# Stable microwave-assisted magnetization switching for nanoscale exchange-coupled composite grain

- Terumitsu Tanaka
^{1}Email author, - Shota Kashiwagi
^{1}, - Yoshitoki Furomoto
^{1}, - Yuto Otsuka
^{1}and - Kimihide Matsuyama
^{1}

**8**:461

**DOI: **10.1186/1556-276X-8-461

© Tanaka et al.; licensee Springer. 2013

**Received: **19 July 2013

**Accepted: **22 October 2013

**Published: **5 November 2013

## Abstract

Magnetization mechanisms of nanoscale magnetic grains greatly differ from well-known magnetization mechanisms of micrometer- or millimeter-sized magnetic grains or particles. Magnetization switching mechanisms of nanoscale exchange-coupled composite (ECC) grain in a microwave field was studied using micromagnetic simulation. Magnetization switching involving a strongly damped or precessional oscillation was studied using various strengths of external direct current and microwave fields. These studies imply that the switching behavior of microwave-assisted magnetization switching of the ECC grain can be divided into two groups: stable and unstable regions, similar to the case of the Stoner-Wahlfarth grain. A significant reduction in the switching field was observed in the ECC grain when the magnetization switching involved precessional oscillations similar to the case of the Stoner-Wohlfarth grain. This switching behavior is preferred for the practical applications of microwave-assisted magnetization switching.

### Keywords

Microwave-assisted magnetization reversal Exchange-coupled composite grain Micromagnetic simulation## Background

Nanoscale magnetic grains are essential for extending the areal density of hard disk drives. These nanoscale grains are found in hard disk drives, in which the problem of writability still remains to be solved. Energy-assisted magnetic recording schemes [1, 2] have already been proposed for solving the writability problems in magnetic recordings. In these recording schemes, microwave-assisted magnetization reversal (MAMR) has recently attracted much attention as an alternative technique for future ultrahigh density recordings. In the case of MAMR, a microwave field is tuned to the ferromagnetic resonance frequency of the recording medium, during which a quasi-direct current (dc) field is also applied, wherein the quasi-dc field is smaller than the switching field in the absence of microwaves. Resonant magnetic precession drives the magnetization over the energy barrier imposed by anisotropy provided that the microwave field amplitude is sufficiently large. Recent experiments [3–6] and simulations [7–13] have demonstrated a reduction in the switching field by applying a large amplitude microwave field with frequencies in the order of gigahertz. To realize ultrahigh density recordings for hard disk drives, magnetic materials with a strong perpendicular magnetic anisotropy (such as *L* 1_{0}-FePt) are required to overcome thermal fluctuations. However, for magnetization reversal, these materials require a strong magnetic head field and microwave field [14] at extremely high frequencies. This is an issue concerning MAMR that needs to be resolved. Recent micromagnetic analysis has shown that an exchange-coupled composite (ECC) structure [15] with both soft and hard magnetic materials effectively reduces the strengths of dc and microwave fields as well as the optimum microwave frequency for magnetization reversal [16–20].

The analytical treatment for the magnetization of a single magnetic vector under circular microwave fields was discussed [14, 21, 22]. In these articles, various steady states of precessional magnetization motions were studied by solving the Landau-Lifshitz-Gilbert (LLG) equation. However, there are so far no reports about the steady state of precessional magnetization motions of ECC structured grain. This study presents the magnetization switching behavior of a nanoscale ECC grain using microwave assistance by drawing comparison with the magnetization motions of Stoner-Wohlfarth grain using LLG simulation.

## Methods

*z*-direction. The anisotropy field of the Stoner-Wohlfarth grain was 60 kOe, and those of the soft and hard sections for the ECC grain were 10 and 60 kOe, respectively. In the ECC grain, the magnetizations of the soft and hard magnetic sections were ferromagnetically coupled at their interfaces through exchange interaction (1.0 × 10

^{−6}erg/cm). All magnetizations were initially arranged in the positive

*z*-direction. The dc pulse field,

*H*

_{dc}, was applied in the negative

*z*-direction and had a pulse width of 10 ns with a rise/fall time of 1 ns. The circularly polarized microwave field with the strength of

*H*

_{ac}was also applied in the

*x*-

*y*plane, where the dc field was constant. These external fields were assumed to be uniformly distributed in the magnetic grains. For all presented results, the exchange stiffness constants for the soft and hard sections were 1.0 × 10

^{−6}erg/cm; the dimensionless Gilbert damping constant was 0.05. The saturation magnetization for the Stoner-Wohlfarth grain was 800 emu/cm

^{3}, and those for the soft and hard sections of the ECC grain were 1,200 and 800 emu/cm

^{3}, respectively.

## Results and discussion

*H*

_{SW}, for the Stoner-Wohlfarth grain as a function of

*H*

_{ac}at 50 GHz. The analytical solutions were obtained by computing the trace and the determinant of the stability matrix expressed by

**A**[20]. It is clearly seen that the stable and unstable switching regions observed in the micromagnetic calculation coincide with the region of det

**A**= 0 and the region bounded by tr

**A**= 0, as derived from Bertotti's analysis. At the boundary of tr

**A**

*=*0,

*H*

_{SW}was confirmed to abruptly increase with decreasing

*H*

_{ac}, which agrees with [14]. Magnetization trajectories during MAMR were calculated using the LLG equation to estimate the switching behavior of the magnetization in the stable and unstable switching regions, which correspond to det

**A**= 0 and the region bounded by tr

**A**= 0, respectively. Figure 3 presents trajectories of the magnetization vectors, which are projected onto the

*x*-

*z*plane for the Stoner-Wohlfarth grain in the unstable switching region (a), at the boundary of tr

**A**= 0 (b), and in the stable switching region (c). The strengths of the dc and microwave fields are

*H*

_{dc}= 46 kOe,

*H*

_{ac}= 2 kOe;

*H*

_{dc}= 33 kOe,

*H*

_{ac}= 3 kOe; and

*H*

_{dc}= 24 kOe,

*H*

_{ac}= 7 kOe for Figures 3a,b,c, respectively. Large angle precession induced by the microwave field is not observed in the early stage of the magnetization switching in the unstable switching region for condition (a). On the other hand, magnetization switching through a quasiperiodic magnetization mode [21] was observed under condition (b), which was also been demonstrated elsewhere [14]. Magnetization was also confirmed to switch through a pure time-harmonic magnetization mode with no generation of higher-order harmonics (P-mode) in the stable switching region (c).

The theoretical treatment is very useful when analyzing the MAMR process. However, applicable field situations of the treatment are limited [21]. Hence, a numerical integration of the LLG equation is necessary for analyzing MAMR processes under various field situations.

*T*= 400 K. The

*H*

_{SW}in MAMR was theoretically shown to steadily decrease with increasing temperature because of thermal fluctuations [14]. As a result, the stable and unstable switching regions shift toward the lower

*H*

_{SW}as shown by the broken lines in Figure 4. In the unstable switching region, the switching events were found to widely distribute in

*H*

_{dc}and

*H*

_{ac}owing to thermal fluctuations. This implies that larger

*H*

_{dc}or

*H*

_{ac}field is necessary for practical applications in magnetic devices utilizing MAMR.

*T*= 0 K. As can be seen in the figure, the strength of

*H*

_{ac}at which an abrupt change in

*H*

_{SW}occurs becomes smaller. The change becomes also smaller when the incident angle increases. Considering the magnetization switching process [21, 22] under microwave fields, these results are reasonable. These results also imply a shift in the unstable switching region toward smaller

*H*

_{ac}and

*H*

_{SW}as well as reduction in the unstable switching region size due to the incident angle. Figure 6 shows trajectories of the magnetization vectors for the Stoner-Wohlfarth grain at an incident angle of 45° when the applied fields are (a)

*H*

_{dc}

*=*31 kOe,

*H*

_{ac}

*=*0.4 kOe and (b)

*H*

_{dc}

*=*30 kOe,

*H*

_{ac}

*=*0.6 kOe. Figure 6a,b also compares the trajectories of the magnetization projected onto the

*x*-

*y*plane. The early stages of magnetization switching are shown in Figure 6c,d. These trajectories are apparently different when large-angle magnetization precession is observed at

*H*

_{dc}= 30 kOe with

*H*

_{ac}= 0.6 kOe. This qualitatively agrees with the magnetization behaviors shown in Figure 3a,b, which also suggests the shift of the unstable region due to the incident angles.

Although the data is not shown, a great reduction in *H*_{SW} was also confirmed at *T* = 400 K when the incident angle was large. These advantages ensure magnetization switching of high *K*_{u} materials by magnetic fields that are practical in device applications such as hard disk drives.

*H*

_{ac}field range. The switching field is minimum when the incident angle is 30°, which is smaller than that for the Stoner-Wohlfarth grain. This tendency is a well-known characteristic in ECC grains in the absence of microwave fields. The abrupt change in

*H*

_{SW}is also clearly seen at

*H*

_{ac}= 0.6 kOe when the incident angle is 0°. This implies that the magnetization behavior of the ECC grain can be classified into the three solution regions of the stability matrix, which is similar to the case of Stoner-Wohlfarth grains. The magnetization switching behaviors were also computed to analyze the switching processes in the stable and unstable switching regions for the ECC grain. Figure 8 shows the trajectories of the magnetization at the top of the hard layer projected onto the

*x*-

*z*plane when the dc and microwave fields are (a)

*H*

_{dc}= 16.6 kOe,

*H*

_{ac}= 0.5 kOe and (b)

*H*

_{dc}= 11.4 kOe,

*H*

_{ac}= 0.6 kOe at an angle of incidence of 0°. Figure 8a shows magnetization switching induced by large damping in the early stage of the switching process. The magnetization switching process seems to be an unstable switching according to the comparison between theoretical analysis and micromagnetic simulation as shown in Figures 2 and 3, respectively. On the other hand, the precessional oscillation is observed at

*H*

_{dc}= 11.4 kOe with

*H*

_{ac}= 0.6 kOe. Magnetization switching involving precessional oscillation was also observed in the stable switching of the Stoner-Wohlfarth grains. This implies that unstable and stable switching occurs under the conditions (a) and (b), respectively, in the ECC grains, indicating that the microwave-assisted switching behavior of the ECC grains qualitatively agrees with the theory predicted by Bertotti [21, 22] and micromagnetic simulation by Okamoto [14].

*T*= 400 K. Figure 9a,b,c,d is for the incident angles of 0°, 15°, 30°, and 45°, respectively. As concluded from the magnetization behavior shown in Figure 8, the switching probability widely distributes in

*H*

_{dc}and

*H*

_{ac}when the incident angle is 0°, which is probably the evidence for unstable switching. On the other hand, the distribution becomes very narrow when the incident angle increases in the same manner as that in Stoner-Wohlfarth grains. This also implies that the reduction in the unstable switching area is due to the incident angles.

## Conclusions

Magnetization switching behavior of a nanoscale ECC grain under microwave assistance has been numerically analyzed by comparing it with that of a Stoner-Wohlfarth grain. The computational simulation indicated that significant switching field reduction due to relatively large microwave field excitation is observed in the ECC grains. Therefore, the magnetization switching in the ECC grain under microwave assistance seems to be divided into two regions of stable and unstable switching depending on applied dc and microwave field strength. Stable switching is more favorable for practical applications when using microwave-assisted magnetization switching in the ECC grain. These results qualitatively agree with the theoretical analysis and the LLG simulation for the Stoner-Wohlfarth grain.

## Authors’ information

TT is an assistant professor in ISEE, Kyushu University. His research interests include micromagnetics, magnetic recording, and high frequency magnetic devices. SK received a B.S. degree in Electrical Engineering from Kyushu University in 2013. YF received an M.S. degree in ISEE from Kyushu University in 2013. YO received a B.S. degree in Electrical Engineering from Kyushu University in 2012. KM is a professor in ISEE, Kyushu University. His research interests include magnetic devices.

## Declarations

### Acknowledgements

This research was partially supported by the Storage Research Consortium (SRC) and a Grant-in-Aid for Young Scientists (A) (grant no. 25709029) 2013 from the Ministry of Education, Culture, Sports, Science, and Technology, Japan.

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.