1. Effects of Arrays arrangements in nano-patterned thin film media
M. El-Hilo
Physics Department, University of Bahrain, P.O , Sakhir, Bahrain

2. Effects of Arrays arrangements in nano-patterned thin film media
In this work, the effect of different arrays arrangements on the magnetic behaviour of patterned thin film media is simulated.
The modelled films consist of 5050 Cobalt grains of uniform diameter (20nm) distributed into two different arrays arrangement: hexagonal (triangular) or regular arrays.
For each arrays arrangement, two cases of anisotropy orientations (planer random and textured films) are considered.
For both arrays arrangements, and media orientations, hysteresis loops at different arrays separation (d) were simulated.

3. Regular arrays arrangement Hexagonal arrays arrangement
Modelled nano magnetic dot Systems
Regular arrays arrangement
Hexagonal arrays arrangement

4. The modelled system is a two dimensional hexagonal arrays separated by a distance d with 5050 particles.
The model is based on a modified Stoner-Wohlfarth theory taking into account thermal reversal of magnetization vector over finite energy barrier.
FIG.1. Modeled hexagonal and regular arrays and the axis system of a particular particle within the film.

5. 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 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];
Where 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;

6. 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.
if the transition is not allowed, standard MC moves are used to determine the equilibrium orientation of magnetic moment within the old energy minimum.
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].
After hundreds of moves the magnetization of the system along the field direction is calculated.

7. Results : Planer Random films
Hexagonal Arrays
Calculated hysteresis loops at different array separations for a planer random system of particles located on a hexagonal lattice.
Regularer Arrays
Calculated hysteresis loops at different array separations (a) for a planer random system of particles located on a regular lattice.

8. Planer Random films
Direction of previously applied saturating field
Direction of previously applied saturating field
Calculated hysteresis loops for a planer random system of particles located on a regular and hexagonal lattices for a maximum packing fraction (array separation a=0)

9. Planer Random films
Variation of Coercivity and remanence ratio vs packing fraction for hexagonal and regular arrays arrangements.

10. Hexagonal Arrays Regularer Arrays
Textured films
Hexagonal Arrays
Calculated hysteresis loops at different array separations (a) for textured system of particles located on a regular lattice.
Regularer Arrays
Calculated hysteresis loops at different array separations (a) for textured system of particles located on a hexagonal lattice.

11. Textured films
Calculated hysteresis loops at different array separations (a) for textured system of particles located on a hexagonal lattice.

12. Conclusions:
Depending on the arrays arrangements, predictions of magnetisation loops shows that dipolar interactions in patterned media can give rise to an increase or decrease in the coercivity, remanence ratio and width of the switching field distribution.
For both random and textured films, the hexagonal (triangular) arrays arrangement give rise to enhanced remanence ratio and narrower SFD compared to the regular arrays arrangement.
For closely packed textured films, the hexagonal arrays arrangements showed a very sharp magnetization reversal unlike the regular arrays arrangements which showed a bimodal SFD.
According to these predictions, a dipolar coupled hexagonal arrays of oriented media will have the advantage of extremely narrow switching field distribution.