Micromagnetic Modeling: Theory and Applications in Magnetic Thin Films
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Iflicromagnetic Modeling: Theory and Applications in Magnetic Thin Films
Modeling of Soft-Magnetic Thin Films
Jian-Gang Zhu Introduction Micromagnetic theory concerns detailed magnetization configurations and the magnetization-reversal processes in a ferromagnetic system. By combining the original micromagnetic theory 1 2 with a dynamic description of magnetization orientations, one can simulate complete magnetization processes and calculate important properties such as magnetic hysteresis and magnetic 3 4 switching dynamics. ' Not only can micromagnetic simulation predict complex magnetic-domain configurations in a ferromagnetic system, it also can generate transient pictures showing how a complex domain configuration forms. Very important among these systems are ferromagnetic thin films, particularly those used in sensors and recording devices. Micromagnetic modeling not only has enriched our understanding of existing magnetic films but has also been used to successfully predict the magnetic properties of new film microstructures created for particular ap5 plications. In this article, a brief introduction of micromagnetic-modeling theory will be given. Modeling of soft and hard magnetic films will be discussed separately through two examples illustrating the essence of micromagnetic-magnetization processes in these films.
Micromagnetic Model Micromagnetic theory considers the free energy in the ferromagnetic material during a magnetization process, which
MRS BULLETIN/OCTOBER 1995
in general includes the following energy terms: • Magnetic-anisotropy energy, • Ferromagnetic exchange energy, • Magnetostatic energy, and • Magnetic-potential energy due to the external fields. The effective magnetic field is then defined by H=
-:—
where E is the total free energy and M is the magnetization. The magnetization orientation follows the Landau-LifshitzGilbert equation — = - y M X H - - MXMXH dt M
(1)
where y is the electron gyromagnetic ratio and A is the damping constant. The first term in the equation describes the gyromagnetic motion (precession of M about H) and the second describes the rotation of the magnetization toward the direction of the effective magnetic field. The m a g n i t u d e of M r e m a i n s u n changed by this equation since the motions generated by both terms in the equation are perpendicular to the magnetization orientation. Only the second term, the damping, yields an energy change in the system. Since A is always positive, the energy always dissipates with a rate linearly proportional to A.
Magnetic thin films usually can be categorized into two types: soft and hard, in terms of their coercivities and permeabilities. The most commonly used soft film in magnetic-recording heads is Permalloy (Ni78Fe22) film. The coercivity of Permalloy film is usually a 3 few oersted (of the order of 10 T) with an initial relative permeability of 2,0003,000. In soft magnetic films, the local anisotropy energy is usually two to three orders of magnitude smaller than that of the magnetostatic interaction ene
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