Download Monte-Carlo Simulations of Thermal Reversal In Granular Planer

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
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ELECTRIC CURRENT
Recording
Head
PATTERN OF
MAGNETISATION
ELECTROMAGNET CORE
Track
Spacing
MAGNETIC FIELD OF HEAD
DIRECTION OF DISK MOTION
Recording Disk
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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
 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.
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  et / 
where t is the measuring time and  1  f0heEB ( , 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 ( ) [0.861.14 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=2106erg/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=5107erg/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