3064 IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 10, OCTOBER 2005 Partitioning of the Perpendicular Write Field Into Head and SUL Contributions T. Schrefl , M. E. Schabes , D. Suess , O. Ertl , M. Kirschner , F. Dorfbauer , G. Hrkac , and J. Fidler Department of Engineering Materials, Sheffield S1 3JD, U.K. Hitachi San Jose Research Center of Hitachi GST, San Jose, CA 95120 USA Institute of Solid State Physics, Vienna University of Technology, 1140 Vienna, Austria We perform multiscale finite element simulation of the write process in perpendicular media. The Landau–Lifshitz–Gilbert equation is solved simultaneously for the head, the data layer, and the soft under layer during the motion of the head. All magnetostatic interac- tions between head, data layer and soft underlayer are concurrently taken into account. This fully integrated recording model enables a detailed analysis of the head field as seen by the media grains. Index Terms—Fast boundary element method, micromagnetics, perpendicular recording, write field. I. INTRODUCTION T HE development of future recording systems with ultra- high storage densities critically depends on a detailed un- derstanding of the write process. The design of the magnetic write head, the data layer, and the soft underlayer (SUL) requires a joint optimization of these components based on their under- lying dynamic magnetization processes. The description of time resolved magnetization dynamics is based on the theory of mi- cromagnetics [1]. In order to calculate the time evolution of the magnetization, Maxwell’s equations are solved simultaneously with an equation of motion for the magnetization vector. In per- pendicular recording all parts of the recording system (current coil, write head, data layer, and SUL) are magnetostatically cou- pled. A precise simulation of the recording process requires to solve the governing equations simultaneously for all these parts while taking into account the movement of the write head [2]. Head field dynamics have been investigated previously using micromagnetic models. Takano [3] showed how the head field rise time is affected by the damping constant, material, yoke length, and pole-tip dimension in ring heads for longitudinal recording. Scholz and Batra [4] solved the dynamic micromag- netic equations using a finite element/boundary element method for a single pole head. They conclude that an intermediate value of the damping constant, short yoke length, and fast current rise time are needed for maximum data rate. Senanan and Victora [5] studied the effect of media permeability on perpendicular recording. They showed that the presence of the medium makes changes to the head field. However, their micromagnetic model used a truncated write poles driven by magnetic charge sheets with explicit time dependence which represent unphysical dy- namic constraints. Here, we follow the approach originally applied for longitu- dinal recording [2] and calculate the magnetization dynamics micromagnetically for the entire recording system, which con- sist of 1) the current coil; Digital Object Identifier 10.1109/TMAG.2005.855227 2) the full three-dimensional (3-D) head structure with the write pole, the yoke and the return pole; 3) the data layer modeled by irregularly shaped Voronoi grains separated by a grain boundary phase with reduced exchange; 4) the SUL. This is a multiscale simulation with the dimensions of the coil and the yoke in the range of 10 000 nm to the grain boundary thickness of 0.5 nm. We compute the head field during recording, taking into account both the back interaction of the data layer onto the head and the SUL and the motion of the head [6]. Here we focus on the time dependence of the dif- ferent contributions to the total head field, which is composed of the field generated by the pole tip, the field generated by the head, and the self-demagnetizing field of the data layer. Besides the magnetic properties, the only input for the simulations are the current profile for the coil excitation and the head velocity. The head field dynamics is calculated from the induced magne- tization processes within the head, the data-layer, and the SUL. Domain wall motion within the yoke of the head, vortex motion within the pole tip of the head, and large-area magnetization processes in the SUL cause a lag of the head field behind the current. Reference [7] provides further details for these effects. II. NUMERICAL BACKGROUND A preconditioned backward differentiation method is applied to solve the Landau–Lifshitz–Gilbert equation for the recording system. At each time step the magnetostatic interaction fields are calculated by using a magnetic scalar potential. We apply a hybrid finite element/boundary element method [8] to compute the magnetic scalar potential. Thus, no mesh is required outside the magnetic parts. All information concerning the mutual in- teraction of the different parts is stored in the boundary element matrix. In order to avoid the matrix elements to be recomputed at each time step due to the movement of the head, we compute the scalar potential at the surface of a so-called field box which moves together with the head. A fast Poisson solver is used to evaluate the potential within the field box at high spatial resolu- tion [9]. Numerical derivation gives the head field which is then 0018-9464/$20.00 © 2005 IEEE