𝑇𝑇'1 , 330 K)𝐷𝐷1
18)∑!," (#!" ()$!" , ,,- .)2!")(/×1)(# ()$+ , ,,- .)2+

> 𝐸𝐸=> ,(4)

the bit is error free where 𝑀𝑀$<? , 𝑇𝑇'<? , and 𝐷𝐷<? are themagnetization, the Curie temperature, and the grain
size of the 𝑖𝑖𝑖𝑖-th grain, respectively.
The readout magnetic field at the reader will bedegraded after 10 years of archiving or writing in the LC
layer. The lowest normalized magnetic field 𝐻𝐻+ thatmust be readable without error can roughly be
represented by 𝐸𝐸=> as(5)

𝐻𝐻+ = 2𝐸𝐸=> − 1.

Table 2 Calculation conditions for information stability.

3. Calculation Results
3.1 LC / HC layer structureFirst, we discuss the structure as shown in Fig. 3 (a)where the upper layer is LC with 𝑇𝑇#" = 650 K and ℎ#"= 4.5 nm, and the lower is HC with 𝑇𝑇!" = 750 K and ℎ!"= 6.0 nm. The 𝑇𝑇#" value was revised to 650 from 625 K
in a previous paper3) due to information stability in the
LC layer during 10 years of archiving.
Figure 3 (b) shows the 𝑧𝑧 component 𝐻𝐻0 of themagnetic field at the track center and the reader position
from the LC and HC layers for the down-track direction
using 3 grains for the cross-track direction. The peak 𝑧𝑧
component 𝐻𝐻0ABC* values are 1151 and 570 Oe from the
LC and HC layers, respectively, where ℎ4)5 is 4.0 nm.
3.1.1 Temperature profile
Figure 4 shows the temperature profiles calculated
employing a heat transfer simulation for the cross-track
direction. The solid lines indicate the temperatures atthe layer boundaries, and the dotted lines indicate thoseat the layer centers.
(a) When writing in the LC layer (LC writing), thetemperature at 𝑦𝑦 = ± 6.0 nm and 𝑧𝑧 = − 2.25 nm is
𝑇𝑇#" + 2𝜎𝜎8#" = 676 K at which 𝜕𝜕𝑇𝑇# /𝜕𝜕𝜕𝜕 is 12.0 K/nm. The
Δ𝑇𝑇!# value is −42 K.

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INDEX(a)(a) 𝜕𝜕𝑇𝑇# /𝜕𝜕𝜕𝜕 = 12.0 K/nm(b)Fig. 3 (a) Layer structure for LC / HC and (b) fieldstrength 𝐻𝐻0 from LC and HC layers for the down-track
direction.
(b) When writing in the HC layer (HC writing), thetemperature at 𝑦𝑦 = ± 6.0 nm and 𝑧𝑧 = − 8.5 nm is
𝑇𝑇!" + 2𝜎𝜎8!" = 780 K at which 𝜕𝜕𝑇𝑇! /𝜕𝜕𝜕𝜕 is 9.0 K/nm. The
𝑇𝑇$%94 value is 957 K. It should be noted that thetemperature of the LC layer (𝑧𝑧 = −2.25 nm) in the centerof adjacent tracks (𝑦𝑦 = ±18.0 nm) is 671 K, which ishigher than 𝑇𝑇#" , and HC writing will erase the data of
the LC layer in the adjacent tracks. Therefore, it isnecessary to devise a suitable writing method to address
this issue, e.g. combination with shingled magnetic
recording.
The results obtained for 𝑇𝑇!" = 750 K are summarizedin Table 3 (a). The 𝑇𝑇$%94 value of 957 K is relatively highsince HC is the lower layer. This is disadvantageous interms of the heat resistance of the writing head and/or
the surface lubricant.
We have reported as regards the thermal gradient in
3D HAMR3):(1) The thermal gradient for the upper layer isintrinsically larger than that for the lower layer due to aheat flow in the in-plane direction in the deep part of thelayer.
(2) The thermal gradient for the HC layer is intrinsicallylarger than that for the LC layer due to their respective
Curie temperatures.
The difference between the thermal gradients for LC andHC writing is relatively small due to the combinations of
the upper LC layer and the lower HC layer.

(b) 𝜕𝜕𝑇𝑇! /𝜕𝜕𝜕𝜕 = 9.0 K/nm
Fig. 4 Temperature profile in the cross-track direction
for an LC (upper) / HC (lower) layer structure whilewriting in the (a) LC and (b) HC layers.
The Δ𝑇𝑇!# value of −42 K is negative, which meansthat the temperature in the HC layer while writing in
the LC layer is lower than that in the LC layer, and thisis advantageous in relation to the information stability
in the HC layer.
By reducing 𝑇𝑇!" , 𝑇𝑇$%94 can be reduced. Furthermore,
the heating power 𝑃𝑃D can also be reduced. The resultsfor 𝑇𝑇!" = 725 K are summarized in Table 3 (b). In
comparison with the result for 𝑇𝑇!" = 750 K, 𝑇𝑇$%94 is
reduced to 920 from 957 K and 𝑃𝑃D can be reduced to 0.94.

3.1.2 Information stability for 10 years of archiving
We estimated the information stability for 10 years ofarchiving with no writing field 𝐻𝐻D using the grain error
probability. The storage temperature is 350 K since wetake a certain margin for temperature into account. The
calculation bit number was 1E+7. The allowable bER is
assumed to be 1E−3.

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Table 3 Results of heat transfer simulation for LC / HClayer structure ((a) 𝑇𝑇!" = 750 and (b) 725 K).
(a)

1.1E−3. On the other hand, bER EFE = 1E−3 is allowable
for the HC layer since there was no change in bER overten years.

(b)

(a)

Grain error distributions are shown in Figs. 5 (a) LC
and (b) HC layers for 10 and 0.001 yrs where 0.001 yrs
corresponds to about 9 hrs. The peaks in the figures
represent grain error, and the 𝐸𝐸[𝑀𝑀$ ] value is negative
for 5 or more grain errors since the total grain number isnine. For (a) the LC layer, 3 grain errors can be seen evenafter 0.001 yrs, and 5 grain errors will occur after 10 yrs
since the LC layer has a low Curie temperature and athin layer. For (b) the HC layer, only 1 grain error canbe seen after both 0.001 and 10 yrs due to a high Curie
temperature and a thick layer.
Figure 6 shows bER as a function of 𝐸𝐸=> for 10 years
of archiving. The second horizontal axis is the lowest 𝐻𝐻+value that must be readable without error, which wasestimated using Eq. (5). 𝐸𝐸=> values of 0.581 and 0.744
are required for the LC and HC layers, respectively.
The information will be degraded in the LC layer andit will be scarcely degraded in the HC layers as shown in
Fig. 5. Figure 7 shows time dependence of bER. Errors
increase over time in the LC layer, and the error does notincrease in the HC layer with both 𝑇𝑇!" = 750 K and 725
K (not shown). The bit error rate bER.+ after 10 years ofarchiving is expressed as
bER.+ = bER EFE + ΔbER,(6)where bER EFE and ΔbER are the initial bit error rate
before archiving and the increase in the bit error rateduring archiving, respectively. For the LC layer, ΔbER
is about 1E−3 for 𝐸𝐸=> = 0.581. Therefore, bER EFE must
be low, for example, 1E−4. In this case, bER.+ will be
20(b)Fig. 5 Number of bits against expected value ofmagnetization during 10 years of archiving for the LC /HC layer structure ((a) LC and (b) HC layers).

Fig. 6 Bit error rate as a function of error threshold andnormalized field amplitude for 10 years of archiving for
the LC / HC layer structure.

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Fig. 7 Time dependence of bit error rate for 10 years ofarchiving for the LC / HC layer structure.
3.1.3 Information stability in HC layer while writing in
LC layer
We estimated the information stability in the HC layer
while writing in the LC layer using the temperature
profile in 3.1.1 and the grain error probability. The
writing field 𝐻𝐻D and time 𝑡𝑡 were assumed to be −10
kOe and 1 ns, respectively. Since the temperature of the
2nd row grains (track center, 𝑖𝑖 = 2) is higher than thatof the 1st row grains (track edge, 𝑖𝑖 = 1), the number ofbits against 𝐸𝐸[𝑀𝑀$< ] averaged over one-row grains isshown in Fig. 8. The 𝐸𝐸[𝑀𝑀$< ] value is negative for 2 or 3
grain errors since the total row grain number is three.
The grain error is higher for 𝑖𝑖 = 2 due to its higher
temperature. For (a) 𝑇𝑇!" = 750 K, only 1 grain error
occurs at most in each row, and the number of errors in
one bit is at most 3 in 9. On the other hand, there is 1
grain error at 𝑖𝑖 = 1, and 2 grain errors at 𝑖𝑖 = 2 for (b)𝑇𝑇!" = 725 K. The number of errors in one bit is at most
4 in 9. Therefore, the information in the HC layer isalmost stable during writing in the LC layer.
Figure 9 shows bER as a function of 𝐸𝐸=> and 𝐻𝐻+
during writing in the LC layer. When 𝑇𝑇!" = 750 K, theresults in Figs. 6 (HC layer) and 9 (𝑇𝑇!" = 750 K) arealmost the same. Therefore, the information in the HC
layer is scarcely degraded. Furthermore, there is a little
degradation in the information for 𝑇𝑇!" = 725 K. Since
there was no change in bER over ten years in the HC
layer, a bER EFE of 1E−3 in the HC layer after writing in
the LC layer can be allowable, and 𝐸𝐸=> values of 0.736
and 0.672 are required for 𝑇𝑇!" = 750 and 725 K,
respectively.
In short, the results obtained in 3.1.2 and 3.1.3 aresummarized in Table 4.
Although the 𝐻𝐻0ABC* value is high for the LC layer asshown Fig. 3 (b), 𝐸𝐸=> and 𝐻𝐻+ are low. On the other hand,
𝐸𝐸=> and 𝐻𝐻+ are high in the HC layer for which 𝐻𝐻0ABC* islow.
The bER value in the HC layer with 𝑇𝑇!" = 725 K ishigher after writing in the LC layer as shown in Fig. 8.
However, the HC layer with 𝑇𝑇!" = 725 K as well as thatwith 𝑇𝑇!" = 750 K may also be a candidate for 3D HAMR
media with the aim of lowering 𝑇𝑇$%94 .

(a)

(b)
Fig. 8 Number of bits against the expected value ofmagnetization in the HC layer while writing in the LC
layer for LC / HC layer structure ((a) 𝑇𝑇!" =750 and (b)725 K).

Fig. 9 Bit error rate in the HC layer as a function of theerror threshold and normalized field amplitude whilewriting in the LC layer for LC / HC layer structure.

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Table 4 Information stability results for LC / HC layer
structure ((a) 𝑇𝑇!" = 750 and (b) 725 K).
(a)

(b)

(a)

3.2 HC / LC layer structure
Next, we discuss the structure as shown in Fig. 10 (a)where the upper layer is an HC layer with 𝑇𝑇!" = 750 K
and ℎ!" = 3.5 nm, and the lower layer is an LC layer
with 𝑇𝑇#" = 550 K and ℎ#" = 7.0 nm. The 𝑇𝑇#" value
must be reduced to realize information stability in the
HC layer while writing in the LC layer since the Δ𝑇𝑇!#
value is positive, which means that the temperature in
the HC layer while writing in the LC layer is higher thanthat in the LC layer. Furthermore, the ℎ#" value must
be increased to realize information stability in the LC
layer for 10 years of archiving since 𝑇𝑇#" became low.
Figure 10 (b) shows 𝐻𝐻0 at the reader from the HC andLC layers for the down-track direction. The 𝐻𝐻0ABC*
values are 1139 and 513 Oe from the HC and LC layers,respectively, where ℎ4)5 is 4.0 nm.

3.2.1 Temperature profile
The results for the HC / LC layer structure aresummarized in Table 5. The 𝑇𝑇$%94 value of 874 K isrelatively low since the HC layer is the upper layer. Thisis advantageous in terms of heat resistance.
The difference between the thermal gradients for HC
and LC writing is relatively large due to the
combinations of the upper HC layer and the lower LC
layer. This may be disadvantageous in relation to HC
and LC writing3). If 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 is too large, the writing
temperature decreases before writing, and write-error
increases. If 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 is too small, it is difficult to reduce
the writing temperature, and the magnetization isreversed by the head field when writing the next bit.
Then, erasure-after-write increases. Furthermore, if𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 is small, the information in tracks adjacent to thewriting track becomes unstable. Therefore, a small
difference in the thermal gradients for HC and LC
writing is preferable in terms of the writing property.
The Δ𝑇𝑇!# value of 35 K is positive. Therefore, the 𝑇𝑇#"value must be reduced to realize information stability in
the HC layer while writing in the LC layer, and ℎ#"must be thick to achieve information stability in the LC
layer during 10 years of archiving.
Table 5 Results of heat transfer simulation for HC / LClayer structure.

(b)
Fig. 10 (a) Layer structure for HC / LC and (b) fieldstrength 𝐻𝐻0 from the HC and LC layers for the downtrack direction.

22

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3.2.2 Information stability for 10 years of archiving
Figure 11 shows the bER as a function of 𝐸𝐸=> and 𝐻𝐻+
for 10 years of archiving. In comparison with the resultsin Fig. 6, the information stability in the HC layer has
degraded since ℎ!" became thin. And although 𝑇𝑇#"
became low, the information stabilities in the LC layer
in Figs. 6 and 11 are roughly the same since ℎ#" became
thick.
The time dependence of bER is shown in Fig. 12. Incomparison with Fig. 7, errors increase over time in boththe HC and LC layers since ℎ!" became thin.

Fig. 13 Bit error rate in the HC layer as a function oferror threshold and normalized field amplitude whilewriting in the LC layer for the HC / LC layer structure.

Fig. 11 Bit error rate as a function of error threshold andnormalized field amplitude for 10 years of archiving for
the HC / LC layer structure.

The results obtained in 3.2.2 and 3.2.3 aresummarized in Table 6.
The 𝐻𝐻0ABC* value is low for the LC layer as shown Fig.
10 (b), and 𝐸𝐸=> and 𝐻𝐻+ for 10 years of archiving are also
low for the LC layer. Increasing the 𝑇𝑇#" or ℎ#" value isnecessary if we are to increase 𝐸𝐸=> and 𝐻𝐻+ . However,increasing the 𝑇𝑇#" value leads to degradation of theinformation in the HC layer when writing in the LC
layer since the writing temperature in the LC layer
increases.
Table 6 Information stability results for HC / LC layer
structure.

Fig. 12 Time dependence of the bit error rate for 10 years
of archiving for the HC / LC layer structure.
3.2.3 Information stability in HC layer while writing in
LC layer
Figure 13 shows the bER in the HC layer as a functionof 𝐸𝐸=> and 𝐻𝐻+ during writing in the LC layer. Since theinformation in the HC layer will degrade during 10 years
of archiving, bER EFE in the HC layer after writing in the
LC layer must be low, for example, 1E−4. Therefore, an
𝐸𝐸=> value of 0.598 is required.

4. Conclusions

We examined the medium layer structure in 3D
HAMR at 2 Tbpsi (total density of 4 Tbpsi), taking
account of a heat transfer simulation and information
stability in high Curie temperature 𝑇𝑇!" (HC) and low
Curie temperature 𝑇𝑇#" (LC) layers.
(1) An LC (𝑇𝑇#" = 650 K, 4.5 nm) / HC (𝑇𝑇!" = 750 K, 6.0nm) layer structure
The medium surface temperature 𝑇𝑇$%94 while writingin the HC layer is relatively high since the HC layer isthe lower layer. This is disadvantageous in terms of the

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heat resistance of the writing head and/or the surface
lubricant.
The temperature in the HC layer while writing in the
LC layer is lower than that in the LC layer, and this isadvantageous in relation to the information stability in
the HC layer.
Although the bit error rate in the HC layer with 𝑇𝑇!"= 725 K is higher than that with 𝑇𝑇!" = 750 K after
writing in the LC layer, the HC layer with 𝑇𝑇!" = 725 K
may also be a candidate for 3D HAMR media with theaim of reducing 𝑇𝑇$%94 .
(2) An HC (𝑇𝑇!" = 750 K, 3.5 nm) / LC (𝑇𝑇#" = 550 K, 7.0nm) layer structure
The 𝑇𝑇#" value must be reduced to realize information
stability in the HC layer while writing in the LC layer.
The difference between the thermal gradients for HC
and LC writing is relatively large due to the
combinations of the upper HC layer and the lower LC
layer. This may be disadvantageous in relation to HC
and LC writing.

24

Acknowledgement We acknowledge the support of theAdvanced Storage Research Consortium, Japan.
References
1) Western Digital: private communication.
2) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 44, 34 (2020).
3) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 44, 122 (2020).
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) T. Kobayashi, Y. Isowaki, and Y. Fujiwara: J. Magn. Soc. Jpn.,
39, 8 (2015).
7) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 43, 114 (2019).
8) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 42, 110 (2018).
R eceiv ed N o v . 2 1 , 2 0 2 0 ; A ccep ted D e c. 1 7 , 2 0 2 0

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J. Magn. Soc. Jpn., 45, 25-29 (2021)<Paper>Spin Wave Resonancein Perpendicularly Magnetized Synthetic Antiferromagnets
M. Ishibashi*, Y. Shiota*, S. Funada*, T. Moriyama*, and T. Ono*, ***Institute for Chemical Research, Kyoto University,

Uji, Kyoto 611-0011, Japan**Center for Spintronics Research Network, Graduate School of Engineering Science, Osaka University

Toyonaka, Osaka 560-8531, Japan,

We report antiferromagnetic spin wave resonance in perpendicularly magnetized synthetic antiferromagnets
consisting of Co/Ni multilayers and a thin Ru spacer layer. Two resonance modes were observed in the finite range ofthe out-of-plane bias magnetic field, where two magnetic moments separated by the Ru layer were
antiferromagnetically aligned. These two modes show an opposite dependence on the bias magnetic field andcorrespond to right- and left-handed polarized spin waves. We also theoretically derive the spin wave dispersion forthe perpendicularly magnetized synthetic antiferromagnets on the basis of an equation of motion. Our experimental
results show good agreement with the theoretical analysis.
Key words: antiferromagnetic spin wave, perpendicularly magnetized synthetic antiferromagnets, polarized spinwaves, spin wave resonance, multilayers
1. Introduction
Spin waves are collective excitations of orderedmagnetic moments in materials and can be used as
information carrier and for processing 1)-3). So far, mostspin-wave devices have been based on ferromagnetic spinwaves, and they mainly use spin wave amplitude 4)- 7) andphase 8)- 10) to encode information. Unlike ferromagnetic
spin waves, spin waves in colinear antiferromagnets
have both right- and left-handed polarizations 11)-12), as
shown in Fig. 1. The polarity of antiferromagnetic spinwaves is attracting much attention in the recent research
field of magnonics, as a new degree of freedom 13)-14), in
addition to the amplitude and phase. In the past several
decades, magnetic resonances with the two kinds ofpolarities
wereobserved
inuniaxial
crystalantiferromagnets such as MnF2 15) or FeF2 16). However, it
is difficult to excite or manipulate spin waves in crystal
antiferromagnets, because they have high resonancefrequency of THz regime due to strong exchange coupling.
Recent works have focused on not only crystal
antiferromagnets but also ferrimagnets for spin wave

Fig. 1 Schematic illustrations of magnetic oscillationsof two antiparallel sublattices for (a) right- and (b) lefthanded polarity.

polarization experiments. In the previous studies, rightand left-handed spin wave polarizations were directly
observed by inelastic neutron scattering in yttrium irongarnet 17) and switching of spin wave polarization wasobserved across the compensated temperature by
Brillouin light scattering in GdFeCo films 18).
In synthetic antiferromagnets (SAFs), two magnetic
moments separated by a thin nonmagnetic spacer are
antiferromagnetically coupled via interlayer exchange
coupling. SAFs show weaker exchange interaction thanthat in crystal antiferromagnets, hence, resonancefrequencies of SAFs are in the range of conventional
microwave electronics (several tens of GHz regime).
These features of SAFs can allow easier detection andmanipulation of the antiferromagnetic spin wave modes.
In this study, we experimentally investigate spin wave
resonance in perpendicularly magnetized SAFs byspectroscopy using a vector network analyzer.
2. Theoretical Analysis
We begin with a theoretical calculation of spin wave
dispersion for interlayer exchange coupled bilayers withperpendicular magnetic anisotropy (PMA). We consider
the system including two ferromagnetic layers FM1, FM2
with the same thickness 𝑡𝑡 , the same saturation
magnetization 𝑀𝑀s , and different magnetic anisotropy
𝐾𝐾1 ≠ 𝐾𝐾2 . Spin wave dispersion with wavevector 𝑘𝑘 can
be derived from an equation of motion (EOM) including
the dynamic dipolar field due to the nonuniform
distribution of local magnetic moments of spin waves.
The effective field 𝐇𝐇𝑖𝑖 ( 𝑖𝑖 = 1, 2 ) acting on themagnetization 𝐦𝐦𝑖𝑖 (|𝐦𝐦𝑖𝑖 | = 1) of the FM 𝑖𝑖 layer is given
by
2𝐾𝐾𝑖𝑖
𝐇𝐇𝑖𝑖 = {𝐻𝐻ext + (− 𝑀𝑀s ) 𝑚𝑚𝑍𝑍𝑍𝑍 } 𝐞𝐞𝑍𝑍 − 𝐻𝐻E 𝐦𝐦𝑗𝑗 + 𝐇𝐇dip,𝑖𝑖𝑖𝑖
𝜇𝜇0 𝑀𝑀s+ 𝐇𝐇dip,𝑖𝑖𝑖𝑖 , (𝑖𝑖, 𝑗𝑗 = 1, 2, 𝑖𝑖 ≠ 𝑗𝑗) (1)

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where 𝐻𝐻E represents the exchange field. The precessionof a magnetic moment in the FM 𝑖𝑖 layer can be expressedby normalized magnetization 𝐦𝐦𝑖𝑖 = ( 𝑚𝑚𝑋𝑋𝑋𝑋 , 𝑚𝑚𝑌𝑌𝑌𝑌 , 𝑚𝑚𝑍𝑍𝑍𝑍 ). The
Z axis is parallel to the direction of the out-of-planemagnetic field 𝐻𝐻ext and X axis is parallel to spin wave
propagation direction. The last two terms correspond to
the self- and mutual-dipolar fields (given in the Appendix
A) 19)-23).
The EOM, d𝐦𝐦𝑖𝑖 ⁄d𝑡𝑡 = −𝜇𝜇0 𝛾𝛾𝐦𝐦𝑖𝑖 × 𝐇𝐇𝑖𝑖 , can be linearized byassuming small deviation of the magnetization from thestatic magnetization direction, |𝑚𝑚𝑋𝑋𝑋𝑋 |, |𝑚𝑚𝑌𝑌𝑌𝑌 | ≪ 1, and thelinearized EOM is given by
𝑚𝑚𝑋𝑋1
𝑚𝑚𝑋𝑋1
𝑚𝑚𝑌𝑌1
𝑚𝑚
̂ ( 𝑌𝑌1 ) = 0 ,𝑖𝑖𝑖𝑖 (𝑚𝑚 ) + 𝜇𝜇0 𝛾𝛾𝐇𝐇
(2)
𝑚𝑚𝑋𝑋2
𝑋𝑋2
𝑚𝑚𝑌𝑌2
𝑚𝑚𝑌𝑌2
where 𝛾𝛾 is the gyromagnetic ratio. The resonancefrequencies 𝑓𝑓 = 𝜔𝜔/(2𝜋𝜋) are obtained as the eigenvalues
̂ , whose elements are explicitlyof the 4th order matrix 𝐇𝐇
given in the Appendix B.
In the case of antiparallel state, 𝑚𝑚𝑍𝑍1 ≃ 1 and 𝑚𝑚𝑍𝑍2 ≃ −1
(as shown in the inset of Fig.4), the two resonancefrequencies are given by
𝜇𝜇0 𝛾𝛾
√𝐻𝐻𝑎𝑎 − √𝐻𝐻𝑏𝑏 ,
𝑓𝑓1 =
(3)
2𝜋𝜋
𝜇𝜇0 𝛾𝛾
√𝐻𝐻𝑎𝑎 + √𝐻𝐻𝑏𝑏 ,
𝑓𝑓2 =
(4)
2𝜋𝜋
2
𝐻𝐻𝑘𝑘1 + 𝐻𝐻𝑘𝑘2 2 𝐻𝐻𝐴𝐴 𝑘𝑘𝑀𝑀s 𝑡𝑡
𝐻𝐻𝑎𝑎 = 𝐻𝐻ext 2 + 𝐻𝐻ext 𝐻𝐻𝐵𝐵 + 𝐻𝐻E 𝐻𝐻𝐴𝐴 +
+
,
2
4
2
2
𝐻𝐻𝐵𝐵
𝐻𝐻𝐵𝐵
𝐻𝐻𝑏𝑏 = 𝐻𝐻𝐴𝐴 {(𝐻𝐻ext + ) (4𝐻𝐻E + 𝐻𝐻𝐴𝐴 ) + (𝐻𝐻ext + ) 𝑘𝑘𝑀𝑀s 𝑡𝑡
2
2
𝐻𝐻𝐴𝐴 𝑘𝑘 2 𝑀𝑀s2 𝑡𝑡 2},+
16
where 𝐻𝐻𝐴𝐴 = 𝐻𝐻𝑘𝑘1 + 𝐻𝐻𝑘𝑘2 , 𝐻𝐻𝐵𝐵 = 𝐻𝐻𝑘𝑘1 − 𝐻𝐻𝑘𝑘2 and the effective
magnetic anisotropy field 𝐻𝐻𝑘𝑘𝑘𝑘 = 2𝐾𝐾𝑖𝑖 ⁄(𝜇𝜇0 𝑀𝑀s ) − 𝑀𝑀s . For
spin waves with 𝑘𝑘= 0 𝜇𝜇m−1 , the resonance frequencies
become simpler forms as below
𝜇𝜇0 𝛾𝛾𝑓𝑓± ={±(2𝐻𝐻ext + 𝐻𝐻𝑘𝑘1 − 𝐻𝐻𝑘𝑘2 )4𝜋𝜋+ √(𝐻𝐻𝑘𝑘1 + 𝐻𝐻𝑘𝑘2 )(4𝐻𝐻𝐸𝐸 + 𝐻𝐻𝑘𝑘1 + 𝐻𝐻𝑘𝑘2 )}. (5)𝑓𝑓+ (𝑓𝑓− ) increases (decreases) linearly with the applied
out-of-plane magnetic field. Here, 𝑓𝑓+ ( 𝑓𝑓− ) is theresonance frequency for right (left)-handed polarization24)-25) shown in Fig. 1.

190 mT). From this result, we determined the saturation
magnetization 𝑀𝑀𝑠𝑠 = 7.0 × 105 A/m and the exchange
field 𝜇𝜇0 𝐻𝐻E = 𝐽𝐽/𝑀𝑀𝑠𝑠 𝑡𝑡 = 180 mT , where the symbol of 𝐽𝐽
represents the interlayer exchange coupling 26).

Fig. 2 Magnetic hysteresis loop measured at 300 K
under out-of-plane magnetic field.
4. Experimental Procedure and Results
The films were patterned into 50 × 100 μm2
rectangular wires and then 80 nm-thick SiO2 was
deposited for electrical isolation. Subsequently, wefabricated coplanar waveguides for spin wave resonance(SWR) as shown in Fig. 3 (a). Coplanar wave guides were
designed for excitation of spin waves with 𝑘𝑘 = 1.2 μm-1.
Re [𝑆𝑆11 ] spectra were obtained by spectroscopy using avector network analyzer at a given out-of-plane magnetic
field. Figure 3 (b) shows a contour plot of SWR spectra
generated from the obtained Re [𝑆𝑆11 ] spectra. The appliedmagnetic field swept from 250 mT to –250 mT with a stepof 10 mT. Two resonance modes were observed from 130
mT to –190 mT, where the two magnetic moments were
antiferromagnetically aligned. The slight difference ofthe field range for the antiparallel state between SQUID
and SWR measurements can be due to undesirable
changes in the properties of the films during thepatterning process. The observed two modes cross at –100 mT and are split by the out-of-plane magnetic field.

3. Magnetic Properties for Sample Films
Films of Ta(3.0) / Pt(2.0) / [Co(0.2) / Ni(0.7)]5 / Co(0.2) /Ru(0.5) / [Co(0.2) / Ni(0.7)]5 / Co(0.2) / Ru(3.0) (unit: nm)
were deposited using dc magnetron sputtering on
thermally oxidized Si substrates. Two ferromagnetic
layers consisting of Co/Ni multilayers are separated by a
0.5 nm-thick Ru layer. Figure 2 shows out-of-planemagnetic
hysteresis
loop
obtainedbyusing
superconducting
quantuminterference
devicemagnetometer. Magnetic moments in the twoferromagnetic layers are perpendicular to the film planeand fully compensated under the out-of-plane magnetic
field from 160 mT to −190 mT (from −160 mT to26

Fig.3 (a) Optical micrograph of device for investigatingof SWR spectra. Bias magnetic field was applied out ofplane. (b) Contour plot of Re [𝑆𝑆11 ].

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5. Discussion
In our experimental case, the attenuation length isestimated to be less than 50 nm from the calculation of
𝐿𝐿 = 𝑣𝑣g ⁄(2𝜋𝜋𝜋𝜋𝜋𝜋) where 𝐿𝐿 represents the attenuation
length, 𝑣𝑣g = 𝜕𝜕(2𝜋𝜋𝜋𝜋)⁄𝜕𝜕𝜕𝜕 represents the group velocity,
𝑓𝑓 represents the resonance frequency expressed by Eqs.
(3) (4) and 𝛼𝛼 = 0.024 represents the damping constantfor Co/Ni multilayers 27). Our coplanar waveguides shownin Fig.3 (a) have a distance of 1 μm between signal andground antennas. These conditions imply that excitedspin waves under one antenna decay before they reachthe other two antennas, and that spin waves under eachantenna can be regard as localized uniform precession
mode. Therefore, we analyzed our experimental datawith the resonance frequencies for spin waves with 𝑘𝑘 = 0
μm−1 . We can obtain the average of PMA for two
ferromagnetic layers (𝐾𝐾1 + 𝐾𝐾2 )⁄2, by linear fitting of theexperimental data above 140 mT and below –200 mT
with Eq.(17) for parallel state (the details are in the
Appendix C). On the other hand, we can obtain the
difference of PMA (𝐾𝐾2 − 𝐾𝐾1 )⁄2 by linear fitting of theexperimental data from –190 to 130 mT with Eq. (5) for
antiparallel state, because the intersection magnetic
field of the two antiferromagnetic resonance modes isgiven by (𝐻𝐻𝑘𝑘2 − 𝐻𝐻𝑘𝑘1 )⁄2 which represents the differenceof the effective magnetic field between the twoferromagnetic layers as predicted in a previous report 28).
While our films consist of two ferromagnetic layers withthe same structure, the experimental results shown in
Fig. 3 (b) suggests that they have different PMA,
indicating the Pt under layer induces the stronger PMA
in the adjacent (lower) ferromagnetic layer.
Figure 4 shows the applied magnetic field dependenceof the resonance frequencies obtained from thetheoretical spin wave dispersion for 𝑘𝑘 = 0 μm−1 (Blacklines represent parallel state case, while red and bluelines represent antiparallel state case.) withexperimentally determined parameters (𝛾𝛾 = 1.88 × 1011
rad/Ts, 𝑀𝑀s = 7.0 × 105 A/m ,𝑡𝑡 =4.7 nm, 𝐽𝐽 = 5.9 × 10−4
J/m2, 𝐾𝐾1 = 5.4 × 105 J/m3, 𝐾𝐾2 = 4.7 × 105 J/m3), which
gives a good agreement with our experimental data
shown in Fig. 3 (b). For the case of parallel state, two
resonance frequencies 𝑓𝑓P_In and 𝑓𝑓P_Out are theoreticallyderived (Eqs. (17) (18) in the Appendix C), corresponding
to in-phase and out-of-phase precession modes. It should
be noted that it is difficult to observe the magnetic
resonance for the out-of-phase precession mode, because
two ferromagnetic layers are almost identical. For thecase of antiparallel state, with comparison of theexperimental results and the theoretical analysis, ourobserved two resonance modes showing opposite
tendencies with the bias magnetic field can be presumed
to be 𝑓𝑓± in Eq. (5), corresponding to right- and lefthanded polarized spin waves. These two oppositely
polarized modes are degenerated at the cross point.
6. Conclusion
In summary, we experimentally and theoreticallydemonstrated spin wave resonance in perpendicularly
magnetized SAFs. In the finite range of the applied outof-plane magnetic field, two resonance modes for
antiferromagnetic state were observed, and theycorrespond to right- and left-handed polarized spin waves.
Our findings will give a route to spin-wave-devices
utilizing spin wave polarization, based on SAFs.
Acknowledgements This work was partially supportedby the JSPS KAKENHI Grant Numbers JP15H05702,
JP18K19021, JP20H00332, JP20K15161, JP20J15421,
and by the Collaborative Research Program of theInstitute for Chemical Research, Kyoto University, andby the Cooperative Research Project Program of the
Research Institute of Electrical Communication, Tohoku
University.

Appendix

Fig.4 Applied magnetic field dependence of resonancefrequencies calculated by theoretical spin wave
dispersion with 𝑘𝑘 = 0 μm−1 [ 𝑓𝑓+ and 𝑓𝑓− are for case of
antiparallel state Eq. (5)]. 𝑓𝑓P_In and 𝑓𝑓P_Out are for caseof parallel state [ Eqs. (17) (18) in Appendix C].

A. Self-dipolar field and mutual dipolar field
For interlayer exchange coupled bilayers with PMA,
magnetostatic energy per unit area is given by
𝜇𝜇0
𝐸𝐸 = − ∑𝜇𝜇0 𝑀𝑀S 𝑡𝑡𝑖𝑖 𝐦𝐦𝑖𝑖 ∙ 𝐇𝐇ext − ∑(𝐾𝐾𝑖𝑖 𝑡𝑡𝑖𝑖 − 𝑀𝑀S 2 )𝑚𝑚𝑍𝑍𝑍𝑍 22𝑖𝑖=1,2𝑖𝑖=1,2+ 𝐽𝐽𝐦𝐦1 ∙ 𝐦𝐦2 ,(6)
where 𝐇𝐇ext = (0, 0, 𝐻𝐻ext ),, 𝑍𝑍 axis is perpendicular to thefilm plane, 𝑋𝑋 axis is parallel to the spin wave
propagation direction, the first term is Zeeman energy,
the second term is demagnetization, the third term is
PMA energy and the last term is interlayer exchange
energy.
The effective field is given by

Journal of the Magnetics Society of Japan Vol.45, No.2, 2021

27

INDEX

𝐇𝐇𝑖𝑖 = −∇𝐦𝐦𝑖𝑖 (𝐸𝐸

𝜇𝜇0 𝑀𝑀S 𝑡𝑡) + 𝐇𝐇dip,𝑖𝑖𝑖𝑖 + 𝐇𝐇dip,𝑖𝑖𝑖𝑖 , (𝑖𝑖, 𝑗𝑗 = 1, 2, 𝑖𝑖 ≠ 𝑗𝑗)(7)
where 𝐇𝐇dip,𝑖𝑖𝑖𝑖 represents the self-dipolar fields and𝐇𝐇dip,𝑖𝑖𝑖𝑖 represents the mutual-dipolar field.
𝐇𝐇dip,𝑖𝑖𝑖𝑖 and 𝐇𝐇dip,𝑖𝑖𝑖𝑖 can be obtained by using the Greenfunction 21)-23), given by−𝐺𝐺𝑃𝑃 0𝑖𝑖𝐺𝐺𝑄𝑄
00
𝐺𝐺𝑋𝑋𝑋𝑋𝑋𝑋 (𝑍𝑍 − 𝑍𝑍 ′ ) = ( 0), (8)
𝑖𝑖𝐺𝐺𝑄𝑄 0 𝐺𝐺𝑃𝑃 − 𝛿𝛿(𝑍𝑍 − 𝑍𝑍′)
where 𝐺𝐺𝑃𝑃 = (𝑘𝑘 ⁄2)exp(−𝑘𝑘|𝑍𝑍 − 𝑍𝑍 ′ |) and 𝐺𝐺𝑄𝑄 = 𝐺𝐺𝑃𝑃 sgn(𝑍𝑍 −𝑍𝑍 ′ ). The self-dipolar fields 𝐇𝐇dip,𝑖𝑖𝑖𝑖 can be calculated by
𝑡𝑡+𝑠𝑠/2
𝑀𝑀𝑠𝑠 𝑡𝑡+𝑠𝑠/2∫
𝑑𝑑𝑑𝑑 ∫
𝑑𝑑𝑍𝑍 ′ 𝐺𝐺𝑋𝑋𝑋𝑋𝑋𝑋 (𝑍𝑍
𝐇𝐇dip,𝑖𝑖𝑖𝑖 =𝑡𝑡 𝑠𝑠/2
𝑠𝑠/2− 𝑍𝑍 ′ )δ𝐦𝐦(𝑍𝑍 − 𝑍𝑍 ′ ). (9)The mutual-dipolar field 𝐇𝐇dip,𝑖𝑖𝑖𝑖 can be calculated by
𝐇𝐇dip,21 =𝑀𝑀𝑠𝑠

𝐇𝐇dip,12 =

𝑀𝑀𝑠𝑠

𝑡𝑡

𝑡𝑡

𝑡𝑡+𝑠𝑠/2

∫𝑠𝑠/2

−𝑠𝑠/2

−𝑠𝑠/2

𝑑𝑑𝑑𝑑 ∫−𝑡𝑡−𝑠𝑠/2 𝑑𝑑𝑍𝑍 ′ 𝐺𝐺𝑋𝑋𝑋𝑋𝑋𝑋 (𝑍𝑍 − 𝑍𝑍 ′ )δ𝐦𝐦(𝑍𝑍 −𝑍𝑍 ′ ), ሺͳͲሻ
𝑡𝑡+𝑠𝑠/2∫−𝑡𝑡− 𝑠𝑠/2 𝑑𝑑𝑑𝑑 ∫𝑠𝑠/2

𝑑𝑑𝑍𝑍 ′ 𝐺𝐺𝑋𝑋𝑋𝑋𝑋𝑋 (𝑍𝑍 − 𝑍𝑍 ′ )δ𝐦𝐦(𝑍𝑍 −𝑍𝑍 ′ ), ሺͳͳሻ

where δ𝐦𝐦(𝑍𝑍 − 𝑍𝑍 ′ ) represents relative perturbation
oscillation of a magnetic moment at 𝑍𝑍 ′ position against
a magnetic moment at 𝑍𝑍 position
𝑚𝑚𝑋𝑋 (𝑍𝑍 ′ )δ𝐦𝐦(𝑍𝑍 − 𝑍𝑍 ′ ) = 𝑒𝑒 −𝑘𝑘|𝑍𝑍−𝑍𝑍′| (𝑚𝑚𝑌𝑌 (𝑍𝑍 ′ )),(12)0
and 𝑠𝑠 represents the thickness of a nonmagnetic spacer
between two ferromagnetic films.
By assuming 𝑘𝑘𝑘𝑘, 𝑘𝑘𝑘𝑘 << 1, we can obtain 𝐇𝐇dip,𝑖𝑖𝑖𝑖 given by𝑘𝑘− 𝑚𝑚𝑋𝑋𝑋𝑋
2
𝐇𝐇dip,𝑖𝑖𝑖𝑖 = 𝑀𝑀s 𝑡𝑡 ( 0 ),0(13)

and we can obtain 𝐇𝐇dip,12 and 𝐇𝐇dip,21 given by𝑘𝑘− 𝑚𝑚𝑋𝑋2
2),
𝐇𝐇dip,12 = 𝑀𝑀s 𝑡𝑡 (0
𝑘𝑘
− 𝑖𝑖 𝑚𝑚𝑋𝑋2(14)

𝐇𝐇dip,21 = 𝑀𝑀s 𝑡𝑡 (

(15)

2

𝑘𝑘

− 𝑚𝑚𝑋𝑋1
20 ).
𝑘𝑘𝑖𝑖 𝑚𝑚𝑋𝑋1
2

B. Resonant frequency for antiparallel state
The spin wave resonant frequency is obtained from theEOM, d𝐦𝐦𝑖𝑖 ⁄d𝑡𝑡 = −𝜇𝜇0 𝛾𝛾𝐦𝐦i × 𝐇𝐇𝑖𝑖 , linearized by assuming|𝑚𝑚𝑋𝑋𝑋𝑋 |, |𝑚𝑚𝑌𝑌𝑌𝑌 | ≪ 1. In the case of antiparallel state, 𝑚𝑚𝑍𝑍1 ≃±1 and 𝑚𝑚𝑍𝑍2 ≃ ∓1, the linearized EOM is explicitly given
by
𝑚𝑚𝑋𝑋1
𝑚𝑚𝑋𝑋1
0
𝐻𝐻14
0 𝐻𝐻12
𝑚𝑚𝑌𝑌1
𝑚𝑚𝑌𝑌
𝐻𝐻21
0 𝐻𝐻230i𝜔𝜔 (𝑚𝑚 ) + 𝜇𝜇0 𝛾𝛾 () (𝑚𝑚 1 ) = 0. (16)0 𝐻𝐻32
0
𝐻𝐻34
𝑋𝑋2
𝑋𝑋2
𝑚𝑚𝑌𝑌2
𝑚𝑚𝑌𝑌2
𝐻𝐻41
0 𝐻𝐻430Here, the components of 4th order matrix of the effective
̂ are given by
field 𝐇𝐇
𝐻𝐻12 = 𝐻𝐻ext ± 𝐻𝐻𝑘𝑘1 ± 𝐻𝐻E ,𝐻𝐻14 = ±𝐻𝐻E ,𝐻𝐻21 = −(𝐻𝐻ext ± 𝐻𝐻𝑘𝑘1 ± 𝐻𝐻E ) ∓ (𝑘𝑘𝑘𝑘𝑘𝑘)⁄2,

28

𝐻𝐻23 = ∓𝐻𝐻E ∓ (𝑘𝑘𝑘𝑘𝑘𝑘)⁄2,
𝐻𝐻32 = ∓𝐻𝐻E ,𝐻𝐻34 = 𝐻𝐻ext ∓ 𝐻𝐻𝑘𝑘2 ∓ 𝐻𝐻E ,𝐻𝐻41 = ±𝐻𝐻E ± (𝑘𝑘𝑘𝑘𝑘𝑘)⁄2,
𝐻𝐻43 = −(𝐻𝐻ext ∓ 𝐻𝐻𝑘𝑘2 ∓ 𝐻𝐻E ) ± (𝑘𝑘𝑘𝑘𝑘𝑘)⁄2,
the resonant frequency 𝑓𝑓 = 𝜔𝜔⁄2𝜋𝜋 is eigenvalue of thê is the 4tĥ + 𝜇𝜇0 𝛾𝛾𝐇𝐇
̂ ] = 0, where 𝟏𝟏
̂ : det[𝑖𝑖𝑖𝑖𝟏𝟏
matrix 𝐇𝐇order identity matrix. The obtained two resonancefrequencies for antiparallel state are already presented
in the main text as Eqs. (3) (4).
C. Resonant frequency for parallel state
In the case of parallel state, 𝑚𝑚𝑧𝑧1 ≃ ± 1 and 𝑚𝑚𝑧𝑧2 ≃ ± 1,
the components of 4th order matrix of the effective field̂ in Eq. (16) are given by
𝐇𝐇
𝐻𝐻12 = 𝐻𝐻ext ± 𝐻𝐻𝑘𝑘1 ∓ 𝐻𝐻E ,𝐻𝐻14 = ±𝐻𝐻E ,𝐻𝐻21 = −(𝐻𝐻ext ± 𝐻𝐻𝑘𝑘1 ∓ 𝐻𝐻E ) ∓ (𝑘𝑘𝑘𝑘𝑘𝑘)⁄2,
𝐻𝐻23 = ∓𝐻𝐻E ∓ (𝑘𝑘𝑘𝑘𝑘𝑘)⁄2,
𝐻𝐻32 = ±𝐻𝐻E ,𝐻𝐻34 = 𝐻𝐻ext ± 𝐻𝐻𝑘𝑘2 ∓ 𝐻𝐻E ,𝐻𝐻41 = ∓𝐻𝐻E ∓ (𝑘𝑘𝑘𝑘𝑘𝑘)⁄2,
𝐻𝐻43 = −(𝐻𝐻ext ± 𝐻𝐻𝑘𝑘2 ∓ 𝐻𝐻E ) ∓ (𝑘𝑘𝑘𝑘𝑘𝑘)⁄2.
As well as the antiparallel state case, two resonancefrequencies can be obtained from the eigenvalues of theEq. (16) for parallel state case. For 𝑘𝑘 = 0 μm−1 , the inphase and out-of-phase resonance frequencies 𝑓𝑓P_In and
𝑓𝑓P_Out for the case of 𝑚𝑚𝑍𝑍1 ≃ 1 and 𝑚𝑚𝑍𝑍2 ≃ 1, (or 𝑚𝑚𝑍𝑍1 ≃− 1 and 𝑚𝑚𝑍𝑍2 ≃ −1) are given by
𝜇𝜇0 𝛾𝛾𝑓𝑓P_In ={2|𝐻𝐻ext | − 2𝐻𝐻E + 𝐻𝐻𝑘𝑘1 + 𝐻𝐻𝑘𝑘2
4𝜋𝜋
𝑓𝑓P_Out =+ √4𝐻𝐻E 2 + (𝐻𝐻𝑘𝑘1 − 𝐻𝐻𝑘𝑘2 )2 }.

(17)− √4𝐻𝐻E 2 + (𝐻𝐻𝑘𝑘1 − 𝐻𝐻𝑘𝑘2 )2 }.

(18)

𝜇𝜇0 𝛾𝛾
{2|𝐻𝐻ext | − 2𝐻𝐻E + 𝐻𝐻𝑘𝑘1 + 𝐻𝐻𝑘𝑘2
4𝜋𝜋

The intercept of Eq. (17) is expressed by 𝐻𝐻E , (𝐻𝐻𝑘𝑘1 + 𝐻𝐻𝑘𝑘2 )and (𝐻𝐻𝑘𝑘1 − 𝐻𝐻𝑘𝑘2 ) . The difference of effective magnetic
anisotropy field between two ferromagnetic layers(𝐻𝐻𝑘𝑘1 − 𝐻𝐻𝑘𝑘2 ) can be obtained by the intersection magnetic
field of two antiferromagnetic resonance modes
expressed by Eq. (5). Therefore, we can obtain the sum ofeffective magnetic anisotropy field (𝐻𝐻𝑘𝑘1 + 𝐻𝐻𝑘𝑘2 ).
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Received Nov. 04, 2020; Accepted Jan. 05, 2021

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J. Magn. Soc. Jpn., 45, 30-36 (2021)<Paper>Vo i d - D e f e c t I nd uc e d M a g ne t i s m a nd S t r uc t ur e Cha ng e o f
Ca r b o n M a t e r i a l s - Ⅰ : G r a p he ne N a no Ri b b o n
Norio Ota and Laszlo Nemes＊

Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tenoudai Tsukuba-city 305-8571, Japan,＊
Research Center for Natural Sciences, Ötvös Lóránd Research Network, Budapest 1519, Hungary

Void-defect is a possible origin of ferromagnetic-like feature of pure carbon material. Applying density functional
theory to void-defect induced graphene-nano-ribbon (GNR), a detailed relationship between multiple-spin-state andstructure change was studied. An equilateral triangle of an initial void having six electrons is distorted to isosceles
triangle by re-bonding carbon atoms. Among possible spin-states of Sz=0/2, 2/2, 4/2 and 6/2, the most stable state
was Sz=2/2. The case of Sz=4/2 is remarkable that initial flat ribbon turned to three dimensionally curled one
having highly polarized spin configuration at ribbon edges. Total energy of Sz=4/2 was very close to that of Sz=2/2,
which suggests coexistence of flat ribbon and curled ribbon. As a model of three dimensional graphite, bi-layered
AB stacked GNR was analyzed for cases of different void position of α-site and β-site. Spin distribution was limited
to the surface layer, nothing to the back layer. Distorted void triangle show 60degree clockwise rotation from α- to
β-site, which was consistent with experimental observation using the scanning tunneling microscope. This study
revealed that void-defect in GNR induces unusual polarized spin state, different with usual ferromagnetic one.
Key words: graphene, GNR, DFT, void, ferromagnetism, spin state, STM

1 . I n tr o d u c tio n
These ten years, it was reported that some carbon
base materials show room temperature ferromagnetic
like hysteresis1)-6). They are graphite and graphene likematerials. Such a light-weight ferromagnetic likematerials will be useful for many applications.
However, such magnetic ordering could not be
thoroughly understood. Possible explanations are thepresence of impurities7), edge irregularities8)-10) or
void-defects11)-16). Here, we like to focus on void-defect.
In experiments, creation of void-defect was done byhigh energy particle irradiation on graphite11)-13).
Void-defect was observed by the scanning tunnelingmicroscope14)-16). Unfortunately, there are little
information on magnetic behaviors and spin
distributions in atomic scale. Theoretical calculations
predicted the importance of the atomic structurechange17)-18). However, there are little explanation on adetailed relationship between the multiple-spin-state
and the structure-change. Here, we try detailed
explanation by the density functional theory (DFT) 19-20).
DFT gives the stable quantum state basically at zerotemperature. In this study, we like focus on
fundamental
propertyofvoid-defectinducedmagnetism and structure change of graphene nanoribbon (GNR). Such analysis will be useful for futureadvanced study on room temperature magnetism andasking Curie-temperature.
There are six unpaired electrons around one void,which suggests a capability of multiple spin-state as
like Sz=6/2, 4/2, 2/2, and 0/2. We need detailed spin
dependent calculation to find the most stable spin stateaccompanying with the structure change Also, we will30

calculate the three-dimensional graphite using themodel of AB-stacked bi-layer GNR. Results will becompared with experimental observation by thescanning tunneling microscope.

2 . C alc u latio n M e th o d an d Mo d e l G N R
We require total energy, optimized molecular
structure and the spin density on a given spin state of
Sz. DFT based generalized gradient approximation(GGA-PBEPBE) 21) was applied utilizing Gaussian09
package22) with an atomic orbital 6-31Gd basis set23).
Total charge is set to be completely zero. Inside of asuper-cell, three dimensional DFT was applied. As
illustrated in Fig. 1, one dimensional periodic boundary
condition was applied to realize an unlimited length
GNR. Calculation is repeated until to meet theconvergence criteria on the root mean square density
matrix less than 10 -8 within 128 cycles.
An initial calculation model of GNR with single
void-defect is shown in left of Fig. 1. Super-cell was[C79H10], where upper and lower zigzag edge carbons
were all hydrogenated to avoid radical carbon edge
complicated situation. Ribbon width was 1.780nm andone-dimensional super-cell length was 1.241nm
repeating to red-line direction. A center positioned
carbon was removed to make a void-defect. Around thisvoid, there are three carbons, which make anequilateral triangle with length of 0.248nm. These
three radical carbons bring six electrons. To investigate
magnetic characteristics, we should consider these six
electrons interaction, which mean to study a detailed
multiple-spin-state analysis.

Journal of the Magnetics Society of Japan Vol.45, No.2, 2021

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was 1.49μB, which coincides well with calculation using
the SIESTA code by Yazyev and Helm17). Spin densities
of Type-A (Sz=2/2) and B (Sz=2/2) were illustrated inFig. 4 at a surface of electron density of 1e/nm3. In bothcases, we can see a large up-spin cloud (red) at a void
triangle’s apex carbon site. We can see fruit pear like
up-spin cloud with sum of 1.37μB, which was 0.12μB
smaller than initial one. Inside of GNR, there appearsup (red) and down (blue) spins alternatively9-10).

Fig. 1 Initial void-defect is created on GNR. Six spinsin a void carry the multiple spin state. Unit cell is[C79H10]. DFT calculation is done three dimensionallyinside of unit cell, which is repeated one dimensionally
toward a red line direction.
.

3 . Mu ltip le Sp in S tate

For six electrons in a void-defect, there are fourcapable spin states of Sz=0/2, 2/2, 4/2 and 6/2. However,
we could not get any converged calculation on singlet
spin state of Sz=0/2. The reason will be explained as
illustrated on right of Fig. 1 that one radical carbon
holds two spins, which should be parallel to avoid
unlimited large coulomb energy due to Hund’s rule24),
in case of one central attractive force by the samecarbon atom. Three pairs of parallel spins enable themultiple-spin-state of Sz=6/2, 4/2, or 2/2. For every spinstate, stable atomic structures are classified to two
types as Type-A and -B as shown in Fig. 2 as (b) and (c).
It should be noted that initial equilateral triangle (a)turned to an isosceles one of (b) and (c). Isosceles
triangle of Type-A was perpendicular to a ribbon axis ofa red line, whereas Type-B tilted. Such distortion
originates from the quantum mechanical re-bonding as
discussed by Yazyev and Helm17). Detailed results wereshown in Fig. 3 and Table 1. Initial non-deformed
ribbon energy was defined to be zero. In Type-A, themost stable spin state was Sz=2/2. Energy level was
reduced to -12.31kcal/mol., where triangle has an angleof 49degree as shown in (b). Type-B show remarkableenergy reduction. In case of Sz=2/2 of Type-B, energy
became -15.62kcal/mol, which is most stable one with asharper angle of 44degree in (c). Distance between
carbon-atom “a” and “c” was shortened to 0.192nm fromoriginal 0.248nm. This suggests a capable origin ofstructure change that original pi-electron conjugatedbond is partially modified to double-bond among
hexagon carbon networks.
Sum of spin density around initial equilateral void

Table 1 Calculated result for mono layer GNR.
Fig. 2 Initial void makes equilateral triangle. Type-A
has an isosceles triangle perpendicular to GNR,
whereas Type-B tilted.

Fig. 3 Energy difference and void structure change.
Type-A show distorted isosceles void triangle of
49degree perpendicular to ribbon as shown in (b).
Type-B shows a tilted triangle with 44degree. In every
type, triplet spin-state of Sz=2/2 is most stable.

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Table 1 Calculated result for mono layer GNR.

4. C u r le d r ibbo n.
Fig. 4 Irregular up-spin cloud (by red) was observed at
centered void triangle for both Type-A and -B. Inside ofribbon, there appear alternate up-spin (red) anddown-spin (blue).

32

Amazing result was obtained in case of Sz=4/2 ofType-B as illustrated on Fig. 5(d), where appears acurled ribbon. While in case of Sz=2/2, ribbon is flat in(c). Void triangle of Sz=4/2 was 40.6degree comparing
with 43.5 degree of Sz=2/2. The spin distribution is
ferromagnetic like for Sz =4/2 as illustrated in Fig. 6(d).
Both of upper and lower ribbon edges carry up-spinclouds. While in case of Sz=2/2 of Fig. 6(c), we can see
anti-ferromagnetic like feature. It should be noted thatenergy of Sz=2/2 was -15.6kcal/mol., whereas Sz=4/2 was-15.5kcal/mol. They are only 0.1kcal/mol. difference.
Such close energy suggests the coexistence both of flat
ribbon and curled ribbon. Spin configuration of Fig
6(d) looks ferromagnetic like arrangement. Edgecarbons are strongly magnetized by up-spins. However,it should be noted that each up-spins are isolated withneighbor edge spins. There is no exchange interaction
between them. On the contrary, as studied in ourprevious paper on FeO-modified GNR25), edge carbons
were highly polarized by up-spins, and also coupledwith neighbor edge spins by super-exchange interaction.
It was usual ferromagnetic coupling. By suchcomparison, void induced GNR show unusual strongly
polarized spin configuration, different with usual
ferromagnetic one.

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5. B i- lay e r G N R

Fig. 5 In case of Sz=4/2 of Type-B, ribbon is curled asshown in (d), whereas for Sz=2/2 ribbon is flat (c).

To simulate three-dimensional graphite, bi-layered AB
stacked GNR was analyzed. In Fig. 7, yellow marked
atoms are surface (first) layer atoms including single
void, whereas gray atoms are back (second) layer
without any void. There are two types of void positions,which one is α-site void positioned over one carbon of
the second layer (back side), whereas β-site positioned
over inter-atom space. Unit cell is [C79H10-C80H10].
Distance between two layers was calculated to be from0.409 to 0.413nm depending on void situation as shownin Table 2. We can see deformed void triangle asclassified by Type-A and Type–B as shown in Fig. 8. In
every Type, the most stable spin state was Sz=2/2. Totalenergy of Type-B was lower (stable) than that of Type-A.
Distorted triangle of Type-B shows small angle of42degree compared with 53degree of Type-A. It should
be noted that, in case of Type-B, total energy is almost
similar for α-site (-14.59kcal/mol.) and β-site(-14.69kcal/mol.). We can expect coexistence of bothsites. Detailed results are summarized in Table 2. In
Fig. 9, spin density of AB-stacked bi-layer GNR was
illustrated. Spin density appeared only to the surface(first) layer. Back (second) layer shows no spin.
Summed spin-density around one void was 1.37μB.

6 . C o m p a r i so n w i t h e x p e r i m e n t s
6 . 1 O b se r v a t i o n o f v o i d - d e f e c t

In 1998, Kerry et al.14) observed void-defect on thesurface of graphite by the scanning tunnelingmicroscope. They observed triangle shape bright spot,
which suggested large excess electrons inside of triangle
void. Our calculation is consistent with suchobservation.

6 . 2 O b se r v a t i o n o f r o t a t i o n a l sy m m e t r y o f v o i dde f e ct

Notable result is the clockwise angle of a void triangle
defined in the figure on bottom of Table 2. The
clockwise angle θ of α-site void triangle was 300degree,whereas β-site 240degree. There appear 60degrees
rotation from β-site to α-site. Such calculation isconsistent with observation on graphite surface done by
Ziatdinov et al.16) using the scanning tunnelingmicroscope.

Fig. 6 In case of Sz=2/2 for Type-B, spin configuration is
ferrimagnetic-like as shown in (c). Whereas in case of
Sz=4/2, it is ferromagnetic-like (d).

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Fig. 7 Void-defect was created on AB-stacked bi-layer GNR with a void at α-site (top panel) and β-site (bottom).
Yellow atoms are surface layer carbon, whereas gray atoms back layer one.
Table 2 Calculated results of bi-layer GNR with single void. Cases are classified for Type-A or Type-B, and for void
positions of α-site or β-site.

34

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Fig. 8 Energy and void triangle are compared in AB-stacked bi-layer GNR.

Fig.9 Spin density configuration of AB-stacked bi-layer GNR, where red cloud shows up-spin and blue one
down-spin. Spin appears only to the surface layer. Back layer shows no spin.

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7 . C o n c l u si o n
Applying density functional theory to a void-defect ingraphene-nano-ribbon (GNR), a relationship between
multiple-spin-state and structure change was studied.
An equilateral triangle of initial void was distorted to
isosceles triangle due to re-bonding of excess six
electrons in a void. Such calculation is consistent withactual observation by the scanning tunnelingmicroscope. Six electrons enable the multiple spin-stateof Sz=6/2, 4/2 and 2/2 due to the Hund’s rule. The moststable spin state was Sz=2/2 showing flat ribbon
structure. Amazing result was obtained for Sz=4/2,
where ribbon was three dimensionally curled, and show
ferromagnetic like spin distribution on both upper andlower edges of the ribbon. Energy of Sz=2/2 and Sz=4/2
were close, almost same. This suggests coexistence offlat and curled ribbon. As a model of three-dimensionalgraphite, bi-layered AB stacked GNR was analyzed for
different void positions of α-site and β-site. Both sites
show similar energy. Void triangle presents 60 degrees
clockwise rotation from β-site to α-site. It should be
noted that such void rotation coincides well with actual
observation. This study revealed that void-defect in
GNR induces unusual highly polarized spin state,different with usual ferromagnetic one.

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and T. Enoki: Phys. Rev. B, 89, 155405 (2014).
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Re c e i v e d O c t . 2 5 , 2 0 2 0 ; Ac c e pt e d J u n . 1 2 , 2 0 2 1

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J. Magn. Soc. Jpn., 45, 37-40 (2021)<Paper>Anomalous Nernst and Seebeck effects in NiCo2 O4 films
Hiroki Koizumi, Atsushi Hidaka, Takashi Komine∗ , and Hideto Yanagihara,∗∗Department of Applied Physics, University of Tsukuba, Tsukuba,1-1-1 Ten-nodai, Tsukuba, Ibaraki 305-8573, Japan∗
Graduate School of Science and Engineering, Ibaraki University,4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan∗∗
Tsukuba Research Center for Energy Materials Science (TREMS), University of Tsukuba,1-1-1 Ten-nodai, Tsukuba, Ibaraki 305-8573, Japan

We investigated both the Seebeck and anomalous Nernst eﬀects in NiCo2 O4 (001) epitaxial films with a preferential magnetization
direction normal to the film plane. Since the thermoelectric signals were extremely small, we custom-built a measurement system todetect the weak voltage signals. To suppress spurious voltage signals originating from the electrical contacts in the measurement
circuit, we employed the following measures. We reduced the number of electrical contacts between the output of a commercial
cryostat with a superconducting magnet and the nano-voltmeters. We employed silver soldering while making the electrical contacts to
reduce the thermal electromotive force voltages at the remaining contacts. By adopting these measures, we have succeeded in detecting
thermoelectric voltages as small as 5 nV. The observed thermoelectric eﬃciency of NiCo2 O4 is quite small compared to conventional
ferromagnetic metals.
Key words: NiCo2 O4 , Anomalous Nernst eﬀect, Perpendicular magnetic anisotropy
1 Introduction
In the recent past, diﬀerent types of energy conversion technologies have been studied due to the increasing need for alternative and sustainable energy sources 1, 2) . Among the energy
conversion technologies, the thermoelectric device has received

perature gradient. Therefore, PMA can be a crucial factor for
generating large ANE voltage 3, 10) .
Oxide-based thermoelectric materials have many advantages
such as the following: they are non-toxic and non-polluting; they
can be synthesized in the air and do not need inert conditions

much attention as it enables the direct conversion of waste heat
energy into electrical energy 3, 4) . Moreover, thermoelectricity isor vacuum; they are stable even at high temperatures. Theseadvantages make oxide thermoelectric materials a potential candidate for practical applications at elevated temperatures. As ainteresting from the perspective of condensed matter physics be-candidate oxide thermoelectric material with PMA, we focusedcause it depends on the electrical and thermal transport phenomena, which are intrinsically related to the electronic state of ma-

on NiCo2 O4 (NCO). NCO has an inverse spinel-type structureterials. Particularly in magnetic materials, the temperature gradient can be converted into electrical voltage through thermomagnetic phenomena, such as the anomalous Nernst eﬀect (ANE) andthe spin Seebeck eﬀect

5, 6). Another transport phenomenon asa counterpart of ANE is known anomalous Hall eﬀect (AHE).
Both the AHE and ANE reflect well the electronic state of materials, they have contributions from the extrinsic and intrinsic(Fd3̄m) and is a conductive ferrimagnet with a high transition
temperature (TC ≈ 400 K) 11) . Further, some previous studies re-ported that NCO has mixed-valence cations and can be expressed
2+
3+
3+
3+
2−
by a general formula, Co2+
x Co1−x [Co Ni1−x Ni x ]O4 (0 < x <1), where tetrahedral (T d ) site is occupied by high spin Co2+ (d7 ,S = 3/2) and Co3+ (d6 , S = 3/2), octahedral (Oh ) site is occupied by low spin Ni2+ (d8 , S = 1), Ni3+ (d7 , S = 1/2), anddiamagnetic low spin Co3+ (d6 , S = 0). The saturation magnetic

mechanisms 3, 7, 8) . However, since the electric field generated bymoment is 2 µB /f.u. irrespective of x. It has been reported that

ANE is smaller than AHE one’s, it hinders to investigate the relation between thermal and electrical transport in various materials.

in the presence of such a large number of states in the system, a large thermoelectric signal can be generated via an increase

Therefore, for understanding the electronic state of materials by
ANE, a measurement system that can detect the weak thermoelectric voltage desired.
The ANE is defined as the generation of an electric field(EANE ) along the direction of the outer product of the magnetization (M) and the temperature gradient (∇T ). Thus, it isexperimentally observed as an anomalous transverse voltage 9) .

in entropy 12, 13) . In addition, NCO film grown on the MgAl2 O4

For example, in the case of ∇T and M parallel to x- and z-axis
respectively, EANE appears along the y-axis direction. In otherwords, ANE in a magnetic material with perpendicular magnetic
anisotropy (PMA) could generate a large thermoelectric voltage
by expanding the area in the vertical direction from the tem-(MAO) substrate exhibits strong PMA 14, 15) , which is approximately 0.3 MJ/m3 at room temperature for a −0.3% epitaxial

strain. A recent theoretical investigation showed that Co at the
T d site is responsible for PMA 16) .

In this study, we designed a measurement system to detect the
weak thermoelectric voltage signal and investigated the thermoelectric properties of NCO. This manuscript is organized as follows. Sample preparation and design of the measurement setup
are explained in Section 2. We present experimental results anddiscussion in Section 3 and summarize the work in the final section.

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2 Experiment
2.1 Sample preparation
Epitaxial NCO thin films with a thickness of 50 nm were grownby reactive radio frequency magnetron sputtering technique (ES250MB: Eiko Engineering Co.,Ltd.)17–19) . We used a 2-inch alloy
target with the ideal composition of Ni:Co= 1 : 2. Before growing the film, a single crystal MAO substrate was ultrasonicallytric measurement as illustrated in Fig.1. Two electrodes placedalong the thermal gradient are for measuring the Seebeck signal(V xx ), and the other two are for measuring the ANE signal (V xy ).
Here, a point contact electrode was fabricated to prevent a decrease in TEMF 22) . The sample was cut into a rectangular shape(5 × 10 mm2 ) to place it on the sample holder and was glued by
GE7031 varnish. We used aluminum wires for making connections between electric pads and the sample puck. One side of

degreased using acetone, ethanol, and deionized water for 5 min
at each step. The growth conditions of NCO thin films were as
follows: Ar and O2 flow rates were set to 10 and 2.5 sccm, respectively; the process temperature was 300◦ C, and the working pres-the sample was heated, and ∇T was induced along the long sideof the rectangle. The voltage induced along the long side (V xx )sure was 1.3 Pa. Thereafter, we annealed the NCO films at 300◦ C

sured as a Nernst signal using Channel 1 of Keithley 2182. For
ANE measurements, a magnetic field perpendicular to the sam-for 30 min under an oxygen pressure of 0.2 Pa

20). The film structure was characterized by reflection high-energy electron diﬀraction (RHEED), X-ray reflectivity (XRR, by Rigaku Smart Lab,

using Co Kα1 radiation), and X-ray diﬀraction (XRD). Magnetic
hysteresis (MH) loops were measured by a vibrating sample magnetometer (VSM) option of the Physical Property Measurement

was measured as a Seebeck voltage using Channel 2 of Keithley
2182, and the voltage induced across the long side (V xy ) was mea-ple plane was applied. Further, to reduce the number of electricalcontacts, we fabricated a signal cable to directly connect abovemeasurement instruments and output connectors of PPMS. In thesample holder and the cable, we used silver soldering at all electrical contact points to reduce contact voltages.

System (PPMS) from Quantum Design.
2.2 Measurement setup
To perform the thermoelectric measurements, we designed andbuilt a sample holder, as illustrated in FIG. 1. Figure 1 shows
schematic illustrations of the sample holder. The sample wasbridged on the top of two Cu plates (5 × 13 × 1 mm3 and 5 × 13 × 3mm3 ). The one Cu plate was directly placed on the sample holder(P102/3A, Quantum Design), where the temperature was measured using the PPMS system. The another Cu plate was placedon the sample holder through Bakelite⃝R (5 × 13 × 2 mm3 ) for ther-

mal insulation. Moreover, a chip resistor (R = 330 Ω, TE Con-nectivity, 3522330RFT) acting as a heater was attached to thisside to raise the temperature. Here, the electrodes on the back of

Direct connection
LEMO

Keithley2400
Fabricated signal cable

PPMS

Keithley196

2107-30 cable
Keithley2182
Indirect connection
LEMO

Terminal
User bridge
cable

Keithley2400

D-sub

PPMS

Keithley196
Signal cable
Keithley2182

the chip resistor were removed by polishing. Input electric power
was supplied to the chip resistor using a source meter (Keithley2400). To monitor the actual temperature diﬀerence between
the Cu plates, we fabricated a type-E thermocouple from chromel

Fig. 1 Structure of the sample holder and configuration for measuring thermoelectric properties. Left panel shows schematics ofthe sample setup, and right panel represents the top view of thesample puck. Bottom panel shows block diagram of indirect and(TFCH-003) and constantan (TFCC-003), supplied by Omega
Engineering Inc. The thermal contact between the thermocouple
and each Cu plate was made using GE7031 varnish via a small

direct connection cable.

piece of thin paper. The thermal electromotive force (TEMF)
of the thermocouple was measured by a voltmeter (Keithley196)
and converted into the temperature diﬀerence (∆T ) using the reference table 21) . In the designed holder, the distance between the
two Cu plates is ℓ = 4 mm. Therefore, the temperature gradientis expressed as ∇T ≈ ∆T/ℓ. The typical width of the sample is
w = 3 mm. Note that we have confirmed the error between theactual temperature diﬀerence of the two Cu plates and the outputof the thermocouple is less than 5%.
Next, the film was patterned by the photolithography technique, and Cr and Au were sputtered as the electrodes. Fourelectrodes were deposited on the top of the films for thermoelec-

38

3

Results and discussion

3.1 Structural characterization
Figures 2 (a)-(d) show the XRD patterns with scattering vector k parallel to MAO[001], [100], and [110], respectively. The
dashed lines indicate the diﬀraction angles expected for the bulk
MAO. All the observed Bragg peaks can be consistently assigned
to a spinel structure. In Figs. 2 (b)-(d), reflections were only confirmed at the Bragg peak positions on the MAO substrate. This
result implies that NCO film has epitaxial distortion, and its lattice constants are a = 8.08 Å and c = 8.27 Å. Based on the lattice
constant of NCO (aNCO = 8.10 Å)11) and MAO (aMAO = 8.08
Å) in bulk, NCO thin films experience a compressive strain of

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36
37
2θ/ϕ (degree)

51

(c)

38

52
53
2θ/ϕ (degree)k// MAO[110]Co Kα176

Temperature (K)
100
200
300

NCO 400

MAO 400

Intensity (a.u.)128

MAO 220

NCO 220k// MAO[110]Co Kα1

126

NCO 440122
124
2θ/ω (degree)

77
78
2θ/ϕ (degree)(d)

S xy (µV/K)−0.005−0.030−0.035

NCO. Figure 3 (c) shows the time dependence of V xy from powering up the heater to measurement start. In this measurement,
the input power is controlled to be ∆T ≈ 10 K (I ≈ 25 mA)

79

3.2 Thermoelectric properties
First, we show the eﬀect of reducing the number of electrical connections on the measurement system. We tested
two diﬀerent ways of connecting the 14-pins LEMO connector(FGG.3B.314.CLAD92) of the interface of the cryostat of
PPMS to the nanovolt-meters; (1) the interface was wired to the
instruments using regular LEMO-D-sub cable with an electric
terminal(indirect connection), (2) the interface was directly
connected to the instruments using the home-built cable as
explained in Section 2 (direct connection). Figure 3 (a) shows
the time dependence of the measured signals V xy for ∆T = 0.
In the case of an indirect connection set up, one can see periodically oscillating ≈ 1 µV of spurious voltage signals, probably
because of the change in the temperature in the laboratory due
to the air conditioner. In contrast, in the case of the direct connection set up, the periodically varying spurious voltage signal
was suppressed, and the standard deviation was approximately 5
nV. This result indicates that thermoelectric voltages generated at
the electrical connections of the measurement system could be aserious problem while measuring weak DC voltage signals.
Using the direct connection setup, we investigated the thermoelectric properties of the sample. Figure 3 (b) shows ∆T dependence of the Seebeck voltage (V xx ) at 300 K. A single data point
represents the average voltage for approximately 5 min after generating a stable ∆T . The relative Seebeck coeﬃcient (S xx ) between NCO and the Al wire is expressed as,
E xx V xx /ℓ V xx
=
=
.
∇T
∆T/ℓ
∆T

S NCO
(µV/K)
xx
2.8
3.6
8.0

temperature dependence of S NCO
xx , which decreases as the temperature decreases.
Next, we describe the results of the ANE measurement of

54

Fig. 2 X-ray diﬀraction patterns of the scattering vector k parallel to (a)[001], (b)[100], and (c-d)[110], respectively .

S xx =

Table 1 Temperature dependence of absolute Seebeck coeﬃNCOcient (S NCOxx ) and anomalous Nernst coeﬃcient (S xy ).

(b)k// MAO[100]Co Kα1

MAO 440120(a)Intensity (a.u.)

118

Intensity (a.u.)

MAO 008k// MAO[001]
Co Kα1
NCO 008

Log Intensity (a.u.)∼ 0.3% due to the lattice mismatch. These results are consistent
with the previous studies 14–16, 20, 23) .

and 50 times averages are taken per point, which takes about 15
minutes from the beginning to the end. From Fig. 3 (c), while
above 200 K, V xy is stable after elapsing 5 min at least; at 100 K,
more than 20 min are needed for the TEMF voltage to become
stable. These results may imply that a new path for thermal
diﬀusion appears at low temperatures. Before we start the ANE
measurement, we need to wait for a suﬃcient duration for theV xy to become stable. S xy is determined from the experimentallymeasured voltages as follows:
S xy =

E xy V xy /w
=
,
∇T
∆T/ℓ

(2)

where w = 3 mm, ℓ = 4 mm. Figure 3 (d) shows the S xy -H loop
at each temperature. Here, the time dependent background component expected from Fig. 3(a) is smaller than the ANE voltage
at each temperatures. In ANE analysis, we extracted only the odd
function components, similar to that in the analysis performed for
the Hall eﬀect. The shape of the S xy -H loop is in good agreementwith a previously reported VSM measurement result (not shown)25). Moreover, a larger saturated S xy appeared at higher temperatures. From Ref.26, the relation between Nernst and Seebeck
coeﬃcient can be written as follow,
S xy ≃ S xx tan θH + ρ xx ϵyx ,(3)where θH is Hall angle, ρ xx is longitudial resistivity, and ϵyx isoﬀ-diagonal element of the thermoelectric tensor. In NCO, θH ∼−10−3 and ρ xx ∼ 10−3 Ωcm 14) . Therefore, the expected S xy from
S xx is approximately 0.01 µV/K, which is almost same with theexperimental results. The little diﬀerence may be attributed to thethermoelectric tensor.
4 Conclusion(1)

Thus, from the slope of this figure, we can determine S xx , whichis 6.4 µV/K. From Ref.24, excluding absolute Seebeck coeﬃcientof the Al, the absolute Seebeck coeﬃcient of the NCO(S NCO
xx )can be estimated, which is 8.0 µV/K at 300 K. Table 1 shows the

In this study, we investigated both the Seebeck eﬀect and ANE
in NiCo2 O4 thin films with PMA. The thermoelectric signals are
extremely small that we needed to build a measurement system todetect the weak thermoelectric voltage signals. To suppress the
spurious voltage signals originating from the electrical contacts atroom temperature of the measurement system, we employed the

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Cornell, Ingo Fetzer, Elena M. Bennett, Reinette Biggs, Stephen R.
Carpenter, Wim de Vries, Cynthia A. de Wit, Carl Folke, Dieter
Gerten, Jens Heinke, Georgina M. Mace, Linn M. Persson, Veerab-

Fig. 3 (a) Comparison of the connection methods between thesample chamber and the measurement instruments. (b) ∆T dependence of relative Seebeck voltage (V xx ) at 300 K. (c) Timedependence of V xy from power input to measurement start. (d)Temperature dependence of anomalous Nernst coeﬃcient S xy .

following solutions: (i) reduction in the number of electrical contacts by directly connecting the output of a commercial cryostat
with a superconducting magnet to the nano-voltmeters, (ii) usedsilver soldering to make electrical contacts to reduce contact voltages. By adopting the aforementioned measures, we succeeded
in detecting thermoelectric voltages as small as 5 nV.
Acknowledgments This project is partly supported by Japan
Science and Technology Agency (JST) under collaborative
research based on industrial demand ”High Performance Magnets: Towards Innovative Development of Next Generation
magnets” (JP-MJSK1415), KAKENHI(19KK0104) , the Ibaraki
University-Tsukuba Joint Coordination Fund, and the Tanigawa Fund Promotion of Thermal Technology. This work
was performed under the approval of the ”Photon Factory
Program Advisory Committee” (proposals No.2017G602 andNo. 2016S2-005). H. K. acknowledges the ”Kato Foundation
for Promotional Science”. H. K. acknowledges support ofGrant-in-Aid for JSPS Fellows (20J10749). H. K. thanks K.
Toko for providing a reference sample that has a large Seebeck
coeﬃcient.
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Recieved Oct. 30, 2020; Revised Dec. 21, 2020; Accepted Jan. 15,
2021

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J. Magn. Soc. Jpn., 45, 41-49 (2021)<Paper>Void-Defect Induced Magnetism and Structure Change ofCarbon Material-Ⅱ: Graphene Molecules
Norio Ota1, Aigen Li2, Laszlo Nemes3 and Masaaki Otsuka4
1-1-1 Tennodai, Tsukuba-City Ibaraki, 305-8571, Japan
Columbia, MO 65211, USA,
3Research Center for Natural Sciences, Ötvös Lóránd Research Network, Budapest 1519, Hungary
4Okayama Observatory, Kyoto University, Asakuchi Okayama, 719-0232, Japan,

1Graduate school of Pure and Applied Sciences, University of Tsukuba,

2Department of Physics and Astronomy, University of Missouri,

Void-defect is a possible origin of ferromagnetic feature on pure carbon materials. In our previous paper, void-defecton graphene-nanoribbon show highly polarized spin configuration. In this paper, we studied cases for graphenemolecules by quantum theory, by astronomical observation and by laboratory experiment. Model molecules for thedensity functional theory are graphene molecules of C23 and C53 induced by a void-defect. They have carbon pentagon
ring within a hexagon network. Single void has three radical carbons, holding six spins. Those spins make several
spin-states, which affects to molecular structure and molecular vibration, finally to infrared spectrum. The stablespin state was triplet, not singlet. This suggests magnetic pure carbon molecule. It was a surprise that thosemolecules show close infrared spectrum with astronomically observed one, especially observed on carbon richplanetary nebulae. We could assign major band at 18.9 micrometer, and sub-bands at 6.6, 7.0, 7.6, 8.1, 8.5, 9.0 and
17.4 micrometer. Also, calculated spectrum roughly coincides with that of laboratory experiment by the laser-induced
carbon plasma, which is an analogy of cosmic carbon creation in interstellar space.
Key words: graphene, void, spin state, DFT, planetary nebula, infrared spectrum

1. Introduction
Graphene and graphite like carbon materials are
candidates
forshowing
ferromagnetic
likehysteresis1)-6). There are many capable explanations
based on impurities7), edge irregularities8)-10) or
defects11)-16). The density functional theory (DFT)shows good coincidence with experiments17)-19) andrevealed reasonable consistency with several
fundamental theories20)-21). Despite such many efforts,
origin of magnetic ordering could not be thoroughly
understood. Our previous study on graphene
nano-ribbon (GNR) revealed that void-defect brings
unusual highly polarized spin configuration andstructure change, which will be opened in this journal
under the same title as number -I. In this paper, welike to apply our study to graphene molecules, smaller
than GNR. Unfortunately, on laboratory experiment,
small pure carbon molecule does not show any
magnetic
feature.
The
reasonmaybemolecule-to-molecule interaction at high density(1010~1023 molecules/cm3) conditions on earth. Radical
carbon’s magnetic feature in small molecules may becancelled out by complex interaction between
molecules. Now, we should look at astronomical
carbon dust floating in interstellar and circumstellar
space. Molecules are kept under peculiar condition ofultra-low density (1~100 molecules/cm3), almost nointeraction each other. Molecular structure affects
molecular vibration and infrared spectrum. In thisstudy, calculated infrared spectrum will be comparedwith the astronomically observed one, also with thelaboratory experiment of the laser induced carbon
plasma.
Fullerene C60 was discovered by Kroto et al.22) (the1996 Nobel Prize) in the sooty residues of vaporized
carbon. They already suggested that “fullerene may be
widely distributed in the universe”.
The presence of
C60 in astrophysical environments was revealed by thedetection of a set of emission bands at 7.0, 8.45, 17.3
and 18.9 μm23)-27). Typical astronomical objects are the
Galactic planetary nebula (PNe) Tc123) and the Small
Magellanic Cloud Lin4928). Observed spectra werecompared with experiment and theory23)29)-31).
However, there remain undetermined observed bands,
not be explained by C60.
It is well known that graphene is a raw material forsynthesizing fullerene32)33). By observation of Lin49,
Otsuka et al.28) suggested the presence of small
graphene. Graphene was first experimentally
synthesized by Geim and Novoselov34) (the 2010 Nobel
Prize). The possible presence of graphene in space wasreported by Garcia-Hernandez et al.35-37).
These
infrared features appear to be coincident with planar
C24 having seven carbon hexagon rings. However, fullobserved bands still cannot be explained by C24 orhexagon network molecules38). Some hints come fromcarbon SP3 defect among SP2 network caused bysingle void-defect in carbon hexagon network by Ota39).
Also, Galue & Leines40) predicted the physical model
supposing pi-electron irregularity. In this paper, weJournal of the Magnetics Society of Japan Vol.45, No.2, 2021

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apply one assumption of single void-defect ongraphene molecule. At the first part, DFT calculation
will be applied to model molecules. Void position
discriminates detailed molecule species. Spindependent calculation will be done to obtain detailed
molecular structure and molecular vibrational
infrared spectrum. At the second part, we willcompare such calculated spectra with astronomicallyobserved one. Finally, we like to compare withlaboratory experiment of laser induced carbon plasma
spectrum41)42), which will be an analogy of cosmic
carbon creation in space.

2. Model Molecules and Calculation
MethodModel molecules are illustrated in Fig. 1 startingfrom C24 having seven carbon hexagon rings35). To findsize dependence, we add larger one of C54. In thispaper, we apply one assumption of single void-defecton such initial molecules. In laboratory experiment,high speed particle can create such void. Similarly, inastronomical space, the cosmic ray as like proton may
attack graphene35-37). As illustrated on top left of Fig. 1,
high speed particle attacks graphene and kick out one
carbon atom. DFT calculation shows molecularconfiguration of void-defect induced graphenemolecules as like C23, and C53, which have one
pentagon ring among hexagon networks. Molecular
structure depends on the void position as marked by a,b, c, d, e, f, in left of Fig. 1. Void induced molecule
species is named by suffixing a, b, and so on, such as(C23-a) and (C23-b). Molecular energy of (C23-a) is 1.04
eV higher than that of (C23-b). In this study, we
supposed isolate molecule, which means nomolecule-to-molecule interaction, and no energy
competition between different void induced species.
While we need energy competition between spin states
for every individual species. It should be noted thatone void has 3 radical carbons and holds 6 spins. Such
spins bring spin-multiplicity, which affect tomolecular structure and molecular vibration, finally to
infrared spectrum.
In calculation, we used DFT43) 44) with theunrestricted B3LYP functional45). We utilized theGaussian09 software package46) employing an atomic
orbital 6-31G basis set47). Unrestricted DFT
calculation was done to have the spin dependent
atomic structure. The required convergence of theroot-mean-square density matrix was 10−8. Based onsuch optimized molecular configuration, fundamental
vibrational modes were calculated, such as C-C
stretching modes, C-C bending modes and so on, using
the Gaussian09 software package. This calculation
also gives harmonic vibrational frequency andintensity in infrared region. The standard scaling isapplied to the frequencies by employing a scale factor

42

of 0.975 for pure carbon system taken from thelaboratory experimental value of 0.965 based oncoronene molecule of C24H1239). Correction due toanharmonicity was not applied to avoid uncertain
fitting parameters. To each spectral line, we assigned
a Gaussian profile with a full width at half maximum(FWHM) of 4cm−1.

3. Spin State Analysis and Structure Change
We tried the multiple spin-state analysis. Example
is shown in Fig. 2 for spin state of Sz=2/2 of (C23-a) and(C23-b). In this study, we dealt total molecular spin S(vector). Molecule is rotatable material, easily follows
to the external magnetic field of z-direction. Projectedcomponent to z-direction is maximum value of Sz,
which is good quantum parameter. In molecularmagnetism, Sz=2/2 is named as triplet spin-state.
Initial void-defect holds 3 radical carbons and allows 6
spins as illustrated in left. Six spins make capablespin-states of Sz=0/2, 2/2, 4/2 and 6/2. Among them,calculated energy of Sz=4/2 and 6/2 resulted unstablehigh energy. Here, we like to compare cases of Sz=0/2
and 2/2. One radical carbon holds two spins, which areforced to be parallel up-up spins (by red arrows in Fig.
2) or down-down spins (blue) for avoiding large
coulomb repulsion due to Hund’s rule58). Spinalignment model is illustrated on middle. Three
couples of spin-pair will be partially cancelled andremain one pair to be Sz=2/2. Such speculation is
confirmed by DFT calculation. Spin cloud is mappedon right at a cutting surface of spin density at 10e/nm3.
We can see up-spin major spin cloud coincident withabove simple speculation.
As shown in panel of (C23-a) in Fig. 1, molecular
structure of Sz=0/2 shows bending top carbon (see a
blue circle of side view), whereas Sz=2/2 shows flat one
as illustrated on right column. It should be noted thatstable spin state is Sz=2/2, not Sz=0/2. Molecularenergy of Sz=2/2 was 0.49 eV lower (stable) than thatof Sz=0/2. Cause of bending carbon of Sz=0/2 comesfrom partial inclusion of SP3 component among SP2
network39)40). Such inclusion increases total molecularenergy. Similar result was confirmed again for a caseof (C23-b).
Other molecules’ structure and energy are listed inFig. 1. Energy change from the spin state Sz=0/2 to theSz=2/2 was noted by ΔE. Stable spin-state is framed bybold green. In most species, Sz=2/2 is stable (lower
energy) than Sz=0/2. Exception is only (C53-a) to show
stable state of Sz=0/2. This comes from complete
structure change, that is, void at a-site induces
SP3-bond among SP2-networks as marked by a red
circle in a column of (C53-a, Sz=0/2).

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Fig. 1 Model graphene molecules. Void-defect positions are classified by suffix a, b, and so on. Calculated molecular
structures are illustrated for both spin-states of Sz=0/2 and Sz=2/2. Total energy difference ΔE was noted in every
column. Stable spin-state was framed by bold green.

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Fig. 2 Spin alignment for (C23-a) and (C23-b) with spin state of Sz=2/2. Initial void holds 3 radical
carbons and allow 6 spins. By re-combination of carbon atoms, there arises partial cancelling of (up-up)
spins by (down-down) one. DFT calculated spin density of Sz=2/2 is illustrated on right.

4. Calculated Infrared Spectrum
Calculated infrared spectra are shown in Fig. 3. Leftcolumns are cases for spin state Sz=0/2, while rightone Sz=2/2. Spectrum of stable spin state was framedby bold green. Astronomically observed major
emission line of 18.9 μm was marked by a green
dotted line. In case of (C23-a), we can see one carbon
pentagon ring and an unusual 9 membered ring.
Calculated infrared spectrum for Sz=2/2 show 18.8 μm
peak close to observed band of 18.9μm. The species of(C23-b, Sz=2/2) [same structure for (C23-c)] have one
pentagon ring and show calculated twin major bands
at 18.9 and 19.1 μm.
In case of (C53-a), stable spin state was Sz=0/2, of
which spectrum show peaks at 21.7 μm and 19.5 μm to
be far from observed one. The spectrum of (C53-b,
Sz=2/2) show a peak at 19.0 μm close to observed one.
Also, (C53-c, Sz=2/2) [same for (C53-d) and (C53-e)]demonstrates major band at 18.9 μm, just the samewith observed one. In case of (C53-f, Sz=2/2), we can see
twin bands at 18.4 and 18.9 μm. Thus, we could obtainseveral species suitable for assigning the astronomical
observation.

44

5. Fundamental Mode Analysis
Fundamental vibrational mode of (C23-b, Sz=2/2)
was analyzed and summarized in Table 1. There are
63 modes for 23 carbon atoms. Energy diagram is
illustrated on top right of Table 1. Zero-point
vibrational energy is 27634 cm-1 (=3.42 eV). The lowest
vibrational energy of Mode-1 is 94.9 cm-1 (=108.06 μm,
0.012 eV). The highest Mode-63 is 2067 cm-1 (=4.96 μm,
0.26 eV). Vibrational behaviors are noted on rightcolumn of the table. They are all carbon to carbon(C-C) in-plane stretching modes parallel to molecularplane. Combination of vibrating bonds is different foreach mode. Bond is named by a, a’, b, b’ etc. illustrated
on a molecule structure. For example, there are two
calculated modes corresponding to observed 18.9 μm
band. One is Mode-24 showing 18.8 μm in-plane C-C
stretching at bonds of c, f, c’, f’, i, l, i’ and l’. Another isMode-23 showing 19.1 μm stretching at c, f, c’, f’, o, p,
and o’. Other major modes will be discussed in next
section by comparing astronomically observed bands.

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Fig. 3 Calculated infrared spectrum. Left figures are spectra for the spin state Sz=0/2, while right one for Sz=2/2.
Stable spin state is framed by bold green.

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Table 1 Fundamental mode analysis of (C23, Sz=2/2).

6. Comparison with Astronomical Observation
6.1 Single molecule spectrum

On top of Fig. 4, astronomically observed infrared
spectra are illustrated for carbon rich planetarynebulae of Lin49 (dark blue curve) and Tc1 (red one).
In both cases, we can see major band at 18.9 μm, alsoa side band at 17.4 μm, and shorter wavelength bands
at 6.6, 7.0, 7.5, 8.1 and 8.5 μm. Sharp atomic emission
lines are marked by arrows of [NeII] and [SIII] forscaling observed wavelength. It should be noted thatthe observed spectra are seen in emission. A nearby
star as like a central star of Tc1 nebula may
illuminate the molecules and excites them to give rise
infrared emission. Detailed discussion was done by Li
and Drain48)49). We regard here that DFT calculated
absorbed spectrum is mirror image of emission one incase of sufficient large photon energy excitation due tothe theory of Einstein’s emission coefficient48),49).
It was amazing to see good coincidence withobserved spectra and calculated one of (C23-b, Sz=2/2).
Detailed comparison is summarized in Table 1.

46

Observed major band at 18.9 μm could be identified by
two modes of Mode-23 (19.1 μm) and Mode-24 (18.8μm). Also, observed 6.6 μm band was reproduced wellby calculated two modes of Mode-55 (6.7 μm) andMode-56 (6.6 μm). Again, observed bands at 7.0, 7.5,
10.0, 16.7, and 17.4 μm could be reproduced wellrespectively by Mode-53 (for 7.1 μm), Mode-52 (7.4μm), Mode-42 (9.9 μm), Mode-27 (16.5 μm), andMode-25 (17.4 μm).
It was amazing again that large molecule cases as
like (C53-c, Sz=2/2) show good coincidence withobservation as compared on a bottom panel of Fig. 4. It
was suggested that there may be little size
dependence. Void-defect induced graphene molecules
generally contribute on cosmic spectra.

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Fig. 4 Astronomically observed emission spectrum forplanetary nebula Tc1 (on top, by red) and Lin49(black) compared with calculated spectrum of (C23-b,
Sz=2/2), and (C53-c, Sz=2/2).

6.2 Weighting sum spectrum

We like to know total contribution of all model
molecules, not depending on peculiar molecularspecies. Favorable way is the weighting sum method.
In case of C23-family, void-a species has 6 identical
positions among 24 carbon sites of C24 mothermolecule. Weighting sum coefficient-p should be
p=6/24. Also, coefficient of void-b species is p’=6/24
and void-c p”=12/24. Weighting sum of epsilon
ε(C23-family) will be obtained by the following
equation (1).
ε(C23-family)=p∙ε(C23-a, Sz=2/2)+p’∙ε(C23-b, Sz=2/2)+p”∙ε(C23-c, Sz=2/2))= (6/24)∙ε(C23-a, Sz=2/2)+(6/24)∙ε(C23-b, Sz=2/2)+(12/24)∙ε(C23-c, Sz=2/2))-------(1)Weighting sum spectrum of C23-family was illustrated
on middle of Fig. 5. It was amazing that we can see
good coincidence between observation and calculation.
In case of larger molecule of C53, weighting sum of
C53-family could well reproduce observed one asshown on bottom of Fig. 5, where void creation
parameter p was noted in Fig. 1.

Fig. 5 Weighting sum spectra for C23-family andC53-family. Void creation capability parameter-p ofeach molecule is considered as weighting sum
coefficient as noted in Fig. 1.

7. Comparison with Laboratory Experiment
Nemes et al.41)42) did the laser induced carbon
plasma experiment as an analogy of carbon dust
creation in interstellar space. Bulk graphite washeated and excited by Nd:YAG laser with wavelengthof 1.064 μm (1.16 eV) in atmospheric pressure Argon
gas. Evaporated carbon molecules emit infrared light.
The emission was recorded by an HgCdTe detector.
Several theories dealt with the carbon dust creatinin space50)-57). Calculated average size of carbon dust isabout 1nm, which is similar size with C23 and C53 inthis study. Temperature of star explosion gas will be2000 K after 300 days of the explosion, and finallycooled as dust cloud57). In case of laser induced plasma
experiment, excited carbon temperature will be 4500
to 7000 K, and finally cooled to room temperature42).
Experimental spectrum is shown in panel (A) of Fig.
6. We compared with weighting sum spectrum ofC23-family and C53-family in panel (B). The
experimental 7.4 μm peak could be reproduced by
calculated 7.5 μm band of C23-family. We can see
plateau from 6 to 7 μm, which may correspond to
calculated bands at 6.7 and 7.2 μm. At a range of 5 μm,
we can suggest some contribution by both C23-family
and C53-family. Also, at a range of 10μm, C23-family
may contribute. It should be noted that void-defect

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induced graphene could roughly explain laboratory
experiment.
Comparison to astronomical observation was shownin panel (C). Astronomically observed bands arefeatured by black dotted lines. We can find again good
reproducibility by calculation.

sub-bands from 6 to 18μm.
(4) By a weighting sum method applied to different
void position species, again we could reproduce wellobserved infrared spectra.
(5) The laboratory experiment on laser induced carbon
plasma was tried as an analogy for carbon dust
creation in space. Experimental infrared emission
spectra could be roughly explained by the weighting
sum spectra of C23 and C53.

Acknowledgement
Aigen Li is supported in part by NSF AST-1311804
and NASA NNX14AF68G.

References(Note on abbreviation of astronomical journals,
ApJ: The Astrophysical Journal
ApJL: The Astrophysical Journal Letters
A&A: Astronomy and Astrophysics
MNRAS: Monthly Notices of the Royal Astronomical Society
PNAS: Proceedings of the National Academy of Sciences)Fig. 6 (A) Infrared spectrum of the laser induced
carbon plasma, (B) calculation for C23-family andC53-family, (C) astronomically observed spectra.

8. Conclusion
Void-defect is a possible origin of ferromagnetic likefeature of graphene and graphite. In this paper,graphene molecules were studied.
(1) Starting model molecules were graphene moleculesof C24 and C54 for the density functional theory
analysis. Single void-defect creates C23, and C53
having carbon pentagon ring among hexagon
networks.
(2) Single void holds six spins to bring spin
multiplicity. DFT calculation show the most stablespin-state to be Sz=2/2, not Sz=0/2.
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expected to avoid complex molecule-to-moleculeinteraction. The triplet spin state of C23 and C53 could
explain astronomically observed spectra of Tc1 and
Lin49 nebulae for a major band at 18.9μm and48

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Journal of the Magnetics Society of Japan Vol.45, No.2, 2021

49

INDEX

Editorial Committee Members・Paper Committee Members
T. Ono and T. Kato (Chairperson), K. Koike, T. Taniyama and K. Kobayashi (Secretary)
H. GotoT. Hasegawa
S. Isogami
K. KamataH. Kikuchi
T. Kouda
S. Kokado
Y. Kota
T. Kubota
T. MakiS. Muroga
T. Nagahama
H. Nakayama
M. NaoeT. Narita
J. OzekiN. PhamT. Sasayama
T. SatoK. Sekiguchi
Y. Shiratsuchi
T. Takura
K. ThamS. YamadaT. Yamamoto

T. Kimura
T. Morita
D. Oyama
T. Shima
K. Yamazaki

N. Adachi
N. Inaba
Y. Kamihara
M. Ohtake
M. Takezawa

S. Honda
K. KatoT. Nozaki
I. Tagawa
S. Yoshimura

K. Bessho
S. Inui
A. Kuwahata
T. SatoT. Tanaka

M. DoiK. ItoK. Masuda
S. Seino
M. Tsunoda

T. DoiY. Kanai
Y. Nakamura
T. Suetsuna
N. Wakiya

K. Hioki
H. KatoK. Nishijima
K. Tajima
S. Yabukami

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編 集 委 員・論 文 委 員
小 野 輝 男 （理事） 加 藤 剛 志 （理事）
磯上慎二
小瀬木淳一
小山大介
小田洋平
後藤博樹
笹山瑛由
THAM KIMKONG
直江正幸
槙
智仁
室賀
翔
森田
孝
安達信泰
桑波田晃弘
土井達也
薮上
信

伊藤啓太
佐藤
拓
土井正晶
吉村
哲

乾
成里
末綱倫浩
仲村泰明
脇谷尚樹

小 池 邦 博 （幹事） 谷 山 智 康 （幹事） 小 林 宏 一 郎 （幹事）
鎌田清孝
菊池弘昭
木村
崇
窪田崇秀
神田哲典
古門聡士
佐藤
岳
嶋
敏之
白土
優
関口康爾
田倉哲也
中山英俊
長浜太郎
成田正敬
長谷川 崇
PHAM NAMHAI
山崎慶太
山田晋也
山本崇史
稲葉信幸
清野智史
西島健一

大竹
充
田河育也
野崎友大

加藤宏朗
竹澤昌晃
日置恵子

加藤和夫
田島克文
別所和宏

金井
靖
田中哲郎
本多周太

神原陽一
角田匡清
増田啓介

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