Journal of Magnetism and Magnetic Materials 109 (1992) 367-374 North-Holland Coercivity angular dependence in longitudinal thin film media Jian-Gang Zhu Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455, USA Received 13 August 1991; in revised form 10 October 1991 Computer simulation study of coercivity out-of-plane angular dependence in thin film longitudinal recording media combined with experimental measurements is presented. A theoretical model developed for studying micromagnetic processes in polycrystalline thin films was utilized for the calculations. Films with crystalline easy axes of the grains randomly oriented in three dimensions as well as in the film plane are investigated. The coercivity angular dependence is analyzed by varying magnetostatic and intergranular exchange interactions in relatively broad ranges. The coercivity angular dependence is characterized by two quantities: the angular position of the coercivity maximum and the normalized difference between the maximum coercivity and in-plane coercivity. The former quantity exhibits significantly different behavior with separately varying the magnetostatic interaction strength and intergranular exchange coupling. The difference may allow us to distinguish the two types of interactions and it may allow us to determine the crystalline anisotropy constant and an effective intergranular exchange coupling strength in the film simultaneously from experimental measurements. Specifically designed experiments are carried out to verify the theoretical calculations. Reasonable agreements between the calculations and experimental measurements are obtained. I. Introduction Angular dependence of coercivity has often been utilized to study the switching mechanism in magnetic recording media, especially in particu- late media [1-3]. However, interactions between magnetic particles in the media results in com- plexities and difficulties in the analysis. It is even more so in thin film recording media in which the collective behavior of the magnetic grains due to strong magnetostatic interactions and possible ino tergranular exchange coupling dominate the mio cromagnetic processes. The purpose of this study is to understand the out-of-plane angular depen- dence of coercivity in the thin film media and its relationship with the magnetostatic and inter- granular exchange interactions in the film. The theoretical calculations were carried out with utilization of a computer simulation model developed earlier [4]. T_ the model, a film is represented by a tw .mensional array of hexagons on a triangular lattice. Each hexagon represents a single crystal grain with uniaxial crystalline anisotropy. The array contains 32 × 32 grains with periodic boundary conditions applied on the opposite sides of the array. The crystalline easy axis of each grain is randomly oriented ei- ther in three dimensions (3D-random) or in the film plane (2D-random). The total effective field on a crystal grain is the sum of the local crys- talline anisotropy field, magnetostatic interaction field, possible intergranular exchange coupling field, and external applied field. Each individual grain is assumed to be always uniformly magne- tized and following Stoner-Wohlfarth coherent rotation. Coupled Landau-Lifshitz equations are utilized to determine simultaneously the magneti- zation orientation of each grain in the array. A value of damping-gyromagnetic ratio [4] ce = h/y = 0.1 was chosen for the calculations. The exter- nal field is applied at an angle 0 with respect to the film plane and 0 is varied in the range from 0° (in-plane) to 90° (vertical). Major hysteresis loops are calculated at the various field angles to obtain the coercivity angular dependence. In a hysteresis loop calculation, the field was varied 0304-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved