Relationship Between Coercivity and Magnetic Domain Structure for Permalloy Thin Film

Transaction of the Materials Research Society of Japan 34[3] 407-409 (2009)

Terumitsu Tanaka1*, Junsuke Matsuzaki2, Hiroki Kurisu2 and Setsuo Yamamoto2 1Graduate School of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishiku, Fukuoka 819-0395, Japan *Fax: 81-92-802-3726, e-mail: [email protected] 2Graduate School of Science and Engineering, Yamaguchi University, 2-16-1 Tokiwadai, Ube, Yamaguchi 755-8611, Japan

Relationship between coercivity and micromagnetic structure was estimated using a micromagnetic simulator assuming permalloy film as a magnetic film. Wire-like shaped magnetic film showed relatively high coercivity and the magnetization reversed thorough coherent rotation. Coercivity was found to relate to the micromagnetic structure, and large sized film tends to configure vortex micromagnetic structure and coercivity becomes small.

Key words: soft magnetic material, micromagnetic simulation, micromagnetic structure, coercivity

1. INTRODUCTION for cell, Gilbert damping constant, saturation Permalloy is one of the strong candidate materials for magnetization and time, respectively. 퐻 eff is given by future storage devices such as magnetic random access a summation of the magnetic field vectors for the memory[1], zig-zag shaped magnetic sensors[2,3] and so anisotropy field, the exchange field between neighboring on. Further increase in a recording density requires cells, the magnetostatic fields, and the external applied magnetic patterns smaller below the order of micrometer. magnetic field. Magnetic properties of micrometer sized permalloy dots and wires are well studied so far[4,5]. However, the magnetic properties strongly depend on the size and the 3. RESULT AND DISCUSSION shape especially for nanometer sized magnetic materials. 3.1 Magnetic property of wire-like shaped film In this study, magnetic properties for the nanometer Figure 2 shows coercivity for the permalloy films as a sized permalloy films were estimated using a function of the length. Initially, the magnetization of micromagnetic simulator, and the relationship between the film was saturated in the –x direction by applying the magnetic properties and micromagnetic structures were external magnetic field of 1T. Then, the external discussed. magnetic field was applied in the direction making an angle  = 1˚ with +x direction in the x-y plane. In the case that w is small and the film is wire-like shape, the 2. CALCULATION magnetization coherently rotates and the coercivity In the simulation, permalloy was assumed as a increases with increase in l. This is due to the increase magnetic material. The saturation magnetization, of the shape anisotropy in the x direction for the film. exchange constant and anisotropy field were set to 860 -6 On the other hand, the small coercivities for the film emu/cc, 1.3×10 erg/cm and 0 Oe, which are typical with large w come from the increase of the magnetically values for permalloy films. The size of the permalloy 2 t isotropic properties in the x-y plane. film was set to be l×w nm ×12.5 nm in the x-y-z Figure 3 shows the coercivity for the wire-like films directions considering recent researches on magnetic as a parameter of the incident angle, . The width of memory devices utilizing magnetic thin films. For the the film is 12.5 nm. When the strength of the external calculation, the cells with the size of 2.5×2.5 nm2×12.5 t magnetic field is close to the coercivity, the nm were assumed to have a single three dimensional magnetizations are in a saddle point of the magnetic magnetization vector as shown in Fig. 1. The cell size energy, which gives such a high coercivity in the case was preliminary confirmed to be small enough to that  is 0˚. When  is not 0˚, the magnetizations calculate micromagnetic structure. The magnetization behavior for the cells were calculated using public available micromagnetic simulator, OOMMF[6] based on the Landau-Lifshitz-Gilbert equation. The Landau-Lifshitz-Gilbert equation is expressed as equation (1).

d푀 훼 d푀 = −γ푀 × 퐻 eff + 푀 × (1) d푡 푀S d푡

Fig. 1 Calculation model. Here, 푀, , MS and t represent the magnetization vector

407 408 Relationship Between Coercivity and Magnetic Domain Structure for Permalloy Thin Film

Fig. 2 Coercivity as a function of length for Fig. 4 Incident angle dependence of remanent permalloy films. coercivity for wire-like permalloy films.

(a) “C” state

Fig. 3 Coercivity as a function of length for 12.5-nm-wide permalloy films.

coherently rotate without stabilizing at the saddle point of magnetic energy and the coercivities are almost the half of that for  = 0˚ above 40 nm of l. The (b) “S” state coercivity becomes 0 because the demagnetizing coefficients for the x, y, and z directions are the same for the film with l = 12.5 nm, resulting in non-shape anisotropy. Coercivity and remanent coercivity for magnetically anisotropic materials depend on incident angles. Figure 4 shows incident angle dependence of the remanent coercivity for the wire-like film, which is a typical profile of magnetic reversal for a single magnetic domain with uniaxial magnetic anisotropy[7] and shows that the magnetizations for the film rotate through coherent magnetization reversal process. The result well explains the high coercivity for the wire-like films (c) Vortex with small w and large l. Fig. 5 Micromagnetic structure for l × w = 150 × 2 100 nm sized permalloy film. T. Tanaka et al. Transaction of the Materials Research Society of Japan 34[3] 407-409 (2009) 409

3.2 Relationship between coercivity and magnetic domain structure Coercivities of the permalloy films were estimated using the micromagnetic simulation concerning micromagnetic structure. Magnetic vectors for the cells were initially arranged in random directions, and the micromagnetic structure was estimated calculating magnetization relaxation. The attempts were performed 10 times for each film size. For the small sized films such as wire-like shape discussed in section 3.1, the relaxed magnetization vectors were confirmed to uniaxially align, and the magnetization vectors rotate all together when reverse magnetic field is applied. This magnetization vector configuration and the magnetization reversal process give relatively large coercivity. Magnetic vector configuration and magnetization reversal process, however, vary depending on the film size and shape. Figure 5 shows the obtained micromagnetic structures for the film with l 2 × w = 150 × 100 nm . Three types of micromagnetic Fig. 6 Probability for appearance of vortex structures appeared depending on the initial micromagnetic structure and coercivity for film magnetization arrangements. Coercivity for the film with the size of l × w. with “C” and “S” states[8] of the micromagnetic structure is found to be relatively small comparing to the wire-like shaped film, and the film with vortex 5. REFERENCES micromagnetic structure gives much smaller coercivity. [1] T. Zhu, J. Shi, K. Nordquist, S. Tehrani, M. Durlam, Figure 6 shows probability for the appearance of vortex E. Chen, and H. Goronkin, IEEE Trans. Magn., 33, micromagnetic structure and coercivity regarding film 3601-3603(1997). size. Film size smaller than 100 nm in l or w showed [2] J. L. Tsai, S. F. Lee, Y. D. Yao, and C. Yu, J. Magn. high coercivity about 1-3 kOe due to the strong shape Magn. Mater., 239, 246-248(2002). anisotropy, and vortex structure does not appear in this [3] F. C. S. da Silva, W. C. Uhlig, A. B. Kos, S. Schima, region. In the case that l is comparable to w, and those J. Aumentado, J. Ungris, and D. P. Pappas, Appl. are greater than 100 nm, vortex micromagnetic structure Phys. Lett., 85, 6022-6024(2004). tends to appear and coercivity deceases. This result [4] R. P. Cowburn, J. Appl. Phys., 93, 9310-9315(2003). translates that the coercivity of the film correlates with [5] E. E. Shalyguina, K. H. Shin, and N. M. Abrosimova, the probability for the appearance of the vortex J. Magn. Magn. Mater., 239, 252-254(2002). micromagnetic structure. [6] M. Donahue, and D. Porter, NIST Interagency Report, also available http://math.nist.gov/oommf. 4. CONCLUSION [7] S. Chikazumi, “KYOUJISEITAI NO BUTSURI”, Coercivities for small sized permalloy films were SYOUKABOU, Japan(1997), p. 256. calculated using a micromagnetic simulator. When [8] J. Li, and C. Rau, J. Appl. Phys., 95, 6527-6529 magnetic field applied in reverse direction to the initial (2004). magnetization direction with tiny incident angle, the coercivities were found to be almost half of that for 0˚ of the incident angle. (Received Januray 6, 2009; Accepted June 18, 2009) A relationship between coercivity and magnetic domain structure was analyzed and the vortex micromagnetic structure was found to have tendency to appear when the film size is larger and coercivity is small.