~ i Jeurnal ef magnetic ~ i materials

ELSEVIER Journal of Magnetism and Magnetic Materials 162 (1996) 362-368

Interface wall structure of exchange-coupled ferrimagnetic bilayer films for magneto-optical recording

Chubing Peng a,*, Seh Kwang Lee b, Soon Gwang Kim b a Department of Physics, Beijing Unit,ersiO', Beijing 100871, China

b Materials Design Laboratory, Korea Institute of Science and Technology, P.O. Box 131, Cheongryang, Seoul 130-650, South Korea

Received 10 November 1995

Abstract

We investigated the static interface wall structure for exchange-coupled double-layer magneto-optical films. Our calculation was based on the mean-field theory and the Landau-Lifshitz-Gilbert motion equation. We obtained the interface wall energy and switching fields in the magnetic hysteresis loops of bilayer films. The calculation shows that the interface magnetic wall structure depends on the magnetic properties of each layer, the external field, and also the thickness of the respective layer. These results have been confirmed by experiments.

Keywords: Interface exchange coupling; Wall energy; Magneto-optical recording

1. Introduction

Recently, exchange-coupled (hereafter denoted EC) ferrimagnetic bilayer and multi-layer films have been extensively studied for their potential advan- tages in magneto-optical recording. Technological advancements towards a higher recording density and a higher data transfer rate such as the use of short wavelength lasers, magnetic superresolution, and direct overwriting, tend to require the use of EC films for one reason or another [1]. The interface coupling in EC films seems to play an important role in MO recording. In 1981, Kobayashi et al. [2] first

* Corresponding author. Materials Design Laboratory, Korea Institute of Science and Technology, P.O. Box 131, Cheongryang, Seoul 130-650, Korea. Fax: + 82-2-958-5409.

investigated the characteristics of the magnetic hys- teresis loops of ferrimagnetic bilayer films. They explained the anomalous and inverted shape of the magnetic hysteresis loops by introducing the concept of an interface magnetic wall. According to their theory, transition metal (TM) and rare-earth (RE) ferrimagnetic bilayer films are classified into two types (types I and II). In type I, the TM moment is larger than the RE moment in one layer, but the RE moment is larger than the TM moment in the other layer. An interface magnetic wall exists when the net moments of both layers are parallel to each other. In type II, the TM (or RE) moment is larger than the RE (or TM) moment in both layers. An interface wall exists when the net magnetization in one layer is antiparallel to that in the other layer. In 1989, Kaneko et al. [3] studied the interface wall structure for magnetic double-layer and triple-layer films us-

0304-8853/96f$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S0304-8853(96)00084-4

C. Peng et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 362-368 3 6 3

ing a macroscopic variation method. However, this method is not valid for illustrating the interface wall for ferrimagnetic EC films, especially for films of type I. Here, we investigate the interface magnetic wall and evaluate the interface wall energy for both type I and type II on the basis of the Landau- Lifshitz-Gilbert motion equation and by use of a mean-field analysis method. We then apply these to evaluate the switching fields of hysteresis loops for G d - F e / T h - F e and ThFeCoNd/TbFeCo bilayer films and compare the calculated results with the experimental value.

2. Theoretical considerations

To study the interface magnetic wall in a bilayer film, we adopt a mean-field model for the amor- phous system. Each layer consists of three magnetic subnetworks [5]. For convenience, the following con- vention is used to represent each subnetwork: n = 1 for the heavy rare earth; n = 2 for the transition metal; and n = 3 for the third magnetic atom. In this study, we place the interface of bilayer films on the x-y plane of our coordinate system. The positive z-axis enters the first layer. The direction of the ion moment at each point is described by (0,4)) in spherical coordinates. Within the very small volume surrounding each point, the direction of the moment for RE ions is assumed to be antiparallel to that for n = 2 and 3 species. Moreover, for simplicity, we also assume that 0 is only a function of z, and that 4~ = -rr/2 for n = 3 species.

The magnetic moment m will proceed under effective magnetic field Hef f. The macroscopic mo- tion equation, the Landau-Lifshitz-Gilbert (LLG) equation, which governs the spin dynamics, is ex- pressed as [4]

dm = " ~ m X n e f f , (1)

dt

where Y is the effective gyromagnetic ratio. Under static equilibrium conditions, the total

torque should vanish:

3

E M, X (Heff) , = 0, (2) n = l

where M, and (Heft.)" are the magnetization of the nth subnetwork and the effective field exerted on the nth subnetwork, respectively.

In our case, the effective field includes the exter- nal, exchange, local anisotropy and the demagnetiz- ing field. Each of these sources will be illustrated as follows.

2.1. Effective field, torque and energy

2.1.1. External field The external field is assumed to be applied along

the direction of the positive z-axis. In terms of spherical coordinates, it can be expressed as:

n ( ex t ) = - H sin 0,

H~ ext)= 0, (3a)

where Ho (ext) a n d n~ ext) are the components of the external field ( H ) in the 0 and ~b direction, respec- tively. The component Ho (ext) tries to pull the net magnetization (M) towards the direction of the ex- ternal field via the shortest path. Therefore, the torque due to the external field can be written as

(torque)ext = M X H = - H M sin Oi, (3b)

where i is the unit vector along the x-axis. The excess Zeeman energy density due to the deviation of the magnetization from the direction of the exter- nal field can be expressed as

Wex t = HM(1 -- cos 0). (3c)

2.1.2. Local anisotropy field The local uniaxial anisotropy is assumed to be

normal to the film plane, and the anisotropy constant is K u. The anisotropy field is:

H 0 (ans) = - - ( gu/Iml)sin 2 O,

n~ ans)= 0. (4a)

This field is in the 0 direction and tries to pull the magnetization towards the easy axis via the shortest path. The anisotropy torque is then

(torque)ans = M X H (arts) = - - g u sin 20i (4b)

and the anisotropy energy density is

Wans = K u sin20. (4c)

364 C. Peng et al./ Journal of Magnetism and Magnetic Materials 162 (1996) 362-368

2.1.3. Exchange field For a pair of ions with angular m o m e n t Jm and

j . , the mutual energy in the classical approximation is given by

emn = - 2 J m n J m "in' (5a)

where J. , . is the exchange constant. If Jm. > 0, the excess energy due to the non-parallel alignment of moments is

Ae"n=2JmnlJmllJn[[ 1 [Z I I-~. [ J"'J"] ' (5b)

and if am. < 0, the excess exchange energy due to non-antiparallel alignment of moments is

Aem = 2J,..lJmllj. l[__ 1 Jm "J. 1 IZl l ] (5c)

The effective field exerted on j . in spherical coordinates is therefore expressed as

2L,.ljml Ho (xfg) - - - [sin 0 cos O,

gn tLB

- c o s (9 sin 01 cos((# - (#j)],

2J...IJml He, (xt~> - - [ s i n 01 s i n ( ( # - (#,)]. (6)

g . / ~

where 0,4) are the angles for j . , and 01,(# l for j .... and g . is the g-factor of the nth species.

Now let us consider a sphere surrounding a site q, and assume that the radius of this sphere is the distance between the nearest neighbors. The proba- bility for the nth magnetic species to take the central q site is x . ( x . is the atomic composition of the nth species), and that for the mth magnetic species to take the surface p position is x m. The position of the site p on the surface of the sphere is described by (Op,(#p). All spins on the surface of this sphere will exert an exchange field on the central ion. Let us first consider the case of n = 3.

For m = 3, 0 = O(z = p ) , 4)= ~r/2 and 01 = O(Z = q), (#l = r r /2 ; from Eq. (6) the exchange field is

H0 (xfg) = 2J33]J31 sin( 01 - 0 ) ,

g3/a'B

H~ "rg)= 0. (7a)

On making the following approximation:

dO sin(O 1 - O) = 01 - O= 7 ( d 3 3 cos 0,) QZ ""

1 d20 +7 dz 2(d" c°s °A2,

(7b)

where d.m (n = 3 and m = 3 in Eq. (7b)) are the nearest distances between the nth and ruth ions, the sum of the exchange fields from all nearest neigh- bors of m = 3 species on the sphere can be ex- pressed as

Ho(Xfg ) _ J331J31 d20 z~ g3 ~B dz2d33 y'~ (cos Op) 2. (7c)

p= 1

In the same way, for m = 2, 4, = "rr/2 and (#i = 'rr/2, the exchange field is

J32]J21 d20 "'3 H0 (xfg) -- d2 E (cos 0p) 2, (7d)

g3/~B dz 2 32p= 1

and for m = 1, 0 t ~ ~ - 0 t and (#1 --*'rr + 7 / 2 the exchange field is

H0(xfg ) J31[Jl[ d20 2 Z3 g3 ~B ~Z2 d31 E (cos op) 2. (7f)

p=l

Similarly, one can obtain the exchange fields for n = 2,3 and m = 1,2,3, respectively.

Finally, the total effective exchange field torque can be written as:

3 d20 (torque)xng = Y'~ M. X H~ (Xfg) = 2a-yzT_2i, (8a)

,,= i dz

where A is the effective exchange stiffness, defined as

1 3 3 Z.

A --N E x . l j . I E • 2 = XmlJ.mllJmld.m E c°s20p • 2 n=l m=l p=l

(8b)

This expression for exchange stiffness is different from that derived by Mansuripur and Ruane [5]. In fact, Eqs. (8a) and (8b) are also suitable for ferro- magnetic alloys. For a simple cubic structure

1 z, , 2" E COS20p = I.

p=l

C. Peng et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 362-368 365

Similar to the derivation of Eqs. (8a) and (8b), from Eqs. (5b) and (5c), one can obtain the excess exchange energy density

( d0) 2. Wxhg = A ~ z (9)

2.1.4. Demagnetization energy In the model considered, the net moment for a

single layer is parallel to the y-z plane. The demag- netizing field is then found to be:

n (dmag) = 4-rrM sin 0 cos 0,

n ~ dmag) = 0. (10a)

This field tries to pull the moment to lie on the film plane. Accordingly, the demagnetization torque on the magnetization is expressed as

(torque)dmag = M X H (dmag) = 4xrM 2 sin 0 cos 0 i,

(10b)

and the demagnetization energy density is

Wdmag = - - 2"rrM 2 sin20. (10c)

2.2. Interface magnetic wall

2.2.1. Interface wall Replacing Eq. (2) with Eqs. (3b), (4b), (8a) and

(10b), one obtains the torque equilibrium equation: (a) z > 0:

d20 -HIMlls in 0 - ( K u ~ - 2r rM?)s in20 + 2A 1 dz 2

=0, (ll) (b) z < 0:

- ( -1)'nlM21sin 0- (gu2 - 2"rrM~)sin 2 0

d20 + 2 A2-S-7_ 2 = 0 , (12)

dz where A i, K~i and M i represent the exchange stiff- ness, anisotropy constant, and the saturation magne- tization for the first (i = 1) and second layer (i = 2). In addition, 1 = 1 for type I and I = 2 for type II.

Eq. (11) can be integrated to give:

al(~z)Z=(K,,-21rM~)sin20

- HIMllcos 0 + constant. (13)

If the layer (z > 0) with thickness Dº is thick enough, the constant can be determined from boundary condi- tions:

d0 at z = D 1, 0 = 0 a n d - - = 0 . (14)

dz

Then Eq. (13) becomes

Al( dz ] = ( Kul - 2 xr M•) sin20 + HIM l I( 1 - cos 0 ).

(15)

Similarly, in the layer z < 0, Eq. (12) becomes

a2~dz(d0)2=(Ku2-2"rrM~)sin20

- ( - l ) tn lMzl( l +cosO). (16)

For type II, it is required that

(Ku2-2~rM~)sinZO-H(l+cosO)>O. (17)

This means that the angle of deviation (0) of the TM moment at the interface (z = 0) must satisfy:

~/ 2[MzIH 0> 2arcsin Ku2 - 2TrM~ " (18)

2.2.2. Interface wall energy From Eqs. (3c), (4c), (9), (10c), (13), (15) and

(16), one can estimate the total interface wall energy per unit area of wall:

°'w = £D2 -2xrMZ)sin20+A[-~z ) ]dz

+ H[lM, l fo°'(1- cos O )dz

+(-1)'[M2lf°_o(l +cosO)dz], (19)

where D 2 is the thickness of the layer in the z < 0 region.

3. The interface wall structure of double layers

In our numerical calculation, we first calculated the interface wall energy at various spin deviations

3 6 6 C. Peng et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 362-368

0 o at z = 0, and then determined the optimal 0 o value at which the interface wall energy achieves a minimum value. All magnetic parameters, including the saturation magnetization, anisotropy constant and exchange stiffness, were estimated through mean- field analysis [5]. Based on the model of Kobayashi et al. [2] for bilayer films, we also calculated the switching fields (H~) in the hysteresis loops. There is a fundamental difference between our calculation and the theory of Kobayashi et al., however. In our model, the interface wall energy depends on the external field: o- w = O-w(H). The switching fields were then estimated in a self-consistent way.

Let us first consider a Gd-Fe (15 n m ) / T b - F e (50 nm) bilayer film. The experimental data was extracted from Refs. [6,7]. The net magnetization is dominated by the Fe subnetwork in the Gd-Fe layer and by the Tb subnetwork in the Tb-Fe layer (type I). The calculated switching fields are 4.02 and 13.00 kOe, in agreement with the experimental values, and the corresponding interface wall energy is 1.61 and 2.47 e r g / c m 2, respectively. The reversal magnetiza- tion process is reproduced as follows: the film is first magnetized to saturation under a strong applied field and the interface wall forms. The magnetic field is then reduced. When the field drops to about 4.10 kOe (one of the switching fields), the net magnetiza- tion of the G d - F e layer is reversed and the interface

"2" ,% 09

,'o v

1 8 0

1 3 5

9 0

4 5

0 - 5 0 0

T b - F e

I - 2 5 0 0 2 5 0 5 0 0

z(~)

Fig. 1. The interface wall structure for a Gd-Fe /Tb-Fe bilayer film at room temperature under an applied magnetic field of (a) 4.0 and (b) 13.0 kOe. The angle 0 of the Fe subnetwork magneti- zation from the normal direction is calculated as a function of the coordinate z in the thickness direction. The parameters used for the calculation are: M~I = 130.0 emu/cm 3, Kut = 1.12× 105 erg/cm 3 and A I = 3.35 × 10-7 erg/cm for the Gd22.4 Fe 77.6 layer, and Ms2 =124.0 emu/cm 3, Ku2 =8.32×105 erg/cm 3 and A, = 2.01 × 10 -7 erg/cm for the Tb26Fe74 layer.

180

1:35

.~ 9o

4 5

0 -500 -zso o z50 500

z(~)

Fig. 2. The interface wall structure for a NTFC/TFC bilayer film at room temperature under an applied magnetic field of (a) 2.78 and (b) 6.30 kOe. The parameters used for the calculation are: M~I = 251 emu/cm 3, Kuj = 6.9X 105 erg/cm 3 and A I = 2.91 x 10 7 erg/cm for the NTFC layer, and M,2 =92 emu/cm 3. Ku2 = 5.0× 105 erg/cm 3 and A 2 = 1.74× 10 - 7 erg/cm for the TFC layer.

wall disappears. Finally, when the field reaches - 1 3 . 0 kOe, the net magnetization of the Tb-Fe layer is also reversed and the interface wall reap- pears. Fig. 1 shows a typical interface wall structure for a G d - F e / T b - F e bilayer film. With a decrease in the external field from 13 to 4 kOe, the interface wall shifts towards the Gd-Fe layer side and the wall energy is reduced.

The second case that we studied was a

Nd I 1 . 3 T b l 2.6 Fe56.5 Co 19.6 (NTFC)/Tbzl.2 Fe68.5 C°10.2 (TFC) bilayer film [8]. This film is characterized by a large Kerr rotation of the NTFC layer at short wavelength (about 0.3 ° at wavelength A = 400 nm) and a high coercivity of the TFC layer. For a 30 nm N T F C / 3 0 nm TFC bilayer film, the calculated switching fields are 2.78 and 6.30 kOe, and the corresponding interface wall energy is 1.09 and 1.95 e r g / c m 2, respectively. When this film is magnetized to saturation, no interface wall exists, which is dif- ferent from the G d - F e / T b - F e case. As the applied field is reduced to about - 2.78 kOe, the net magne- tization of the NTFC layer is reversed, and the interface wall forms. Finally, when the field reaches - 6 . 3 0 kOe, the net magnetization of the TFC layer is also reversed, and the interface wall collapses. Fig. 2 shows a typical interface wall structure for a N T F C / T F C bilayer film. With an increase in the external field, the interface wall tends to shift to- wards the TFC layer side.

C. Peng et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 362-368 367

Table 1 Switching fields (H s) and interface wall energy (tr w) at the respective switching field for NTFC/TFC bilayer films at room temperature. For comparison, the experimental values for the switching fields are also listed

Sample H~ (exp.) H~ (cal.) ~r w (cal.) (kOe) (kOe) (erg/cm 2 )

NTFC 100 nm 2.06 NTFC 20 nm/TFC 15 nm 2.36 3.10 1.14

4.00 4.64 1.43 NTFC 10 nm/TFC 20 nm 4.69 5,11 NTFC 15 nm/TFC 20 nm 4.31 4.04 1.29

4.90 5,38 1.63 NTFC 30 nm/TFC 30 nm 2.94 2.78 1.09

6.66 6.30 1.95 NTFC 50 nm/TFC 50 nm 2.55 2.49 1.07

7.84 7.25 2.37 TFC 100 nm 9.41

The switching fields and interface wall energy for N T F C / T F C films of various thickness are summa- rized in Table 1. The interface wall energy is about 1-2.5 e r g / c m 2. It is seen that the calculated switch- ing fields are in good agreement with experimental values. From the table, it is also interesting to note that, for a 10 nm N T F C / 2 0 nm TFC bilayer film, the magnetization reversals in the NTFC and TFC layers occur in the same field and the interface wall does not form in the reversal process. This indicates that the two layers are well exchange-coupled at the interface and that the bi layer film has a coercivity value that is intermediate between the coercivities of the two isolated films.

The temperature dependence of the switching fields and interface wall energy (if it exists) above room temperature was also calculated for the 30 nm N T F C / 3 0 nm TFC bilayer film, as shown in Table 2. The Curie temperature is about 460 and 391 K the for NTFC and TFC single layer, respectively. Obvi-

ously, the magnetization reversal process is sensitive to the temperature. Above 350 K, the two layers are well exchange-coupled, and the reversals in both layers occur simultaneously. The coercivity for the bilayer film is much larger than those for single layers. This indicates that a higher external field is required than in the case of a single layer if the temperature for wr i t ing /e ras ing is lower than the Curie temperature of the NTFC layer. This feature was confirmed by the present authors and others [7].

4. Conclusions

The interface wall structure of magnetic bilayers of types I and II has been studied on the basis of the LLG equation and by use of the mean-field analysis method. The interface wall energy and hence the switching fields have been shown to depend on the magnetic properties of each layer, the external field and the thickness of the respective layer. The calcu- lated results for G d - F e / T b - F e and N d T b F e C o / TbFeCo bilayers are in agreement with experiment. Moreover, the temperature dependence of the switch- ing fields has indicated that the coupling between two layers may have a great effect on the MO recording.

Acknowledgements

The authors would like to thank Mr. Jung-gu Lee for providing some of the experimental data and also Dr. Byung-ki Cheong for a careful review of the manuscript. One of the authors (C.B.P,) acknowl- edges KOSEF for financial support for his stay in

Korea.

Table 2 Switching field (H~) and interface wall energy (~w) at various temperatures (T) for a 30 nm NTFC/30 nm TFC bilayer film

T (K) 330 350 370 390 400

H s (kOe) 2.51, 3.41 2.14 1.45 0.90 0.25 ~w (erg/cm2) 0.95, 1.26

References

[1] R.J. Gambino, T.S. Plaskett and R.R. Ruf, IEEE Trans. Magn. 24 (1988) 2557; see also N.A. Bojarczuk, R.J. Gambino, T.S. Plaskett, P. Fumagalli and R. Ruf, Proc. Magneto-Optical Recording Int. Symp. '92, p. 48.

[2] T. Kobayashi, H. Tsuji, S. Tsunashima and S. Uchiyama, Jpn. J. Appl. Phys. 20 (1981) 2089.

368 C. Peng et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 362-368

[3] M. Kaneko, K. Aratani, Y. Mutoh, A. Nakaoki, K. Watanabe and H. Makino, Jpn. J. Appl. Phys. 28 (Suppl. 28-3) (1989) 27.

[4] M. Mansuripur, J. Appl. Phys. 63 (1988) 5809. [5] M. Mansuripur and M.F. Ruane, IEEE Trans. Magn. 22

(1986) 33.

[6] S. Tsunashima, H. Tsuji, T. Kobayashi and S. Uchiyama, IEEE Trans. Magn. 17 (1981) 2840.

[7] P. Hansen, C. Clausen, G. Much, M. Rosenkranz and K. Witter, J. Appl. Phys. 66 (1989) 756.

[8] Jung-Gu Lee, M.S. Thesis, Taegu University, Korea, 1994, p. 42.