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Spin Wave Excitation and Propagation Properties in a Permalloy Film

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2013 Jpn. J. Appl. Phys. 52 083001(http://iopscience.iop.org/1347-4065/52/8R/083001)
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REGULAR PAPER

Japanese Journal of Applied Physics 52 (2013) 083001
http://dx.doi.org/10.7567/JJAP.52.083001

Spin Wave Excitation and Propagation Properties in a Permalloy Film
Kazuto Yamanoi1 , Satoshi Yakata2;3 , Takashi Kimura2;3 , and Takashi Manago1
1

Department of Applied Physics, Fukuoka University, Fukuoka 814-0180, Japan
Advanced Electronics Research Division, INAMORI Frontier Research Center, Kyushu University, Fukuoka 819-0395, Japan
3
CREST, Japan Science and Technology Agency, Chiyoda, Tokyo 102-0075, Japan
E-mail: manago@fukuoka-u.ac.jp
2

Received March 12, 2013; accepted June 4, 2013; published online July 18, 2013
Spin wave excitation and propagation properties in a permalloy were investigated using a vector network analyzer for the magnetostatic surface
wave (MSSW) and magnetostatic backward volume wave (MSBVW) configurations. In the MSSW configuration, the excitation and transmission
spectra show many peaks. They originate at the distance of antenna lines of the coplanar waveguide, and the waveguide design is important for
selecting the excitation and transmission wave vectors of the spin wave. The attenuation length of the MSSW was estimated to be 7.1 m, and thegroup velocity of the MSSW with a wave number of 0.26 m 1 was estimated to be about 8.6 m/ns for an external magnetic field of 20 mT. In the
MSBVW configuration, however, the excitation spin wave spectrum shows a single peak, since many quantized peaks overlap. A transmission
signal with a single peak was also detected, but this could be an artifact such as an induced current.
# 2013 The Japan Society of Applied Physics

1. Introduction

Progress in spin current research1–9) has led to various
spintronic applications such as race track memory,10,11) spin
torque diodes,12,13) spin torque oscillators,14–16) and so on.
In these studies, the carriers of the spin current are spinpolarized electrons that ﬂow in ferromagnetic metals or are
injected from ferromagnetic metals to nonmagnetic metals.
Recently, spin pumping17,18) and spin Seebeck eﬀects19,20)
have attracted attention for the generation of a pure spincurrent, but these are also based on the motion of spinpolarized electrons. The diﬀusion length of the spin current
by conduction electrons is more or less 1 m because of
the spin ﬂip caused by the thermal eﬀect or spin orbit
interaction. A spin wave that conveys spin information
can also be called a spin current without the ﬂow of spinpolarized electrons. The advantage of the spin wave is its
long-range propagation over a millimeter scale in yttrium
iron garnet (YIG), and over a 10 m scale in a permalloy(Py),21) which is much larger than the spin diﬀusion lengthof the charge spin current. Additionally, spin wave devices
are expected to be ultrafast logical gate devices.22–24) There
have been many studies using YIG for microwave devices,but metals such as Py were not satisfactory in spite of being
important for integration with a Si process for spintronic
devices. The ﬁrst study of spin wave propagation spectroscopy for Py, which shows that magnetostatic surface
waves propagate as far as 40 m in Py, was reported by
Bailleul et al.21) Time-resolved measurement of spin wave
propagation using a pulse excitation method was also
reported.25) Recently, it has been found that spin-polarized
current can induce the Doppler shift of a spin wave.26–28)
The basic propagation properties in metallic ﬁlms, however,are still not very clear. They will be important for futureapplications.22–24) In this paper, we report spin excitation andpropagation properties of a continuous sinusoidal wave
using a vector network analyzer in detail.
2. Experimental Procedure

A 30-nm-thick Py thin ﬁlm with a width of 100 m was
fabricated on a Si/SiO2 substrate by sputtering, e-beamlithography, and wet etching. These were covered with a

w

2 μm

w + 2 μm

7 μm

y

G S
Port 2xw

B
Py

for MSSW
configuration

100 μmk
Cu Port 1
G S
Bfor MSBVW
configuration
Fig. 1. (Color online) SEM image of the sample. The space between the
two CPWs, w, was varied from 10 to 100 m.

35-nm-thick SiO2 sputtered ﬁlm for insulation, and a pair of
coplanar waveguides (CPWs) for excitation and detection
antennas was formed by depositing a 300-nm-thick Cu
above the Py ﬁlm by e-beam lithography, e-beam evaporation, and a liftoﬀ technique. Figure 1 shows a scanningelectron microscopy (SEM) image of the sample. The CPWs
were of the signal-ground (SG) type and were connected at
the end of electrical pads. The line width of the antenna was
2 m, and the distance between centers of the signal andground lines was 7 m. The space w between the two CPWs,deﬁned in Fig. 1, was varied from 10 to 100 m.
Spin wave excitation and transmission measurements
were performed using a vector network analyzer (VNA;
HP8510C) and a microprobe station (Cascade Microtech
Summit 9000), which was modiﬁed to apply an in-planestatic magnetic ﬁeld. Two types of conﬁguration were used
for these measurements, depending on the relative orienta-

083001-1# 2013 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 52 (2013) 083001

K. Yamanoi et al.

tions of the magnetization direction M and in-plane wave
vector k. As is shown in Fig. 1, one is the MSSW conﬁguration, where the external magnetic ﬁeld is applied along
the y-axis and k is along the x-axis, resulting in M ? k. The
other is the MSBVW conﬁguration, where the external
magnetic ﬁeld is applied along the x-axis and k is along
the x-axis, resulting in M k k. The dispersion relationships
between frequency and wave vector for these conﬁgurations29,30) aresﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
 2

Ms
f¼
ð1  e2kd Þ for MSSW;BðB þ Ms Þ þ2
2
ð1Þ
sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1  ekd
B B þ Msf¼
2kd
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃBðB þ Ms Þ ðkd  1Þ;for MSBVW;
¼
2
ð2Þ

3. Results and Discussion
3.1 MSSW configuration

Figure 2(a) shows the reﬂection spectra (Re S11 ) undervarious external magnetic ﬁelds for the conﬁguration. There
are some peaks, and the interval between peaks decreases
with increasing magnetic ﬁeld. In our antenna conﬁguration,
the signal and ground lines are shorted, and then the spinwave excitation occurs under both the signal and groundlines almost simultaneously. Therefore, a boundary condition is given and a standing wave is excited to maximize theamplitude under both the signal and ground lines. Assumingthat l is the length determined by this boundary condition,
the wave number is given by k ¼ n=l, where n is the mode
number. The peaks in the spectra correspond to the spin

Py width 100 μm
Thickness 30 nm

Re ΔS

11

100 mT

0.1

20 mT

0
4

5

6

7

8

9

10

11 12

Frequency (GHz)
(b)

12
10

Frequency (GHz)where  is the gyromagnetic ratio, B is the static magnetic
ﬁeld, Ms is the saturation magnetization, k is the wave
number, and d is the ﬁlm thickness.
The spin wave was excited at the antenna of port 1,
and the propagated spin wave was detected at the antennaof port 2. For spin wave excitation measurement, one-port
reﬂection measurement was performed and the S11 parameter was measured. For spin wave propagation measurement,
two-port transmission measurement via a Py ﬁlm was performed and the S21 parameter was measured. The incident
microwave power was 0 dBm, which was conﬁrmed in thelinear response regime judging from the power dependenceof the spectral shape. Signals obtained under a static magnetic ﬁeld were analyzed by subtracting the backgroundsignal obtained without magnetic ﬁeld. Hereafter, we call thesubtracted signals S11 and S21 the reﬂection and transmission signals, respectively. The real part of these signals
was analyzed. The choice of the real part as the characteristic parameter was mainly based on the fact that it
is suitable for the determination of the resonant frequency
because it exhibits a peak at the resonant frequency when
the phase shift is eﬃciently small. On-chip full two-port
calibration was carried out by using a calibration wafer,and the phase shift induced by the antennas was suﬃciently
small, judging from the shape of the approximately symmetric spectra of Re S11 in the MSBVW conﬁguration.
All measurements were performed at room temperature.

(a) 0.2

n=4
8
60 mT

n=1

6

n=2

n=1

n=3
n=4

4
6

7

8 9 10 11 12
Frequency (GHz)

2
20

(c)

40
60
80
Magnetic field (mT)

G

7 μm

100

S

Cu
SiO2
Py

Substrate
Fig. 2. (Color online) (a) Reﬂection spectra (Re S11 ) in MSSW
conﬁguration. (b) Dispersion relationship of the reﬂection signal. The solidlines are the ﬁtting curves with the dispersion relation of the MSSW
[Eq. (1)]. (c) Schematic cross section of the sample. The standing wave
arises between the signal and ground lines.

wave signals with diﬀerent wave numbers. Such MSSW
excitation with a speciﬁc wave number was also demonstrated using a resonator structure of an excitation
antenna.31,32) The peak frequency is shown as a function ofmagnetic ﬁeld in Fig. 2(b). The solid lines are the ﬁtting
curves with the dispersion relation of MSSW [Eq. (1)]. The
parameters used are Ms ¼ 1:08 T and =2 ¼ 29:7 GHz/T.
The obtained wave numbers k and l ¼ n=k are summarizedin Table I. The value of l of 5.7–7.7 m is appropriate forour antenna geometry, because the distance between thesignal and ground lines is 7 m, as illustrated in Fig. 2(c).
The origin of the decrease in l with increasing n is not clear.
It alludes to the necessity of eﬀective boundary conditions
similar to the eﬀective ‘‘pinning’’ boundary conditions
in conﬁned magnetic structures.33) Thus, an MSSW was

083001-2# 2013 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 52 (2013) 083001

K. Yamanoi et al.

Table I. Fitted results of wave numbers and related values obtained from
relationship between frequency and magnetic ﬁeld for MSSW.

(a) 0.03

Port 1 (S11 reﬂection measurement)k(1/m)l ¼ n=k
(m)

0.02

20 mT

kd

1

0:41  0:02

7:7  0:4

0.012

2

1:01  0:02

6:3  0:2

0.030

3

1:60  0:02

5:9  0:1

0.048

4

2:20  0:03

5:7  0:1

0.066

Re ΔS21n

w = 10 μm
40 mT 60 mT

80 mT
100 mT

0.01
0

-0.01

Port 2 (S21 transmission measurement)k(1/m)l ¼ n=k
(m)

kd

1
2

0:26  0:02
0:55  0:03

11:9  0:9
11:5  0:6

0.008
0.016

3

0:93  0:03

10:2  0:3

0.028

4

1:20  0:03

10:4  0:3

0.036

5

1:59  0:03

9:9  0:2

0.048

-0.02
4

5

6

7
8
9 10 11Frequency (GHz)

12

12

(b)

10

successfully excited in this conﬁguration. Note that spinwaves with not only the wave number corresponding to
the peak frequency but also various wave numbers are
excited, since the spectra are spread over a wide frequency
range.
The transmission spectra (Re S21 ) for w ¼ 10 m areshown in Fig. 3(a). The peak frequency of Re S21 is not
the same as that of Re S11 , and its oscillation is ﬁne.
Figure 3(b) shows the magnetic ﬁeld dependence of peakfrequency. Peak indexes were determined and are shownin the inset of Fig. 3(b). Some peaks have a shoulder
or become slightly broad. It seems that the peak shape isaﬀected by that of the excitation spectra, because Re S11
has a local minimum around the frequency where Re S21
becomes broad or has a shoulder. Therefore, we eliminate
the shoulderlike peak to ﬁx the indexes. The ﬁtting curvesof n ¼ 1{5 of the MSSW [Eq. (1)] are also shown, and theﬁtted results are indicated in Table I. The obtained l isapproximately 12 m, which is roughly in agreement withthe distance between the excitation and detection antennas,
as illustrated in Fig. 3(c), although a decrease in l with n
is observed similarly to the result of S11 analysis. As shownin a snapshot image of the spin wave [Fig. 3(c)], a large
spin wave signal can be detected when the magnetization modulation is large under the detection antenna. This is
explained as follows. The S parameter is deﬁned by S21 ¼
S2 =S1 ¼ jS2 j exp i2 =jS1 j exp i1 ¼ jS2 j=jS1 j exp ið2  1 Þ,
where S1 is the incident signal and S2 is the detectedsignal. When 2  1 ¼ 2n, Re S21 becomes maximum.
This means that the propagation wave should have themaximum amplitude under the detection antenna when
the incident wave has the maximum amplitude under theincident antenna in the snapshot image. Therefore, when the
wavelength matches the distance between the excitationand detection antennas, the detection antenna can pick up
the real part of the spin wave signal eﬀectively. Thus, we
can analyze the multipeak spectra similarly to in standing
wave analysis. The transmission properties of the spin wave
depend on the distance between the two antennas, though astanding wave does not arise between the two antennas ofFrequency (GHz)

n

8

n=5
40 mT

n=2

6

n=1

n=1

4

6

2

(c)

n=3
n=4
n=5

20

7
8
Frequency (GHz)

40
60
80
Magnetic field (mT)Port 1

12 μm

9

100

Port 2Cu
SiO2
Py

Substrate
Fig. 3. (Color online) (a) Transmission spectra (Re S21 ) for w ¼ 10 m
in MSSW conﬁguration. (b) Dispersion relationship of the transmission
signal. The ﬁtting curves with the dispersion relation of the MSSW
[Eq. (1)] are also shown. The inset shows the peak indexes of the signal.
(c) Schematic cross section of the sample and the eﬃciently detectablespin waves.

ports 1 and 2. This result shows the possibility of realizing awave vector ﬁlter by controlling the distance between theantennas.
Figure 4(a) shows the transmission spectra (Re S21 ) for
various w under an external ﬁeld of 20 mT. The spin wave
signal can be seen up to 40–50 m, which is consistent withthe previous reports.21,28) The signal intensity is deﬁned as
the largest peak-to-peak value, and plotted as a function of w
in Fig. 4(b). The inset of Fig. 4(b) shows the same data witha semi-logarithmic scale. The intensity decreases exponentially and the attenuation length of the MSSW was estimatedto be 7.1 m.
Since the spin wave with a diﬀerent k is clearly observed
owing to the oscillation of the spectrum, one can the
deduced group velocity of the spin wave from the interval

083001-3# 2013 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 52 (2013) 083001

12

B = 20 mT

10Frequency (GHz)Re ΔS21w = 10 μm

20 μm

Py width 100 μm
Thickness 30 nm

0.01

30 μm
40 μm

8
0.04
0.03

4

50 μm

5

6

10

11

0.03

4 5 6 7 8 9 10 11 12
Frequency (GHz)

0

12

0

0

20

40
60
80
Magnetic field (mT)

100

120

Fig. 5. (Color online) Dispersion relationship of reﬂection signal in
MSBVW conﬁguration. The inset shows the reﬂection spectra (Re S11 ) of
the MSBVW conﬁguration.

10
Intensity

Intensity

0

-1

0.04

20 mT

2

7
8
9
10
Frequency (GHz)(b) 0.05

0.02
0.01

100 μm
4

100 mT

6
11

Intensity

Re ΔS

(a)

K. Yamanoi et al.

-2

10

-3

10

3.2 MSBVW configuration

10-4

0.02

0

10

20
30
w (μm)

40

50

0.01
B = 20 mT
0
0

10
20
30
40
Space between antennas w (μm)

50Fig. 4. (Color online) (a) Transmission spectra (Re S21 ) for various w
under external ﬁeld of 20 mT. (b) Signal intensity as a function of w. The
inset shows the same data with a semi-logarithmic scale. The attenuation
length of the MSSW was estimated to be 7.1 m.

between the peaks of the spectrum. The group velocity of the
MSSW with wave number k is theoretically expressed as
 2
d!
Ms
d expð2kdÞ
sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
¼
:
vg ¼
 2
dk
2
Ms
ð1  e2kd ÞBðB þ Ms Þ þ2
ð3Þ
The vg depends on k ¼ n=l, that is, the index of n. Whenn ¼ 1, vg is calculated to be 9.9 m/ns for w ¼ 10 m(l ¼ 12 m) and B ¼ 20 mT. Experimentally, one can use
two neighboring peaks of the spectrum (n ¼ 1),
vg ¼

!
2f
¼
¼ 2lf :
k
n=l

ð4Þ

In the case of w ¼ 10 m (l ¼ 11:9 m: experimental value)and B ¼ 20 mT, the group velocity of n ¼ 1 is deduced to beapproximately 8.6 m/ns using the frequency diﬀerence fbetween the ﬁrst peak (n ¼ 1) and the second peak (n ¼ 2),
which is in close agreement with the theoretical groupvelocity of 9.9 m/ns.

Figure 5 shows the relationship between the peak frequencyof the reﬂection spectra and the external magnetic ﬁeld,
and the inset shows the reﬂection spectra (Re S11 ) undervarious magnetic ﬁelds for the MSBVW conﬁguration. Onlya single peak was obtained for each magnetic ﬁeld. Since
kd is much smaller than unity, as shown in Table I, thedispersion relation of the MSBVW [Eq. (2)] becomes thesame as Kittel’s equation for thin ﬁlms. Therefore, even if
many standing waves are excited, their quantized peaks
overlap, and consequently only one peak is observed. The
solid curve shows the result calculated using Eq. (2), whichis in good agreement with the experimental result.
Regarding the transmitted property shown in Fig. 6(a),a similar dispersion relation is obtained, compared withthe reﬂection properties of the MSBVW. The intensity of thespectra, however, is much lower than that of the MSSW
signals. As shown in Fig. 3(a) for the MSSW, the signal
intensity decreases with increasing magnetic ﬁeld because
the damping term in the LLG equation increases with increasing magnetic ﬁeld. On the other hand, for the transmission signal in the MSBVW conﬁguration, the intensity
increases with increasing magnetic ﬁeld, as shown in theinset of Fig. 6(a). It seems that the intensity increase
observed in the reﬂection spectra in the inset of Fig. 5
aﬀects the transmission signal. It is, however, not clear why
the intensity of the reﬂection spectra increases with themagnetic ﬁeld at present. Additionally, Fig. 6(b) shows thatthe intensity of the transmission signal does not dependon the distance between the antennas. If this is the MSBVW
signal, it should decrease with increasing distance between
the antennas because of the decay. Therefore, we consideredthat these spectra are not attribute to the MSBVW
propagation, and could reﬂect a kind of induced current ina Py strip. Further investigation is necessary for an MSBVW
in metallic ﬁlms.

083001-4# 2013 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 52 (2013) 083001

K. Yamanoi et al.

implies that the transmission signal does not originate from
the MSBVW, and it could indicate a kind of induced current.
One should thus take care in the MSBVW measurement
using a VNA.

(a)

Py width 100 μm
Thickness 30 nm
w = 10 μm

8Acknowledgments

This work was partly supported by JSPS KAKENHI Grant
Number 24560034. This work was partly supported byfunds (Nos. 115002 and 127005) from the Central ResearchInstitute of Fukuoka University. The authors thank Dr. Kasaiof the National Institute for Materials Science (NIMS) for
fruitful discussions.

0.00086

w = 10 μm
Re ΔS21Frequency (GHz)1040.0004

100 mT

20 mT

02-0.0004
4 5 6 7 8 9 10 11 12
Frequency (GHz)

0
0

20

(b)

100

120

Phys. Rev. Lett. 84 (2000) 3149.

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B = 100 mT
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Re ΔS210.000240
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12)

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14)

15)

10

20
50
100
Space between antennas w (μm)16)

Fig. 6. (Color online) (a) Dispersion relationship of transmission signal
in MSBVW conﬁguration. The inset shows the transmission spectra(Re S21 ) of the MSBVW conﬁguration. (b) Antenna distance dependenceof Re S21 .

17)
18)
19)
20)

4. Conclusion

21)

We investigated the spin wave excitation and propagation
properties of a continuous sinusoidal wave using a VNA.
In the MSSW conﬁguration, the excited spin wave spectra
show some peaks, owing to the standing wave excitation
between signal and ground lines. The transmission spinwave spectra also show many peaks in contrast to the excitedspin wave spectra. The peaks depend on the distance
between the antennas of the two ports. These properties
suggest that the distance between the antennas can control
the wave vector of the transmitted spin wave; thus, they canbe used as a wave vector ﬁlter. The attenuation length of the
MSSW was estimated to be 7.1 m, and the group velocityof n ¼ 1 was deduced to be approximately 8.6 m/ns for
B ¼ 20 mT. In the MSBVW conﬁguration, the excited spinwave spectra show a single peak for each magnetic ﬁeld.
This is due to the overlapping of many quantized peaks
because of a very small kd. The transmission signal does
not depend on the antenna distance. Therefore, this result

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