- Email: [email protected]
Al multilayers
N'H
~ -,7-"
ELSEVIER
Journal of Magnetism and Magnetic Materials 166 (1997) 277-282
journal of magnetism and magnetic materials
Magnetic anisotropy of Ni/A1 multilayers S.S. Kang a,*, J.W. Feng b G.J. Jin a, M. Lu a, X.N. Xu a, A. Hu a, S.S. Jiang a, H. Xia c a National Laboratory of Solid State Microstructures and Center for Advanced Studies in Science and Technology of Micros~ructures, Nanjing University, Nanjing 210093, China b Wuhan Institute of Physics, Academia Sinica, Wuhan 430071, China c Beijbzg General Institute of Non-ferrous Metals, Beijing 100080, China
Received 20 September 1995
Abstract The magnetic anisotropy of Ni/A1 multilayers has been investigated by vibrating sampIe magnetometer (VSM) and ferromagnetic resonance (FMR) techniques. The FMR spectra are obtained as a function of the orientation of the applied magnetic field from in-plane to out-of-plane, and are fitted theoretically to determine the magnetic anisotropy. From VSM and FMR, a positive vaIue for Ni/AI interface anisotropy, favoring a perpendicular easy axis, is obtained. Furthermore, for the ultrathin magnetic layer below a critical Ni thickness of 20 A, a perpendicular easy axis of magnetization can be extrapolated. Keywords: Magnetic multilayers; Magnetic anisotropy;Ferromagnetic resonance
1. Introduction In the last few years there has been a rapidly increasing interest in the magnetic anisotropy of ultrathin metallic films and multilayers. The magnetic anisotropy, together with the coercive field, the remanence, the saturation magnetization and KelT rotation, play an important role in information storage and retrieval processes. For instance, media for magneto-optic or perpendicular magnetic recording are required to have an easy axis perpendicular to the
Corresponding author. Fax: + 86-25-3300535.
film plane. In general, for ultrathin films the easy axis of magnetization is expected to lie in the plane of the film owing to the demagnetizing energy. Recently, a change from a perpendicular orientation of the easy axis of the magnetization for film thickness d below a few monolayers to an in-plane orientation for larger d has been reported in Fe/Ag(001) [1], Fe/On(001)[2], C o / A u ( l l l ) [ 3 ] , and Ni/Cu(001) [4]. The possible mechanism, such as shape anisotropy, magnetocrystalline anisotropy, magneto-elastic anisotropy, and the reduced symmetry of the structure at the surface (or interfaces) has been proposed to explain the perpendicular anisotropy. The orientational dependence of the magnetic anisotropy is also considered [5,6]. In particular, the interface anisotropy (including the interface rough-
0304-8853/97/$17.00 Copyright© 1997 Elsevier Science All rights reserved. PI1 S0304-8853(96)00608-7
278
S.S, Kang el al. / JourT~alof Magnetism and Magnetic Materials 166 (1997) 277-282
ness and lattice mismatch), as one of important factors in understanding the perpendicular anisotropy, has been investigated extensively [5,7-9]. In this paper, the magnetic properties of Ni/A1 multilayers, investigated by FMR and VSM methods, are reported. The interface anisotropy energy constant K s of Ni/A1 multilayers is found to be a positive value, favoring a perpendicular easy axis. In order to interpreting the magnetic anisotropy the intrinsic stress is taken into account. Moreover, a critical thickness, below which the easy axis of multilayers switches from parallel to perpendicular to the film plane, is revealed by extrapolating.
2. Experimental techniques The samples were prepared by alternately sputtering layers of Ni and A1 onto glass substrates with a 500 A A1 seed layer. The background pressure was 5 X 10 -7 Torr, and the deposition was carried out at an Ar pressure of 7.5 X 10 .3 Torr with the substrate temperature about 350 K. The sputtering rates of Ni and A1 for all Ni/A1 multilayers were kept constant, 15 and 12 ]~/s respectively. The thickness of the Ni and A1 layers were controlled by the exposure time. Finally, an overlayer of 200 A A1 was deposited. A detailed description of sample preparation can be found in Ref. [16]. The multilayers under investigation were designated as [Ni(x)/A!(35 A)] X 60 where x denotes Ni layer thickness in A, x ranging from 15 to 70 A. The Ni/A1 multilayers just after preparation were studied using an X-ray diffractometer with a 12 kW Rigaku rotating anode X-ray source (a Cu anode in high brilliance 0.2 X 2 mm 2 spot mode) and a symmetric graphite (002) monochromator. Magnetic measurements were performed by using VSM at room temperature. With an electronic paramagnetic resonance spectrometer model ER-200D SRC at a frequency of 9.78 GHz, FMR measurements were carried out to determine the anisotropy energies and the easy axis of magnetization from analyzing the angular dependence of the resonance field /'/res. Assuming uniaxial anisotropy and a homogeneous
magnetization distribution, the resonance field H can be calculated from the following expression [10]:
+ Hk2(3 cos°'0 sin20 -- cos40 )] x [ I-I c o s ( 0 - 0 , , ) - A cos20 -
where
A=4'rrM-Hk,
2Kt/M,
Hk2 = 4 K 2 / M .
Hk = H k l + H k 2 ,
], (1)
k2cos40
Hkt=
~o is the microwave fre-
quency, 3, the gyromagnetic ratio, 0 and OH are angles of magnetization M and the applied field H with respect to the film normal, K t and K e the first and second order perpendicular anisotropy constants. According to the equilibrium condition of the magnetization vector M we have M H s i n ( O H - 0) = (2"rrM 2 - K t - 2K2)sin20
+ 4Kzsin 0 cos30.
(2)
By fitting the data from the angle-dependent FMR measurements, the information about the perpendicular anisotropy can be extracted.
3. Results 3.1. Sm~cu~re
Fig. ta and Fig. lb show the low- and high-angle X-ray diffraction (XRD) pattern of the Ni(25 A)/Al(35 A) muttilayer, respectively. In the low-angle region, Bragg reflections up to the second order are observed which confirms that the multilayer is of periodic structure. Considering the X-ray refractive corrections [11], the period deduced from these Bragg peak positions agrees well with the designed value. The high-angle XRD pattern shows that both A1 and Ni layers have fcc(111) texture, with an interplanar spacing of 2.304 and 2.05 A, respectively. The interplanar spacing of A1 is 1.5% smaller than that of bulk A1 (2.338 *), while the interplanar spacing of Ni is 1% larger than that of bulk fcc N i ( l l l ) planes
279
S.S. Kang et aL ~Journal of Magnetism and Magnetic Materials 16d (1997) 277-282
(a)
g
_= 0.5
2
.~
4 2e (deg.)
Ni (111)
35
40 45 28 (deg.)
50
rections are all of the easy-plane type. The area between perpendicular and parallel magnetization curves per unit Ni volume, from which the effective anisotropy energy can be determined, obviously decreases. These facts illustrate that the easy-plane anisotropy is stronger for Ni(50 A)/Al(35 A) than that for Ni(25 ~.)/A1(35 A). This result is also obtained by FMR measurements described in the next section. In addition, for the samples with thin Ni layers, there exist a high saturation field and nonzero remanence in perpendicular orientation (see Fig. 2b). These facts may result from the relatively weak easy-plane anisotropy discussed above and inhomogeneous magnetization due to structural fluctuations and domains. The magnetization of Ni is determined by VSM with the applied magnetic field perpendicular to the film plane at room temperature (see Table 1). The result illustrates that the magnetization decreases with decreasing Ni layer thickness. For samples with a Ni layer thickness less than 20 A, no hysteresis loop has e
Fig. 1. X-ray diffractionpattern of Ni(25 A)/Al(35 A) multilayer in (a) low- and (b) high-angle regions.
(2.034 A). It indicates a contraction of the A1 lattices and a expansion of the Ni lattices along the growth direction, which is due to the lattice mismatch between A1 and Ni. 3.2. V S M m e a s u r e m e n t
The two typical hysteresis loops for Ni(50 A)/Al(35 A) and Ni(25 A)/Al(35 A) multilayers are shown in Fig. 2a and Fig. 2b, respectively, with the applied magnetic field parallel and perpendicular to the film plane. From Fig. 2a, a square loop can be seen when the applied field is oriented along the film plane. It indicates that the easy magnetization direction is of the easy-plane type. In Fig. 2b, the saturation is reached gradually with the applied field along the film plane. The ratio of the remanence in parallel orientation is larger than that in perpendicular orientation and the easy magnetization direction is still of the easy-plane type. From Fig. 2a and Fig. 2b, it is shown that the characters of the hysteresis loops are obviously different although easy magnetization di-
(a)
-1 P
t
p
-3
-2
-1 0 H(kG)
-1
1
2
3
(b/ -2
-1
0 H(kG)
2
Fig. 2. Magnetic hysteresis loops for (a) Ni(50 A)/AI(35 A) and (b) Ni(25 A)/Al(35 A) multilayerrespectively,with applied dc field parallel (ID and perpendicular( _1_) to the film plane.
S.S. Kang et al. ~Journal of Magnetism and Magnetic Materials 166 U997) 277-282
280
Table 1 The values of the parameters A and the Land~ factor g and the second order perpendicular anisotropy field Hk2 and saturate magnetization M s for the Ni/A1 multilayers Samples
A (Oe)
g
H~:~ (Oe)
M s (G)
Ni(25 A)/AI(35 A)
1154
2.I9
50
230
Ni(35 ,~)/A1(35 A)
i555
2.2
200
390
Ni(50 ,~.)/A1(35 i )
2152
2.21
i00
415
Ni(70 ,~)/A1(35 A)
2398
2.18
150
440
been observed at room temperature due to the decrease of the Curie temperature.
5. ©
© "~4" IJ_
r-. o
2
3'0 6'0 Angle ( deg. )
90
Fig. 4. The resonance field versus angle in the film plane for the Ni(35 A.)/AI(35 A) multilayer. The solid line is a fit obtained with A = 4.2 kOe, g = 2.2 and Hk2 = 200 Oe,
3.3. Ferromagnetic resonance
The two typical FMR spectra for Ni(50 A)/Al(35 A) and Ni(25 A)/Al(35 A) multilayers are shown in Fig. 3a and Fig. 3b, respectively, with the external magnetic field parallel and perpendicular to the film ":'. 4 ._>
2
.r'- 0
O
(a)
g:-4o
,
,
2
4 H(kG)
5 4 0~ >
2
>
•r-
0
"O
-2 O if)
~-4
i
0
2
r
4 H(kG
1
(b)
6
Fig. 3. FMR signal for (a) Ni(50 ,~,)/A1(35 i ) muitilayer and (b) Ni(25 A.)/Al(35 ,~_)multilayer. (11)Applied dc field along the film plane (0 N = 90°), and ( J_ ) applied dc field perpendicular to the film plane (OH = 0°).
plane. The differences between the resonance fields are obvious. When an applied field is oriented along the film plane, the resonance field Hr~ s i n c r e a s e s with decreasing thickness of the Ni layers. But Hr~~ decreases with decreasing thickness of the Ni layers when the external magnetic field is oriented perpendicular to the film plane. These behaviors are attributed to the decrease of the bulk anisotropy energy with decreasing Ni thickness. Fig. 4 shows the dependence of the resonance field on the angle of the external magnetic field from in-plane to out-of-plane for the Ni(35 ,~)/AI(35 A) multilayer. From Eqs. (1) and (2), parameters A = 1.6 kOe, g = 2.2, and Hk2 = 200 Oe are obtained by fitting the data of resonance field versus angle similar to A u / C o / A u [10,12] and F e / C u [13]. The calculated result (solid curve) is shown in Fig. 4. The experimental result is in good agreement with the theoretical description. Some of the results under the investigation are summarized in Table 1. As shown in Table 1, the parameter A, characteristic of the internal field along the film normal, increases with increasing Ni thickness. This behavior can be explained in terms of the positive interface anisotropy (including reduction of the magnetization in the vicinity of the interface and the structural imperfections of the interface). Following the method of analysis previously used, in particular that in Refs. [14,15], the surface (or interface) induced magnetic anisotropy in multilayers can be studied through the dependence of the perpendicular anisotropy on the thickness of the magnetic layers, x, if the interface anisotropy essentially
S.S. Kang et al. ~Journal of Magnetism and Magnetic Materials 166 (1997) 277-282
enhances the first-order anisotropy. Then the firstorder anisotropy energy, K t (see Eq. (1)), can be separated in thickness-independent (volume contribution) and thickness-dependent (interface contribution) terms:
(3)
a:, = Kv + 2 K s ~ x ,
where K v is the homogeneous volume anisotropy energy (excluding the demagnetizing energy). When the demagnetizing energy is included, Eq. (3) can be written as Keff ----K'v + 2 K s / x ,
(4)
where K'v = K v - 2 , r r M ~ , Keff = K l - 2 , r r M 2 = - A M J 2 (according to the definition given in Eq. (1), H~2 is small enough to be neglected here (see Table 1)). Kef f and K 'v are the effective perpendicular anisotropy energy and effective volume anisotropy energy, respectively (including the demagnetizing energy). For the multilayers having a different Ni layer thickness (25, 35, 50, and 70 A), Kef f is calculated and plotted as a function of 1 / x in Fig. 5. A linear variation of Keff v e r s u s 1 / x is obtained, indicating that the data are reasonable. From the slope of the straight line fitted, the interface anisotropy constant K s is deduced, K 5 = 0.076 e r g / c m 2. A positive K s value means that the interface anisotropy confines the magnetization to the direction of the film normal. Also, from the intersection with the coordinate axis, the effective perpendicular volume anisotropy energy
4=Ms
~" 6O v
< i
4"
K'v is obtained as - 7 . 5 × 105 e r g / c m 3. If the demagnetizing energy is excluded, the volume anisotropy energy K v is about 7.3 × 105 e r g / c m 3, which lies above the magnetocrystalline anisotropy energy for bulk Ni at 5 × 10 4 e r g / c m 3. In addition, a critical Ni thickness, below which the easy axis of the multilayers switches from along to perpendicular to the film plane, can be deduced (see Fig. 5). However, this linear extrapolation assumes that M s is independent of the film thickness. This condition is not fulfilled for the thinnest films due to their low Curie temperature. For the same reason no obvious FMR peaks can be found in this thickness range. From Table 1, the Landg factor g can be found to increase slightly with increasing Ni thickness up to 50
4. Discussion and conclusion
As mentioned in Section 3, the perpendicular volume anisotropy K v is much larger than the magnetocrystalline anisotropy, and such a large volume anisotropy may be interpreted by the magnetostriction, according to the relation K• = 3 h E e , where E is the Young modulus and e the strain. Taking the typical magnetostriction constant A = - 2 4 × 10 - 6 , K v = 7.3 × 105 e r g / c m 3, this yields about 1.1% strain, which is on the same order of magnitude as the strain of 1% determined by XRD. As for the interface anisotropy, due to the large lattice mismatch between the adjacent layers (15%), N i / A l multilayers are expected to have an incoherent interface above the critical thickness of 2 ~, and misfit dislocations at the interface are formed to reduce the strain. Since Ni has a negative magnetostriction constant h, the magneto-elastic anisotropy energy density K,~ should be positive in N i / A l and is given by [7] =
o.&
0.04
o.o'8
0.08
1/t(A ~ ) Fig. 5. Variation of Keef versus 1/oX for Ni/A1 multilayerswith a fixed A1 layer thickness of 35 A. The reorientation transition occurs at ~ 20 A.
281
-
}acz,,
where G is the shear modulus and b the Burgers vector. Taking A11~ = - 2 4 × 10 -6 and G = 7 . 7 × 10 .1 d y n / c m 2, K~ should be about 0.07 e r g / c m 2. The magneto-elastic anisotropy K~ is slightly smaller than the perpendicular interface anisotropy K s o b -
282
S.S. Kang et aI. / Journal of Magnetism and Magnetic Materials 166 (1997) 277-282
tained (0.076 erg/cm2). If the intermixing at the interface is considered [8], the interface roughness gives rise to an effective perpendicular anisotropy (about 0.01 e r g / c m 2 for Ni(111)). Furthermore, taking the shape anisotropy to be that of Ni layers, perpendicular magnetization should occur for a Ni thickness below about 20 A by extrapolating. This thickness dependence, namely, a crossover from inplane to out-of-plane orientation of magnetization at critical Ni thickness, is opposite to our finding in N i / A g [16] multilayers. In conclusion, the magnetic anisotropy of the N i / A 1 multilayers has been investigated by FMR and VSM measurements. In the FMR measurement, resonance field data as a function of the field orientation from along to perpendicular to the film plane are obtained and are fitted theoretically. A positive interface anisotropy constant favoring a perpendicular easy axis is revealed by FMR data. The magnetic anisotropy is discussed by considering the intrinsic stress and magnetostriction. Furthermore, the perpendicular easy axis of magnetization below a critical Ni thickness may be expected from the anisotropy constants measured.
Acknowledgements This work is supported by the National Natural Science Foundation of China and the Provincial Natural Science Foundation of Jiangsu.
References [I] Z.Q. Qiu, J. Pearson and S.D. Bader, Phys. Rev. Lett. 70 (i993) I006. [2] R. Allenspachand A. Bischof, Phys. Rev. Lett. 69 (1992) 3385. [3] R. Allenspach,M. Stampanoniand A. Bisehof, Phys. Rev. Lett. 65 (i990) 3344. [4] Chin-AnChang, J. Magn. Magn. Mater. 97 (1991) 102. [5] M.T. Johnson, J.J. de Vries, N.W.E. McGee, J. aan de Stegge and F.J.A. den Breeder, Phys, Rev. Lett. 69 (1992) 3575. [6] B.N. Engel, C.D. England, R.A. van Leeuwen, M.H. Wiedmann and C.M. Falco, Phys. Rev. Lett, 67 (1991) 1910. [7] F.J.A. den Breeder, W. Hoving and P.J.H. Bloemen, J. Magn. Magn. Mater. 93 (1991) 562. [8] P. Bruno, J. Appl. Phys. 64 (1988) 3153. [9] F.J.A. den Breeder, E. Janssen,A. Mud and J.M. Kerkhof, J. Magn. Magn, Meter. 126 (1993) 563; F.J.A. den Breeder, E. Janssen, W. Hoving and W.B. Zeper, IEEE Trans. Magn. 28 (1992) 2760; R. Jungblut,M.T. Johnson,J. aan de Stegge, A. Reinders and F.J.A. den Breeder, J. Appl. Phys. 75 (1994) 6424. [10] C. Chappert, K. Le Dang and P. Beauvillain,Phys. Rev. B 44 (i992) 3193. [i1] S.S. Jiang, J. Zou, D.J.H. Cockayne, A. Sikorski, A. Hu and R.W. Peng, Phys. Stat. Sol. (a) 130 (1992) 373. [12] Peng Chubing,Dai Daosheng, Fang Ruiyi, Phys. Rev. B 46 (1992) 12022. [13] S.M. Rezende, J.A.S. Moura, F.M. de Aguiar and W.H. Schreiner, Phys. Rev. B 49 (I994) 15105. [I4] G.T. Rado, Phys. Rev. B 26 (1982) 295. [15] U. Gradmann,J. Magn. Magn. Mater. 54-57 (1986) 733. [16] J.W. Feng, S.S. Kang,F.M. Pan, G.J. Jin, M. Lu, A. Hu, S.S. Jiang and D. Feng, J. Magn. Magn. Mater. 152 (1996) 27.
~ -,7-"
ELSEVIER
Journal of Magnetism and Magnetic Materials 166 (1997) 277-282
journal of magnetism and magnetic materials
Magnetic anisotropy of Ni/A1 multilayers S.S. Kang a,*, J.W. Feng b G.J. Jin a, M. Lu a, X.N. Xu a, A. Hu a, S.S. Jiang a, H. Xia c a National Laboratory of Solid State Microstructures and Center for Advanced Studies in Science and Technology of Micros~ructures, Nanjing University, Nanjing 210093, China b Wuhan Institute of Physics, Academia Sinica, Wuhan 430071, China c Beijbzg General Institute of Non-ferrous Metals, Beijing 100080, China
Received 20 September 1995
Abstract The magnetic anisotropy of Ni/A1 multilayers has been investigated by vibrating sampIe magnetometer (VSM) and ferromagnetic resonance (FMR) techniques. The FMR spectra are obtained as a function of the orientation of the applied magnetic field from in-plane to out-of-plane, and are fitted theoretically to determine the magnetic anisotropy. From VSM and FMR, a positive vaIue for Ni/AI interface anisotropy, favoring a perpendicular easy axis, is obtained. Furthermore, for the ultrathin magnetic layer below a critical Ni thickness of 20 A, a perpendicular easy axis of magnetization can be extrapolated. Keywords: Magnetic multilayers; Magnetic anisotropy;Ferromagnetic resonance
1. Introduction In the last few years there has been a rapidly increasing interest in the magnetic anisotropy of ultrathin metallic films and multilayers. The magnetic anisotropy, together with the coercive field, the remanence, the saturation magnetization and KelT rotation, play an important role in information storage and retrieval processes. For instance, media for magneto-optic or perpendicular magnetic recording are required to have an easy axis perpendicular to the
Corresponding author. Fax: + 86-25-3300535.
film plane. In general, for ultrathin films the easy axis of magnetization is expected to lie in the plane of the film owing to the demagnetizing energy. Recently, a change from a perpendicular orientation of the easy axis of the magnetization for film thickness d below a few monolayers to an in-plane orientation for larger d has been reported in Fe/Ag(001) [1], Fe/On(001)[2], C o / A u ( l l l ) [ 3 ] , and Ni/Cu(001) [4]. The possible mechanism, such as shape anisotropy, magnetocrystalline anisotropy, magneto-elastic anisotropy, and the reduced symmetry of the structure at the surface (or interfaces) has been proposed to explain the perpendicular anisotropy. The orientational dependence of the magnetic anisotropy is also considered [5,6]. In particular, the interface anisotropy (including the interface rough-
0304-8853/97/$17.00 Copyright© 1997 Elsevier Science All rights reserved. PI1 S0304-8853(96)00608-7
278
S.S, Kang el al. / JourT~alof Magnetism and Magnetic Materials 166 (1997) 277-282
ness and lattice mismatch), as one of important factors in understanding the perpendicular anisotropy, has been investigated extensively [5,7-9]. In this paper, the magnetic properties of Ni/A1 multilayers, investigated by FMR and VSM methods, are reported. The interface anisotropy energy constant K s of Ni/A1 multilayers is found to be a positive value, favoring a perpendicular easy axis. In order to interpreting the magnetic anisotropy the intrinsic stress is taken into account. Moreover, a critical thickness, below which the easy axis of multilayers switches from parallel to perpendicular to the film plane, is revealed by extrapolating.
2. Experimental techniques The samples were prepared by alternately sputtering layers of Ni and A1 onto glass substrates with a 500 A A1 seed layer. The background pressure was 5 X 10 -7 Torr, and the deposition was carried out at an Ar pressure of 7.5 X 10 .3 Torr with the substrate temperature about 350 K. The sputtering rates of Ni and A1 for all Ni/A1 multilayers were kept constant, 15 and 12 ]~/s respectively. The thickness of the Ni and A1 layers were controlled by the exposure time. Finally, an overlayer of 200 A A1 was deposited. A detailed description of sample preparation can be found in Ref. [16]. The multilayers under investigation were designated as [Ni(x)/A!(35 A)] X 60 where x denotes Ni layer thickness in A, x ranging from 15 to 70 A. The Ni/A1 multilayers just after preparation were studied using an X-ray diffractometer with a 12 kW Rigaku rotating anode X-ray source (a Cu anode in high brilliance 0.2 X 2 mm 2 spot mode) and a symmetric graphite (002) monochromator. Magnetic measurements were performed by using VSM at room temperature. With an electronic paramagnetic resonance spectrometer model ER-200D SRC at a frequency of 9.78 GHz, FMR measurements were carried out to determine the anisotropy energies and the easy axis of magnetization from analyzing the angular dependence of the resonance field /'/res. Assuming uniaxial anisotropy and a homogeneous
magnetization distribution, the resonance field H can be calculated from the following expression [10]:
+ Hk2(3 cos°'0 sin20 -- cos40 )] x [ I-I c o s ( 0 - 0 , , ) - A cos20 -
where
A=4'rrM-Hk,
2Kt/M,
Hk2 = 4 K 2 / M .
Hk = H k l + H k 2 ,
], (1)
k2cos40
Hkt=
~o is the microwave fre-
quency, 3, the gyromagnetic ratio, 0 and OH are angles of magnetization M and the applied field H with respect to the film normal, K t and K e the first and second order perpendicular anisotropy constants. According to the equilibrium condition of the magnetization vector M we have M H s i n ( O H - 0) = (2"rrM 2 - K t - 2K2)sin20
+ 4Kzsin 0 cos30.
(2)
By fitting the data from the angle-dependent FMR measurements, the information about the perpendicular anisotropy can be extracted.
3. Results 3.1. Sm~cu~re
Fig. ta and Fig. lb show the low- and high-angle X-ray diffraction (XRD) pattern of the Ni(25 A)/Al(35 A) muttilayer, respectively. In the low-angle region, Bragg reflections up to the second order are observed which confirms that the multilayer is of periodic structure. Considering the X-ray refractive corrections [11], the period deduced from these Bragg peak positions agrees well with the designed value. The high-angle XRD pattern shows that both A1 and Ni layers have fcc(111) texture, with an interplanar spacing of 2.304 and 2.05 A, respectively. The interplanar spacing of A1 is 1.5% smaller than that of bulk A1 (2.338 *), while the interplanar spacing of Ni is 1% larger than that of bulk fcc N i ( l l l ) planes
279
S.S. Kang et aL ~Journal of Magnetism and Magnetic Materials 16d (1997) 277-282
(a)
g
_= 0.5
2
.~
4 2e (deg.)
Ni (111)
35
40 45 28 (deg.)
50
rections are all of the easy-plane type. The area between perpendicular and parallel magnetization curves per unit Ni volume, from which the effective anisotropy energy can be determined, obviously decreases. These facts illustrate that the easy-plane anisotropy is stronger for Ni(50 A)/Al(35 A) than that for Ni(25 ~.)/A1(35 A). This result is also obtained by FMR measurements described in the next section. In addition, for the samples with thin Ni layers, there exist a high saturation field and nonzero remanence in perpendicular orientation (see Fig. 2b). These facts may result from the relatively weak easy-plane anisotropy discussed above and inhomogeneous magnetization due to structural fluctuations and domains. The magnetization of Ni is determined by VSM with the applied magnetic field perpendicular to the film plane at room temperature (see Table 1). The result illustrates that the magnetization decreases with decreasing Ni layer thickness. For samples with a Ni layer thickness less than 20 A, no hysteresis loop has e
Fig. 1. X-ray diffractionpattern of Ni(25 A)/Al(35 A) multilayer in (a) low- and (b) high-angle regions.
(2.034 A). It indicates a contraction of the A1 lattices and a expansion of the Ni lattices along the growth direction, which is due to the lattice mismatch between A1 and Ni. 3.2. V S M m e a s u r e m e n t
The two typical hysteresis loops for Ni(50 A)/Al(35 A) and Ni(25 A)/Al(35 A) multilayers are shown in Fig. 2a and Fig. 2b, respectively, with the applied magnetic field parallel and perpendicular to the film plane. From Fig. 2a, a square loop can be seen when the applied field is oriented along the film plane. It indicates that the easy magnetization direction is of the easy-plane type. In Fig. 2b, the saturation is reached gradually with the applied field along the film plane. The ratio of the remanence in parallel orientation is larger than that in perpendicular orientation and the easy magnetization direction is still of the easy-plane type. From Fig. 2a and Fig. 2b, it is shown that the characters of the hysteresis loops are obviously different although easy magnetization di-
(a)
-1 P
t
p
-3
-2
-1 0 H(kG)
-1
1
2
3
(b/ -2
-1
0 H(kG)
2
Fig. 2. Magnetic hysteresis loops for (a) Ni(50 A)/AI(35 A) and (b) Ni(25 A)/Al(35 A) multilayerrespectively,with applied dc field parallel (ID and perpendicular( _1_) to the film plane.
S.S. Kang et al. ~Journal of Magnetism and Magnetic Materials 166 U997) 277-282
280
Table 1 The values of the parameters A and the Land~ factor g and the second order perpendicular anisotropy field Hk2 and saturate magnetization M s for the Ni/A1 multilayers Samples
A (Oe)
g
H~:~ (Oe)
M s (G)
Ni(25 A)/AI(35 A)
1154
2.I9
50
230
Ni(35 ,~)/A1(35 A)
i555
2.2
200
390
Ni(50 ,~.)/A1(35 i )
2152
2.21
i00
415
Ni(70 ,~)/A1(35 A)
2398
2.18
150
440
been observed at room temperature due to the decrease of the Curie temperature.
5. ©
© "~4" IJ_
r-. o
2
3'0 6'0 Angle ( deg. )
90
Fig. 4. The resonance field versus angle in the film plane for the Ni(35 A.)/AI(35 A) multilayer. The solid line is a fit obtained with A = 4.2 kOe, g = 2.2 and Hk2 = 200 Oe,
3.3. Ferromagnetic resonance
The two typical FMR spectra for Ni(50 A)/Al(35 A) and Ni(25 A)/Al(35 A) multilayers are shown in Fig. 3a and Fig. 3b, respectively, with the external magnetic field parallel and perpendicular to the film ":'. 4 ._>
2
.r'- 0
O
(a)
g:-4o
,
,
2
4 H(kG)
5 4 0~ >
2
>
•r-
0
"O
-2 O if)
~-4
i
0
2
r
4 H(kG
1
(b)
6
Fig. 3. FMR signal for (a) Ni(50 ,~,)/A1(35 i ) muitilayer and (b) Ni(25 A.)/Al(35 ,~_)multilayer. (11)Applied dc field along the film plane (0 N = 90°), and ( J_ ) applied dc field perpendicular to the film plane (OH = 0°).
plane. The differences between the resonance fields are obvious. When an applied field is oriented along the film plane, the resonance field Hr~ s i n c r e a s e s with decreasing thickness of the Ni layers. But Hr~~ decreases with decreasing thickness of the Ni layers when the external magnetic field is oriented perpendicular to the film plane. These behaviors are attributed to the decrease of the bulk anisotropy energy with decreasing Ni thickness. Fig. 4 shows the dependence of the resonance field on the angle of the external magnetic field from in-plane to out-of-plane for the Ni(35 ,~)/AI(35 A) multilayer. From Eqs. (1) and (2), parameters A = 1.6 kOe, g = 2.2, and Hk2 = 200 Oe are obtained by fitting the data of resonance field versus angle similar to A u / C o / A u [10,12] and F e / C u [13]. The calculated result (solid curve) is shown in Fig. 4. The experimental result is in good agreement with the theoretical description. Some of the results under the investigation are summarized in Table 1. As shown in Table 1, the parameter A, characteristic of the internal field along the film normal, increases with increasing Ni thickness. This behavior can be explained in terms of the positive interface anisotropy (including reduction of the magnetization in the vicinity of the interface and the structural imperfections of the interface). Following the method of analysis previously used, in particular that in Refs. [14,15], the surface (or interface) induced magnetic anisotropy in multilayers can be studied through the dependence of the perpendicular anisotropy on the thickness of the magnetic layers, x, if the interface anisotropy essentially
S.S. Kang et al. ~Journal of Magnetism and Magnetic Materials 166 (1997) 277-282
enhances the first-order anisotropy. Then the firstorder anisotropy energy, K t (see Eq. (1)), can be separated in thickness-independent (volume contribution) and thickness-dependent (interface contribution) terms:
(3)
a:, = Kv + 2 K s ~ x ,
where K v is the homogeneous volume anisotropy energy (excluding the demagnetizing energy). When the demagnetizing energy is included, Eq. (3) can be written as Keff ----K'v + 2 K s / x ,
(4)
where K'v = K v - 2 , r r M ~ , Keff = K l - 2 , r r M 2 = - A M J 2 (according to the definition given in Eq. (1), H~2 is small enough to be neglected here (see Table 1)). Kef f and K 'v are the effective perpendicular anisotropy energy and effective volume anisotropy energy, respectively (including the demagnetizing energy). For the multilayers having a different Ni layer thickness (25, 35, 50, and 70 A), Kef f is calculated and plotted as a function of 1 / x in Fig. 5. A linear variation of Keff v e r s u s 1 / x is obtained, indicating that the data are reasonable. From the slope of the straight line fitted, the interface anisotropy constant K s is deduced, K 5 = 0.076 e r g / c m 2. A positive K s value means that the interface anisotropy confines the magnetization to the direction of the film normal. Also, from the intersection with the coordinate axis, the effective perpendicular volume anisotropy energy
4=Ms
~" 6O v
< i
4"
K'v is obtained as - 7 . 5 × 105 e r g / c m 3. If the demagnetizing energy is excluded, the volume anisotropy energy K v is about 7.3 × 105 e r g / c m 3, which lies above the magnetocrystalline anisotropy energy for bulk Ni at 5 × 10 4 e r g / c m 3. In addition, a critical Ni thickness, below which the easy axis of the multilayers switches from along to perpendicular to the film plane, can be deduced (see Fig. 5). However, this linear extrapolation assumes that M s is independent of the film thickness. This condition is not fulfilled for the thinnest films due to their low Curie temperature. For the same reason no obvious FMR peaks can be found in this thickness range. From Table 1, the Landg factor g can be found to increase slightly with increasing Ni thickness up to 50
4. Discussion and conclusion
As mentioned in Section 3, the perpendicular volume anisotropy K v is much larger than the magnetocrystalline anisotropy, and such a large volume anisotropy may be interpreted by the magnetostriction, according to the relation K• = 3 h E e , where E is the Young modulus and e the strain. Taking the typical magnetostriction constant A = - 2 4 × 10 - 6 , K v = 7.3 × 105 e r g / c m 3, this yields about 1.1% strain, which is on the same order of magnitude as the strain of 1% determined by XRD. As for the interface anisotropy, due to the large lattice mismatch between the adjacent layers (15%), N i / A l multilayers are expected to have an incoherent interface above the critical thickness of 2 ~, and misfit dislocations at the interface are formed to reduce the strain. Since Ni has a negative magnetostriction constant h, the magneto-elastic anisotropy energy density K,~ should be positive in N i / A l and is given by [7] =
o.&
0.04
o.o'8
0.08
1/t(A ~ ) Fig. 5. Variation of Keef versus 1/oX for Ni/A1 multilayerswith a fixed A1 layer thickness of 35 A. The reorientation transition occurs at ~ 20 A.
281
-
}acz,,
where G is the shear modulus and b the Burgers vector. Taking A11~ = - 2 4 × 10 -6 and G = 7 . 7 × 10 .1 d y n / c m 2, K~ should be about 0.07 e r g / c m 2. The magneto-elastic anisotropy K~ is slightly smaller than the perpendicular interface anisotropy K s o b -
282
S.S. Kang et aI. / Journal of Magnetism and Magnetic Materials 166 (1997) 277-282
tained (0.076 erg/cm2). If the intermixing at the interface is considered [8], the interface roughness gives rise to an effective perpendicular anisotropy (about 0.01 e r g / c m 2 for Ni(111)). Furthermore, taking the shape anisotropy to be that of Ni layers, perpendicular magnetization should occur for a Ni thickness below about 20 A by extrapolating. This thickness dependence, namely, a crossover from inplane to out-of-plane orientation of magnetization at critical Ni thickness, is opposite to our finding in N i / A g [16] multilayers. In conclusion, the magnetic anisotropy of the N i / A 1 multilayers has been investigated by FMR and VSM measurements. In the FMR measurement, resonance field data as a function of the field orientation from along to perpendicular to the film plane are obtained and are fitted theoretically. A positive interface anisotropy constant favoring a perpendicular easy axis is revealed by FMR data. The magnetic anisotropy is discussed by considering the intrinsic stress and magnetostriction. Furthermore, the perpendicular easy axis of magnetization below a critical Ni thickness may be expected from the anisotropy constants measured.
Acknowledgements This work is supported by the National Natural Science Foundation of China and the Provincial Natural Science Foundation of Jiangsu.
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