ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 279 (2004) 82–90
Magnetization reversal in the pinned layer of CoFe/PtMn bilayers Y.G. Wang*, A.K. Petford-Long Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK Received 29 November 2003; received in revised form 7 January 2004
Abstract The magnetization reversal of the ferromagnetic (FM) layer in CoFe/PtMn exchange-coupled bilayer films has been investigated using bulk magnetometry. These films exhibit very complex angular dependence and the easy axis is perpendicular to the field applied during deposition and post-annealing. Holding the film at negative saturation of the FM layer for up to 17 h results in no change in the exchange field. We believe that this is a thermally stable exchangecoupled system. Only limited thermal activation with a small time constant appears and no thermally activated reversal of the antiferromagnetic layer with a large time constant exits. r 2004 Elsevier B.V. All rights reserved. PACS: 75.60.Jk; 75.70.Cn; 75.50.Ss Keywords: Exchange coupling; Magnetization reversal; Thermal activation; Hysteresis; CoFe/PtMn bilayer
1. Introduction A great deal of attention has been focused on the exchange coupling at the interface between a ferromagnetic (FM) layer and an antiferromagnetic (AFM) layer due to its importance in spinvalve heads for high density recording systems and related giant magnetoresistance devices. For good reviews see Refs. [1,2]. In these exchange-coupled systems, the AFM layer pins the adjacent FM layer through the action of the exchange coupling at the AFM/FM interface. This gives rise to the
*Corresponding author. Present address: Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK. Tel.: +44-141-330-4707; fax: +44-141-3304464. E-mail address:
[email protected] (Y.G. Wang).
shift of the hysteresis loop along the field axis and an enhanced coercivity of the FM layer which was originally observed by Meiklejohn and Bean [3] and is generally referred to as exchange-bias. The offset of the hysteresis loop of the FM layer is explained by considering the disorder at the AFM/ FM interface and predicting that competing magnetic interactions at the interface lead to the formation of domains in the AFM layer [4], in addition to the effect of the defects themselves [5]. Experimental and theoretical studies have also suggested that the enhanced coercivity may result from interface roughness [6–9], spin rearrangement at the interface [10–12], higher-order anisotropy [13], instabilities in the AFM order in the grains [14,15], or inhomogeneities in the AFM layer [16]. The magnetization reversal of the FM layer in exchange-coupled systems is a complex process. In
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2004.01.049
ARTICLE IN PRESS Y.G. Wang, A.K. Petford-Long / Journal of Magnetism and Magnetic Materials 279 (2004) 82–90
addition to the loop shift and coercivity enhancement described above, several phenomena have also been observed in this process such as the asymmetry of the magnetizing and demagnetizing reversal mechanisms [8,11,12,16–22], a training effect [22–27], a sweep rate dependence [28,29] and a reduction of the loop shift with respect to zero field after holding the FM layer at negative saturation, i.e. keeping the FM layer saturated in the direction antiparallel to unidirectional easy axis (UEA) of the system [21,22,28–32]. The complexity of the reversal process is believed to be a result of the thermally activated reversal of parts of the AFM layer. This can occur either during reversal of the FM layer or following reverse saturation of the FM layer, driven by exchange coupling from the neighbouring FM layer [21,22,28,30]. Two mechanisms have been proposed: coherent reversal of single AFM domains [21] or the formation of domain walls within the AFM layer [15,29,33]. Observations of the magnetization reversal of the FM layer in IrMn/CoFe exchange-coupled bilayers with different AFM layer thicknesses (dAFM ) showed a very complex magnetization process. This included many of the processes described above such as a shift of the hysteresis loop, coercivity enhancement, asymmetry of reversal, and a reduction of the loop shift with respect to zero field while holding the FM layer at negative saturation [22,34,35]. The reversal mechanisms that were observed were dependent on the thickness of the AFM layer, dAFM : We fitted our results to a model that assumed that two energy barrier distributions with different time constants coexist, of which the thermally activated reversal of the AFM layer with a large time constant results in an increasing shift of the entire hysteresis loop towards zero field with increased period of time spent at negative saturation, because of a reduction in the overall unidirectional anisotropy in the films. Thermal activation with a small time constant contributes to the coercivity enhancement, the asymmetry of reversal mechanism, and the training effect. As dAFM decreases, the energy barriers for thermally activated reversal of the AFM layer decrease. The changes in the AFM layer then become more significant, resulting in a
83
greater effect on the reversal of the FM layer and contributing to the dAFM dependence of the magnetization reversal in this system. One of the factors that contributes to the magnetic anisotropy of the AFM layer in an exchange-coupled system is the magnetocrystalline anisotropy of the AFM material [36]. IrMn is believed to be a disordered AFM material which gives a unidirectional anisotropy constant larger than 0.39 erg/cm2 in CoFe/IrMn system [37,38], and the question arises as to how an exchangecoupled system with an ordered AFM layer acts. One example is ordered PtMn, which leads to a unidirectional anisotropy constant of 0.26 erg/cm2 in CoFe/PtMn system [39]. The as-deposited polycrystalline PtMn has a metastable, nonmagnetic disordered face-centred cubic (FCC) structure, which transforms to an ordered AFM facecentred tetragonal (FCT) phase after a high temperature anneal. In addition, because the thermal activation tends to make exchangecoupled systems thermally unstable, there has been considerable effort to find systems which have increased thermal stability, and in particular to find new AFM materials for the pinning layer. One of the most promising candidates in terms of thermal stability is PtMn [39–42] which has a blocking temperature higher than 500 K. In order to compare with study on disorder AFM biased CoFe/IrMn system, this paper presents magnetic measurements which study in detail the magnetization reversal of the FM layer and the related thermally activated processes in exchange-coupled CoFe/PtMn bilayers.
2. Experimental details A series of //seed(5 nm)/CoFe(10 nm)/PtMn (dAFM nm)/Ta(2 nm) exchange-coupled films with dAFM ¼ 3; 5, 7, 10, 15 and 20 were deposited by magnetron sputtering in an orienting field on silicon wafers substrates with a thermally oxidized layer. After deposition the films were annealed at 300 C for 4 h in a magnetic field of 1 T parallel to the orienting field. The microstructure of similar films deposited on Si3N4 membranes at the same time was analysed using transmission electron
ARTICLE IN PRESS Y.G. Wang, A.K. Petford-Long / Journal of Magnetism and Magnetic Materials 279 (2004) 82–90
microscopy. This showed them to be polycrystalline with strong /1 1 1S texture. The magnetometry measurements were made using a vibrating sample magnetometer at room temperature. The sweep-rate during the reversal was kept constant at 2.5 Oe/s in order to keep contributions from time-dependent effects the same for all the specimens. In the waiting-time experiment at negative saturation of the FM layer, a similar procedure was used to that for the IrMn/ CoFe films [35]. Starting at positive field, the applied field was swept to a negative value which saturates the FM layer in the opposite direction to its initial state. Then the films were held at negative saturation of the FM layer for a given period of time (tns ). During this period, some proportion of the AFM layer could reverse by thermal activation as a result of the exchange coupling between the FM and AFM layers. The demagnetising branch of the hysteresis loop was then measured as the applied field was returned to the initial value. The field was swept positive to saturate the FM layer in its original direction and the magnetizing branch of the loop was then measured without waiting at positive saturation of the FM layer. The procedure was then repeated for a different value of tns so that a cumulative effect of waiting time was observed.
Hard-axis Ha θ Easy-axis
PtMn
CoFe
(a) 1.0 θ = 90o θ = 0o Hc
0.8 0.6 0.4 M x 103 (emu)
84
Hex
0.2 0.0 -0.2 -0.4 -0.6
NS
-0.8 -1.0 -1000
(b)
-500
0 Ha (Oe)
500
1000
Fig. 1. (a) Schematic for the measurements of angular dependence of exchange field and coercivity. (b) Representative easy axis (y ¼ 0 ) and hard axis (y ¼ 90 ) hysteresis loops for a CoFe(10 nm)/PtMn(15 nm) film.
3. Results and discussion We have firstly investigated the angular dependence of the exchange coupling in the CoFe/PtMn bilayers. The magnitude of the exchange coupling and coercivity of FM/AFM bilayers was measured in an applied field, which makes an angle y with the anisotropy axis of the FM layer as defined in Fig. 1(a). Hysteresis loops were obtained at different values of y by rotating the sample in the plane of film surface with respect to the applied field. The hard axis hysteresis loop was easily found since it had the smallest coercivity and the exchange field was zero. Therefore, the hysteresis loop measurements are defined with respect to an origin at 90 to the hard axis direction. The exchange field Hex and coercivity Hc for each angle y are defined as the displacement and the half-
width of the loop, respectively. Examples of such loops are seen in Fig. 1(b), which shows easy axis (i.e. y ¼ 0 ) and hard axis (i.e. y ¼ 90 ) hysteresis loops for a CoFe(10 nm)/PtMn(15 nm) bilayer. An interesting observation for all the CoFe/PtMn bilayer films analysed is that the hard axis direction is parallel to the direction of the field applied during deposition and during post-deposition annealing, i.e. the easy axis of the FM layers lies perpendicular to the deposition field. This effect has been observed in Fe/FeF2 [10] and Fe3O4/CoO [43] systems and is usually referred as perpendicular coupling. Fig. 2 shows the angular dependence of the exchange field and coercivity for the CoFe(10 nm)/ PtMn(15 nm) bilayer in which a well defined
ARTICLE IN PRESS Y.G. Wang, A.K. Petford-Long / Journal of Magnetism and Magnetic Materials 279 (2004) 82–90
400
350 Hc Hex
300 200 100 0
Hex Hc
300 Hex & Hc (Oe)
Hc, Hex (Oe)
85
250 200 150 100
-100 50 -200 0
90
180
270 360 θ (degree)
450
540
Fig. 2. Angular dependence of the exchange field Hex and coercivity Hc for an exchange-coupled CoFe(10 nm)/ PtMn(15 nm) bilayer. Measurements were made every 10 and data are shown by dots. The solid lines are guides to the eye.
exchange-bias field effect can be obtained. The largest exchange field was observed at an angle of about 40 away from the easy axis. The variation in exchange field is not symmetric about the axis at 90 to the hard axis (termed the easy axis direction). As pointed out above, the main uniaxial anisotropy is perpendicular to the field applied during deposition and post-annealing and defines a main UEA. The residual effect of the field applied during deposition and post-annealing, however, results in different behaviour appearing for a field applied at 90 and 270 to the UEA. A two-fold odd symmetry exists in the angulardependence of the exchange field for the CoFe(10 nm)/PtMn(15 nm) bilayer with respect to the easy and hard axes, i.e. Hex ðy þ 3p=2Þ ¼ Hex ð3p=2 yÞ and Hex ðy þ p=2Þ ¼ Hex ðp=2 yÞ: However, a two-fold even symmetry exists for the coercivity with respect to the easy and hard axes, i.e. Hc ðy þ 3p=2Þ ¼ Hc ð3p=2 yÞ and Hc ðy þ p=2Þ ¼ Hc ðp=2 yÞ: Fig. 3 summarizes the results of the hysteresis loop measurements for y ¼ 0 ; i.e. field applied
0 2
4
6 8 10 12 14 16 18 PtMn Thickness, dAFM (nm)
20
22
Fig. 3. The exchange field Hex and coercivity Hc as a function of PtMn thickness dAFM of the CoFe(10 nm)/PtMn(dAFM nm) bilayers. The solid lines are guides to the eye.
parallel to the easy axis of the FM CoFe layer. The figure shows the dependence of exchange field Hex and coercivity Hc on PtMn thickness, dAFM ; for bilayers with a 10 nm thick CoFe layer. The exchange field and coercivity were obtained from the hysteresis loops for fields applied along the easy axis of the CoFe layer and after several cycles, i.e. no training effect is involved. These data show that Hex becomes observable when dAFM exceeds about 7 nm, and then increases with dAFM : The coercivity, on the other hand, shows an initial peak and then reduces to a steady state value as dAFM increases. The coercivity is 18 Oe at dAFM ¼ 3 nm, and increases to a maximum of 308 Oe at dAFM ¼ 10 nm, then slightly decreases to a nearly constant value of about 235 Oe for dAFM X15 nm. These data show that for all the samples we studied here the AFM thickness is smaller than that needed to establish well-defined exchange bias. Similar complex angular dependence of exchange field and coercivity was also observed by Xi and White [44] in NiFe/CrMnPt systems and can be explained from effects due to the thickness of AFM layer. For systems with AFM layer thickness large enough to support well-defined exchange bias both an even symmetry with respect to the easy axis and an odd symmetry with respect to the hard axis appeared. For systems with thinner AFM layer these two symmetries are not
ARTICLE IN PRESS 86
Y.G. Wang, A.K. Petford-Long / Journal of Magnetism and Magnetic Materials 279 (2004) 82–90
fully developed. The even symmetry is broken and the maximum exchange fields on each side of the easy axis have different values. With decreasing AFM layer thickness, the angular-dependent exchange field deviates from the even symmetry more and more, and finally loses the symmetry totally. The location of the maximum exchange field, which was found to be determined by the ratio of the exchange field to the coercivity along the easy axis, moves further away from the easy axis as well. On the other hand, in many systems, in particular those exhibiting spin-flop coupling, such as Fe/MnPd [13] or Fe/MnF2 [45], higher order terms in the energy (and thus Hex and Hc ) have been observed and may also contribute to the complex angular dependence of exchange field and coercivity. As for the NiFe/CrMnPt bilayers [44], this asymmetric angular behaviour of the exchange field in CoFe/PtMn systems can be understood in terms of an interfacial spin flop [5,46]. We expect the ordered FCT polycrystalline AFM PtMn to have a spin structure in which the moments point along the /1 1 1S directions so that it is internally compensated and the interface between the FM and the AFM layers will be compensated. As pointed out in Refs. [5,46,47], spin-flop coupling can appear between a compensated AFM layer and a FM layer. This perpendicular coupling can be understood within a microscopic Heisenberg model where, due to frustration of the moments at the interface, the FM layer minimizes the energy of the system when it aligns perpendicular to the AFM easy axis. The spin-flop coupling gives rise to a uniaxial anisotropy which in turn causes the large coercivity and the interfacial defects leads to shift of hysteresis loop, i.e. the exchange bias [5]. On annealing the AFM PtMn moments at the interface are aligned perpendicular to the FM CoFe magnetization along the easy axis induced by the aligning field. Subsequently the AFM layers will twist back to the easy axis established by the aligning field to reduce system energy. If the AFM layer is thick enough, the AFM moments at the back of the bilayer will be aligned along the external field, and therefore, a well-defined easy axis of the AFM layer will be established. If the AFM is thin, which is our case, the back of the
AFM displays a residual spin-flop configuration which results in the asymmetry of the angular dependence of exchange field. Defects such as roughness at the interface lower the degree of compensation at the interface and cause canting of the interfacial spins, which might be the another origin of the lack of even symmetry of the exchange field about the easy axis direction [48]. As for the IrMn/CoFe system a training effect is observed for the CoFe/PtMn system, as shown in Fig. 4 for y ¼ 0: This is believed to be a result of thermal activation with a small time constant [35]. The exchange field induced by the FM layer at negative saturation [at point NS in Fig. 1(b)] enables the AFM layer to relax to its lowest energy configuration. This most likely results in some proportion of the AFM layer reversing such that the magnitude of the UEA anisotropy decreases. As the number of magnetization cycles increases this reversed proportion approaches some equilibrium value so that the difference between one loop and the next becomes smaller. Fig. 5 shows the total training effect T and that in between the first and the second rounds of the hysteresis loop T12 as a function of PtMn thickness dAFM of the CoFe(10 nm)/PtMn(dAFM nm) bilayers. We define the total training effect as T ¼ ½Hc ð1stÞ Hc ðNthÞ=Hc ðNthÞ and the training effect in between the first and second rounds of the hysteresis loop as T12 ¼ ½Hc ð1stÞ Hc ð2ndÞ=Hc ð2ndÞ; where Hc (Nth), Hc (1st) and Hc (2nd) are the coercivities of the Nth, 1st and 2nd hysteresis loops, respectively. In practice Hc in Fig. 3 is used instead of Hc (Nth). One can see that the training effect becomes stronger as the AFM PtMn layer thickness increases. This implies that the exchange coupling at the FM/AFM interface contributes to the training effect. As the AFM layer thickness increases the exchange coupling at the FM/AFM interface strengthens so the training effect becomes more effective. One also notices for systems with thicker AFM layer (dAFM X10), the slopes of the increase of training effects, especially for T12, are much smaller than those for systems with thinner AFM layer. This would be expected since for
ARTICLE IN PRESS Y.G. Wang, A.K. Petford-Long / Journal of Magnetism and Magnetic Materials 279 (2004) 82–90
2.0
2.0 1st loop 2nd loop 3rd loop
M x 103 (emu)
1.0
1.5 1.0 M x 103 (emu)
1.5
0.5 0.0 -0.5 -1.0 -1.5
0.5
1st loop 2nd loop 3rd loop 4th loop
0.0 -0.5 -1.0 -1.5
-2.0 -200 -150 -100 -50 (a)
0 50 Ha (Oe)
-2.0 -1200
100 150 200
2.0 1st loop 2nd loop 3rd loop
1.5 M x 103 (emu)
1.0
-800
(c)
1.5
M x 103 (emu)
87
0.5 0.0 -0.5
1.0 0.5 0.0
-400 0 Ha (Oe)
400
800
-400 0 Ha (Oe)
400
800
1st loop 2nd loop 3rd loop 4th loop 5th loop
-0.5 -1.0
-1.0
-1.5
-1.5 -200 -150 -100 -50 0 50 (b) Ha (Oe)
-2.0 -1200
100 150 200 (d)
-800
Fig. 4. Some examples of successive hysteresis loops showing a training effect for (a) CoFe(10 nm)/PtMn(3 nm), (b) CoFe(10 nm)/ PtMn(5 nm), (c) CoFe(10 nm)/PtMn(10 nm), and (d) CoFe(10 nm)/PtMn(20 nm) bilayer films.
50 T12 T
T & T12 (%)
40 30 20 10 0 2
4
6
8
10
12
14
16
18
20
22
PtMn Thickness, dAFM (nm) Fig. 5. The total training effect T and that in between the first and the second rounds of the hysteresis loop T12 as a function of PtMn thickness dAFM of the CoFe(10 nm)/PtMn(dAFM nm) bilayers. The solid lines are guides to the eye.
thicker AFM layers the AFM anisotropy will be more fully developed and hence the AFM spins will, on the other hand, be more difficult to be rearranged by the FM. Fig. 6 shows examples of hysteresis loops for CoFe(10 nm)/PtMn(10 nm) and CoFe(10 nm)/ PtMn(15 nm) measured after holding the sample at negative saturation of the FM layer, i.e. point NS in Fig. 1(b), for different periods of time tns : The slight difference seen in Fig. 6(a) on the magnetizing branch of the loop is believed to be a result of the training effect. Holding the CoFe/ PtMn bilayers at negative saturation of the FM CoFe layer does not result in a decrease of the exchange field. This indicates that there is no reversal in the bulk of the AFM layer over these rather long time periods. This does not preclude reversible changes of the magnetization in regions
ARTICLE IN PRESS Y.G. Wang, A.K. Petford-Long / Journal of Magnetism and Magnetic Materials 279 (2004) 82–90
88
2.0
0.8
1.5
M/Ms
M x 103 (emu)
0.5 0.0 -0.5 -1.0
tns = 0 tns = 17 hr.
-1.5
-2.0 -1000 -750 -500 -250 0 250 500 750 1000 (a) Ha (Oe)
-0.4
-1.2 101
102
(a)
103 Time (s)
104
105
0.016
1.0
0.012
0.5 S/Ms
M x 103 (emu)
0.0
-0.8
1.5
0.0
0.008 0.004
-0.5 tns = 0 tns = 5 hr. tns = 10.5 hr.
-1.0 -1.5 -1000 -750 -500 -250 (b)
-240 Oe -280 Oe -320 Oe -350 Oe -400 Oe -800 Oe
0.4
1.0
0
250 500 750 1000
Ha (Oe)
0.000 -0.004 -900 -800 -700 -600 -500 -400 -300 -200 (b) Ha (Oe)
Fig. 6. Hysteresis loops measured after holding the sample at negative saturation of the FM layer for different periods of time tns for (a) CoFe(10 nm)/PtMn(10 nm); (b) CoFe(10 nm)/ PtMn(15 nm).
Fig. 7. (a) Time dependence of magnetization at various values of applied field, and (b) the normalized viscosity coefficient S=Ms as a function of applied field Ha for a CoFe(10 nm)/ PtMn(15 nm) bilayer. The solid line is a guide to the eye.
of the AFM layer on a much shorter time-scale, for example the formation of twist domain walls, which could contribute to the training effect and the loop broadening. This result is different from that observed for the IrMn/CoFe system [35]. Although other effects, such as grain size, blocking temperature or distribution of temperatures and their dependence with thickness, could also play a role we believe that this is mainly because of the crystallographic order in the PtMn AFM layer. Spins are tied strongly to crystal structure and reversal or rotation of the moments in bulk regions of the AFM layer has to overcome a much higher energy barrier and the energy induced by the applied field is not high enough to overcome this barrier.
As first observed by Street and Woolley [49], the time dependence for reversal is expected to follow a logarithmic law: MðHa ; tÞ ¼ MðHa ; 0Þ7SðHa Þln t; where SðHa Þ ¼ 7dM=dln t is the magnetic viscosity which goes through a maximum near Ha = Hc : The magnitude of SðHa Þ is dependent on the value of f(E) at a critical energy barrier E activated by the applied field Ha and has been shown to be [50–52] SðHa Þ ¼ 2Ms kTf ½EðHa Þ; where Ms is the saturation magnetization. As shown in Fig. 7(a), a linear relation of MðtÞ was observed for CoFe(10 nm)/PtMn(15 nm) bilayers
ARTICLE IN PRESS Y.G. Wang, A.K. Petford-Long / Journal of Magnetism and Magnetic Materials 279 (2004) 82–90
at various values of applied field and in Fig. 7(b) a maximum is observed at Hc on the curve of SðHa Þ=Ms in agreement with this model. The linear dependence of MðtÞ; and thus of the viscosity coefficient, on time remains constant over long time periods, implying that the activation energy distribution present in the sample is wide. This may result from several factors, such as a distribution of AFM domain size, a distribution of Ne! el axis orientation in the AFM domains, and random pinning sites and helical domain walls at the FM/AFM interface [35]. The curvature of the active region of the f(E) curve remains small as the total magnetization changes, which agrees with the fact that no decrease of exchange field is observed when the bilayers are held at tns ; and with the very small value observed for S=Ms :
4. Conclusions Based on our studies of the magnetization reversal of CoFe/PtMn bilayers we believe that this is a thermally stable exchange-coupled system. Only thermal activation with a small time constant appears, which is likely to be an interface-initiated change, such as the formation of helical domain walls within the AFM layer. Holding the CoFe/ PtMn film at negative saturation of the FM layer over long time periods does not lead to a decrease of the exchange field confirming the better thermal stability of the PtMn-based system. The angular dependence of exchange field shows an asymmetric behaviour. A spin-flop coupling configuration in which the AFM moments lie perpendicular to the FM magnetization at interface can be applied to interpret the results.
Acknowledgements This work was supported by EPSRC. The authors would like to acknowledge Seagate Technology for partial financial support and Deirdre O’Neill for the provision of samples. We are also grateful to K. O’Grady for provision of magnetometry facilities.
89
References [1] J. Nogues, I.K. Schuller, J. Magn. Magn. Mater. 192 (1999) 203. [2] R.L. Stamps, J. Phys. D 33 (2000) R247. [3] W.H. Meiklejohn, C.P. Bean, Phys. Rev. 102 (1956) 1413. [4] A.P. Malozemoff, Phys. Rev. B 35 (1987) 3679; A.P. Malozemoff, J. Appl. Phys. 63 (1988) 3874. [5] T.C. Schulthess, W.H. Butler, Phys. Rev. Lett. 81 (1998) 4516. [6] S. Zhang, D.V. Dimitrov, G.C. Hadjipanayis, J.W. Cai, C.L. Chien, J. Magn. Magn. Mater. 198–199 (1999) 468. [7] D.V. Dimitrov, S. Zhang, J.Q. Xiao, G.C. Hadjipanayis, C. Prodos, Phys. Rev. B 58 (1998) 12090. [8] Z. Li, S. Zhang, Phys. Rev. B 61 (2000) R14897; Z. Li, S. Zhang, Appl. Phys. Lett. 77 (2000) 423. [9] Z. Qian, J.M. Sivertsen, J.H. Judy, J. Appl. Phys. 83 (1998) 6825. [10] T.J. Moran, J. Nogus, D. Lederman, I.K. Schuller, Appl. Phys. Lett. 72 (1998) 617. [11] V.I. Nikitenko, V.S. Gornakov, L.M. Dedukh, Yu.P. Kabanov, A.F. Khapikov, A.J. Shapiro, R.D. Shull, A. Chaiken, R.P. Michel, Phys. Rev. B 57 (1998) R8111. [12] J. Wang, W.N. Wang, X. Chen, H.W. Zhao, J.G. Zhao, W.Sh. Zhan, Appl. Phys. Lett. 77 (2000) 2731. [13] Y.J. Tang, B. Roos, T. Mewes, S.O. Demokritov, B. Hillebrands, Y.J. Wang, Appl. Phys. Lett. 75 (1999) 707. [14] H. Xi, R.M. White, Phys. Rev. B 61 (2000) 80. [15] M.D. Stiles, R.D. McMichael, Phys. Rev. B 59 (1999) 3722; M.D. Stiles, R.D. McMichael, Phys. Rev. B 60 (1999) 12950. [16] C. Leighton, I.K. Schuller, Phys. Rev. B 63 (2001) 174419. [17] M.D. Stiles, R.D. McMichael, Phys. Rev. B 63 (2000) 064405. [18] V.I. Nikitenko, V.S. Gornakov, A.J. Shapiro, R.D. Shull, K. Liu, S.M. Zhou, C.L. Chien, Phys. Rev. Lett. 84 (2000) 765. [19] M.R. Fitzsimmons, P. Yashar, C. Leighton, I.K. Schuller, J. Nogues, C.F. Majkrzak, J.A. Dura, Phys. Rev. Lett. 84 (2000) 3986. [20] C. Leighton, M.R. Fitzsimmons, P. Yashar, A. Hoffmann, J. Nogues, J. Dura, C.F. Majkrzak, I.K. Schuller, Phys. Rev. Lett. 86 (2001) 4394. [21] X. Portier, A.K. Petford-Long, A. de Morais, N.W. Owen, H. Laidler, K. O’Grady, J. Appl. Phys. 87 (2000) 6412. [22] Y.G. Wang, A.K. Petford-Long, T. Hughes, H. Laidler, K. O’Grady, M.T. Kief, J. Magn. Magn. Mater. 242–245 (2002) 1073. [23] C. Schlenker, J. Phys. (France) 28 (1967) 611. [24] H. Fujiwara, K. Zhang, T. Kai, T. Zhao, J. Magn. Magn. Mater. 235 (2001) 319. [25] D. Suess, M. Kirschner, T. Schrefl, J. Fidler, R.L. Stamps, J.-V. Kim, Phys. Rev. B 67 (2003) 054419. [26] J. Keller, P. Milt!enyi, B. Beschoten, G. Guntherodt, . U. Nowakw, K.D. Usadel, Phys. Rev. B 66 (2002) 014431.
ARTICLE IN PRESS 90
Y.G. Wang, A.K. Petford-Long / Journal of Magnetism and Magnetic Materials 279 (2004) 82–90
[27] S.G.E. te Velthuis, A. Berger, G.P. Felcher, B.K. Hill, E. Dan Dahlberg, J. Appl. Phys. 87 (2000) 5046. [28] A.M. Goodman, K. O’Grady, H. Laidler, N. Owen, X. Portier, A.K. Petford-Long, F. Cebollada, IEEE Trans. Magn. 37 (2001) 565. [29] R.L. Stamps, Phys. Rev. B 61 (2000) 12174. [30] P.A.A. van der Heijden, T.F.M.M. Maas, W.J.M. de Jonge, J.C.S. Kools, F. Roozeboom, P.J. van der Zaag, Appl. Phys. Lett. 72 (1998) 492. [31] E. Fulcomer, S.H. Charap, J. Appl. Phys. 43 (1972) 4190. [32] T. Hughes, H. Laidler, K. O’Grady, J. Appl. Phys. 89 (2001) 5585. [33] D. Mauri, H.C. Siegmann, P.S. Bagus, E. Kay, J. Appl. Phys. 62 (1987) 3047. [34] Y.G. Wang, A.K. Petford-Long, H. Laidler, K. O’Grady, M.T. Kief, IEEE Trans. Magn. 38 (2002) 2773. [35] Y.G. Wang, A.K. Petford-Long, J. Appl. Phys. 92 (2002) 6699. [36] M. Takahashi, M. Tsunoda, J. Phys. D: Appl. Phys. 35 (2002) 2365. [37] K. Yagami, M. Tsunoda, M. Takahashi, J. Appl. Phys. 89 (2001) 6609. [38] M. Tsunoda, K. Nishikawa, T. Damm, T. Hashimoto, M. Takahashi, J. Magn. Magn. Mater. 239 (2002) 182.
[39] T. Sato, M. Tsunoda, M. Takahashi, J. Magn. Magn. Mater. 240 (2002) 277. [40] R.F.C. Farrow, R.F. Marks, S. Gider, A.C. Marley, S.S.P. Parkin, D. Mauri, J. Appl. Phys. 81 (1997) 4986. [41] M. Saito, N. Hasegawa, F. Koike, H. Seki, T. Kuriyama, J. Appl. Phys. 85 (1999) 4928. [42] G.W. Anderson, Y. Huai, M. Pakala, J. Appl. Phys. 87 (2000) 5726. [43] Y. Ijiri, J.A. Borchers, R.W. Erwin, S.-H. Lee, P.J. van der Zaag, R.M. Wolf, Phys. Rev. Lett. 80 (1998) 608. [44] H. Xi, R.M. White, J. Appl. Phys. 86 (1999) 5169; H. Xi, R.M. White, Phys. Rev. B 61 (2000) 1318. [45] I.N. Krivorotov, C. Leighton, J. Nogu!es, I.K. Schuller, E. Dan Dahlberg, Phys. Rev. B 65 (2002) 100402. [46] N.C. Koon, Phys. Rev. Lett. 78 (1997) 4865. [47] L.L. Hinchey, D.L. Mills, Phys. Rev. B 34 (1986) 1689. [48] J.V. Kim, R.L. Stamps, B.V. McGrath, R.E. Camley, Phys. Rev. B 61 (2000) 8888. [49] R. Street, J.C. Woolley, Proc. Phys. Soc. A 62 (1949) 562. [50] R. Street, J.C. Woolley, P.B. Smith, Proc. Phys. Soc. B 65 (1952) 679. [51] P. Gaunt, G.J. Roy, Philos. Mag. 34 (1976) 781. [52] P. Gaunt, J. Appl. Phys. 59 (1986) 4129.