Monte-Carlo Simulations of Thermal Reversal In Granular Planer Media Monte-Carlo Simulations of Thermal Reversal In Granular Planer Media M. El-Hilo Physics Department, University of Bahrain, P.O , Sakhir, Bahrain

Magnetic Recording  Top view of a 36 GB, 10,000 RPM, IBM SCSI server hard disk. The disk has 10 stacked platters. Recording Head Recording Disk (“Media”) Bit Length Track Spacing Areal Density = Tracks per inch) x (Bits per inch) PATTERN OF MAGNETISATION ELECTRIC CURRENT ELECTROMAGNET CORE MAGNETIC FIELD OF HEAD DIRECTION OF DISK MOTION DISK MEDIUM READOUT SIGNAL READOUT SIGNAL DECODED DIGITAL SIGNAL Bit Length For 3.5  RPM The time where the head crossing a 0.1  m longbitis: 100ns

Abstract: A general model is developed to simulate thermally agitated magnetization reversal in granular planar media. The modeled system is a two dimensional (2D) hexagonal array with 40  40 grains. In this work, two systems were modeled; one consist of cobalt nanoparticles (D=20nm) with an average anisotropy coupling constant a(=KV/kT)=200, and another consist of FePt nanoparticles (D=5nm) with a=80. For both media, the time dependence of thermal coercivity at different array separation (d) is simulated. These simulations showed that interaction effects slow down the time variation of thermal coercivity

D d E asy-axis x y z     HaHa HTHT FIG.1. Modeled hexagonal arrays and axis system of a particular particle within the film.  The modeled system is a two dimensional hexagonal arrays separated by a distance d with 40  40 particles.  The model is based on a modified Stoner-Wohlfarth theory taking into account thermal reversal of magnetization vector over finite energy barrier.

  The total energy of a particle i within the film is given by:  For a thermally stable particle (blocked), the test for a magnetization reversal over the energy barrier is achieved by calculating the transition probability Where and HK is the anisotropy field.  In this study, the approximate numerical expression of Wang et al [2] for the pre-exponential factor f 0h is also used; where t is the measuring time and is the inverse of relaxation time with  EB is the height of the total energy barrier for reversal.  In the calculation of the approximate numerical expression of Pfeiffer is used [1];

Monte Carlo simulations (MC) is performed as follows;  At a any given state of magnetization, the magnetic moment of each particle is tested for a reversal using the transition probability Pr.  The reversal is allowed when Pr is greater than the generated random number.  If the reversal is allowed the direction of moment in the new energy minimum is determined using a technique described in previous work [3].  if the transition is not allowed, standard MC moves are used to determine the equilibrium orientation of magnetic moment within the old energy minimum.  After hundreds of moves the magnetization of the system along the field direction is calculated.

Results/Co Medium FIG.2. The simulated room temperature hysteresis loops for the Co medium when the array separation d=90nm (a) and d=1nm (b). (b) (a) D=20nm, K=2  10 6 erg/cc, Msb=1400 emu/cc.

Results/ Co Medium FIG.3- Predicted time dependence of thermal coercivity at different array separations for the Co medium. Conclusion These predictions lead to an interesting result, that is: the time variation of thermal coercivity can be inhibited by promoting interaction effects.

FIG.4-a- The simulated room temperature hysteresis loops for the FePt medium when the array separation d=0.5nm. FIG.4b- Predicted time dependence of thermal coercivity at different array separations for the FePt medium. Results/ FePt Medium [1] H. Pfeiffer, Phys. Status Solidi 118 (1990), p [2] X. Wang, H.N. Bertram and V.L. Safonov, J. Appl. Phys. 92(2002), p [3] M. El-Hilo, R. Chantrell and K. O’Grady. J. Appl. Phys. 84(1998), p [4] M. El-Hilo, J. Mag. Mag. Mater (2004), p [5] M. El-Hilo, K. O’Grady and R. Chantrell J. Mag. Mag. Mater. 120(1993), p.244 Dm=5nm and standard deviation of 0.25nm (i.e. 5%), K=5  10 7 erg/cc, Msb=1200