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Monte-Carlo Simulations of Thermal Reversal In Granular Planer Media M. El-Hilo Physics Department, University of Bahrain, P.O. 32038, Sakhir, Bahrain Magnetic Recording Bit Length ELECTRIC CURRENT Recording Head PATTERN OF MAGNETISATION ELECTROMAGNET CORE Track Spacing MAGNETIC FIELD OF HEAD DIRECTION OF DISK MOTION Recording Disk (“Media”) DISK MEDIUM Bit Length READOUT SIGNAL DECODED DIGITAL SIGNAL Areal Density = Tracks per inch) x (Bits per inch) Top view of a 36 GB, 10,000 RPM, IBM SCSI server hard disk. The disk has 10 stacked platters. For 3.5 HDD @10000 RPM The time where the head crossing a 0.1mm long bit is: 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 4040 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 The modeled system is a two dimensional hexagonal arrays separated by a distance d with 4040 particles. The model is based on a modified Stoner-Wohlfarth theory taking into account thermal reversal of magnetization vector over finite energy barrier. z y d D x Ha HT m Easy-axis FIG.1. Modeled hexagonal arrays and axis system of a particular particle within the film. The total energy of a particle i within the film is given by: ET KVi sin 2αi mi [ H a xˆ H ij ] j i For a thermally stable particle (blocked), the test for a magnetization reversal over the energy barrier is achieved by calculating the transition probability Pr 1 et / where t is the measuring time and 1 f0heEB ( , HT ) / KT is the inverse of relaxation time with EB is the height of the total energy barrier for reversal. In the calculation of EB ( , HT ) the approximate numerical expression of Pfeiffer is used [1]; EB ( HT , ) KV 1 HT / H K g ( ) [0.861.14 g ( )] Where g ( ) cos 2 / 3 sin 2 / 3 3/ 2 and HK is the anisotropy field. In this study, the approximate numerical expression of Wang et al [2] for the pre-exponential factor f0h is also used; 4 KV f 0h Q H K k BT g 3 ( ) HT 1 H g ( ) K 2 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 0.9 t=1s t=10ms t=10ns 0.6 0.3 -2 0 0 -1 1 -0.3 -0.6 -0.9 Applied Field H(kOe) (a) 2 Reduced Magnetisation M/Ms Reduced Magnetisation M/Ms D=20nm, K=2106erg/cc, Msb=1400 emu/cc. t = 1s t = 10ms t = 10 ns 0.9 0.6 0.3 -2 -1 0 0 1 2 -0.3 -0.6 -0.9 Applied Field H(kOe) (b) FIG.2. The simulated room temperature hysteresis loops for the Co medium when the array separation d=90nm (a) and d=1nm (b). Results/ Co Medium Reduced Coercivity Hc(t)/HK 0.50 d=1 nm d=4 nm d=10 nm d=90 nm 0.45 0.40 0.35 0.30 0.25-10 10 -7 10 -4 10 -1 10 2 10 Conclusion These predictions lead to an interesting result, that is: the time variation of thermal coercivity can be inhibited by promoting interaction effects. Time t (s) FIG.3- Predicted time dependence of thermal coercivity at different array separations for the Co medium. Results/ FePt Medium 0.9 t=1s t=1ms t=10ns 0.6 0.3 -80 -60 -40 -20 0 0 20 40 60 -0.3 -0.6 80 Reduced Coercivity Hc(t)/HK Reduced Magnetisation M/Ms Dm=5nm and standard deviation of 0.25nm (i.e. 5%), K=5107erg/cc, Msb=1200 -0.9 0.4 d = 20 nm d = 0.5 nm 0.3 0.2 -10 10 Applied Field H(kOe) FIG.4-a- The simulated room temperature hysteresis loops for the FePt medium when the array separation d=0.5nm. 10 -7 -4 10 -1 10 10 2 Time t(s) FIG.4b- Predicted time dependence of thermal coercivity at different array separations for the FePt medium. [1] H. Pfeiffer, Phys. Status Solidi 118 (1990), p. 295. [2] X. Wang, H.N. Bertram and V.L. Safonov, J. Appl. Phys. 92(2002), p.2064.. [3] M. El-Hilo, R. Chantrell and K. O’Grady. J. Appl. Phys. 84(1998), p.5114.. [4] M. El-Hilo, J. Mag. Mag. Mater. 272-276(2004), p1700.. [5] M. El-Hilo, K. O’Grady and R. Chantrell J. Mag. Mag. Mater. 120(1993), p.244