ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 292 (2005) 65–71 www.elsevier.com/locate/jmmm
Temperature dependence of interlayer coupling and magnetization in amorphous-FeNiB/Ru multilayers S.M. Zhoua,c,, L. Sunb a
Surface Physics Laboratory (National Key Laboratory), Department of Physics, Fudan University, 220 Handan Rd, Shanghai 200433, China b Department of Physics and Astronomy, The Johns Hopkins University, Baltimore MD 21218, USA c State Key Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China Received 1 August 2004; received in revised form 13 October 2004 Available online 10 November 2004
Abstract For amorphous-FeNiB (2.0 nm)/Ru multilayers, an oscillatory interlayer coupling is observed with the variation of the Ru spacer thickness. At 0.8 nm thick Ru layer, near the first antiferromagnetic coupling maximum, the energy of the effective interlayer coupling at low temperature T is found to change as a linear function of T 3=2 : At the same time, the spontaneous magnetization of the samples at low temperature scales as a linear function of T. Therefore, the temperature dependence of the energy of the effective coupling might be controlled by thermal spin waves in the ferromagnetic layers. r 2004 Elsevier B.V. All rights reserved. PACS: 75.30.Et; 75.70.Cn; 75.30.Ds; 75.50.Kj Keywords: Magnetic multilayer; Interlayer coupling; Temperature
The oscillatory interlayer coupling between ferromagnetic (FM) transition metal layers through nonmagnetic (NM) spacers has been studied extensively over the last decade because Corresponding author. Surface Physics Laboratory (Na-
tional Key Laboratory), Department of Physics, Fudan University, 220 Handan Rd, Shanghai 200433, China. Tel.: 862165642316; fax: 862165104949. E-mail address:
[email protected] (S.M. Zhou).
of its important applications in magneto-electronic devices and its intriguing physics [1,2]. The interlayer coupling is found to decrease monotonically with increasing temperature [3–6]. The experimental results can be analyzed by two major theoretical models [7–10]. Some experiments show that the (bilinear) interlayer coupling at finite temperatures is controlled by the electron distribution near the Fermi surface [4,7,8]. However, experiments in Ni/Cu/Co and Ni/Cu/Ni trilayers
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2004.10.096
ARTICLE IN PRESS 66
S.M. Zhou, L. Sun / Journal of Magnetism and Magnetic Materials 292 (2005) 65–71
and Fe/V multilayers show that at low temperatures the bilinear coupling is a linear function of T 3=2 [6]. The T 3=2 dependence coincides with the second model, in which the temperature dependence is assumed to originate from the magnetic excitation (thermal spin waves) [9,11]. Therefore, more experiments are required to clarify the mechanism of the temperature dependence of the bilinear coupling. In this community, in order to suppress the effect of temperature variation of the magnetization, most measurements were made at temperatures far below the Curie temperature T C of these FM materials (Fe, Co, Ni, and their alloys). Since the decrement of the normalized magnetization MðTÞ=Mð0Þ is very small in the measured temperature range, the effect of the NM spacer on the temperature variation of the interlayer coupling can be addressed well. Alternatively, in order to reveal the effect of magnetization on temperature dependence of interlayer coupling, it will be helpful to use FM materials with low T C : For magnetic multilayers with antiferromagnetic (AFM) interlayer coupling, the magnetization reversal process depends not only on the interlayer coupling but also on the anisotropy of the FM layers. In general, it is not enough to calculate the interlayer coupling energy from hysteresis loops. When the FM anisotropy energy is much smaller than the AFM coupling energy, however, the hysteresis loop is slanted and magnetization reversal process can be described by magnetization coherent rotation model. As it is well known, pinholes usually exist in sputtered magnetic multilayers. As a result, the strength of the bilinear coupling is reduced and the biquadratic coupling is induced [12]. Therefore, biquadratic coupling should be considered in calculations of hysteresis loops. The remanent ratio is equal to zero if the bilinear coupling is stronger than the biquadratic coupling and J 1 o4J 2 o0: In this way, for HoH S (saturation field), one can have the following relationship [13]: " # 4 MH MH 3 H¼ ð4J 2 J 1 Þ 8J 2 ; tM S MS MS
(1)
where M H and M S are the magnetization component along the external field and the saturation magnetization of the constituent FM layers, respectively. t is the FM layer thickness, and J 1 and J 2 are the energies of the bilinear and biquadratic couplings, respectively. At H ¼ 0 we can have the following equation: J eff ¼
M 2S t ; 4a
(2)
where a ¼ @M H =@H is the slope of the magnetization curve at H ¼ 0; which can be calculated from the measured magnetization curve near the zero field, and the effective interlayer coupling energy J eff ¼ 4J 2 J 1 : An approximation that the saturation magnetization is replaced by spontaneous magnetization for fields near zero field can be made. Note that M S refers to spontaneous magnetization below. In this paper, we study the temperature dependence of the interlayer coupling and the magnetization in amorphous-FeNiB/Ru multilayers. Note that the transition metal Ru can induce strong AFM interlayer coupling [2]. With amorphous FM materials, low T C can be obtained by compositional modification [14]. In this way, the interlayer coupling can be studied in a wide range of normalized temperature T=T C : More importantly, the amorphous FM materials normally have very small intrinsic anisotropy and the AFM coupling can, therefore, be accurately determined from the slanted hysteresis loops. The FM and AFM couplings between amorphous FM layers are found to change alternatively with the Ru layer thickness. At the first AFM coupling maximum, the effective interlayer coupling energy decreases with decreasing temperature as linear functions of the T 3=2 : A correlation between the interlayer coupling and the spontaneous magnetization as a function of temperature is found. A large specimen (0:5 cm 5 cm) of [Ru (0–3.0 nm)/Fe4 Ni76 B20 ð¼ FeNiBÞð2:0 nmÞ40 multilayer was deposited onto Si(1 0 0) substrates by DC magnetron sputtering with a base pressure of 108 Torr: The FM and NM layers were made from FeNiB and Ru targets, respectively. Their deposition rates are 0.1 and 0.2 nm/s with the Ar pressure of 5 m Torr during deposition. A 10.0 nm thick Ru buffer layer was deposited to make a
ARTICLE IN PRESS S.M. Zhou, L. Sun / Journal of Magnetism and Magnetic Materials 292 (2005) 65–71
smooth growth of the multilayer. Wedged-Ru layers were made to avoid run-to-run variation because it is crucially important to have an identical FM layer thickness. Each location on the sample along the wedge direction corresponds to a specific Ru layer thickness. The large specimen was cut into many small pieces along the wedge direction, which have the same FM layer and different Ru layer thickness. A uniform [Ru (2.0 nm)/FeNiB (2.0 nm)]40 multilayer and a 200 nm thick FeNiB film were prepared to define the structural characteristic. A superconductor quantum interference device (SQUID) was used to measure hysteresis loops.
Intensity (arb. units)
105
103
67
Fig. 1 shows the typical results about the X-ray diffraction spectra of the FeNiB (2.0 nm)/Ru (2.0 nm) multilayer in low- and high-angle ranges. Several diffraction peaks in the low-angle range demonstrate that the multilayer has a good periodicity. The main diffraction peak in the high-angle range comes from Ru(0 0 0 1), which is inherited from the 10 nm thick Ru buffer layer. Around the main peak, there are two satellite peaks. The deduced value of the bilayer thickness from low- and high-angle ranges is in good agreement with the designed value of 4.0 nm. In experiments, the 200 nm thick FeNiB single film was found to be amorphous. Fig. 2 shows the representative hysteresis loops of FeNiB(2.0 nm)/Ru multilayers with various Ru layer thickness at low temperature of 5 K. The hysteresis loops are squared for Ru layer thickness of 0.5, 1.65, and 2.7 nm and slanted for Ru layer thickness of 0.8 and 2.0 nm. The saturation field is about 500 and 3000 Oe, respectively, for 0.8 and 2.0 nm thick spacers, as demonstrated by the long tail below the saturation field. As shown in Fig. 3,
101
1.0
0.5 nm
1.65 nm
0.8 nm
2.0 nm
1.2 nm
2.7 nm
0.5 0.0
0
2
4 2θ (deg)
6
8
M
10-1
-0.5 -1.0 1.0
5
0.5 0.0 M
Intensity (arb. units)
4
3
-0.5 -1.0 1.0 0.5
2
0.0
0 35
M
1
40
45
50
-0.5 -1.0 -1000 -500
0 500 1000 H(Oe)
-1000 -500
0 500 1000 H(Oe)
2θ (deg) Fig. 1. X-ray diffraction of FeNiB(2.0 nm)/Ru (2.0 nm) multilayers at low and high angles.
Fig. 2. Hysteresis loops of FeNiB (2.0 nm)/Ru multilayers with various Ru layer thickness at 5 K. The inserted numbers refer to the Ru layer thickness.
ARTICLE IN PRESS S.M. Zhou, L. Sun / Journal of Magnetism and Magnetic Materials 292 (2005) 65–71
68
HS (kOe)
3
2
1
0 0.5
1.0
1.5
2.0
2.5
3.0
tRu (nm) Fig. 3. For FeNiB (2.0 nm)/Ru multilayers, the saturation field oscillates with the Ru layer thickness at 5 K.
the saturation field oscillates with the Ru layer thickness with a period of about 1.2 nm, as fingerprint of oscillatory interlayer coupling. This oscillation period is very close to observations in other crystalline-FM/NM multilayers [2]; thus confirming that the oscillation period is determined only by the microstructure and orientation of the Ru layers. Few papers have reported on the oscillatory interlayer coupling between amorphous FM layers [15–17]. The saturation field of the first AFM coupling maximum is found to be smaller than that of the second AFM coupling because of discontinuous growth of 0.8 nm Ru layer with pinholes. The pinholes not only reduce the AFM coupling strength but also induce biquadratic coupling [12]. At the second AFM coupling maximum, the interlayer coupling energy is about 0:045 erg=cm2 ; which is about one order smaller than that of 0:28 erg=cm2 in Co/Ru multilayers [2]. Among many factors, the FM magnetization is a major reason for the difference of the interlayer coupling strength between Co/Ru and FeNiB/Ru multilayers because the magnetization of FeNiB layers is much smaller than that of Co layers. This
will also be manifested by the following temperature dependence of the interlayer coupling. Before addressing the temperature dependence of the interlayer coupling, it is essential to study the temperature dependence of the spontaneous magnetization M S and the T C of the multilayer. In order to determine the T C ; we measured the magnetization versus temperature curve with applied magnetic field larger than the saturation field. Three representative M2T curves for single thick FM films, AFM and FM coupled multilayers are shown in Fig. 4(a). The T C decreases in the order of the single thick film, FM-coupled multilayer of FeNiB(2.0 nm)/Ru(0.5 nm) and AFMcoupled one of FeNiB(2.0 nm)/Ru(0.8 nm). Apparently, the T C of multilayers is generally smaller than that of corresponding single thick FM films. For example, FeSi/Cr multilayers with thick spacer layers and thin FM layers have a very low T C ; compared to corresponding single thick films [15]. In epitaxially grown Co/Cu/Ni sandwiches [18], the T C of the ultrathin Ni layer is also lower than Ni bulk value and especially changes as a function of the Cu spacer layer thickness, which was attributed to the effect of oscillatory interlayer coupling. Fig. 4(b) shows the susceptibility of the FeNiB(2.0 nm)/Ru(0.8 nm) multilayer above the T C : The inverse susceptibility is a linear function of temperature, obeying the Curie–Weiss law very well with a paramagnetic Curie temperature of 116 K, close to the ferromagnetic one. With hysteresis loops at various temperatures, the spontaneous magnetization M S of all samples can be exploited from the M versus H curve in high field range according to the law of approach to saturation. Fig. 5 shows the temperature dependence of M S for single thick film and multilayers of FeNiB(2.0 nm)/Ru with Ru spacer of 0.5, 0.6, 0.8, and 1.0 nm. For single thick film and the multilayer with 0.5 nm thick Ru spacers, the spontaneous magnetization can be described very well by the Bloch law, i.e. M S ðTÞ ¼ M S ð0Þ½1 BT 3=2 : The spin-wave parameter B of the multilayer is larger than that of the single thick film. This phenomenon can be explained in terms of the finite size effect of the T C and surface effect on the spin-wave constant. Firstly, B is propor3=2 tional to T C and the T C of magnetic multilayers
ARTICLE IN PRESS S.M. Zhou, L. Sun / Journal of Magnetism and Magnetic Materials 292 (2005) 65–71
1.0
1.0 single film, 0.1 kOe
0.8
MS (arb. units)
0.8 nm, 0.7 kOe M (arb. units)
69
0.5 nm, 0.7 kOe
0.6 TC TC
0.4
single thick film
0.9 0.5 nm
0.2
0.0 0 (a)
100
200
0.8
300
T (K)
0
50
100
150
200
250
300
T3/2 (K3/2)
(a)
MS (arb. units)
χ-1 (arb. units)
1.0
0.9
0.6 nm 0.8
0.8 nm 1.0 nm
100 (b)
200 T (K)
300
0.7 0 (b)
Fig. 4. In (a) temperature dependence of the measured magnetization for the FeNiB(2.0 nm)/Ru multilayers, and single thick film, the determined ferromagnetic T C is about 109, 119 and 142 K for 0.8 and 0.5 nm thick Ru spacers, and for single thick films, respectively. In (b) for the multilayer FeNiB(2.0 nm)/Ru(0.8 nm), the measured inverse susceptibility (solid squares) and a linear fit (dashed line). The insert numbers refer to Ru spacer layer thickness and corresponding external magnetic field.
is lower than that of corresponding single thick FM films in Fig. 4(a), demonstrating a finite size effect. Secondly, the spin-wave constant of multilayers is usually larger than the bulk value, due to a surface effect. For multilayers with 0.5–1.0 nm thick Ru spacers, the magnetization can be described very well by a linear function M S ðTÞ ¼ M S ð0Þ½1 B0 T: This dependence also holds for other large Ru layer thickness. Similar phenomena
10
20
30
40
50
T (K)
Fig. 5. Temperature dependence of the measured spontaneous magnetization (solid squares) for single thick FeNiB film and multilayer FeNiB(2.0 nm)/Ru(0.5 nm) (a) and FeNiB(2.0 nm)/ Ru multilayers with thick Ru spacers (b). The dotted lines refer to T 3=2 (a) and T (b) fits, and the insert numbers refer to Ru spacer layer thickness.
have already been observed in FeSi/Si multilayers [19], in which the spontaneous magnetization is a linear function of T and T 3=2 ; respectively, for thick and thin Si layers. Recently, the temperature dependence of the magnetization in Fe/Cr multilayers was found to depend strongly on the interlayer coupling [20]. M is found to be a linear function of T, T 3=2 ; and T 2 ; respectively, for samples without any interlayer coupling and with
ARTICLE IN PRESS S.M. Zhou, L. Sun / Journal of Magnetism and Magnetic Materials 292 (2005) 65–71
70
FM and AFM coupling. In a word, the temperature dependence of the spontaneous magnetization can be explained as a result of an interplay between the interlayer coupling and low-dimensional effect [19,20]. The linear T dependence in the AFM-coupled FeNiB/Ru multilayers might be also related to compositional short-range ordering in the amorphous FM layer. In what follows, we will discuss the temperature dependence of the interlayer coupling. For 0.8 nm thick Ru layers, the strength of the effective interlayer coupling J eff can be calculated by Eq. (2) and using the data of the a and the M S at various temperatures. The experimental results are shown in Fig. 6. The effective interlayer coupling energy in the temperature range from 5 to 50 K can be fitted smoothly by the equation J eff ðTÞ ¼ J eff ð0Þ½1 ðT=T 1 Þ3=2 : Above 50 K, the variation of the magnetization deviates from the linear dependence. The parameter T 1 is found to be 108.5 K. Strikingly, this value is very close to the ferromagnetic T C of the multilayer. As shown in Figs. 5 and 6, the effective interlayer coupling energy increases with increasing spontaneous
Jeff (erg/cm2)
0.032
0.028
0.024
0.020 0
100
200
300
400
T3/2 (K3/2)
Fig. 6. Temperature dependence (solid squares) of the effective coupling energy for the FeNiB(2.0 nm)/Ru(0.8 nm) multilayer. The dashed line refers to a T 3=2 linear fit.
magnetization as a function of temperature. Therefore, it is suggested that the temperature characteristic of the effective interlayer coupling is mainly controlled by the FM layers. Since the bilinear coupling in the first model is only related to the Fermi–Dirac statistics of the electrons in the NM spacer, it cannot be used to describe the foregoing results [7,8]. It favors to explain the temperature dependence of the bilinear coupling at low temperatures, which is mainly controlled by the nonmagnetic spacers, if the T C of FM layers is very high. In the second model, the temperature variation of the bilinear coupling energy is controlled by the thermal excitation of spin waves in the FM layers [9–11]. In FeNi/Ag multilayers, the coefficient of the bilinear coupling J 12 ð¼ J 1 =M 2S Þ is almost a constant of the temperature in a wide temperature range. Therefore, J 1 will be a linear function of T 3=2 in the low temperature range [13], if the sponataneous magnetization of the FeNi/Ag multilayers is a linear function of T 3=2 : Note that the T 3 term is usually very small. More recently, the bilinear interlayer coupling energy was found to be a linear function of T 3=2 in variety of magnetic multilayers [6]. Therefore, J 1 may be of a linear function of T 3=2 in the present FeNiB/Ru multilayers. From the phenomenon that the saturation field of the first AFM coupling maximum is smaller than that of the second AFM coupling maximum, one can know the existence of the pinholes in thin Ru layers. Since the direct biquadratic coupling is induced by the pinholes in the Ru layers [12], it is strongly related to thermal fluctuation of FM spins near interfaces. In summary, the oscillatory interlayer coupling was observed in FeNiB (amorphous)/Ru multilayers. The Curie temperature T C of the multilayer is lower than that of single thick films, due to finite size effect. The spontaneous magnetization at low temperatures obeys the Bloch law for single thick film and multilayers with very thin Ru spacers. For multilayers with thick Ru spacers, however, the spontaneous magnetization has a linear temperature dependence. At the first antiferromagnetic coupling maximum, the energy of the effective coupling changes as a linear function of T 3=2 in a very wide range of normalized temperature T=T C :
ARTICLE IN PRESS S.M. Zhou, L. Sun / Journal of Magnetism and Magnetic Materials 292 (2005) 65–71
A correlation has been found between the effective interlayer coupling and the spontaneous magnetization. In addition to the temperature dependence, the amplitude of the interlayer coupling at a given temperature should be strongly related to the FM spins. This important issue needs further detailed studies, which might also be helpful to understand the mechanism of the interlayer coupling. This work was supported by NSF of China Grant No. 10174014 and 60271013, and the State Key Project of Fundamental Research of China Grant no. 2002CB613504.
References [1] P. Gru¨nberg, R. Schreiber, Y. Pang, M.B. Brodsky, H. Sowers, Phys. Rev. Lett. 57 (1986) 2442. [2] S.S.P. Parkin, N. More, K.P. Roche, Phys. Rev. Lett. 64 (1990) 2304. [3] M.D. Stiles, in: B. Heinrich, J.A.C. Bland (Eds.), Ultrathin Magnetic Structures, vol. 3, Springer, Berlin, 1994. [4] Z. Zhang, L. Zhou, P.E. Wigen, K. Ounadjela, Phys. Rev. Lett. 73 (1994) 336. [5] N. Persat, A. Dinia, Phys. Rev. B 56 (1997) 2676. [6] J. Lindner, C. Ru¨dt, E. Kosubek, P. Poulopoulos, K. Baberschke, P. Blomquist, R. Wa¨ppling, D.L. Mills, Phys. Rev. Lett. 88 (2002) 167206.
71
[7] D.M. Edwards, J. Mathon, R.B. Muniz, M.S. Phan, Phys. Rev. Lett. 67 (1991) 493. [8] P. Bruno, Phys. Rev. B 52 (1995) 411 and therein. [9] N.S. Almeida, D.L. Mills, M. Teitelman, Phys. Rev. Lett. 75 (1995) 733. [10] Z.P. Shi, R.S. Fishman, Phys. Rev. Lett. 78 (1997) 1351. [11] K.B. Hathaway, in: B. Heinrich, J.A.C. Bland (Eds.), Ultrathin Magnetic Structures, vol. 2, Springer, Berlin, 1994, pp. 45–81. [12] J.F. Bobo, H. Kikuchi, O. Redon, E. Snoeck, M. Piecuch, R.L. White, Phys. Rev. 60 (1999) 4131. [13] B. Rodmacq, K. Dumesnil, P. Mangin, M. Hennion, Phys. Rev. B 48 (1993) 3556. [14] I. Vincze, T. Kemeny, A.S. Schaafsma, A. Lovas, F. van der Woude, in: Cs. Hargitai, I. Bakonyi, T. Kemny (Eds.), Chemical and Topological Short-Range Order in Metallic Glasses, Conference on Metallic Glasses: Science and Technology, vol. 1, Budapest, 1980, p. 361. [15] Y.H. Liu, Y.M. Zhang, S.S. Yan, X.D. Ma, Phys. Rev. B 48 (1993) 10266. [16] Y.K. Lin, T. Novet, D.C. Johnson, J.M. Valles Jr., Phys. Rev. B 53 (1996) 4796. [17] K. Inomata, K. Yusu, Y. Saito, Mater. Sci. Eng. B 31 (1995) 41. [18] A. Ney, F. Wilhelm, M. Farle, P. Poulopoulos, P. Srivastava, K. Baberschke, Phys. Rev. B 59 (1999) R3938. [19] C. Aron, P. Auric, C. Jeandey, Solid State Commun. 79 (1991) 217. [20] Z.Q. Qiu, J.E. Mattson, C.H. Sowers, U. Welp, S.D. Bader, H. Tang, J.C. Walker, Phys. Rev. B 45 (1992) 2252.
