JOURNAL OF APPLIED PHYSICS 107, 09D309 共2010兲
High frequency magnetic field imaging by frequency modulated magnetic force microscopy Hitoshi Saito,a兲 Wei Lu,b兲 Kodai Hatakeyama, Genta Egawa, and Satoru Yoshimura Center for Geo-Environment Science, Faculty of Engineering and Resource Science, Akita University, Akita 010-8502, Japan
共Presented 19 January 2010; received 31 October 2009; accepted 14 January 2010; published online 7 May 2010兲 High frequency ac magnetic field from magnetic recording head was successfully imaged by using our newly developed frequency-modulated magnetic force microscopy 共FM-MFM兲, which uses the frequency modulation of cantilever oscillation caused by applying ac magnetic field to a mechanically oscillated cantilever. The FM-MFM has been demonstrated and the experimental results show good agreement with our proposed models for FM-MFM. The amplitude and phase images of an ac magnetic field can be obtained separately by using the FM-MFM technique with a lock-in amplifier. By taking advantage of this technique, the present FM-MFM method opens a possibility to evaluate the magnetic field characteristics of magnetic recording head with high spatial resolution. © 2010 American Institute of Physics. 关doi:10.1063/1.3368706兴 I. INTRODUCTION
Magnetic force microscopy 共MFM兲 is a powerful tool to investigate microscopic magnetic domain structures of high density magnetic recording media and nanoscale magnetism. MFM applications in the design and development of disk drive components have expanded rapidly over the past few years because of the need to explore nanometer scale phenomena that limit recording density and MFM is an ideal tool to investigate the nanoscale magnetism due to the high spatial resolution for static magnetic fields from a magnetic sample.1 The maximum lateral resolution of this technique is about 10 nm.2 However, for the detection of alternating magnetic field 共ac magnetic field兲, conventional MFM is only sensitive to the ac magnetic fields that have a frequency component near the mechanical resonant frequency of a MFM cantilever 共0 = 2 f 0兲, such as the sinusoidal magnetic field3 and the amplitude-modulated magnetic field with a modulation frequency that equals 0.4 Because the cantilever acts as a mechanical amplifier near the resonance of the cantilever, signals of which frequency are not close to 0 are not amplified and disappear below the detection threshold. Recently, we developed a new MFM imaging technique for ac magnetic fields with wide frequency range.5 This method uses the frequency modulation 共FM兲 of a cantilever oscillation by applying ac magnetic field to a mechanically oscillated tip. We found that ac magnetic field caused the FM of a cantilever oscillation when ac magnetic field does not oscillated the cantilever by itself in the case that the frequency of ac magnetic field is far from the resonant frequency of the cantilever. By using frequency-demodulated
signals of the cantilever oscillation, we can image the gradient of ac magnetic field. We mentioned this method as FMMFM. The principle of FM-MFM can be explained that the displacement of a harmonic oscillator whose spring constant has a term of periodically changed with different frequency from that of oscillation force, m
共1兲
where z is the displacement of the tip in perpendicular direction, m is the effective mass of the tip, ␥ is the damping factor of the oscillation, k0 is the intrinsic spring constant of the cantilever, ⌬k is the effective change of the spring constant of the cantilever, and F0 is the force which is driven by a piezoelectric element with a constant force at a frequency near the resonance frequency c共=2 f c兲. When a MFM tip behaves as a monopole type tip,6 ⌬k was given by ⌬k =
qtipHz cos共mt兲. z
共2兲
where qtip is the magnetic charge at the tip-end, Hz is the normal component of ac magnetic field which is applied to the MFM tip with respect to the sample surface, m共=2 f m兲 is the frequency of the magnetic field. Then, the frequency modulation of cantilever displacement occurs in the following expression:5
Electronic mail:
[email protected]. b兲 Current address: School of Materials Science and Engineering, Shanghai Key Laboratory of D&A for Metal-Functional Materials, Tongji University, Shanghai, 200092, China. 107, 09D309-1
冋
F0 ⌬k sin ct + cos共mt兲 m␥c m␥c
z共t兲 =
a兲
0021-8979/2010/107共9兲/09D309/3/$30.00
dz共t兲 d2z共t兲 + 共k0 + ⌬k兲z共t兲 = F0 cos共ct兲, + m␥ dt2 dt
⬵
冉
册
F0 ⌬k sin共ct兲 + 兵cos关共c + m兲t兴 m␥c 2m␥c
+ cos关共c − m兲t兴其
冊
© 2010 American Institute of Physics
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FIG. 2. 共Color online兲 共a兲 Topographic, 共b兲 amplitude, and 共c兲 phase images of the ac magnetic field for a writing head at main pole region.
FIG. 1. Schematic diagram of ac magnetic field measurement of a magnetic recording head by FM-MFM.
= z0 sin共ct兲 + c
Hz 兵cos关共c + m兲t兴 z
+ cos关共c − m兲t兴其.
共3兲
where z0 is the amplitude of the cantilever and c is a constant. Therefore an ac magnetic field gradient Hz / z was obtained by using the frequency demodulation. In this study, we demonstrates a higher frequency imaging of ac magnetic field for single-pole head of hard disk drive by adjusting the oscillation frequency c in the way that c − m = 0. In this case, the Eq. 共3兲 becomes the following expression due to the mechanical filtering effect, z共t兲 ⬇ z0 sin共ct兲 + c = z0 sin共ct兲 + c
Hz cos关共c − m兲t兴 z
Hz cos共0t兲. z
10 kOe. The magnetization direction of the tip was perpendicular to a sample surface and the gradient of the normal component of magnetic field to a sample surface with respect to the normal direction was detected. All the experiments were performed in air atmosphere. The ac magnetic field was generated by a single pole type writing head which was driven by a sinusoidal ac current with a zero-to-peak amplitude of 20 mA and frequency of 100 kHz. The ac magnetic field measurement was done by using lift mode after topographic measurement and the c was changed to satisfy the condition that c − m = 0 as above mentioned. The lift height is 50 nm. Amplitude and phase information of the ac field signal was extracted by using a lock-in amplifier. The signal is the output of an optical sensor. We got the reference by using a multiplier and a lowpass filter from the applied voltages of a piezo and a head. The measurable frequency of the ac magnetic field 共m兲 can be increased up to 2 MHz. III. RESULTS AND DISCUSSIONS
共4兲
Therefore, the ac magnetic field images can be obtained by detecting the amplitude of the side-band component. In this paper, we report the magnetic imaging of a high frequency ac magnetic field which is generated from a magnetic recording head by using the newly developed FMMFM. This FM-MFM technique will open a possibility to evaluate the magnetic field characteristics of magnetic recording head with high spatial resolution. II. EXPERIMENT
Figure 1 shows the schematic diagram of ac magnetic field measurement of a magnetic recording head by FMMFM. The system used in this method was based on a conventional JSPM-5400 共JEOL Ltd.兲 scanning probe microscope. The cantilever is oscillated by using a piezoelectric element, while an ac magnetic field is applied to a MFM cantilever by a sample. The cantilever deflections are sensed by laser beam deflection. Here the oscillation frequency c of the piezoelectric element was near the resonant frequency of the cantilever 共0兲 for the measurement of topographic images. The value of 0 of the cantilever with the MFM tip was about 256 kHz and the value of Q was about 500. In this experiment, we used a high-coercivity MFM tip 共SI-MF40Hc, Nitto Optical Co. Ltd兲 and a magnetic recording head as a sample. The MFM tip was coated with a 20 nm L10-FePt film and the radius is 50 nm. The coercivity is approximately
Figure 2 shows the 2 ⫻ 2 m2 topographic, amplitude, and phase images of the writing head. Figure 2共a兲 shows a typical shielded SPT head structure with a trailing shield/ return pole, which is very close to the main pole in the trailing direction. The main pole, the gap 共around 50 nm兲 between main pole and trailing shield, and a nonmagnetic layer connected with main pole are also clearly observed. Figure 2共b兲 is the corresponding MFM amplitude image of the main pole region. As shown in the image, the main pole position 共bright area兲 is clearly seen. It also can be observed that strong amplitude of ac magnetic field is measured near the pole position. The highest intensity is obtained at the pole, near the middle of main pole and small peak of the intensity is obtained at the trailing shield near the gap. In addition, the MFM contrast of amplitude image in the area away from the main pole region is almost the same and there is no significant MFM signal contrast, which indicates that no phase information is included in the amplitude image. Figure 2共c兲 shows the corresponding MFM phase image of the main pole region 共obtained at the same scan as amplitude image兲. From the phase image, the polarity of the field can be observed clearly. The bright area corresponds to the inphase magnetic field of the main pole while the dark area indicates a phase difference of 180° and it can be concluded that the perpendicular component of the magnetic field at the position of main pole region is opposite to that at the position of trailing shield/return pole. The MFM amplitude and phase images demonstrate that FM-MFM performs very well in the imaging of ac magnetic fields. The spatial resolution is al-
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most the same as that of conventional MFM. Now the limitation of measurable frequency is about 2 MHz, which corresponds to the limit of the photodetector. With extended apparatus such as laser Doppler vibrometry to measure the high frequency oscillation of the cantilever, it is possible to image an ac magnetic field with a frequency up to several hundred megahertz by using the newly developed FM-MFM. IV. CONCLUSIONS
In summary, the FM-MFM has been developed and it has demonstrated the ability to image ac magnetic fields with high spatial resolution. The experimental results show good agreement with the proposed models of this phenomenon. The amplitude and phase images of an ac magnetic field from magnetic recording head were obtained separately by using the newly developed FM-MFM technique. By taking advantage of this phenomenon, the present FM-MFM method can be applied to image high frequency ac magnetic field with a frequency up to several hundred MHz. And this
FM-MFM technique is thought to be effective in highresolution imaging of ac magnetic field and will open a possibility in the evaluation of magnetic field characteristics of magnetic writing head. ACKNOWLEDGMENTS
We would like to thank Dr. Y. Uehara from Fujitsu Ltd. for providing the single-pole head. This work was supported by JST/SENTAN, the Storage Research Consortium and Akita Prefectural Government. 1
D. Rugar, H. J. Mamin, P. Guethner, S. E. Lambert, J. E. Stern, I. McFadyen, and T. Yogi, J. Appl. Phys. 68, 1169 共1990兲. 2 H. Saito, R. Sunahara, Y. Rheem, and S. Ishio, IEEE Trans. Magn. 41, 4394 共2005兲. 3 Y. Martin and H. K. Wickramasinghe, Appl. Phys. Lett. 50, 1455 共1987兲. 4 M. R. Koblischka, J. D. Wei, and U. Hartmann, J. Phys. Conf. Ser. 61, 591 共2007兲. 5 H. Saito, H. Ikeya, G. Egawa, S. Ishio, and S. Yoshimura, J. Appl. Phys. 105, 07D524 共2009兲. 6 H. Saito, J. Chen, and S. Ishio, IEEE Trans. Magn. 35, 3992 共1999兲.
