J01317

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Micromagnetic study of exchange interaction effect on magnetization reversal mode of

CoFeAl

Umi Muflihatun Nurul Azizah, Suryasatriya Trihandaru, and Nur Aji Wibowo

Citation: AIP Conference Proceedings 1710, 030014 (2016); doi: 10.1063/1.4941480 View online: http://dx.doi.org/10.1063/1.4941480

View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1710?ver=pdfcov Published by the AIP Publishing

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Micromagnetic Study of Exchange Interaction Effect on

Magnetization Reversal Mode of CoFeAl

Umi Muflihatun Nurul Azizah

1,c)

, Suryasatriya Trihandaru

2, b)

and Nur Aji

Wibowo

2, a)

1_{Department of Physics Education, Faculty of Science and Mathematics, Satya Wacana Christian University,}

Salatiga 50711, Central Java, Indonesia

2

Department of Physics, Faculty of Science and Mathematics, Satya Wacana Christian University, Salatiga 50711, Central Java, Indonesia

a)_{nurajiwibowo@gmail.com} b)_{suryasatrya@gmail.com} c)_{192011005@student.uksw.edu}

Abstract. A magnetization switching dynamics of perpendicular magnetic anisotropy material CoFeAl has been simulated. This simulation was conducted using Landau-Lifshift Gilbert equation. The used magnetic parameters are magnetic anisotropy 2.3 × 106_{erg/cm3, magnetic saturation 10 kG, medium Gilbert damping 0.3 and various exchange} constants in a range of (1.5 – 4.0) × 10-7 erg/cm. CoFeAl is modeled as a parallel-pipe with the dimension is 50×50×20 nm3_{. As a result, this simulation predicts that the chosen materials exhibit good thermal stability which is greatly affected} by exchange energy. Magnetization reversal mechanism is dominated by domain wall propagation process. Moreover, the simultaneous distribution of thermal with external magnetic field on the materials reduces the writing field which reaches the minimum value when exchange constant is 3.5 × 10-7_erg/cm.

INTRODUCTION

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In this research, micromagnetic simulation method is used to observe the behaviors of nano-dot magnetization in micro scale [2]. What is researched in this study is the effect of magnetic parameter, which is exchange constant of CoFeAl towards magnetization reversal process of magnetic-based storage material. Exchange constant is important to study because it is closely related to interaction between the adjacent spins in the media [8] which affects the behaviors of nano-dot magnetization reversal. Behaviors of magnetization reversal have to be researched to understand the potential of materials to be applied in magnetic-based storage media [2].

METHOD

The total energy of a micromagnetic system is known as the Gibbs free energy, Etot, which is affected by

magnetization polarization, external field, and a number of magnetic parameters. Etotincludes Zeeman energy,

magneto static energy, magnetocrystal energy, and exchange energy. Etotis formulated in Equation (1)[9].

2

1

2

tot x y z ext magn

E A K_A . . . dV

:

§ § · ·

³¨_© ¨_© m m m ¸_¹ a m J H J H ¸_¹

(1)

Where

0Ms . ,t , 1

P

J r m r m

(2)

In this equation, m is magnetic moment of cell unit

m M Ms

with M is the magnetization and Ms is the

magnetic saturation, mx,y ,zis the space gradient of magnetic moment components which are normalized towards

x, y, and z axis, KAis anisotropy constant, a is vector unit parallel to easy axis, J is magnetic polarization which is shown by Equation (2) where P0is vacuum permeability, Hextis external magnetic field, Hmagnis magnetostatic

field, and A is the function of exchange constant shown by equation _A _{JS c d}2 _{, where J is the sum of exchange,}

S2 is square of the spin, d is the distance between the nearest spins, and c is crystal structure [9].

In equilibrium-magnetized state, magnetic moments of cell units are in line with the direction of effective magnetization fieldHeff . The function of Heffis shown in Equation (3) [9].

2 2

eff ext magn

s s K A . M M A '

H m a m a H H

(3)

WhereMsis magnetic saturation, and the function of 'mis shown in Equation (4)[10].

2 2 2

2 x 2 y 2 z

x y z

w w w

'

w w w

m m m m

(4)

magn

H is calculated using Equation (5)[9].

magn U

H

(5)

WhereU is scalar magnetic potential calculated using Equation (6).

0 in s out U M U ' ' m

(6)

Where

Uin

and

Uout

are scalar magnetic potentials inside and outside nano-dot with limitations as stated in

Equation. (7)[9].

in out in out s U U U U M . w w

wn wn m n

(7)

Before the magnetic moment reach the equilibrium state, it will evolves according to Equation (8) which is known as Landau-Lifshiftz-Gilbert equation [8][11].

[ ]

eff T

s

d

γ

dt

M

dt

D

u

m

m H

H

m

(8)

030014-2

(4)

Withα is Gilbert damping constant, and γ is gyromagnetic ratio (1.76×107_oe-1_.s-1_{) and} T

H is stochastic thermal field.

Equation (8) is solved numerically using magnetic parameters, which are exchange constant Aex, anisotropy

constant K_A, and magnetic saturation Ms which depends on the temperature, as shown in Equation (9), (10) and (11)

[12].

2 0

0 s ex

s M T

A T A

M

§ ·

¨ ¸

© ¹

(9)

2 0

0 s s

M T

K T K

M

A A

§ ·

¨ ¸

© ¹

(10)

0 5

0 ₁ .

s s c

M T M T / T

(11)

Where T is operation temperature and Tc is Curie temperature (1000 K).

After m is calculated using Equation 8, the total energy, Etotcan be calculated. Because m evolves towards time,

then E_totalso changes towards time. In the time interval given, E_totwill reach its maximum value

Emax

and

minimum value

Emin

. When it reachesEmax, Hextis equal toHc.Eminis calculated before and after the magnetic

moments reversal process. In particular temperature T andH_ext, the difference between E_maxandE_min can be

calculated. The difference is called barrier energy EB for magnetic moments reversal. Its magnitude is calculated

using Equation (12).

B max min

E E E

(12)

The total of temperature fluctuation field is assumed to follow Gaussian distribution with amplitude calculated using fluctuation-dissipation theorem as shown in Equation (13 – 14) [3][11].

( )

0

i T

H t

(13)

B

s

2k T

α

σ

=

γ

VM

Δ

t

(14)

Where kB = Boltzman constant, V = nano-dot volume, and 't = time difference (0.25×10-12s).

The perpendicular anisotropy material used as a model in this research is CoFeAl with magnetic parameters KA=

2.3 × 106 _erg/cm3_{, 4}_S_M

s = 10 kG, α = 0.3, and Aex = (1.5 – 4.0) × 10-7 erg/cm. CoFeAl is modeled in the form of

block with a size of 50×50 nm2_{and width of 20 nm called nano-dot or a one-bit information storage. The nano-dot}

consists of 15u15 cell units. Each of them has dimension of 3.3u3.3u20 nm3_{and represents one direction of}

magnetic moments m. The size is chosen to realize HDD with density of ~250 Gbit/inch2_{. This CoFeAl model is}

shown in Fig. 1.

FIGURE 1. Model of nano-CoFeAl with volume of 50u50u20 nm3_{consisting of 15}_u_{15 cell units.}

y

z

x

w

l

(5)

RESULT AND DISCUSSION

FIGURE 2. Scheme of micromagnetic simulation of Nano-CoFeAl in room temperature.

Nano-CoFeAl which is evaluated numerically in this research has in-line magnetization directions with +x axis. Then, it is given with external magnetic field in the direction of –x which magnitude increases linearly from 0 to 20

kOe in room temperature (298 K) for 2.5 ns as shown in Fig. 2. An important thing to research in the magnetization reversal mechanism of nano-CoFeAl is the existence of barrier energy which separates two stable conditions of magnetization, which are initial condition and magnetized condition. Initial condition is a condition where the magnetization direction of nano-CoFeAl is opposite to the direction of external magnetic field. Meanwhile, magnetized condition is a condition where the magnetization direction of nano-CoFeAl is already in line to the given external magnetic field. The existence of the barrier energy shows that energy is required to reverse the magnetization direction of nano-CoFeAl from its initial equilibrium state into its second equilibrium state.

FIGURE 3. Energy profile which has to be overcome in the magnetization reversal of nano-CoFeAl for variations of material intrinsicproperty, which is exchange constant (Aex) =

(1.5 – 4.0) × 10-7 erg/cm in room temperature

H_T 0

.

FIGURE 4. Barrier energy and coercive field change in magnetization reversal of nano-CoFeAl towards the increase of

exchange constant (Aex) = (1.5 – 4.0) × 10-7 erg/cm in room temperature.

Figure 3 shows the energy barrier (EB) profile of nano-CoFeAl for six variations of exchange constant values

(Aex) during the external magnetic field induction,Hext. It is shown that the higher the Aex value (the higher the EB)

has to be overcome. It is known that Aex contributes to the magnitude of exchange energy which further affects the

magnitude of EB. Exchange energy will decrease if the direction of the nearest magnetic moments in the material is

parallel [9]. For a number of Aex values which have been researched, it is observed that the peak of EB can be

reached at the same time. The peak of EB is a condition in which the magnetization direction of nano-CoFeAl will

exactly reverse. This shows that exchange constant tends to have less effect on the time required for magnetization reversal. It is also observed that Aex affects the width of barrier energy 'G where the constriction of 'G takes

place along with the increase of Aex.

The manipulation of material characteristics using a number of Aex variations affects the magnitude of EB and

coercive field (Hc), as shown in Fig. 4. The magnitude of EB can be found by calculating the difference between the

peak energy and the base energy formed during external field induction, as shown in Fig. 2. If EB is quite small, the

0 1 2

2000 3000 4000 5000 6000

E

(

kB

T)

t (ns)

Aex = 1.5Ć10-7_erg/cm

EB

ċģ

1 2 3 4

2500 3000 3500 4000

EB

(

kB

T)

Aex (Ć10-7_erg/cm)

H

c_(O

e)

EB

Hc 298

2.5 t (ns) 2.5 t (ns)

20

Hext (kOe)

T (K)

030014-4

(6)

media magnetization becomes unstable for a long time. The EB value required for HDD media to have good thermal

stability and survival rate over than 10 years is ≥ 60 kBT [6][8]. The result shows that EB for all exchange constant

values are over 60 kBT. Therefore, it is known that CoFeAl with composition of those material intrinsic properties

can also be used as HDD media with good thermal stability for over 10 years. It is also shown that EB tends to get

stronger along with the increase of Aex. It is related to the effect of crystal structure towards the magnitude of

exchange interaction. A media with high exchange interaction will have high c value. With high c value, crystal structure will have a tendency towards particular directions. Because crystal structure tends to align to particular directions along with the increase of Aex, the magnetization direction of CoFeAl will be more difficult to reverse and

have high EB value. In addition to barrier energy, Hc, which is required in magnetization reversal of nano-CoFeAl, is

also getting higher along with the increase of exchange interaction, where Hc is the required field to reverse the

direction of media magnetizations up to 50% [10]. The interesting part is the difference in the increasing patterns of EB and Hc. It is observed that EB tends to increase linearly along with the increase of Aex, whereas Hc is not having

same phenomenon.

FIGURE 5. The magnitude difference of nucleation field in magnetization reversal of nano-CoFeAl for exchange constant

(Aex) = (1.5 – 4.0) × 10-7 erg/cm in room temperature

H_T 0

.

FIGURE 6. Magnetization reversal curve of nano-CoFeAl for variations of the material intrinsic property, which is exchange constant (Aex) = (1.5 – 4.0) × 10-7 erg/cm in room temperature.

Figure 5 shows the exchange constant dependence of nucleation field (Hn). Hn is the required field to force

magnetization directions of the material reverse from its initial conditions [13]. When Aex< 3× 10-7 erg/cm, Hn

decreases significantly for a small change of Aex. However, when Aex> 3.0 × 10-7 erg/cm, Hn tends to be stable

towards Aex increase. The interesting part is when EB and Hcare getting stronger along with the increase of exchange

constant, as shown in Fig. 4. However, nucleation field is getting smaller along with the increase of Aex. This is

caused by the constriction of 'G for stronger exchange interaction.

Figure 6 shows the magnetization reversal curve of nano-CoFeAl for the various exchange constants during the external field induction, Hext. The initial direction of nano-dot magnetizations (t = 0 ns) before the field induction

is in line with +x axis. The external field is submitted in the direction of –x axis and increased from 0 – 2 T for 2.5

ns. This magnetization dynamics is represented by the value of M/Msat. M is instantaneous magnetization direction in

the direction of x axis and Msat is the initial magnetization direction of nano-CoFeAl. If the value of M/Msat is 1, it

shows that M and Msat has the same magnitude and magnetization direction. If the value of M/Msat is 0, it shows that

the total magnetization of M and Msat is zero. In that condition, magnetization of nano-CoFeAl will exactly reverse

and become parallel toHext. On the other hand, if the value of M/Msat is -1, it shows the magnetized condition,

which is the condition when M and Msat has the same magnitude of magnetization with opposite direction, or the

condition where material magnetizations are already in line withHext. During the field induction, the direction of

media magnetization changes along with time until magnetization directions are in line withHext. Through media

inducing process withHext, magnetization direction of nano-CoFeAl can be reversed. It is shown that media with

high Aex requires faster time for the reversal of its magnetization directions compared to media with low Aex. For all

values of simulated Aex, magnetization reversal curve tends to form the S shape. This curve pattern shows that

magnetization reversal process of nano-CoFeAl is more dominated by domain wall propagation process than domain wall nucleation. Moreover, it is shown that when Aex is 1.5 × 10-7 erg/cm and 2.0 × 10-7 erg/cm, magnetization

dissipation occurs, so that the reversal process is slowed. This happens because exchange energy decreases, whereas

2 3 4

6000 7000 8000 9000 10000

Aex (Ć10-7_erg/cm)

Hn

(O

e)

0 1 2

-1 0

1 Aex = 1.5Ć10-7_erg/cm

t (ns)

Mx

/

Msa

(7)

contributions from other energy increase. This result shows that by using the distributed field induction, nano-CoFeAl can be magnetized.

FIGURE 7. Micrograph of magnetization reversal mechanism of nano-CoFeAl with K_┴ = 2.3 u 106 erg/cm3, D 0.3and

4SMs 10kG for variations of exchange constants (Aex) = (1.5 – 4.0) × 10-7 erg/cm in room temperature

H_T 0

Magnetization reversal modes from the simulated values of Aex have identical patterns as shown in Fig. 7. At

first, nano-dot consists of only one domain which magnetic moments are in line with +x axis. This domain is shown in black color. Along with the increase ofHext, white domain starts to form in the center of the nano-dot with a

pattern resembling Z letter. This domain has magnetic moments parallel toHext. Between the two domains, a grey

area, which acts as their boundaries, is formed. This area is known as domain wall. The domain wall propagates to all directions until the magnetization of nano-dot are parallel toHext. This magnetization is marked with the

nano-dot’s change of color from black to white. The forming of the white domain, which starts from the center, shows that

magnetic moments reversal easily occurs in the center compared to other regions. This is caused by the dominance of exchange interaction in the center of the nano-dot. With this domination, magnetic moments in the center of nano-CoFeAl will be less stable compared to magnetics moments in other sides. This instability causes magnetic moments in the center to reverse easier and faster compared to other sides.

1.5u10-7_erg/cm

t = 0.000 ns t = 0.344 ns t = 0.409 ns t = 0.699 ns t = 1.042 ns

2.0 u10-7_erg/cm

2.5 u10-7_erg/cm

3.0 u10-7_erg/cm

3.5 u10-7_erg/cm

4.0 u10-7_erg/cm

030014-6

(8)

(a) _(b)

FIGURE 8. (a) Simulation scheme of magnetization reversal using writing field pulse and thermal pulse, (b) Dependence pattern of threshold field (Hth) in magnetization reversal of nano-CoFeAl for exchange constant (Aex) = (1.5 - 4.0) u10-7 erg/cm.

In the magnetization reversal scheme in room temperature – without thermal stimulation, reversal field required

for various simulated Aex reaches 5520 – 10000 Oe. This value is classified as too high to use in magnetic-based

recording technology. Therefore, in the second part of this paper, thermal field is also inducted simultaneously to magnetic field, as shown in Fig. 8 (a). Both fields increase linearly from 0 Tesla and 298 K for Hw and Tw

consecutively until it reaches particular magnitude, is constant at that value for a period of time, and then decreases linearly to reach its initial value. In this case, Tw increases near Curie temperature. All of this process is done in 5 ns

[1][6]. To evaluate the stochastic effect because of the temperature stimulant effect in magnetization process, this simulation is performed using 20 different random numbers [3]. Using thermal stimulation, there is thermal field (H_T) which is also contributed to the magnitude of Heffin Equation (3).

Using this scheme, the required field to magnetizes the media or what is called as writing field can be determined by calculating the threshold field (Hth). Hth is the minimum magnetic field required until the reversal probability

from the 20 random numbers has a value of 1. The Aex dependence of Hth is shown in Fig. 8 (b). The required Hth for

various simulated Aex (1.5 – 4.0) u10-7 erg/cm is between 1350 – 2500 Oe. Fluctuation of Hth in the range of given

Aex is appropriate to sixth degree of polynomial function as shown in fitted dashed line. It can be seen that Hth tends

to stable for Aex ≥ 3.0 u10-7 erg/cm and has the highest magnitude, which is 2500 Oe, for Aex is 1.75 u10-7 erg/cm.

The result is lower than the reversal field required in a case without any thermal pulse stimulation.

CONCLUSION

Micromagnetic simulation study of nano-CoFeAl for magnetic recording media application using HAMR technology has been performed by solving Landau – Liftshitz Gilbert equation. It is found that with a variety of

exchange constants in a range of (1.5 - 4.0) u10-7 erg/cm, CoFeAl is able to be used as HDD media because it meets the thermal stability requirements of materials. The requirement is having enormous barrier energy in an interval of 2230 – 3390 kBT. This barrier energy magnitude affects the strength of material coercivity, which causes high

reversal field. The magnitude of reversal field can be overcome by stimulation of thermal field so it can be lowered from a range of 5520 – 10000 Oe into a range of 1350 – 2500 Oe. Magnetization reversal mode of nano-CoFeAl is

dominated by domain wall propagation process, which starts with domain forming from the center of nano-dot and propagates into all directions.

ACKNOWLEDGMENTS

This research is funded by Department of Education, Central Java Province, through University Facilitation Young Lecturer Research Program.

1 2 3 4

1500 2000 2500

Hth

(O

e)

Aex(×10-7 erg/cm) 5

0 T 298

H, T

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030014-8