Stability of standing spin wave in permalloy thin film studied by anisotropic
magnetoresistance effectK. Yamanoi, Y. Yokotani, X. Cui, S. Yakata, and T. Kimura
Citation: Journal of Applied Physics 118, 233909 (2015); doi: 10.1063/1.4937918
View online: http://dx.doi.org/10.1063/1.4937918
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/118/23?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Spin wave spectra in perpendicularly magnetized permalloy rings
Appl. Phys. Lett. 106, 112403 (2015); 10.1063/1.4916029
Spin wave resonance excitation in ferromagnetic films using planar waveguide structures
J. Appl. Phys. 108, 023907 (2010); 10.1063/1.3435318
High-intensity Brillouin light scattering by spin waves in a permalloy film under microwave resonance pumping
J. Appl. Phys. 102, 103905 (2007); 10.1063/1.2815673
Ferromagnetic resonance saturation and second order Suhl spin wave instability processes in thin Permalloy
films
J. Appl. Phys. 102, 023904 (2007); 10.1063/1.2756481
Multiple ferromagnetic resonance in mesoscopic permalloy rings
J. Appl. Phys. 97, 10A712 (2005); 10.1063/1.1851932

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 133.5.164.140 On: Tue, 23 Aug 2016
10:59:34

JOURNAL OF APPLIED PHYSICS 118, 233909 (2015)

Stability of standing spin wave in permalloy thin film studied by anisotropic
magnetoresistance effectK. Yamanoi,1 Y. Yokotani,1 X. Cui,2 S. Yakata,3 and T. Kimura1,4,a)1

Department of Physics, Kyushu University, 6-10-1 Hakozaki, Fukuoka 812-8581, Japan
Graduate School of Information Science and Electrical Engineering, Kyushu University, 744 Motooka,
Fukuoka 819-0395, Japan3
Department of Information Electronics, Fukuoka Institute of Technology, 3-30-1 Wajiro-higashi, Higashi-ku,
Fukuoka 811-0295, Japan
4
Research Center for Quantum Nano-Spin Sciences, Kyushu University, 6-10-1 Hakozaki, Fukuoka 812-8581,
Japan
2(Received 14 August 2015; accepted 2 December 2015; published online 21 December 2015)
We have investigated the stability for the resonant spin precession under the strong microwave
magnetic field by a specially developed detection method using the anisotropic magnetoresistanceeffect. The electrically separated excitation and detection circuits enable us to investigate theinfluence of the heating effect and the nonuniform spin dynamics independently. The large
detecting current is found to induce the field shift of the resonant spectra because of the Joule
heating. From the microwave power dependence, we found that the linear response regime for the
standing spin wave is larger than that for the ferromagnetic resonance. This robust characteristic of
the standing spin wave is an important advantage for the high power operation of the spin-wave
C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4937918]
device. V

I. INTRODUCTION

Dynamic detection and manipulation of the magnetization properties in a metallic ferromagnetic film have grown
rapidly with the development of the physics on spin dynamics.1–3 Especially, the spatially modulated spin configuration
stabilized in the patterned ferromagnetic nanostructures isknown to excite the non-uniform coherent spin precession
with a spatial periodical modulation, namely, spin wave.4–7
Owing to its fast time scale in GHz range and high compatibility with a Si-based semiconductor integrated circuits, thespin waves in ferromagnetic thin films are expected to havevarious potential applications in future telecommunication
devices, such as a microwave filter,8–10 oscillator,11–13 andfast spin-information transportation.14,15 In addition, the development of high-performance spin-based telecommunication devices also makes an innovation in military andsecurity applications. Moreover, the fundamental material
parameters in ferromagnet, such as the spin polarization andthe damping constant, can be deduced from the characteristics of the spin wave propagation.16 Therefore, the dynamical
property of the spin wave and the exploration of their precise
manipulation techniques may create important milestones
both from fundamental and technological viewpoints.17
Especially, for seeking the further possibility of spin-based
electronic devices, understanding the thermal stability andthe non-linear response induced by the large amplitude RF
magnetic field are indispensable.
The spin dynamics for the uniform magnetization,
namely, ferromagnetic resonance (FMR) has been intensively
investigated in nonlinear regime.18–22 However, the nonlinear
dynamics for the spin wave are also important for developinga)t-kimu@phys.kyushu-u.ac.jp

0021-8979/2015/118(23)/233909/5/$30.00

aforementioned telecommunication devices. So far, the spinwaves are mainly controlled by using geometrically induced
magneto-static interaction.1,23,24 However, the tunability forsuch systems is not so high because the modulation magnitudeis fixed by their shapes. Instead of the direct patterning of theferromagnetic film, a patterned periodical electrode is known
as an alternative method for controlling the spatial distributionof the spins in a ferromagnetic thin film.8,10,25 Recent developments for the nano-fabrication techniques made it possible toprepare well-defined patterned electrode with high accuracy.
In this method, we can adjust the modulation magnitude andphase. Moreover, since one does not need to consider the deterioration of the ferromagnet during the nano patterning andnon-uniformity due to the edge roughness and oxidation, themagnetic properties as high as the bulk values will be
expected. The impedance transmission measurements basedon the vector network analyzer have been mainly used forcharacterizing these systems. However, the detectable spinwaves are limited by the electrode design because the interlinkage magnetic flux is canceled out. Moreover, the input
power is restricted by the output power of the network analyzer. Here, we demonstrate a sensitive detection method forthe spin wave excited by the patterned electrodes. Electricallyseparated excitation and detection circuits enable us to detect
the standing spin waves for various wave lengths sensitively
and to investigate their stabilities against the heating and large
microwave magnetic field.
II. EXPERIMENT

Our spin-wave device consists of a 40-nm-thick ferromagnetic Permalloy (Py) film and the 200-nm-thick ladder-typenonmagnetic Cu electrode, which are electrically separated bya 100-nm-thick SiO2 sputtered film. A schematic illustration

118, 233909-1

C 2015 AIP Publishing LLC
V

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 133.5.164.140 On: Tue, 23 Aug 2016
10:59:34

233909-2

Yamanoi et al.

J. Appl. Phys. 118, 233909 (2015)

FIG. 1. Schematic illustration of thefabricated spin wave device together
with the circuit diagram for the spinwave excitation and detection andscanning electron microscope image ofthe representative fabricated device.

for the fabricated device together with a scanning electron
microscope (SEM) image of the representative device isshown in Fig. 1. The Py film is grown by a magnetron sputtering at the base pressure of 2  108 Torr on a conventional Si substrate. Here, the pressure during the sputtering is
2 mTorr, and the deposition rate is 2 nm/s. The Cu narrowwires, 200 nm in width, were fabricated by a conventional
lift-off technique with an electron-beam lithography. The
center-center interval L between the Cu wires is 8 lm. The
width and length for the Py film are 200 lm and 600 lm,
respectively. The periodical electrodes were put on the middle part of the Py film (200 micron). The external magnetic
field is applied along the Cu wire direction (y direction) inorder to fix the precession axis of the magnetizations. The
magneto-static surface spin waves (MSSWs) propagating
perpendicular to the magnetization were generated by flowing a high frequency ac current with 7 GHz in the nonmagnetic ladder-type electrodes and were detected by monitoring
the resistance of the Py film through the AMR. Here, toimprove the signal/noise ratio of the detected voltage, we
adapt the pulse modulated RF current with the lock-in detection technique.26,27

FIG. 2. (a) Field dependence of the resistance for Py film under the microwave magnetic field with the magnitude of 10 mW. (b) Numerical curve
reproduced by superimposing several Lorentzian curves with different resonant magnetic fields.

III. RESULTS AND DISCUSSIONS

Figure 2(a) shows the representative result for the fielddependence of the voltage induced in the Py film under theRF magnetic field with the power of 10 mW. Here, the DC
current for the measurement is 60 mA. The induced voltage
clearly exhibits the resonant features consisting of the multiple peaks. We found that each voltage peak is reproduced byseveral Lorentzian curves with different resonant magnetic
field, as shown in Fig. 2(b). To explore the origin of theresonant-like features, we fitted the resonant magnetic fields
to the dispersion relationship for the MSSW given by the following equation:5
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
c
H0 ðH0 þ 4pMS Þ þ 4p2 MS2 ð1  e4pt=k Þ: (1)fMSSW ¼
2pHere, c is the gyromagnetic ratio given by 18.4 MHz/Oe, Ms
is the saturation magnetization 4pMs ¼ 9:8 kOe. t and k are
the thickness for the ferromagnetic film and the wavelength,
respectively. As shown in Fig. 3(a), the resonant magnetic
fields are well explained by the MSSW along the x-axis withassuming that the half wave length of the standing spin wave
is given by the fraction of the integer number of the electrodespacing L and the ferromagnetic resonance with the infinite
wave length. This means that the present method is moresensitive to the previously developed method based on vector network analyzer because the previous method only can
detect the standing spin wave whose wave length is the

FIG. 3. (a) Theoretical dispersion relationship between the FMR and MSSW
frequencies and the external magnetic field together with the experimentallyobtained values (Solid circle). Here, we assume k ¼ 2L=n. (b) Schematic
illustration of standing spin waves with the different n stabilized by periodical Cu electrodes.

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 133.5.164.140 On: Tue, 23 Aug 2016
10:59:34

233909-3

Yamanoi et al.

fraction of the integer number of the electrode spacing L.10
We may have to consider the standing spin wave perpendicular to the film place (along z-axis). However, it is difficult to
induce such a spin wave by the present frequency range
because of its short wave length. The shape of the spectra
seems to be broader than those in the vector network analyzer measurements. This is because the signal comes fromthe whole sample in the present measurement while the signal in the network analyzer measurement mainly comesfrom the surface of the ferromagnetic film. Since the magnitude of the ac magnetic field induced by present excitation
method gradually decreases with increasing z because of thethin SiO2 thickness, the spin precession perpendicular to thefilm plane (along z-axis) becomes inhomogeneous. As aresult, the spectra obtained from the resistance measurement
become broad compared with that by the network analyzer.
Here, we discuss the reason why the present method can
induce and detect the standing spin wave with k=2 ¼ L=n.
Since the methods for exciting the spin wave in both experiments are same, the difference should be caused by thedetection scheme. As shown in Fig. 3(b), the standing spinwaves for n ¼ 2 or other even numbers can be imaged byassuming that the anti-node of the wave is located underneath the electrode. These spin waves can be reproduced bysuperimposing the wave given by cosðkx þ xtÞ and thatgiven by cosðkðx  LÞ  xtÞ with the condition kL ¼ 2pm,
where m is the integer. In these spin waves, the time derivative of the magnetic flux underneath the electrode should belarge, leading to the RF voltage generation in the Cu electrode.3 In the case for n ¼ 3 or other odd numbers, the standing wave with the node underneath the electrode satisfies
such a condition. This kind of spin wave can be reproducedby superimposing the wave cosðkx þ xtÞ and that given bycosðkðx  LÞ  xtÞ with the condition kL ¼ pð2m þ 1Þ,
where m is the integer. In this situation, the magnetic flux
around the electrode is always zero, leading to no voltage
drop in the Cu electrode. Therefore, the vector network analyzer measurement can detect the standing spin wave with
odd numbers but cannot detect that with even numbers.10 On
the other hand, in the present method using the anisotropic
magnetoresistance, the signal is not related to the local structure of the spin wave but to the averaged angle of the spinsin a whole sample. Therefore, the standing spin waves stabilized in the film are effectively detected. Here, we emphasizethat the resonant precessions for the FMR and MSSW occur
in the different regions of the Py film. For the FMR, the resonantly precessional motion is excited underneath the Cu
electrode while the standing spin wave is formed in theregion between the electrodes. This indicates that the total
volume for the spin wave becomes much larger than that for
the FMR. Indeed, the resistance change due to the MSSW
excitation is much larger than the FMR. However, the difference of the resistance change is not so large. This is because
the average precession angle for the spin wave is smaller
than that for the FMR. We also note that the resistancechange due to the spin wave excitation decreases withdecreasing the wave length. This is because the averageangle decreases with decreasing the wave length due to theincrease of the exchange energy. Similar tendency is

J. Appl. Phys. 118, 233909 (2015)

expected by changing the electrode spacing. However, since
the decoherence of the spin wave increases with increasing
the electrode spacing, the resistance change also decreases
with increasing the electrode spacing. The systematic study
on the electrode spacing dependence may provide the dynamical information about the spin wave propagation.
We then investigate the dc dependences of the resonant
features. Figure 4(a) shows the resistance spectra of the samedevice for various dc. The minimum current was 50 mA
because the signal-to-noise ratio in the spectra becomesworse below 50 mA. The measurement with smaller current
can be performed by further optimization of the sample
structure, such as increasing the length or decreasing the
thickness of the Py film. In the measurements, the shape ofthe spectra does not show significant change. However, theresonant fields for the FMR and standing spin waves were
found to increase with increasing the bias current. According
to Eq. (1), we naively expect that the increase of the resonant
fields is related to the modification of the saturation magnetization because it seems to be difficult to change other parameters, such as the wave length, by the dc current. Figure4(b) shows the dc dependence of the saturation magnetization estimated from Eq. (1). It should be noted that the saturation magnetizations estimated from the standing MSSW
for various wave number (n  1) show almost same current
dependence although that for the FMR shows different signature. The saturation magnetization estimated from MSSW
shows a small reduction when the current increases. Since
the reduction of the saturation magnetization is caused byelevating the temperature of the ferromagnetic thin film, theobserved reduction can be understood by the Joule heatingof the detecting dc. Regarding the large difference in thesaturation magnetization estimated from FMR, it should be
noted that the value is estimated by assuming the uniform
precession, meaning infinite wave length. However, in realistic situation, the precession area is only restricted underneath the electrode. Therefore, the saturation magnetizationin the FMR was overestimated. The relatively large current
dependence in the FMR is also related to the inhomogeneous precession. Since the FMR condition in the pattered

FIG. 4. (a) Voltage spectra for various DC. (b) Resonant fields for FMR andMSSWs as a function of the DC. (c) Saturation magnetizations estimatedfrom the experimental results with Eq. (1) as a function of the dc.

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 133.5.164.140 On: Tue, 23 Aug 2016
10:59:34

233909-4

Yamanoi et al.

structure is affected by the demagnetizing fields, the dependence of the saturation magnetization becomes large. It
also should be noted that we did not see any influence ofthe spin transfer torque because of the insufficient current
density  1010 A/cm2
Finally, we investigate the microwave-power dependence of the resonant properties. Figure 5(a) shows the resistance spectra for various microwave powers. We summarize
the resonant field and its relative values as a function of the
microwave power in Figs. 5(b) and 5(c), respectively. Whenthe microwave power is smaller than 10 mW, the resonant
fields for the FMR and MSSW show a small reduction without significant changes in the resonant properties. However,when the microwave power exceeds 32 mW (15 dBm), theresonant magnetic field for the FMR significantly reduces.
Here, it should be noted that the resonant fields for the standing spin waves do not show any large change even the powerover 32 mW. These features cannot be explained by the simple heating effect discussed earlier and indicate that, under
the high microwave power, the standing spin wave is morestable than the FMR. At the moment, the reason for the poor
stability of the FMR is not clear. However, we should beaware of the difference in the excitation regions between the
FMR and the standing spin wave. So, one of the possible reasons for the poor power tolerance for the FMR is related tothe inhomogeneous excitation of the spin precession. Whenthe large spin precession is locally excited underneath the Cu
electrode, the in-plane stray field is induced by the magnetic
charge at the border of the electrode. Such a situation may
assist the transformation of the spin excitation mode fromthe FMR into the spin wave with a long wave length, giving
rise to the significant reduction of the peak magnetic field for
the FMR. Regarding the small reduction of the resonant field
for the standing spin wave observed in Figs. 5(b) and 5(c),we may have to take into account the non-sinusoidal distribution of the RF magnetic field. Especially, around the central area of the electrode, the constant magnetic field aroundthe center of electrode significantly prevents to stabilize thestanding spin wave in the center of the Cu electrode as

FIG. 5. (a) Voltage spectra for various input microwave powers. (b)Resonant fields for FMR and MSSWs as a function of the microwave power.
(c) Relative change of the resonant magnetic fields for FMR and MSSW as afunction of input microwave power.

J. Appl. Phys. 118, 233909 (2015)

shown in Fig. 3(b). As a result, the wave length for the standing spin wave decreases. From Eq. (1), the reduction of theresonant magnetic field can be understood by decreasing thewave length of the standing spin wave.
IV. CONCLUSION

We have developed a method for detecting the standing
spin wave using electrically separated excitation and detection circuits. By changing the detecting dc and the exciting
RF current independently, we investigated the stability of theresonant spin precession. The influence of the detecting current is simply understood by the reduction of the saturation
magnetization due to the Joule heating. The microwavepower dependence indicates that the standing spin wave has
a superior stability for the strong RF magnetic field compared with the ferromagnetic resonance because the wave
length of the spin wave is protected by the patterned electrode. This robust property for the standing spin wave is anadvantage for the spin wave application with the high power
operation.
ACKNOWLEDGMENTS

This work was partially supported by Grant-in-Aid for
Scientific Research on Innovative Area, “Nano Spin
Conversion Science” (26103002) and that for Scientific
Research (S) (25220605). The author (X. C.) acknowledges
the China Scholarship Council for Young Scientists.
1

Spin Dynamics in Confined Magnetic Structures III, edited by B.
Hillebrands and A. Thiaville (Springer-Verlag, Berlin, Heidelberg, 2006).
A. Scholl, L. Baumgarten, R. Jacquemin, and W. Eberhardt, Phys. Rev.
Lett. 79, 5146 (1997).
3
T. J. Silva, C. S. Lee, T. M. Crawford, and C. T. Rogers, J. Appl. Phys. 85,7849 (1999).
4
F. J. Dyson, Phys. Rev. 102, 1217 (1956).
5
R. W. Damon and J. R. Eshbach, J. Phys. Chem. Solids 19, 308 (1961).
6
L. K. Brundle and N. J. Freedman, Electron. Lett. 4, 132 (1968).
7
K. Yamanoi, S. Yakata, T. Kimura, and T. Manago, “Spin wave excitationand propagation properties in a permalloy film,” Jpn. J. Appl. Phys., Part 1
52, 083001 (2013).
8
C. S. Tsai, J. Su, and C. C. Lee, IEEE Trans. Magn. 35, 3178 (1999).
9
B. Kuanr, Z. Celinski, and R. E. Camley, Appl. Phys. Lett. 83, 3969 (2003).
10
K. Kiseki, S. Yakata, and T. Kimura, Appl. Phys. Lett. 101, 212404 (2012).
11
V. E. Demidov, S. Urazhdin, and S. O. Demokritov, Nat. Mater. 9, 984(2010).
12
M. Madami, S. Bonetti, G. Consolo, S. Tacchi, G. Carlotti, G. Gubbiotti,
F. B. Mancoff, M. A. Yar, and J. Åkerman, Nat. Nanotechnol. 6, 635(2011).
13
F. Macia, F. C. Hoppensteadt, and A. D. Kent, Nanotechnology 25,
045303 (2014).
14
M. P. Kostylev, A. A. Serga, T. Schneider, B. Leven, and B. Hillebrands,
Appl. Phys. Lett. 87, 153501 (2005).
15
M. Jamali, J. H. Kwon, S. M. Seo, K. J. Lee, and H. Yang, Sci. Rep. 3,3160 (2013).
16
K. Sekiguchi, K. Yamada, S.-M. Seo, K.-J. Lee, D. Chiba, K. Kobayashi,
and T. Ono, Phys. Rev. Lett. 108, 017203 (2012).
17
J. H. Kwon, S. S. Mukherjee, P. Deorani, M. Hayashi, and H. Yang, Appl.
Phys. A 111, 369–378 (2013).
18
Y. S. Gui, A. Wirthmann, and C. M. Hu, Phys. Rev. B 80, 184422 (2009);
80, 060402(R) (2009).
19
E. Schl€oomann, J. Appl. Phys. 31, 1647 (1960).
20
Y. K. Fetisov, C. E. Patton, and V. T. Synogach, IEEE Trans. Magn. 35,
4511–4521 (1999).
21
C. T. Boone, J. A. Katine, J. R. Childress, V. Tiberkevich, A. Slavin, J.
Zhu, X. Cheng, and I. N. Krivorotov, Phys. Rev. Lett. 103, 167601 (2009).
2

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 133.5.164.140 On: Tue, 23 Aug 2016
10:59:34

233909-5
22

Yamanoi et al.

T. Gerrits, P. Krivosik, M. L. Schneider, C. E. Patton, and T. J. Silva,
Phys. Rev. Lett. 98, 207602 (2007).
23
J. P. Park, P. Eames, D. M. Engebretson, J. Berezovsky, and P. A.
Crowell, Phys. Rev. Lett. 89, 277201 (2002).
24
S. Saha, R. Mandal, S. Barman, D. Kumar, B. Rana, Y. Fukuma, S. Sugimoto,Y. Otani, and A. Barman, Adv. Funct. Mater. 23, 2378–2386 (2013).

J. Appl. Phys. 118, 233909 (2015)25

E. Schloemann, R. Tustison, J. Weissman, H. J. Van Hook, and T.
Varitimos, J. Appl. Phys. 63, 3140 (1988).
26
M. Jamali, K. Narayanapillai, J. H. Kwon, and H. Yang, Appl. Phys. Lett.
101, 062401 (2012).
27
X. Cui, S. Hu, M. Hidegara, S. Yakata, and T. Kimura, Sci. Rep. 5, 17922(2015).

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 133.5.164.140 On: Tue, 23 Aug 2016
10:59:34