Observation of Zigzag-Shaped Magnetic Domain Boundaries in Granular Perpendicular Magnetic Recording Media Using Alternating Magnetic Force Microscopy

Abstract

In granular media for perpendicular magnetic recording, zigzag-shaped magnetic domain boundaries form between magnetic grains isolated by a non-magnetic grain boundary phase. They are the main source of jitter noise caused by the position fluctuation of magnetic bit transitions. The imaging of zigzag boundaries thus becomes an important task to increase recording density with decreasing bit size, when the zigzag and bit sizes become comparable. We visualized the zigzag boundaries of magnetic domains in as-sputtered granular media with a spatial resolution of less than 3 nm using our developed Alternating Magnetic Force Microscopy (A-MFM). We used a soft magnetic amorphous FeCoB tip with high saturation magnetization, which further enhances the spatial resolution through the inverse magnetostrictive effect. The zigzag size ranged from 2 to 8 nm in media with an estimated grain size of around 5 nm. Additionally, we observed zigzag bit boundaries in commercially recorded granular media with a recording density of 500 kfci.

1. Introduction

Perpendicular magnetic recording remains one of the most used types of digital data storage due to its relatively low price, nonvolatility, reliability and large storage capacity, which makes it a primary choice, especially for secondary storage devices [1]. Growing progress in the development of magnetic recording has led to an increase in recording density above 1 Tb/in² and has reduced bit sizes to the nanometer range, approaching the superparamagnetic limit. So, magnetic media with a fine grain size and significantly high perpendicular magnetic anisotropy, such as SmCo, CoCrPt or L1₀ FePt- alloys, have been developed [2]. However, the increased magnetic anisotropy requires stronger magnetic fields during the recording process in HDDs. To enable magnetic recording and overcome the so-called “magnetic trilemma”, special energy-assisted methods were developed, including microwave-assisted magnetic recording (MAMR) and heat-assisted magnetic recording (HAMR). The realistic potential recording density for these methods is up to 4–5 Tb/in² [3,4,5], whereas the theoretical limit is over 100 Tb/in² [2].

Perpendicular magnetic recording media are designed in two ways: bit-patterned thin film and continuous media. In bit-patterned media, magnetic recording bits are physically patterned initially; however, these media are expensive due to the high cost of lithography. Conventional continuous media consist of randomly deposited nanosized grains, which are separated by a non-magnetic, mostly oxide, layer, making them noticeably cheaper. One recorded bit represents a spatial area consisting of adjacent grains or their magnetic clusters, so the bit boundary is not a straight line and follows the granular or cluster structure. Zigzag boundaries thus become the main source of transition position fluctuations and jitter noise in HDDs [6,7,8,9] and their contribution increases as the bit size decreases, limiting the possible recording density. Moreover, microstructural defects, originating from grain size distribution, misorientation, shape irregularity or imperfect isolation (coalescence), cause spatial inhomogeneity of coercivities [10] and affect the bit zigzag boundary [11,12]. Thus, magnetic characterization of the microstructure in granular recording media is an important task for developing recording devices with increased magnetic recording density.

Precise magnetic imaging is required to characterize fine granular structures with sufficient resolution and sensitivity. Significant progress has been made in micromagnetic simulations, where TEM provides precise information on microstructure, but this method predicts magnetic properties indirectly [7,9,10,12,13]. Zigzag bit boundaries were observed with spin-polarized SEM; however, the method requires a high vacuum and complex instrumentation [14,15]. The resolution of spin-stand testers [16,17] and SQUID-on-a-tip [18] is limited by the size of the sensing element and its distance from the sample, whereas for magneto-optical methods such as MOKE [19], the spatial resolution is limited by the optical wavelength. Conventional MFM imaging is also performed at a distance above the sample surface to avoid Van der Waals forces, which results in imaging the gradient of the stray magnetic field with lower resolution.

We developed an advanced MFM with higher spatial resolution, named Alternating Magnetic Force Microscopy (A-MFM) [20,21]. A-MFM enables the selective detection of magnetic forces even near the sample surface, where non-magnetic surface short-range forces are dominant. A-MFM uses the frequency modulation of the tip oscillation, which is caused by the periodic change in the effective spring constant of the cantilever due to the interaction between the magnetic tip and the magnetic field source. A-MFM performs measurements at a short tip-sample distance using lock-in detection of the frequency-demodulated signal from the tip oscillation near the sample surface, achieving higher spatial resolution of less than 5 nm in air atmosphere [22].

For DC magnetic field measurements, a soft magnetic tip is used, whose magnetic moment is periodically changed by an off-resonance AC magnetic field applied normal to the sample plane. In the experiment, we used a homemade amorphous FeCoB alloy-coated Si tip, which enables high resolution of less than 5 nm by using the inverse magnetostrictive effect [23]. The amorphous alloy-coated tip has a sharp tip end with a very smooth surface because the amorphous alloy has no crystal grain structure. The experimental scheme is similar to that shown in previous work [24].

In this study, we demonstrated the imaging of zigzag-shaped domain boundaries in granular perpendicular magnetic recording media, both with and without recorded bits.

2. Experimental Protocol

We investigated two groups of CoCrPt–oxide granular media using A-MFM with a Si tip coated with homemade amorphous magnetostrictive Fe₆₀Co₂₀B₂₀, which is a soft magnetic material with a high saturation magnetization of above 1000 emu/cm³ [23]. One group of media includes unrecorded as-sputtered granular magnetic films without a coating layer and with different grain sizes, approximately ~5 and ~10 nm. Another group of media consists of granular CoCrPt–SiO₂ perpendicular magnetic media with a protective coating layer and a recording density of 500 kfci, which is used as a PMR medium in hard disk technology.

A-MFM measurements were performed at room temperature in air using a non-contact atomic force microscope (NanoNavi L-trace II, Hitachi High-Tech Science Corporation, Tokyo, Japan), operated with a tip oscillation frequency of around 300 kHz. Pyramidal silicon tips with a ~40 N/m spring constant for the cantilever were coated with a 15 nm amorphous magnetostrictive Fe₆₀Co₂₀B₂₀ film (Figure 1a) using a DC sputtering procedure. The measurements of the DC magnetic field of the sample were performed after a topography scan, in lift mode, less than 5 nm above the surface. The full setup is shown in Figure 1b. The samples were placed over a soft magnetic ferrite core, which was used to generate an AC field, $H_z^{ac}\cos ({\omega }_{m}t)$, where ω_m/2π = 89 Hz and $H_z^{ac}$ (the zero-to-peak amplitude) was 150 Oe. A phase-locked loop (easyPLL, Nanosurf AG, Liestal, Switzerland) was used as a frequency demodulator. Amplitude and phase data were extracted using a lock-in amplifier (LI5640, NF Corporation, Yokohama, Japan), with X as the in-phase and Y as the quadrature components of the signal [24]. The X images of the maximal out-of-plane gradient were analyzed using a homemade program in Wolfram Mathematica to map the zero-crossing position and calculate power spectra. The pixel size of the measured images was 2.5 nm.

The A-MFM measurement procedure is the same as described in previous works [23,24]. We applied an AC magnetic field ${\mathit{H}}_{ex}^{ac}\left(=H_z^{ac}\cos ({\omega }_{m}t){\mathit{e}}_z\right)$ to the tip. Here, the unit vector of the z direction ${\mathit{e}}_z$ was normal to the sample plane. The AC magnetic field causes a periodic change in the tip magnetization (${\mathit{m}}_{tip}$) through the magnetization rotation process. The periodic change in ${\mathit{m}}_{tip}$ is expressed by ${\mathit{m}}_{tip}^{ac}=m_z^{ac}\cos ({\omega }_{m}t){\mathit{e}}_z+m_x^{ac}\sin ({\omega }_{m}t){\mathit{e}}_x$, when ${\mathit{m}}_{tip}^{ac}$ rotates in the x–z plane. The alternating magnetic force gradient ($F_z^{\prime }$), which corresponds to the signal of A-MFM, is given by the following expression:

$$\begin{array}{l}{F}_z^{\prime }={\displaystyle \frac{\partial F_z}{\partial z}}={\displaystyle \frac{\partial }{\partial z}}\left(-{\displaystyle \frac{\partial U}{\partial z}}\right)=-{\displaystyle \frac{{\partial }^2}{\partial z^2}}\left(-{\mathit{m}}_{tip}^{ac}\mathbf{·}{\mathit{H}}_{sample}^{dc}\right)={\displaystyle \frac{{\partial }^2}{\partial z^2}}\left(m_z^{ac}{H}_z^{dc}\cos ({\omega }_{m}t)+m_x^{ac}{H}_x^{dc}\sin ({\omega }_{m}t)\right)\\ =m_z^{ac}{\displaystyle \frac{{\partial }^2{H}_z^{dc}}{\partial z^2}}\cos ({\omega }_{m}t)+m_x^{ac}{\displaystyle \frac{{\partial }^2{H}_x^{dc}}{\partial z^2}}\sin ({\omega }_{m}t)\end{array}$$

Here, ${\mathit{H}}_{sample}^{dc}\left(=H_x^{dc}{\mathit{e}}_x+H_y^{dc}{\mathit{e}}_y+H_z^{dc}{\mathit{e}}_z\right)$ is the DC magnetic field from the sample and $U\left(=-{\mathit{m}}_{tip}^{ac}\mathbf{·}{\mathit{H}}_{sample}^{dc}\right)$ is the magnetic energy of ${\mathit{m}}_{tip}^{ac}$ in ${\mathit{H}}_{sample}^{dc}$.

The lock-in extracted A-MFM signals at angular frequency (${\omega }_m$) are as follows:

$$X=m_z^{ac}{\displaystyle \frac{{\partial }^2{H}_z^{dc}}{\partial z^2}}, Y=m_x^{ac}{\displaystyle \frac{{\partial }^2{H}_x^{dc}}{\partial z^2}}$$

Here, $X$ is the in-phase component of ${\omega }_m$ and $Y$ is the quadrature component of ${\omega }_m$.

The $X$ signal is dominant and has high spatial resolution because the magnetic charge ($q_m$) of $m_z^{ac}$ concentrates at the tip end near the sample surface. In contrast, the $Y$ signal is smaller than the $X$ signal and has lower spatial resolution. In the case of the $Y$ signal, the magnetic charges $q_m$ and $-q_m$ of $m_x^{ac}$ are located at opposite sides of the pyramidal tip and are separated by the tip width. Thus, the large in-plane distance between opposite-sign magnetic charges degrades the resolution, and the large vertical distance between the magnetic charges at the tip sides and the sample surface degrades both the resolution and sensitivity.

Therefore, we used the $X$ signal for DC magnetic field imaging. In the measurement, we used the maximum value of the $X$ signal by adjusting the lock-in phase with respect to the lock-in reference signal. As the reference signal, we used the output voltage of the AC magnetic field source for lock-in synchronization.

By using the $X$ signal, it is noted that A-MFM enables imaging of the transition boundary of perpendicular magnetization domains by detecting zero-crossing positions of the ${\partial }^2{H}_z^{dc}/\partial z^2$ signal. As the magnetic transition boundary in perpendicular granular magnetic recording media is crossed, $H_z^{dc}$ changes the sign by crossing the zero value. Therefore, ${\partial }^2{H}_z^{dc}/\partial z^2$ also changes the sign when passing the transition boundary.

3. Results and Discussion

3.1. Granular Media

In Figure 2, we can see the images of the topography (a,d) and the gradient of the out-of-plane magnetic field ${\partial }^2{H}_z^{dc}/\partial z^2$ (b,e) for the uncoated magnetic media with coarse and fine grain sizes, respectively. The pixel size in the images is 2.5 nm square. Here, the magnetic layer is not coated with a protective layer, so we see that in Figure 2a, the minimal grain size in the coarse medium roughly corresponds to the expected 10 nm. In the topography image of the fine medium in Figure 2d, the surface is smoother, and individual shapes of about 5 nm are not distinguishable. In the images (b,e), bright and dark areas correspond to positive and negative polarities of ${\partial }^2{H}_z^{dc}/\partial z^2$, respectively.

The domains are separated by zero magnetic transition lines, which mark the zero-crossing of the magnetic field gradient, as shown in Figure 2c,f on a pixel net. Zigzag boundaries are seen in both coarse and fine granular media and are observed along the slow scan direction (y). In the case of coarse grains (a–c), the lines are smoother, with zigzag sizes of about 3–10 px (7.5–25 nm), whereas in the case of fine grains (c, d), the zigzag boundaries are more pronounced, with sizes of about 1–3 px (2.5–7.5 nm), which roughly corresponds to the expected grain size values in the media. The yellow circles, which indicate the evaluated average grain size, fit the curvature of the domain boundary. As a result, we concluded that the zigzag-shaped magnetic transition boundary of granular media was observed using the proposed A-MFM method.

For a more detailed analysis of the zigzag size, we approximated the zero transition line using a segmented straight line. To exclude noise, we selected only the straight-line segments of three pixels or larger. Red was used for three-pixel segments, green for four-pixel segments and blue for all the larger segments (five-pixel and longer). The results are shown in Figure 3. In Figure 3a, we can see that the ratio of shorter segments (red and green) is lower than the ratio in Figure 3b. So, the media with fine particle size has shorter segments in the zero transition boundary and, consequently, shorter zigzag lengths. The summary is presented in Figure 3c, where the zigzag distribution in fine particle media has a maximum at ≤3 px, and in coarse media, it peaks at about 7 pixels. Both distributions are asymmetric, with the maximum shifted toward smaller sizes. This distribution shape is typical of a lognormal distribution and may indicate magnetic clustering and interparticle interaction.

3.2. Recorded Media

The A-MFM image of the lock-in $X$ signal for the coated recorded media with a 500 kfci recording density is shown in Figure 4a. In a similar manner to Figure 2, the bright and dark stripes, which correspond to the magnetic bits with positive and negative perpendicular magnetization, are separated by the zigzag-shaped magnetic transition boundary lines. In Figure 4b, the corresponding magnetic surfaces are presented in a 3D image of the magnetic signal $m_z^{ac}{\displaystyle \frac{{\partial }^2{H}_z^{dc}}{\partial z^2}}$ vs. spatial (x,y) coordinates, where they appear corrugated, indicating a granular magnetic structure. The zero transition lines exhibit zigzag roughness of about 2–5 px, or several nanometers (Figure 4c).

To confirm that the observed boundaries were not related to imaging noise, different thresholds d of zero crossing were applied to recognize the magnetic transition. The d parameter is defined as a percentage of I_max-I_min, which denotes the difference between the maximum and minimum signal intensities across all the pixels. Then, d was compared with the signal intensity difference (∆I) between two neighboring pixels with opposite signs on the magnetic transition. When the two nearest pixels, belonging to adjacent positive and negative bits, have $\Delta I>d[\%]\times {\displaystyle \frac{I_{\max }-I_{\min }}{100[\%]}}$, zero crossing points are recognized as the magnetic transition. In contrast, when $\Delta I<d[\%]\times {\displaystyle \frac{I_{\max }-I_{\min }}{100[\%]}}$, zero crossing points are not recognized as the magnetic transition. The resulting magnetic transition boundaries for d = 0–2% are shown in Figure 4c–e. They demonstrate the same zigzag shape, with points dropping out only when the threshold exceeded d ~2%. Therefore, the transition boundary exhibits some steepness (Figure 4b), where noise has only a minor effect, and the zigzag boundaries originate from internal properties, such as the magnetization of individual grains.

The ability of A-MFM to visualize zigzag boundaries was confirmed using the power spectrum in Figure 5. The spectrum was calculated for line profiles taken from Figure 4a for 500 kfci recorded media, where the peak at k_x= 1/λ≈ 10 µm⁻¹ corresponds to the recorded bit size of 50 nm [23,24]. The marked onset point at k_x≈ 160 µm⁻¹ indicates the threshold between the visible signal and the white noise level. As can be seen from the onset point, the maximum wave number k_x≈ 160 µm⁻¹ corresponds to the minimum detectable wavelength or spatial resolution λ/2= 1/(2k_x) ≈3 nm, which is comparable to the pixel size of 2.5 nm. So, the observed zigzag boundaries correspond to the observed spatial resolution. For uncoated media, the expected resolution should be even finer due to the smaller distance between the tip end and the surface of the magnetic media compared to the coated film.

4. Conclusions

We performed magnetic imaging of the magnetic transition region in perpendicular magnetic recording media using our previously developed Alternating Magnetic Force Microscopy (A-MFM) with enhanced spatial resolution. We equipped it with a tip coated with a sensitive amorphous FeCoB soft magnetic film with high magnetostriction, which uses the inverse magnetostrictive effect to increase the effective magnetic volume by facilitating magnetic reversal at the tip end.

The zigzag size was found to be in the range of 2–8 nm for the media with an estimated grain size of around 5 nm, using boundary detection based on the zero perpendicular magnetic field. Therefore, the presented microscopy technique could be useful for the development of high-density magnetic recording media with decreased jitter noise.