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Magnetic force microscopy using tip magnetization modulated by ferromagnetic resonance
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Nanotechnology 26 125701 (http://iopscience.iop.org/0957-4484/26/12/125701) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 130.56.64.29 This content was downloaded on 31/05/2017 at 16:07 Please note that terms and conditions apply.
You may also be interested in: Recent progress in high-resolution magnetic imaging using scanning probe techniques M Bode, M Dreyer, M Getzlaff et al. Surface potential imaging with atomic resolution by frequency-modulation Kelvin probe force microscopy without bias voltage feedback Lili Kou, Zongmin Ma, Yan Jun Li et al. Local field loop measurements by magnetic force microscopy Marco Coïsson, Gabriele Barrera, Federica Celegato et al. Magnetic force imaging of a chain of biogenic magnetite and Monte Carlo analysis of tip–particle interaction André Körnig, Markus A Hartmann, Christian Teichert et al. Modulation of Step Heights of Thin Pb Films by the Quantum Size Effect Observed by Non-Contact Atomic Force Microscopy Mao Han-Qing, Li Na, Chen Xi et al. Quantitative analysis of the magnetic properties of a carbon nanotube probe T Arie, N Yoshida, S Akita et al. Dual-tip magnetic force microscopy with suppressed influence on magnetically soft samples Marián Precner, Ján Fedor, Ján Šoltýs et al. Effective AFM cantilever tip size: methods for in-situ determination Carlo Maragliano, Ayoub Glia, Marco Stefancich et al.
Nanotechnology Nanotechnology 26 (2015) 125701 (6pp)
doi:10.1088/0957-4484/26/12/125701
Magnetic force microscopy using tip magnetization modulated by ferromagnetic resonance Eiji Arima1, Yoshitaka Naitoh1, Yan Jun Li1, Satoru Yoshimura2, Hitoshi Saito3, Hikaru Nomura4, Ryoichi Nakatani4 and Yasuhiro Sugawara1 1
Department of Applied Physics, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita 565-0871, Japan 2 Center for Geo-environment Science, Graduate School of Engineering and Resource Science, Akita University, Akita 010-8502, Japan 3 Research Center for Engineering Science, Graduate School of Engineering and Resource Science, Akita University, Akita 010-8502, Japan 4 Division of Materials and Manufacturing Science, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan E-mail: [email protected] Received 3 September 2014, revised 17 December 2014 Accepted for publication 22 December 2014 Published 4 March 2015 Abstract
In magnetic force microscopy (MFM), the tip–sample distance should be reduced to analyze the microscopic magnetic domain structure with high spatial resolution. However, achieving a small tip–sample distance has been difficult because of superimposition of interaction forces such as van der Waals and electrostatic forces induced by the sample surface. In this study, we propose a new method of MFM using ferromagnetic resonance (FMR) to extract only the magnetic field near the sample surface. In this method, the magnetization of a magnetic cantilever is modulated by FMR to separate the magnetic field and topographic structure. We demonstrate the modulation of the magnetization of the cantilever and the identification of the polarities of a perpendicular magnetic medium. S Online supplementary data available from stacks.iop.org/NANO/26/125701/mmedia Keywords: ferromagnetic resonance, magnetic force microscopy, magnetic material surface, ferromagnetism, scanning force micrscopy (Some figures may appear in colour only in the online journal) 1. Introduction
measured in the same scan under a constant tip–sample distance (≅15 nm) after a topographic scan using a so-called ‘lift mode’ measurement. This method has been widely used because it is very easy to decrease the nonmagnetic tip– sample interaction and detect magnetic interaction with high resolution. To analyze the magnetic property of the magnetic domain with high spatial resolution, the tip–sample distance should be reduced. However, in lift-mode MFM, it is difficult to image the magnetic domain structure at a small tip–sample distance because of the superimposition of interaction forces such as van der Waals and electrostatic forces induced by the
Techniques to analyze the surface of magnetic memory devices with high spatial resolution are very important to develop today’s information technology. Magnetic force microscopy (MFM) [1–4] is a powerful tool for imaging the microscopic magnetic domain structure. In conventional MFM, a cantilever with a magnetic tip is oscillated at/near the resonance frequency, and the amplitude or phase change is measured as magnetic information of the sample. In general, the amplitude and phase of the oscillating cantilever are 0957-4484/15/125701+06$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
E Arima et al
Nanotechnology 26 (2015) 125701
sample surface on the magnetic interaction force. As an alternative, MFM with a soft magnetic tip driven by an ac magnetic field was proposed to separate the magnetic interaction from the van der Waals and electrostatic interactions [5]. Direction detectable static magnetic field imaging was demonstrated; however, this method of MFM is not applicable to soft magnetic materials because of the use of the external magnetic field. In this study, we propose a new MFM technique using ferromagnetic resonance (FMR) that can detect only the magnetic interaction force between the magnetic tip and the magnetic sample surface near the surface without affecting the magnetization of the sample. In this method, a highcoercivity MFM tip coated with a thin ferromagnetic film is irradiated with a frequency-modulated microwave, and then, the magnetization of the ferromagnetic tip can be modulated [6]. The magnetic field on the surface is measured by detecting the modulation component of the frequency shift Δf of the oscillating cantilever. There is no effect of the microwave on the sample because the resonance frequency fres of the FMR of the sample is different from that of the cantilever. We demonstrate the identification of the polarities of a perpendicular magnetic medium with high spatial resolution.
sample plane. The magnetic force Fmag is given by Fmag = μ 0 m z
(
)
⎪
∫
(3)
(
)
(4)
where mz(dc) and mz(ac) are the amplitude of the dc component and ac component of the magnetic dipole, respectively [5]. The fres of a magnetic sample in the external magnetic field B is given by fres 2 =
⎛ γ ⎞2 ⎡ ⎜ ⎟ B + Ny − Nz μ 0 M ⎤⎦ ⎝ 2π ⎠ ⎣ × ⎡⎣ B + ( Nx − Nz ) μ M ⎤⎦ .
(
)
0
(5)
Here, γ is the electron gyromagnetic ratio, M is the saturation magnetization of the magnetic coated cantilever, and μ0 is the magnetic permeability. Nx, Ny, and Nz are the demagnetization factors [10]. In an MFM cantilever, mainly the tip apex interacts with the sample surface. The tip apex is composed of oblate ellipsoidal magnetic grains. The demagnetization factor Nl along the long axis l and Na along the short axis a for the oblate ellipsoid are given by [11]. Nl = 1 −
(1)
Na =
⎤ ⎡ ⎞ ⎛ 2 r2 r −1⎟ ⎥. ⎢ sin−1⎜⎜ 1 − ⎟ ⎥ r r 2 − 1 ⎢⎣ r 2 − 1 ⎠ ⎝ ⎦ 1
(
)
1 (1 − Nl ). 2
(6)
Here, r is the proportion of l0/a0, where l0 and a0 are the length of the long axis and the short axis, respectively. When B is parallel in the short axis a, using the following relationships Nx = Ny = Nl and Nz = Na, fres is given from equation (5) by
where frf, fm, and fd are the microwave frequency, modulation frequency and modulation bandwidth, respectively. The magnetic force Fmag between the tip and sample surface is given by [7, 8]. Fmag = μ 0 Mtip ⋅ Hsample dv .
.
m z = m z (dc) + m z (ac) cos 2πfm t ,
FMR occurs when an MFM cantilever coated with a thin ferromagnetic film is irradiated with a microwave with its fres. The magnetization of the MFM cantilever is modulated by irradiation with the frequency-modulated microwave. The frequency-modulated microwave is expressed as
⎪
∂z
Here, mz and Hz are the field-dependent dipole moment of the tip and the perpendicular component of the magnetic field with respect to the sample plane, respectively. The value of Hz depends on the perpendicular distance z from the sample surface. When the frequency-modulated microwave is irradiated with the MFM tip, mz is given by
2. Theory
⎧ ⎫ fd sin 2πfm t ⎬ , f (t ) = cos ⎨ 2πfrf t + fm ⎩ ⎭
∂H z
(2)
fres =
Here, Mtip and Hsample are the magnetization vector of the magnetic tip and the magnetic stray field of the sample, respectively. In MFM, the tip can be described using two types of models, a monopole model or a dipole model. The monopole model of the MFM tip applies to a high-aspectratio long cylinder thin tip [7]. Some MFM experiments can be explained well with the monopole model [9]. However, this model cannot be used for a conventional MFM tip. The conventional MFM tip is assumed to be a dipole tip, and the dipole model describes MFM images very well [8]. In this method, we treat the MFM tip as a simple dipole oriented and vibrated along the z-axis, which is perpendicular to the
γ ⎡ ⎣ B + ( Nl − Na ) μ 0 M ⎤⎦ . 2π
(7)
In frequency-modulation dynamic force microscopy (FM-DFM), the relationship between the frequency shift Δf of the oscillation cantilever and the tip–sample conservative interaction force (Fts) is given by Δf = −
f0 ∂Fts . 2 k ∂z
(8)
Here, f0, k, and ∂Fts/∂z are the resonance frequency, stiffness of the cantilever and tip–sample force gradient, respectively. Equation (8) is valid when the oscillation amplitude is much smaller than the decay length of the interaction force. From equations (3) and (8), the frequency 2
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Nanotechnology 26 (2015) 125701
signal of the PLL circuit and measured as the magnetic component of the surface. Experiments were performed using a laboratory-built FM-DFM system operating under ultra-high vacuum conditions at room temperature. The deflection of the cantilever was detected by an optical beam deflection sensor [13, 14]. As magnetic tips, we used high-coercivity MFM tips coated with a 20 nm thick L10-FePt film (SI-MF-40-Hc: Nitto Optical). Their magnetization and coercivity were approximately 560 emu cm−3 and 14.4 kOe, respectively. The magnetization direction of the tips was perpendicular to the sample surface. The stiffness, resonance frequency, and quality factor of the MFM tips were k = 45 N m−1, f0 = 276 kHz, and Q = 8600, respectively. From a transmission electron microscopy image of the MFM tip apex (supplementary data figure 1), the ellipsoidal magnetic grain at the tip apex has a dimension of l0 = 32.25 nm along the long axis and a0 = 29.8 nm along the short axis, and r = lo/a0 was estimated to be approximately 1.09. As a nonmagnetic tip, we used a silicon cantilever (PPP-NCHR: Nanosensors) with a spring constant of k = 40 N m−1, resonance frequency of f0 = 270–280 kHz, and quality factor of Q = 2663. We selected oscillation amplitudes for both cantilevers of 10 nm. These values are thought to be sufficiently small to use equation (8) because the decay length of the magnetic force is large, which is in the range of domain size (100 nm). A SmCo magnet with a magnetic field of 120 mT was used as a sample to measure the microwave-frequency dependence of the tip magnetization. The frequency of the FMR of the SmCo magnet was over 10 GHz. A CoCrPt–SiO2 perpendicular magnetic recording medium was used to image the local magnetic field distribution, which was prepared using an in-line-type magnetron sputtering system. A transmission electron microscopy image of the medium revealed CoCrPt nanoparticles with a diameter of approximately 5.9 nm and an average interparticle distance of approximately 1.6 nm. The recording signals (50 kiloflux change in.) were written using a perpendicular single-pole inductive head.
Figure 1. Block diagram of frequency-modulated magnetic force
microscopy using ferromagnetic resonance. The microwave is frequency-modulated at fmod. The magnitude R and phase ϕ of the modulated component Δfm of the frequency shift Δf are detected with the lock-in amplifier.
shift Δfmag induced by the magnetic interaction is given by Δfmag = −
f0 2k
μ0 m z
∂ 2Hz ∂z 2
.
(9)
The modulated magnetic force is also the conservative force. Therefore, the magnetization of the magnetic cantilever is modulated at a frequency of fmod with FMR. From equations (4) and (9), the modulation components of the frequency shift of the magnetic cantilever Δfm is given by Δfm = −
f0 2k
(
μ 0 m z (ac) cos fmod t
)
∂ 2Hz ∂z 2
.
(10)
From equation (10), the magnetic field gradient ∂2Hz/∂z2 on the surface can be obtained by measuring the modulation component Δfm of Δf.
3. Experimental details 4. Results and discussion Figure 1 presents a block diagram of MFM using FMR. The tip–sample interaction was measured using the frequency modulation (FM) detection method [12]. The cantilever was self-oscillated at its resonance frequency (f0) with a constant amplitude (A) using an oscillator controller (OC4: Specs Zurich GmbH). Δf of the oscillating cantilever caused by the tip–sample interaction was detected by a phase-locked-loop (PLL) circuit (OC4: Specs Zurich GmbH). The surface topography was obtained from the change in Δf in constantheight mode. A frequency-modulated microwave was generated by a microwave signal generator (MG3694B: Anritsu) and irradiated into the cantilever to modulate the magnetization. As an antenna, the center core of a coaxial cable was used to radiate the near-field microwave [6]. The distance between the antenna and cantilever was set to within 0.5 mm. The modulation component Δfm of Δf was detected with a lock-in amplifier (LD2: Specs Zurich GmbH) from the output
First, we investigated whether the magnetization of the ferromagnetic tip could be modulated using FMR. Figure 2 shows the experimentally measured frf dependence of Δf on the SmCo magnet surface in the microwave frequency range of 2.40–3.00 GHz. The frf dependence of Δf was measured while the distance between the tip and the surface was kept constant by interrupting the feedback loop to control the distance. The black dotted line shows the dependence for the nonmagnetic Si cantilever, whereas the red solid line shows the dependence for the magnetic FePt-coated cantilevers. For the Si cantilever, the frf dependence of Δf has no peak. In contrast, for the FePt-coated cantilever, the frf dependence of Δf has a significant negative peak at frf ≅ 2.70 GHz. The negative peak for the FePt-coated cantilever indicates that the magnetization of the tip was changed by the FMR at frf ≅ 2.70 GHz. The bandwidth of half maximum (BWHM) of 3
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Nanotechnology 26 (2015) 125701
Figure 2. Frequency shift (Δf) of the oscillating cantilever as a
Figure 3. Frequency shift (Δf) of the oscillating cantilever as a
function of the microwave frequency (frf) measured on a SmCo magnet surface. The black dotted and red solid lines correspond to Si and FePt-coated cantilevers, respectively. The stiffness, resonance frequency, and Q value of the FePt-coated cantilever (Si cantilever) were 40 N m−1 (40 N m−1), 276.4 kHz (159.6 kHz), and 8588 (15 638), respectively. The amplitude of the FePt-coated cantilever (Si cantilever) was A = 10 nm (10 nm). The power of the microwave was 15 dBm.
function of microwave frequency (frf) measured for the FePt-coated cantilever on the SmCo magnet surface. The black dashed and red solid lines were obtained at Δf = −5 Hz and Δf = −10 Hz, respectively. (MFM tip was same as one used in figure 1).
I and II, respectively. Thus, fres increases with increasing external magnetic field B, which is consistent with the theoretical prediction from equation (7). This result also indicates that the magnetization of the tip was changed by the excitation of the FMR. This report is the first of the magnetization of a magnetic tip being modulated using FMR. Thus far, only the FMR in the sample surface has been detected [18]. Finally, we performed MFM imaging of the surface of a CoCrPt–SiO2 perpendicular magnetic recording medium with a magnetic domain structure of recorded bits (figure 4(a)) to demonstrate the usefulness of MFM using FMR. In figures 4(b) and (c), we present the magnitude and phase images measured using MFM FMR, respectively. In the magnitude image in figure 4(b), we can clearly observe the bright and dark regions, which correspond to the recorded bits and boundaries among the recorded bits, respectively. However, in the phase image in figure 4(c), we can also observe bright and dark regions, where the interval between two bright regions is twice as large as that in the magnitude image. This result indicates that the bright and dark regions in the phase image correspond to the upward and downward directions of the perpendicular magnetic medium, respectively. Figures 4(d) and (e) present line profiles of the magnitude and phase images, respectively. In figure 4(d), the peak interval is estimated to be approximately 100 nm, which is equal to the bit length. In figure 4(e), the peak interval is estimated to be approximately 200 nm, which is twice the bit length. The difference in the phase between the bright and dark regions is estimated to be approximately 180°. These results indicate that the magnitude and phase images correspond to the strength and polarity of the magnetic field of the sample surface, respectively [5]. The profile of the magnitude image appears as a series of rounded peaks, and the profile of phase image contains flattened peaks with flat valleys. This result indicates that the strength of the magnetic field is maximized at the center of the bit and that its polarity dramatically changes between each bit. There is an inherent superiority to imaging polarity. Thus, we demonstrated
the peak at 2.70 GHz was 0.50 GHz. Note that a slight oscillation appears in the frf dependence of Δf for the FePtcoated cantilever. The experimentally obtained fres is in good agreement with the numerically obtained value calculated from equations (6) and (7) to be r = 1.09. This finding indicates that FMR for the MFM tip occurred at frf = 2.70 GHz. The measured peaks were always negative, which indicates that the attractive interaction between tip and sample was increased. The magnetic force appears to be modulated from repulsion to attraction due to FMR. The BWHM of the obtained FMR peak was somewhat larger than that of the FePt thin film deposited on a flat surface [14]. There are two possible reasons for this difference: the magnetic anisotropy of the tip apex was low [15, 16] and/or some FePt grains with different fres near the apex affect the BWHM of the FMR peak [16]. Slight oscillation in the result appears to be due to the excitation of standing spin waves in the ferromagnetic thin film [17]. We measured the FMR peaks with other tips, which ranged from 2.55 GHz to 2.75 GHz. These results indicate that the reproducibility of this experiment was good. When the end of the antenna was brought less than 0.5 mm from the cantilever, the negative peak was observed. However, when the antenna was further than 0.5 mm, the negative peak was not observed at all. According to equation (7), the microwave frequency at the FMR fres should depend on the external magnetic field B. Next, we investigated the B dependence of fres. Figure 3 shows the frf dependence of Δf measured on the SmCo magnet surface for the FePt-coated cantilever. To change the external magnetic field B acting on the MFM tip, the frequency shift before interrupting the feedback loop for distance control was set to Δf = −5 Hz (case I) or Δf = −10 Hz (case II). The frf dependence of Δf showed negative peaks in both cases. The microwave frequencies at the FMR fres were estimated to be approximately fres = 2.705 GHz and fres = 2.720 GHz for cases 4
E Arima et al
Nanotechnology 26 (2015) 125701
Figure 4. (a) Structure of CoCrPt–SiO2 perpendicular magnetic recording medium. (b) Magnitude R and (c) phase ϕ images obtained with MFM using ferromagnetic resonance. Cross-sectional profiles along the red lines in the (d) magnitude and (e) phase images (MFM tip was different from the one used in figures 1 and 2).
could detect the magnetic field near the sample surface without affecting the magnetization of the sample. This technique is very simple and has the potential capability to be applied to other techniques such as magnetic exchange microscopy for detecting the magnetic state of atoms [23, 24] and molecules [25–27].
identification of the polarities of the perpendicular magnetic medium with high spatial resolution with MFM using FMR. In the magnitude image, we approached the tip to the sample, and the signal became larger. However, we could not quantitatively measure the magnetic field because it was difficult to measure how much magnetic force was modulated by FMR [19, 20]. With conventional MFM, imaging 10 nm domain contrast has been reported [21, 22]. With our proposed method, we could obtain only 100 nm domain contrast. There are two possible reasons why a higher resolution could not be achieved: fmic could not be less than on the order of 0.001 GHz and the parameter of the cantilever was not good. By applying a high spring constant and frequency cantilever, the oscillation amplitude decreases, and the magnetic force can be detected more sensitively.
Acknowledgments This work was supported by a Japan Society for the Promotion of Science and a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports, and Culture of Japan.
References 5. Conclusions [1] Rugar D, Mamin H J, Guethner P, Lambert S E, Stern J E, McFadyen I and Yogi T J 1990 Appl. Phys. Lett. 68 1169 [2] Hartman U, Goeddenhenrich T and Heiden C 1991 J. Magn. Magn. Mater. 101 263 [3] Grutter P, Meyer E, Heiselmann H, Rosenthaler L, Hidber H R and Guntherodt H J 1988 J. Vac. Sci. Technol. A 6 279 [4] Martin Y and Wickramasinghe H K 1987 Appl. Phys. Lett. 50 1455 [5] Saito H, Ito R, Egawa G, Li Z and Yoshimura S 2011 J. Appl. Phys. 109 07E330 [6] An T, Ohnishi N, Eguchi T, Hasegawa Y and Kabos P 2010 IEEE Magn. Lett. 1 3500104 [7] Hug H J et al 1998 J. Appl. Phys. 83 5609
We proposed a new method of MFM using FMR to measure magnetic information on the magnetic surface. In this method, a high-coercivity MFM tip coated with a thin ferromagnetic film was irradiated with a frequency-modulated microwave to modulate the magnetization of the ferromagnetic tip. The magnetic field on the surface was measured by detecting the modulation component of the frequency shift of the oscillating cantilever. We demonstrated the first ever modulation of a magnetization of the magnetic cantilever. Furthermore, we demonstrated the identification of the polarities of a perpendicular magnetic medium with high spatial resolution. We 5
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Nanotechnology 26 (2015) 125701
[8] Hartmann U 1999 Annu. Rev. Mater. Sci. 29 53 [9] Saito H, Chen J and Ishio S 1999 IEEE Trans. Magn. 35 3992 [10] Kittel C 1995 Introduction to Solid State Physics 7th edn (NewYork: Wiley) p 504 [11] Bozorth R M 1951 Ferromagnetism (New York: Van Nostrand) p 845 [12] Albrecht T R, Grütter P, Horne D and Rugar D 1991 J. Appl. Phys. 69 668 [13] Yokoyama K, Ochi T, Uchihashi T, Ashino M, Sugawara Y, Suehira N and Morita S 2000 Rev. Sci. Instrum. 71 128 [14] Mansilla M V, Gomez J and Butera A 2008 IEEE Trans. Magn. 44 2883 [15] Hurben M J and Patton C J 1998 J. Appl. Phys. 83 4344 [16] Butera A, Zhou J N and Barnard J A 1999 Phys. Rev. B 60 12270 [17] Martins A, Trippe S C, Santos A D and Pelegrini F 2007 J. Magn. Magn. Mater. 308 120 [18] Nozaki Y, Ohta M, Taharazako S, Tateishi K, Yoshimura S and Matsuyama K 2007 Appl. Phys. Lett. 91 082510
[19] Kappenberger P, Schmid I and Hug H J 2005 Adv. Eng. Mater. 7 332 [20] Proksch R, Skidmore G D, Dahlberg E D, Foss S, Schmidt J J, Merton C, Walsh B and Dugas M 1996 Appl. Phys. Lett. 69 2599 [21] Koblischka M R, Hartmann U and Sulzbach T 2004 J. Magn. Magn. Mater. 272 2138 [22] Moser A, Xiao M, Kappenberger P, Takano K, Weresin W, Ikeda Y, Do H and Hug H J 2005 J. Magn. Magn. Mater. 287 298 [23] Gross L, Mohn F, Moll N, Lijeroth P and Meyer G 2009 Science 325 1110 [24] Fahrendorf S, Atodiresei N, Besson C, Caciuc V, Matthes F, Blügel S, Burgler D E and Schneider C M 2013 Nat. Commun. 4 2425 [25] Kaiser U, Schwarz A and Wiesendanger R 2007 Nature 446 522 [26] Schmidt R, Lazo C, Kaiser U, Schwarz A, Heinze S and Wiesendanger R 2011 Phys. Rev. Lett. 106 257202 [27] Pielmeier F and Giessibl F J 2013 Phys. Rev. Lett. 110 266101
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My IOPscience
Magnetic force microscopy using tip magnetization modulated by ferromagnetic resonance
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Nanotechnology 26 125701 (http://iopscience.iop.org/0957-4484/26/12/125701) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 130.56.64.29 This content was downloaded on 31/05/2017 at 16:07 Please note that terms and conditions apply.
You may also be interested in: Recent progress in high-resolution magnetic imaging using scanning probe techniques M Bode, M Dreyer, M Getzlaff et al. Surface potential imaging with atomic resolution by frequency-modulation Kelvin probe force microscopy without bias voltage feedback Lili Kou, Zongmin Ma, Yan Jun Li et al. Local field loop measurements by magnetic force microscopy Marco Coïsson, Gabriele Barrera, Federica Celegato et al. Magnetic force imaging of a chain of biogenic magnetite and Monte Carlo analysis of tip–particle interaction André Körnig, Markus A Hartmann, Christian Teichert et al. Modulation of Step Heights of Thin Pb Films by the Quantum Size Effect Observed by Non-Contact Atomic Force Microscopy Mao Han-Qing, Li Na, Chen Xi et al. Quantitative analysis of the magnetic properties of a carbon nanotube probe T Arie, N Yoshida, S Akita et al. Dual-tip magnetic force microscopy with suppressed influence on magnetically soft samples Marián Precner, Ján Fedor, Ján Šoltýs et al. Effective AFM cantilever tip size: methods for in-situ determination Carlo Maragliano, Ayoub Glia, Marco Stefancich et al.
Nanotechnology Nanotechnology 26 (2015) 125701 (6pp)
doi:10.1088/0957-4484/26/12/125701
Magnetic force microscopy using tip magnetization modulated by ferromagnetic resonance Eiji Arima1, Yoshitaka Naitoh1, Yan Jun Li1, Satoru Yoshimura2, Hitoshi Saito3, Hikaru Nomura4, Ryoichi Nakatani4 and Yasuhiro Sugawara1 1
Department of Applied Physics, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita 565-0871, Japan 2 Center for Geo-environment Science, Graduate School of Engineering and Resource Science, Akita University, Akita 010-8502, Japan 3 Research Center for Engineering Science, Graduate School of Engineering and Resource Science, Akita University, Akita 010-8502, Japan 4 Division of Materials and Manufacturing Science, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan E-mail: [email protected] Received 3 September 2014, revised 17 December 2014 Accepted for publication 22 December 2014 Published 4 March 2015 Abstract
In magnetic force microscopy (MFM), the tip–sample distance should be reduced to analyze the microscopic magnetic domain structure with high spatial resolution. However, achieving a small tip–sample distance has been difficult because of superimposition of interaction forces such as van der Waals and electrostatic forces induced by the sample surface. In this study, we propose a new method of MFM using ferromagnetic resonance (FMR) to extract only the magnetic field near the sample surface. In this method, the magnetization of a magnetic cantilever is modulated by FMR to separate the magnetic field and topographic structure. We demonstrate the modulation of the magnetization of the cantilever and the identification of the polarities of a perpendicular magnetic medium. S Online supplementary data available from stacks.iop.org/NANO/26/125701/mmedia Keywords: ferromagnetic resonance, magnetic force microscopy, magnetic material surface, ferromagnetism, scanning force micrscopy (Some figures may appear in colour only in the online journal) 1. Introduction
measured in the same scan under a constant tip–sample distance (≅15 nm) after a topographic scan using a so-called ‘lift mode’ measurement. This method has been widely used because it is very easy to decrease the nonmagnetic tip– sample interaction and detect magnetic interaction with high resolution. To analyze the magnetic property of the magnetic domain with high spatial resolution, the tip–sample distance should be reduced. However, in lift-mode MFM, it is difficult to image the magnetic domain structure at a small tip–sample distance because of the superimposition of interaction forces such as van der Waals and electrostatic forces induced by the
Techniques to analyze the surface of magnetic memory devices with high spatial resolution are very important to develop today’s information technology. Magnetic force microscopy (MFM) [1–4] is a powerful tool for imaging the microscopic magnetic domain structure. In conventional MFM, a cantilever with a magnetic tip is oscillated at/near the resonance frequency, and the amplitude or phase change is measured as magnetic information of the sample. In general, the amplitude and phase of the oscillating cantilever are 0957-4484/15/125701+06$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
E Arima et al
Nanotechnology 26 (2015) 125701
sample surface on the magnetic interaction force. As an alternative, MFM with a soft magnetic tip driven by an ac magnetic field was proposed to separate the magnetic interaction from the van der Waals and electrostatic interactions [5]. Direction detectable static magnetic field imaging was demonstrated; however, this method of MFM is not applicable to soft magnetic materials because of the use of the external magnetic field. In this study, we propose a new MFM technique using ferromagnetic resonance (FMR) that can detect only the magnetic interaction force between the magnetic tip and the magnetic sample surface near the surface without affecting the magnetization of the sample. In this method, a highcoercivity MFM tip coated with a thin ferromagnetic film is irradiated with a frequency-modulated microwave, and then, the magnetization of the ferromagnetic tip can be modulated [6]. The magnetic field on the surface is measured by detecting the modulation component of the frequency shift Δf of the oscillating cantilever. There is no effect of the microwave on the sample because the resonance frequency fres of the FMR of the sample is different from that of the cantilever. We demonstrate the identification of the polarities of a perpendicular magnetic medium with high spatial resolution.
sample plane. The magnetic force Fmag is given by Fmag = μ 0 m z
(
)
⎪
∫
(3)
(
)
(4)
where mz(dc) and mz(ac) are the amplitude of the dc component and ac component of the magnetic dipole, respectively [5]. The fres of a magnetic sample in the external magnetic field B is given by fres 2 =
⎛ γ ⎞2 ⎡ ⎜ ⎟ B + Ny − Nz μ 0 M ⎤⎦ ⎝ 2π ⎠ ⎣ × ⎡⎣ B + ( Nx − Nz ) μ M ⎤⎦ .
(
)
0
(5)
Here, γ is the electron gyromagnetic ratio, M is the saturation magnetization of the magnetic coated cantilever, and μ0 is the magnetic permeability. Nx, Ny, and Nz are the demagnetization factors [10]. In an MFM cantilever, mainly the tip apex interacts with the sample surface. The tip apex is composed of oblate ellipsoidal magnetic grains. The demagnetization factor Nl along the long axis l and Na along the short axis a for the oblate ellipsoid are given by [11]. Nl = 1 −
(1)
Na =
⎤ ⎡ ⎞ ⎛ 2 r2 r −1⎟ ⎥. ⎢ sin−1⎜⎜ 1 − ⎟ ⎥ r r 2 − 1 ⎢⎣ r 2 − 1 ⎠ ⎝ ⎦ 1
(
)
1 (1 − Nl ). 2
(6)
Here, r is the proportion of l0/a0, where l0 and a0 are the length of the long axis and the short axis, respectively. When B is parallel in the short axis a, using the following relationships Nx = Ny = Nl and Nz = Na, fres is given from equation (5) by
where frf, fm, and fd are the microwave frequency, modulation frequency and modulation bandwidth, respectively. The magnetic force Fmag between the tip and sample surface is given by [7, 8]. Fmag = μ 0 Mtip ⋅ Hsample dv .
.
m z = m z (dc) + m z (ac) cos 2πfm t ,
FMR occurs when an MFM cantilever coated with a thin ferromagnetic film is irradiated with a microwave with its fres. The magnetization of the MFM cantilever is modulated by irradiation with the frequency-modulated microwave. The frequency-modulated microwave is expressed as
⎪
∂z
Here, mz and Hz are the field-dependent dipole moment of the tip and the perpendicular component of the magnetic field with respect to the sample plane, respectively. The value of Hz depends on the perpendicular distance z from the sample surface. When the frequency-modulated microwave is irradiated with the MFM tip, mz is given by
2. Theory
⎧ ⎫ fd sin 2πfm t ⎬ , f (t ) = cos ⎨ 2πfrf t + fm ⎩ ⎭
∂H z
(2)
fres =
Here, Mtip and Hsample are the magnetization vector of the magnetic tip and the magnetic stray field of the sample, respectively. In MFM, the tip can be described using two types of models, a monopole model or a dipole model. The monopole model of the MFM tip applies to a high-aspectratio long cylinder thin tip [7]. Some MFM experiments can be explained well with the monopole model [9]. However, this model cannot be used for a conventional MFM tip. The conventional MFM tip is assumed to be a dipole tip, and the dipole model describes MFM images very well [8]. In this method, we treat the MFM tip as a simple dipole oriented and vibrated along the z-axis, which is perpendicular to the
γ ⎡ ⎣ B + ( Nl − Na ) μ 0 M ⎤⎦ . 2π
(7)
In frequency-modulation dynamic force microscopy (FM-DFM), the relationship between the frequency shift Δf of the oscillation cantilever and the tip–sample conservative interaction force (Fts) is given by Δf = −
f0 ∂Fts . 2 k ∂z
(8)
Here, f0, k, and ∂Fts/∂z are the resonance frequency, stiffness of the cantilever and tip–sample force gradient, respectively. Equation (8) is valid when the oscillation amplitude is much smaller than the decay length of the interaction force. From equations (3) and (8), the frequency 2
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signal of the PLL circuit and measured as the magnetic component of the surface. Experiments were performed using a laboratory-built FM-DFM system operating under ultra-high vacuum conditions at room temperature. The deflection of the cantilever was detected by an optical beam deflection sensor [13, 14]. As magnetic tips, we used high-coercivity MFM tips coated with a 20 nm thick L10-FePt film (SI-MF-40-Hc: Nitto Optical). Their magnetization and coercivity were approximately 560 emu cm−3 and 14.4 kOe, respectively. The magnetization direction of the tips was perpendicular to the sample surface. The stiffness, resonance frequency, and quality factor of the MFM tips were k = 45 N m−1, f0 = 276 kHz, and Q = 8600, respectively. From a transmission electron microscopy image of the MFM tip apex (supplementary data figure 1), the ellipsoidal magnetic grain at the tip apex has a dimension of l0 = 32.25 nm along the long axis and a0 = 29.8 nm along the short axis, and r = lo/a0 was estimated to be approximately 1.09. As a nonmagnetic tip, we used a silicon cantilever (PPP-NCHR: Nanosensors) with a spring constant of k = 40 N m−1, resonance frequency of f0 = 270–280 kHz, and quality factor of Q = 2663. We selected oscillation amplitudes for both cantilevers of 10 nm. These values are thought to be sufficiently small to use equation (8) because the decay length of the magnetic force is large, which is in the range of domain size (100 nm). A SmCo magnet with a magnetic field of 120 mT was used as a sample to measure the microwave-frequency dependence of the tip magnetization. The frequency of the FMR of the SmCo magnet was over 10 GHz. A CoCrPt–SiO2 perpendicular magnetic recording medium was used to image the local magnetic field distribution, which was prepared using an in-line-type magnetron sputtering system. A transmission electron microscopy image of the medium revealed CoCrPt nanoparticles with a diameter of approximately 5.9 nm and an average interparticle distance of approximately 1.6 nm. The recording signals (50 kiloflux change in.) were written using a perpendicular single-pole inductive head.
Figure 1. Block diagram of frequency-modulated magnetic force
microscopy using ferromagnetic resonance. The microwave is frequency-modulated at fmod. The magnitude R and phase ϕ of the modulated component Δfm of the frequency shift Δf are detected with the lock-in amplifier.
shift Δfmag induced by the magnetic interaction is given by Δfmag = −
f0 2k
μ0 m z
∂ 2Hz ∂z 2
.
(9)
The modulated magnetic force is also the conservative force. Therefore, the magnetization of the magnetic cantilever is modulated at a frequency of fmod with FMR. From equations (4) and (9), the modulation components of the frequency shift of the magnetic cantilever Δfm is given by Δfm = −
f0 2k
(
μ 0 m z (ac) cos fmod t
)
∂ 2Hz ∂z 2
.
(10)
From equation (10), the magnetic field gradient ∂2Hz/∂z2 on the surface can be obtained by measuring the modulation component Δfm of Δf.
3. Experimental details 4. Results and discussion Figure 1 presents a block diagram of MFM using FMR. The tip–sample interaction was measured using the frequency modulation (FM) detection method [12]. The cantilever was self-oscillated at its resonance frequency (f0) with a constant amplitude (A) using an oscillator controller (OC4: Specs Zurich GmbH). Δf of the oscillating cantilever caused by the tip–sample interaction was detected by a phase-locked-loop (PLL) circuit (OC4: Specs Zurich GmbH). The surface topography was obtained from the change in Δf in constantheight mode. A frequency-modulated microwave was generated by a microwave signal generator (MG3694B: Anritsu) and irradiated into the cantilever to modulate the magnetization. As an antenna, the center core of a coaxial cable was used to radiate the near-field microwave [6]. The distance between the antenna and cantilever was set to within 0.5 mm. The modulation component Δfm of Δf was detected with a lock-in amplifier (LD2: Specs Zurich GmbH) from the output
First, we investigated whether the magnetization of the ferromagnetic tip could be modulated using FMR. Figure 2 shows the experimentally measured frf dependence of Δf on the SmCo magnet surface in the microwave frequency range of 2.40–3.00 GHz. The frf dependence of Δf was measured while the distance between the tip and the surface was kept constant by interrupting the feedback loop to control the distance. The black dotted line shows the dependence for the nonmagnetic Si cantilever, whereas the red solid line shows the dependence for the magnetic FePt-coated cantilevers. For the Si cantilever, the frf dependence of Δf has no peak. In contrast, for the FePt-coated cantilever, the frf dependence of Δf has a significant negative peak at frf ≅ 2.70 GHz. The negative peak for the FePt-coated cantilever indicates that the magnetization of the tip was changed by the FMR at frf ≅ 2.70 GHz. The bandwidth of half maximum (BWHM) of 3
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Figure 2. Frequency shift (Δf) of the oscillating cantilever as a
Figure 3. Frequency shift (Δf) of the oscillating cantilever as a
function of the microwave frequency (frf) measured on a SmCo magnet surface. The black dotted and red solid lines correspond to Si and FePt-coated cantilevers, respectively. The stiffness, resonance frequency, and Q value of the FePt-coated cantilever (Si cantilever) were 40 N m−1 (40 N m−1), 276.4 kHz (159.6 kHz), and 8588 (15 638), respectively. The amplitude of the FePt-coated cantilever (Si cantilever) was A = 10 nm (10 nm). The power of the microwave was 15 dBm.
function of microwave frequency (frf) measured for the FePt-coated cantilever on the SmCo magnet surface. The black dashed and red solid lines were obtained at Δf = −5 Hz and Δf = −10 Hz, respectively. (MFM tip was same as one used in figure 1).
I and II, respectively. Thus, fres increases with increasing external magnetic field B, which is consistent with the theoretical prediction from equation (7). This result also indicates that the magnetization of the tip was changed by the excitation of the FMR. This report is the first of the magnetization of a magnetic tip being modulated using FMR. Thus far, only the FMR in the sample surface has been detected [18]. Finally, we performed MFM imaging of the surface of a CoCrPt–SiO2 perpendicular magnetic recording medium with a magnetic domain structure of recorded bits (figure 4(a)) to demonstrate the usefulness of MFM using FMR. In figures 4(b) and (c), we present the magnitude and phase images measured using MFM FMR, respectively. In the magnitude image in figure 4(b), we can clearly observe the bright and dark regions, which correspond to the recorded bits and boundaries among the recorded bits, respectively. However, in the phase image in figure 4(c), we can also observe bright and dark regions, where the interval between two bright regions is twice as large as that in the magnitude image. This result indicates that the bright and dark regions in the phase image correspond to the upward and downward directions of the perpendicular magnetic medium, respectively. Figures 4(d) and (e) present line profiles of the magnitude and phase images, respectively. In figure 4(d), the peak interval is estimated to be approximately 100 nm, which is equal to the bit length. In figure 4(e), the peak interval is estimated to be approximately 200 nm, which is twice the bit length. The difference in the phase between the bright and dark regions is estimated to be approximately 180°. These results indicate that the magnitude and phase images correspond to the strength and polarity of the magnetic field of the sample surface, respectively [5]. The profile of the magnitude image appears as a series of rounded peaks, and the profile of phase image contains flattened peaks with flat valleys. This result indicates that the strength of the magnetic field is maximized at the center of the bit and that its polarity dramatically changes between each bit. There is an inherent superiority to imaging polarity. Thus, we demonstrated
the peak at 2.70 GHz was 0.50 GHz. Note that a slight oscillation appears in the frf dependence of Δf for the FePtcoated cantilever. The experimentally obtained fres is in good agreement with the numerically obtained value calculated from equations (6) and (7) to be r = 1.09. This finding indicates that FMR for the MFM tip occurred at frf = 2.70 GHz. The measured peaks were always negative, which indicates that the attractive interaction between tip and sample was increased. The magnetic force appears to be modulated from repulsion to attraction due to FMR. The BWHM of the obtained FMR peak was somewhat larger than that of the FePt thin film deposited on a flat surface [14]. There are two possible reasons for this difference: the magnetic anisotropy of the tip apex was low [15, 16] and/or some FePt grains with different fres near the apex affect the BWHM of the FMR peak [16]. Slight oscillation in the result appears to be due to the excitation of standing spin waves in the ferromagnetic thin film [17]. We measured the FMR peaks with other tips, which ranged from 2.55 GHz to 2.75 GHz. These results indicate that the reproducibility of this experiment was good. When the end of the antenna was brought less than 0.5 mm from the cantilever, the negative peak was observed. However, when the antenna was further than 0.5 mm, the negative peak was not observed at all. According to equation (7), the microwave frequency at the FMR fres should depend on the external magnetic field B. Next, we investigated the B dependence of fres. Figure 3 shows the frf dependence of Δf measured on the SmCo magnet surface for the FePt-coated cantilever. To change the external magnetic field B acting on the MFM tip, the frequency shift before interrupting the feedback loop for distance control was set to Δf = −5 Hz (case I) or Δf = −10 Hz (case II). The frf dependence of Δf showed negative peaks in both cases. The microwave frequencies at the FMR fres were estimated to be approximately fres = 2.705 GHz and fres = 2.720 GHz for cases 4
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Figure 4. (a) Structure of CoCrPt–SiO2 perpendicular magnetic recording medium. (b) Magnitude R and (c) phase ϕ images obtained with MFM using ferromagnetic resonance. Cross-sectional profiles along the red lines in the (d) magnitude and (e) phase images (MFM tip was different from the one used in figures 1 and 2).
could detect the magnetic field near the sample surface without affecting the magnetization of the sample. This technique is very simple and has the potential capability to be applied to other techniques such as magnetic exchange microscopy for detecting the magnetic state of atoms [23, 24] and molecules [25–27].
identification of the polarities of the perpendicular magnetic medium with high spatial resolution with MFM using FMR. In the magnitude image, we approached the tip to the sample, and the signal became larger. However, we could not quantitatively measure the magnetic field because it was difficult to measure how much magnetic force was modulated by FMR [19, 20]. With conventional MFM, imaging 10 nm domain contrast has been reported [21, 22]. With our proposed method, we could obtain only 100 nm domain contrast. There are two possible reasons why a higher resolution could not be achieved: fmic could not be less than on the order of 0.001 GHz and the parameter of the cantilever was not good. By applying a high spring constant and frequency cantilever, the oscillation amplitude decreases, and the magnetic force can be detected more sensitively.
Acknowledgments This work was supported by a Japan Society for the Promotion of Science and a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports, and Culture of Japan.
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We proposed a new method of MFM using FMR to measure magnetic information on the magnetic surface. In this method, a high-coercivity MFM tip coated with a thin ferromagnetic film was irradiated with a frequency-modulated microwave to modulate the magnetization of the ferromagnetic tip. The magnetic field on the surface was measured by detecting the modulation component of the frequency shift of the oscillating cantilever. We demonstrated the first ever modulation of a magnetization of the magnetic cantilever. Furthermore, we demonstrated the identification of the polarities of a perpendicular magnetic medium with high spatial resolution. We 5
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