IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 11, NOVEMBER 2015

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Detection of Vortex Core Oscillation Using Second-HarmonicVoltage Detection Technique
Xiaomin Cui1 , Satoshi Yakata2, and Takashi Kimura3,4,5
1 Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka 819-0395, Japan
2 Department of Information Electronics, Fukuoka Institute of Technology, Fukuoka 811-0295 Japan
3 Department of Physics, Kyushu University, Fukuoka 812-8581, Japan
4 Research Center for Quantum Nano-Spin Sciences, Kyushu University, Fukuoka 812-8581, Japan
5 Core Research for Evolutionary Science and Technology, Japan Science and Technology Agency, Tokyo 102-0075, Japan

A sensitive and reliable detection method for magnetic vortex core dynamics at the remanent state has been demonstrated. Perfectly
symmetric potential created in a circular-shaped disk produces twofold symmetry in the position dependence of the resistance ofthe ferromagnetic disk. We find that the detectable second-harmonic voltage can be induced by flowing the dc current when thecircular-shaped core oscillation is excited by the microwave magnetic field. The consistent features have been observed in the currentdependence and field dependence of the signals, indicating that the present method is a powerful technique to characterize the coredynamics, even at the remanent state.
Index Terms— Anisotropic magnetoresistance (AMR) effect, RF magnetic field, second harmonic, vortex dynamics.

I. I NTRODUCTIONMAGNETIC vortex stabilized in the micrometer-sizedor submicrometer-sized ferromagnetic disk has been
intensively studied, because it opens up the possibilities ofadvanced spintronic applications, such as high-density spintronic memory devices, vortex-based spin-torque oscillators,
as well as logic operation devices [1]–[4]. The attention onmagnetic vortices also arises from the numerous advantages,including negligible magnetostatic interaction, high thermalstability, and remarkably low-frequency dispersion at theresonant oscillation state [1], [5], [6]. Moreover, the staticand dynamic characteristics of the magnetic vortex canbe controlled by the geometrical confinement, such as theshape of the dot and the ratio between the thickness andthe diameter [7]–[9]. However, further developments in theexperimental characterization of the vortex characteristics,
especially for the vortex dynamics, are indispensable for thefurther manipulation of magnetic vortices and the promotionof the practical application. So far, numerous methods forevaluating the dynamic properties of the magnetic vortex
have been demonstrated [10]–[13]. In particular, electricalmeasurement techniques, such as homodyne detection andhigh-frequency impedance measurement, sensitively detect thevortex motion in small ferromagnetic disks. These electricaltechniques are based on monolithic RF measurement scheme.
However, this simplification strongly regulates the situationof vortex excitation and prevents the detailed study of thedynamic characteristic.
Recently, we have developed a novel detection method
for vortex dynamics, in which the excitation and detection
circuits are electrically separated [14]. This technique provides

AManuscript received March 20, 2015; accepted May 17, 2015. Dateof publication May 22, 2015; date of current version October 22, 2015.
Corresponding author: T. Kimura (e-mail: t-kimu@phys.kyushu-u.ac.jp).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMAG.2015.2435024

sensitive detection and the flexible experimental situations,leading to a detailed study of the dynamic response of themagnetic vortex. However, owing to its detection scheme, it isdifficult to measure the core dynamics at the remanent state,
which is the spatially symmetric domain structure. To improve
this disadvantage in our evaluation method, in this paper,
we develop a novel method based on the second-harmonic
detection technique.
II. E XPERIMENTAL P ROCEDURE
Fifty permalloy (Py) ferromagnetic circular disks wereprepared on nondoped Si substrate using electron-beamlithography in combination with the conventional liftoff
technique. The circular Py disks with a thickness of 40 nm
and a diameter of 2 µm were deposited using electron-beam
evaporation equipment under high vacuum. The center-tocenter interval between the disks is 4 µm. The Py dots areconnected by the Cu pads in order to make a series circuit of
the chained disk. In addition, periodic Cu strip lines, which
generate microwave magnetic field with high frequency, areformed on each Py disk. Here, the electrical connection
between Py disks and Cu electrodes was insulated by thepatterned SiO2 film with the thickness of 100 nm.
Here, we explain the detection mechanism of vortex
oscillation at the remanent state. Fig. 1(a) shows the schematicof the anisotropic magnetoresistance (AMR) measurement
together with the scanning electron microscopy image of a partof the device. The resistance of the chain of the Py disks as afunction of the core position is shown in Fig. 1(b). We obtained
this plot by changing the magnitude and the direction of themagnetic field. Here, we assume that the vortex core linearly
displaces perpendicularly to the direction of the external field
when the applied magnetic field is sufficiently smaller than
the annihilation field of the magnetic vortex [15], [16]. It isclearly seen that the resistance change shows the twofold
symmetry. This indicates that when the vortex core has a0018-9464 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 11, NOVEMBER 2015

Fig. 1. (a) Scanning electron microscopy image of a part of the fabricateddevice together with the probe configuration for AMR measurement.
(b) Resistance of the circular disks as a function of the vortex core position.
(c) and (d) Schematic of the second-harmonic signal generation due to thecircular core oscillation.

Fig. 2. (a) Circuit diagram used for the second-harmonic signal measurement
together with the scanning electron microscopy image of a part of thefabricated device. (b) Representative voltage spectrum under the microwave
magnetic field with the frequency of 182 MHz ( ON-resonant state) and(c) that with the frequency of 150 MHz (OFF-resonant state).

circular trajectory with the frequency f , the second-harmonic
resistance change is expected. Therefore, when the dc current
flows in the disk, the second-harmonic voltage will be induced,
as shown in Fig. 1(c) and (d). Using spectrum analyzer, we
can detect the signal related to the vortex oscillation.
Fig. 2(a) shows the diagram of the measurement circuit.
We flow the microwave current with the specific frequency fin
in the periodical Cu electrodes. This induces the voltagechange with the frequency 2 f in under the dc current flow.
In particular, when the vortex core is resonantly excited,the induced voltage with the frequency 2 f in becomes large.
However, when f in is far from the resonant frequency ofthe vortex core, the core oscillation becomes very small.
Therefore, by changing the input microwave frequency fin
with monitoring the spectrum of the voltage, we cancharacterize the resonant motion of the magnetic vortex core.
III. R ESULT AND D ISCUSSIONFirst, to confirm the validity of the aforementioned detection
scheme, we measured the spectrum of the voltage induced

Fig. 3. (a) Voltage spectra for various input RF frequencies in the range of150–208 MHz. Here, the spectrum was measured every 4 MHz, and each
spectrum was vertically shifted to clarify. (b) Voltage spectra for various
input RF frequencies signals without offset. (c) Frequency dependence ofthe dc voltage measured by the previously developed lock-in technique undera small in-plane magnetic field.

by the dc current under the microwave magnetic field.
Fig. 2(b) and (c) show the voltage spectra for f in = 182 MHz
and f in = 150 MHz, respectively. We confirmed that a clear
voltage peak exists at f = 364 MHz corresponding to 2 f in in
the spectra for f in = 182 MHz. However, for f in = 150 MHz,
only a small peak at a level similar to the noise level isobserved. This indicates that the resonant frequency of thevortex core is close to 182 MHz.
To evaluate the resonant property more clearly, we measure
the spectra for various input RF frequencies around 180 MHz.
Here, the spectra under the input RF frequency in the rangeof 150–208 MHz were measured every 4 MHz. As can be seenin Fig. 3(a), the spectra for various input frequencies show
the resonant feature. From the results, the resonant frequency
can be recognized as 182 MHz, where the signal becomesthe maximum value. To verify the reliability of the present
results, we confirmed the resonant properties of the magnetic
vortex using our previously developed technique [14]. Here,to introduce the spatial asymmetry, we introduce a small
in-plane magnetic field with the magnitude of 30 Oe, muchsmaller than the annihilation field of the magnetic vortex.
Since the resonant frequency of the magnetic vortex confinedin the circular disk is almost independent of the core position,
the resonant property similar to the remanent state is expected.
As can be seen in Fig. 3(c), we confirmed that the resonant
frequency of the vortex is ∼180 MHz, which is consistent
with the results in Fig. 3(a) and (b).
We then investigate the dc current dependence of theinduced voltage. Since the voltage is linearly proportional
to the current, we expect a logarithmic dependence on thedc current in the signal. Fig. 4(a) shows the spectrum inducedby the RF magnetic field with the frequency of 182 MHz
for various dc current. The peak magnitude monotonicallyincreases with increasing the dc current. Moreover, as can beseen in Fig. 4(b), its dependence clearly shows the logarithmic
dependence.
Finally, we investigate the field dependence of the spectrum
under the RF magnetic field with 182 MHz. As can be seen

CUI et al.: DETECTION OF VORTEX CORE OSCILLATION

4300303show the features consistent with the previously reported
results. This technique may be extended to the higher orderfrequency generator voltage, faster than the intrinsic precession
frequency.
ACKNOWLEDGMENT

Fig. 4.
(a) Voltage spectra under the microwave magnetic field withthe frequency of 182 MHz for various dc current in the absence of themagnetic field. (b) Current dependence of the amplitude of the resonantpeak of the second-harmonic signal. Solid line: logarithmic curve fitted tothe experimental data.

Fig. 5. Voltage spectra under the microwave magnetic field with the frequencyof 182 MHz for various static in-plane magnetic fields.

in Fig. 5, the signal does not show a significant change lessthan 65 Oe both for the positive and the negative magneticfields. However, above 90 Oe, the peak amplitude starts todecrease and finally disappears. This is because the corepotential deviated from the ideal parabolic shape when themagnetic field is close to the annihilation [7], [17]. When themagnetic field exceeds 120 Oe, the vortex core annihilates,
resulting in the perfect elimination of the twofold symmetry
in the resistance.
IV. C ONCLUSION
To investigate the magnetic vortex core dynamics at theremanent state, we have developed a novel method basedon the electrically separated excitation and detection circuitswith the spectrum analyzer. The signature of the vortex coreresonance is well detected as the second-harmonic signal
induced by the twofold symmetric resistance change. The
current and field dependence of the second-harmonic signal

This paper was supported in part by the Ministry of Education, Culture, Sports, Science, and Technology through Nano
Spin Conversion Science under Grant 26103002 and in part by
Grant-in-Aid for Scientific Research under Grant 25220605.
X. Cui would like to thank the China Scholarship Council for
Young Scientists.
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