- Email: [email protected]
Simulation of structural anisotropy in rare-earth transition metal multilayers
3ournal ot Magnetism and Magnetic Materials 177-181 (1998) 1173-1174
~
ELSEVIER
Journalof magnetism and magnetic materials
Simulation of structural anisotropy in rare-earth transition metal multilayers Y. Fujiwara, T. Masaki, X.Y. Yu, S. Tsunashima*, S. Iwata Department of Electronics, Nagoya University, Chikusa-Ku, Nagoya 464-01, Japan
Abstract UniaxiaI structural anisotropy in rare-earth transition-metaI amorphous multilayers has been simulated by using a close-packed superlattice as an initial condition and solving a one-dimensional diffusion equation. The simulation has revealed that the degree of the short-range anisotropic atomic order becomes the maximum at a certain bilayer period depending on the degree of the interlayer diffusion. The calculated trend of the structural anisotropy agrees with the experimental one obtained by extended X-ray absorption fine structure spectroscopy. © 1998 Elsevier Science B.V. All rights reserved.
Keywords: Multilayers; EXAFS; A n i s o t r o p y - uniaxial
Perpendicular magnetic anisotropy (PMA) in amorphous rare-earth transition-metal (RE-TM) films is known to be enhanced by introducing a multilayer structure and to show the maximum at a bilayer period of about 1.0 nm [11. In order to explain the enhanced magnetic anisotropy, Extended X-ray absorption fine structure (EXAFS) experiments were performed on Tb/Fe amorphous multilayers (MLs) and it was found that perpendicular structural anisotropy (SA) measured in the first peak of Fourier-transformed EXAFS was closely correlated with the PMA [2]. We have considered that the SA originated from the difference of the coordination number between film normal and in-plane directions. In this study, we will perform a simple simulation of the SA in order to reproduce and explain the experimental results. Hereafter we calculate the difference of the coordination numbers using a simplified multilayer model, where FCC(1 1 1) planes of A or B atoms with the same atomic size are piled up successively to form an ideal superlattice. Interlayer atomic diffusion which leads the superlattice to the random solid solution is introduced according to the one-dimensional diffusion equation with the same diffusion constants for A and B atoms. Then simulation can be carried out by using the following
differential equation:
*Corresponding author. Tel.: + 81 52 789 3639; fax: + 81 52 789 3153; e-mail: [email protected].
PSA
Cx(z, t + At) = Cx(z, t) - D{Cx(z - d, t) + Cx(z + d, t) -- 2Cx(z, t)}d- ZAt,
(1)
where Cx(z, t) is the concentration o f X ( = A or B) atoms at the position z in the film normal and at time t, D the diffusion coefficient, and d the lattice spacing between the (1 1 1) planes. Starting from the ideal superlattice, we can calculate the concentration Cx(z, t) as a function of time. Using this concentration, we can calculate the expectation value for the number of the nearest neighbor Y atoms seen from X atoms, Nxy (Y = A or B) for any bond directions in the FCC lattice. Effective coordination number N~.r, which could be obtained from EXAFS of X atoms, is given by
N*r = Zi Z}+ ~- zZk3Cx(zi, t) Cr(zj, t) cos201jk ~iCx(zi, t) ,
(2)
where i and j are atomic layer numbers, k represents nearest-neighbor bond direction, 01jk the angle between the directions of a particular X - Y bond and the X-ray polarization. In order to discuss the perpendicular structural anisotropy, we define the perpendicular structural anisotropy PSA as
0304-8853/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 3 4 3 - 0
N~A[I -- N~A± , , N~A [I + NAA.I-
(3)
1174
Z Ftdiwara et al. /Journal of Magnetism and Magnetic Materials 177-181 (1998) 1173-1174
25
' I
. . . . . . .
\ Dd-2t= 0.0
2O
Table 1 Integrated intensities of the first low-angle X-ray diffraction peaks for muttilayers with 4 monolayers normalized with those of 18 monolayers
\
15
0=2\ \
t0
x
5
0.5 . - - .
\
Relative intensity
\
\ "...
Simulation (Dd- 2t = 0.0) Simulation (Dd- 2t = 1.0) Simulation (Dd- zt = 1.5) Experiment
1.144 x 10- l 2.019 x 10- 3 0.119 x 10- 3 0,559 x 10- s
0 , "" I ~ S : Z 0 2 4 6 8 101214161820 Bilayer period (monolayers)
Bilayer period (nm) 2 4 6 8
0 3.5
Fig. 1. Calculated perpendicular structural anisotropy PSA as a function of bilayer periods, where the degree of the diffusion (see text) is chosen as a parameter.
\
3
Dd -2t \
2.5
\
- -
--O-"
2 where N~ and N* are the effective coordination numbers for the glancing (10° with respect to the fitm plane) and normal incident of X-ray, respectively [21. Fig. 1 shows the calculated PSA as a function of hilayer period for A/B multilayers with various degree of diffusion. When Dd-ar is small, the PSA simply increases with decreasing bilayer period. When the Dd-2t becomes more than 1.0, the PSA increases with decreasing bilayer period and exhibits the maximum, followed by abrupt decrease at a certain bilayer period. The maximum PSA decreases with the progress of the interlayer diffusion. Using the results of the simulation, we have calculated the small-angle X-ray diffraction pattern of the multilayers for various degrees of diffusion by a recursive method based on the optical model [3]. The integrated intensities of the low-angle first peak were calculated as a function of the bilayer period. As shown in Table 1, the calculated intensity is consistent with the experimental one when Dd-at is assumed to be as large as 1.0. The comparison of the calculated and experimental PSA is shown in Fig. 2, where the experimental one was estimated from the peak intensity of the Fourier-transformed Fe EXAFS [2"]. If we assume Dd-Jt is 1.0, the value of the calculated PSA as a function of bilayer periods, not only its magnitude but also the peak position, agrees with those estimated from the results of EXAFS. This fact shows that the model of this simulation can describe the structural characteristics of the amorphous multilayers. Furthermore, the origin of the enhanced PMA in the multilayers is thought to be closely related to the short-range anisotropic atom pair order introduced with the multilayer structure.
0.7 1.0 1.5
sire.---
1.5 1
0.5 0 -0.5
+
0
,
t
,
T
P
•
1
5 10 15 20 25 30 35 Bilayer period (monolayers)
Fig. 2. Comparison of calculated and experimental perpendicular structural anisotropy obtained from the simulation and Fe EXAFS, respectively.
In conclusion, a simple simulation of the diffusion process in the multilayer structure showed the appearance of the maximum PSA at a certain bilayer period depending on the degree of diffusion. The results of the simulation are consistent with those of EXAFS and lowangle XRD. The authors thank Professor M. Matsui, Nagoya University, for kind discussions.
References
[1] S. Tsunashima, T. Ohtani, X.Y. Yu, S, Iwata, S. Uchiyama, J. Magn. Magn. Mater. 104-107 (1992) 1021. [2] Y. Fujiwara, X.Y. Yu, S. Tsunashima, S. Iwata, M. Sakurai, K. Suzuki, J. Appl. Phys. 79 (8) (t996) 6270. [3-1 J.H. Underwood,T.W. Barbee Jr., Appl. Opt. 20 (1981)3027.
~
ELSEVIER
Journalof magnetism and magnetic materials
Simulation of structural anisotropy in rare-earth transition metal multilayers Y. Fujiwara, T. Masaki, X.Y. Yu, S. Tsunashima*, S. Iwata Department of Electronics, Nagoya University, Chikusa-Ku, Nagoya 464-01, Japan
Abstract UniaxiaI structural anisotropy in rare-earth transition-metaI amorphous multilayers has been simulated by using a close-packed superlattice as an initial condition and solving a one-dimensional diffusion equation. The simulation has revealed that the degree of the short-range anisotropic atomic order becomes the maximum at a certain bilayer period depending on the degree of the interlayer diffusion. The calculated trend of the structural anisotropy agrees with the experimental one obtained by extended X-ray absorption fine structure spectroscopy. © 1998 Elsevier Science B.V. All rights reserved.
Keywords: Multilayers; EXAFS; A n i s o t r o p y - uniaxial
Perpendicular magnetic anisotropy (PMA) in amorphous rare-earth transition-metal (RE-TM) films is known to be enhanced by introducing a multilayer structure and to show the maximum at a bilayer period of about 1.0 nm [11. In order to explain the enhanced magnetic anisotropy, Extended X-ray absorption fine structure (EXAFS) experiments were performed on Tb/Fe amorphous multilayers (MLs) and it was found that perpendicular structural anisotropy (SA) measured in the first peak of Fourier-transformed EXAFS was closely correlated with the PMA [2]. We have considered that the SA originated from the difference of the coordination number between film normal and in-plane directions. In this study, we will perform a simple simulation of the SA in order to reproduce and explain the experimental results. Hereafter we calculate the difference of the coordination numbers using a simplified multilayer model, where FCC(1 1 1) planes of A or B atoms with the same atomic size are piled up successively to form an ideal superlattice. Interlayer atomic diffusion which leads the superlattice to the random solid solution is introduced according to the one-dimensional diffusion equation with the same diffusion constants for A and B atoms. Then simulation can be carried out by using the following
differential equation:
*Corresponding author. Tel.: + 81 52 789 3639; fax: + 81 52 789 3153; e-mail: [email protected].
PSA
Cx(z, t + At) = Cx(z, t) - D{Cx(z - d, t) + Cx(z + d, t) -- 2Cx(z, t)}d- ZAt,
(1)
where Cx(z, t) is the concentration o f X ( = A or B) atoms at the position z in the film normal and at time t, D the diffusion coefficient, and d the lattice spacing between the (1 1 1) planes. Starting from the ideal superlattice, we can calculate the concentration Cx(z, t) as a function of time. Using this concentration, we can calculate the expectation value for the number of the nearest neighbor Y atoms seen from X atoms, Nxy (Y = A or B) for any bond directions in the FCC lattice. Effective coordination number N~.r, which could be obtained from EXAFS of X atoms, is given by
N*r = Zi Z}+ ~- zZk3Cx(zi, t) Cr(zj, t) cos201jk ~iCx(zi, t) ,
(2)
where i and j are atomic layer numbers, k represents nearest-neighbor bond direction, 01jk the angle between the directions of a particular X - Y bond and the X-ray polarization. In order to discuss the perpendicular structural anisotropy, we define the perpendicular structural anisotropy PSA as
0304-8853/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 3 4 3 - 0
N~A[I -- N~A± , , N~A [I + NAA.I-
(3)
1174
Z Ftdiwara et al. /Journal of Magnetism and Magnetic Materials 177-181 (1998) 1173-1174
25
' I
. . . . . . .
\ Dd-2t= 0.0
2O
Table 1 Integrated intensities of the first low-angle X-ray diffraction peaks for muttilayers with 4 monolayers normalized with those of 18 monolayers
\
15
0=2\ \
t0
x
5
0.5 . - - .
\
Relative intensity
\
\ "...
Simulation (Dd- 2t = 0.0) Simulation (Dd- 2t = 1.0) Simulation (Dd- zt = 1.5) Experiment
1.144 x 10- l 2.019 x 10- 3 0.119 x 10- 3 0,559 x 10- s
0 , "" I ~ S : Z 0 2 4 6 8 101214161820 Bilayer period (monolayers)
Bilayer period (nm) 2 4 6 8
0 3.5
Fig. 1. Calculated perpendicular structural anisotropy PSA as a function of bilayer periods, where the degree of the diffusion (see text) is chosen as a parameter.
\
3
Dd -2t \
2.5
\
- -
--O-"
2 where N~ and N* are the effective coordination numbers for the glancing (10° with respect to the fitm plane) and normal incident of X-ray, respectively [21. Fig. 1 shows the calculated PSA as a function of hilayer period for A/B multilayers with various degree of diffusion. When Dd-ar is small, the PSA simply increases with decreasing bilayer period. When the Dd-2t becomes more than 1.0, the PSA increases with decreasing bilayer period and exhibits the maximum, followed by abrupt decrease at a certain bilayer period. The maximum PSA decreases with the progress of the interlayer diffusion. Using the results of the simulation, we have calculated the small-angle X-ray diffraction pattern of the multilayers for various degrees of diffusion by a recursive method based on the optical model [3]. The integrated intensities of the low-angle first peak were calculated as a function of the bilayer period. As shown in Table 1, the calculated intensity is consistent with the experimental one when Dd-at is assumed to be as large as 1.0. The comparison of the calculated and experimental PSA is shown in Fig. 2, where the experimental one was estimated from the peak intensity of the Fourier-transformed Fe EXAFS [2"]. If we assume Dd-Jt is 1.0, the value of the calculated PSA as a function of bilayer periods, not only its magnitude but also the peak position, agrees with those estimated from the results of EXAFS. This fact shows that the model of this simulation can describe the structural characteristics of the amorphous multilayers. Furthermore, the origin of the enhanced PMA in the multilayers is thought to be closely related to the short-range anisotropic atom pair order introduced with the multilayer structure.
0.7 1.0 1.5
sire.---
1.5 1
0.5 0 -0.5
+
0
,
t
,
T
P
•
1
5 10 15 20 25 30 35 Bilayer period (monolayers)
Fig. 2. Comparison of calculated and experimental perpendicular structural anisotropy obtained from the simulation and Fe EXAFS, respectively.
In conclusion, a simple simulation of the diffusion process in the multilayer structure showed the appearance of the maximum PSA at a certain bilayer period depending on the degree of diffusion. The results of the simulation are consistent with those of EXAFS and lowangle XRD. The authors thank Professor M. Matsui, Nagoya University, for kind discussions.
References
[1] S. Tsunashima, T. Ohtani, X.Y. Yu, S, Iwata, S. Uchiyama, J. Magn. Magn. Mater. 104-107 (1992) 1021. [2] Y. Fujiwara, X.Y. Yu, S. Tsunashima, S. Iwata, M. Sakurai, K. Suzuki, J. Appl. Phys. 79 (8) (t996) 6270. [3-1 J.H. Underwood,T.W. Barbee Jr., Appl. Opt. 20 (1981)3027.