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Thin Solid Films 275 ( 1996) 199-202
Bilinear and biquadratic exchange coupling in epitaxial Fe/Cr/Fe/Ag/GaAs( 100) structures R.J. Hicken, C. Daboo, M. Gester, A.J.R. Ives, S.J. Gray, J.A.C. Bland The Cavendish Laboratory. University of Cambridge, Madingley Road. Cambridge CB3 OHE, UK
Abstract
The interlayer exchange coupling has been investigated in epitaxial Fe( 20 A) lCrlFe(20 A) /Ag/GaAs( 100) structures that contain a wedge-shaped (O-40 A) Cr layer. Longitudinal and polar magneto optical Kerr effect (MOKE) and Brillouin light scattering (BLS) measurements have been combined to determine values for the bilinear and biquadratic coupling strengths. While the phase and period of the oscillations in the interlayer coupling agree well with those reported by other researchers, the magnitude of the coupling strength is found to be reduced. The dependence of the biquadratic coupling strength upon the Cr thickness is well described by a simple power law and may provide a useful test of extrinsic biquadratic coupling models. We show that the combination of MOKE and BLS measurements are very effective in investigating the ultrathin Cr region and that ferromagnetic (FM) coupling produces large changes in the polar MOKE saturation field. Keywords: Epitaxy; Magnetic properties and measurements; Light scattering; Chromium
1. Introduction Antiferromagnetic (AFM) interlayer exchange coupling through a transition metal spacer layer was first observed in Fe/Cr/Fe trilayer structures [ I]. Although interlayer coupling has now been observed in many different materials [ 21 there are a number of reasons why Fe/Cr remains one of the most interesting systems to study. Firstly the antiferromagnetism of the Cr may be modified in an ultrathin film, with phase slips occurring in the magnetic order [ 3-51 and frustration effects resulting from interfacial roughness [ 61. Secondly, Fe/Cr structures are known to exhibit biquadratic coupling [ 4,7,8]. A number of intrinsic mechanisms [ 91, that apply to ideal structures, and extrinsic mechanisms [ lo] , that depend upon some form of structural defect, have been proposed to explain the existence of the biquadratic coupling. In this paper we present a study of the interlayer coupling in Fe/Cr/Fe trilayer structures, containing wedge-shaped Cr layers, grown on Ag/GaAs( 100) substrates. Although shortperiod coupling oscillations can be obtained for such structures grown at elevated temperatures [ 111, our samples were grown at lower temperatures. We therefore expect our samples to contain structural defects that may favour extrinsic biquadratic coupling. We have combined in-plane magneto optical Kerr effect (MOKE), polar MOKE and Brillouin light scattering (BLS) measurements in order to determine 0040-6090/96/$15.00
0 1996 Elsevier Science S.A. All rights reserved
SSDlOO40-6090(95)07042-7
how the bilinear and biquadratic coupling strengths depend upon the value of the Cr thickness. Both BLS and polar MOKE are sensitive to the perpendicular anisotropy of the constituent Fe layers and interlayer coupling of either sign. We will show how this allows us to observe the nature of the coupling in the ultrathin Cr limit.
2. Experimental consideration The epitaxial Fe/Cr/Fe structures described in this paper were grown on GaAs( 100) substrates capped with thick Ag( 100) buffer layers. In-situ structural characterisation was performed by means of low-energy electron diffraction (LEED) and reflection high-energy electron diffraction (RHEED) . Further details of both the growth and the structural characterisation will be given elsewhere [ 121. The samples were capped with a protective Cr layer approximately 20 w thick before being removed from the growth chamber for ex-situ magnetic characterisation. In-plane MOKE measurements were recorded with the field applied parallel to both the in-plane easy, Fe(OOl), and hard, Fe(Ol1) axes. Let us assume the interlayer coupling energy to be a surface energy of the form E coupling= -2A,2~,.~~-2B,2(~,.~*)2
(1)
200
R.J. Hicken et al. / Thin Solid Films 275 (I 996) 199-202
in which M, and M2 are the magnetization vectors of the two Fe layers and Al2 and B,, are the bilinear and biquadratic coupling constants respectively. By considering the condition for the saturated state to become unstable we find that for the case of antiferromagnetic coupling the in-plane saturation field has the form H
sat
= +2K, --IV
4(~,,+2~,~) Md
(2)
in which K,, M and d are the cubic anisotropy constant, magnetization and thickness of the Fe layers (assumed to be equal) respectively. The positive and negative signs refer to the hard and easy axis directions respectively. Although the saturation field in Eq. (2) gives the total coupling strength the individual values of A,, and B,, can sometimes be deduced by considering other features in the hysteresis loop -0.5u
[7,81.
0
Let us consider a trilayer structure in which the two magnetic layers are identical apart from their interface anisotropies. We define the quantity H,,,=~TM---~
2K1
4K,i
M
Md
(3)
in which KS,; is the interface anisotropy constant averaged over the two interfaces of layer i, where i = 1 or 2. We may assume that close to saturation the magnetisation vectors and the surface normal are coplanar, and then we obtain the following expression for the polar saturation field A
=Md(H,,,-H,,,)(H,,,-H,,2)
+2B
12
12 2(%,
+X,2
-
(4)
=LA
For the samples to be described here Ha,, f Ha,*, (contrary to the assumption made in Ref. [ 131) and then Eq. (4) predicts that the polar saturation field has a non-linear dependence upon the coupling field and is sensitive to both ferromagnetic (FM) and AFM coupling. Since the polar curves are generally rounded near the saturation point, the polar MOKE saturation field was taken to be that at which the polar Kerr intensity reached 96% of its maximum value [ 131. Further details of the MORE and BLS experiments will be given elsewhere [ 121. We note however that since the sample must be repositioned for each of the three experiments, the Cr thickness scale in these experiments are subject to a systematic error of up to 0.7 A.
3. Results In-plane and polar MORE and BLS measurements were made at various points on a Fe( 20 A) /Cr( O-38 A) /Fe( 20 A) wedge structure (Sample I). BLS measurements were made with a field of 5 kOe applied parallel to the Fe hard axis which was sufficient to saturate the sample at all points along the wedge. The spin wave frequencies and the MOKE saturation fields are plotted in Fig. 1. The in-plane easy axis
5 10 15 20 25 30 35 Cr thickness (A)
Fig. 1, The following quantities are plotted as a function of Cr thickness for sample I: (a) BLS mode frequencies, where the open and closed symbols denote the acoustic and optical spin wave modes respectively; (b) the polar MOKE loop saturation field; (c) the in-plane easy axis MOKE saturation field (closed symbols), or the coercive field, plotted as a negative quantity, if the loop is square (open symbols). The inset in panel (c) is an expanded view of the data for small Cr thicknesses
saturation field (Fig. 1 (c) ) reveals the oscillatory nature of the coupling. Where an open symbol has been used in Fig. 1 (c) the easy axis loops are square, indicating that the sample is either FM coupled or simply uncoupled. We have identified the beginning of the wedge as the point at which the coercivity of the easy axis loop decreases abruptly to about half its previous value (see inset in Fig. 1 (c)). This change may occur because the inclusion of a partial Cr layer provides new sites for domain nucleation. The first AFM region (4-15 A> is also clearly visible in the polar MOKE scan but the second AFM (20-38 A) region is less we11 defined. In the region where the Cr thickness varies from 0 to 4 A we see a sharp reduction of the polar MOKE saturation field which we believe is due to strong ferromagnetic coupling of the two Fe layers. As Cr is introduced into the middle of the 40 A Fe layer the saturation field decreases, because of the additional perpendicular anisotropy associated with the Cr layer, until a full monolayer of Cr is present. It is known that a monolayer of Cr orders antiferromagnetically with a neighbouring Fe layer [5,14], so we expect the two 20 A Fe layers to be strongly FM coupled through the Cr monolayer. As the Cr thickness is increased the FM coupling decreases and the polar MORE saturation field increases. When the Cr thickness reaches a value of about 4 A the coupling becomes antiferromagnetic and the saturation field increases further in a manner similar to the in-plane MORE saturation field. For a Cr thickness of 16 A the two Fe layers are essentially uncoupled and then the polar MOKE saturation field is seen to lie about half way between the two extremal values observed for smaller Cr thicknesses.
R. J. Hicken et al. /Thin Solid Films 275 (1996) 199-202
The two spin wave modes observed in the BLS experiment correspond to an in-phase and out-of-phase precession of the magnetizations in the two Fe layers and are referred to as the acoustic and optical spin wave modes respectively [ 151. We see from Fig. 1 (a) that the frequency of the optical mode varies strongly as a function of Cr thickness although it was only sufficiently intense as to be observable for Cr thicknesses between 11 and 30 A. The optical mode is seen to lie lower than the acoustic mode for Cr thicknesses between 16 A and 20 A where the easy axis MOKE loops are square. This means that the exchange coupling can only be very weakly FM in this region and is insufficient to overcome the dipolar coupling which is weakly AFM. In fact from a detailed calculation we have determined that the quantity A,* + 2B,, must lie in the range of 0.0 to 0.034 erg cm-*. In order to determine the values of the interface and cubic anisotropy fields for the Fe layers in the structure we have performed BLS field scans at appropriate positions on the wedge [ 121. The parameter values obtained from the fitting procedure are shown in Table 1. The value of the cubic anisotropy constant, K,, for the 20 %, Fe layers is found to be reduced relative to the value of 4.5 X lo5 erg cm-3 for bulk Fe. We note however that reduced values of K, have been observed previously for the Fe/Ag( 100) system [ 161. In the first AFM coupling peak it was possible to fit the easy axis Table 1 The parameter
values determined
Layer
K, (
Cr/Fe(20 A)/Ag Cr/Fe( 20 A)/Cr Cr/Fe(40 A)/Ag
3.1 3.1 4.3
by BLS for the Fe layers in sample X
I
K, (erg cm-‘)
lo5 erg cmm3)
0.60 0.30 0.72
Values of 1710 emu cm-j and 2.09 were assumed for the magnetization and R factor of the Fe layers.,
201
in-plane MOKE loops by assuming that the system occupies the minimum energy state. The parameter values in Table 1 were assumed and the coupling parameters A,, and B12 were varied to obtain the best fit. BLS field scans were also used to investigate the interlayer coupling. The easy and hard axis MOE loops and the BLS field scan for a Cr thickness of 10 A are shown in Fig. 2. For the BLS scan both spin wave modes are observed only when the layer magnetizations begin to cant apart from the applied field direction. At a smaller field of approximately 0.4 kOe the magnetizations jump to an almost antiparallel alignment and then the Stokes and antiStokes modes are observed to have slightly different frequencies as has been observed previously [ 11. The procedure for fitting the BLS data will be described elsewhere [ 121. Values of - 0.14 and - 0.010 erg cm-* were obtained for A,, and B,* respectively from the fit to the BLS field scan. These values were used to calculate the theory curves plotted with the experimental data in Fig. 2(a) and 2(b) . The saturation and switching fields of both the easy and hard axis loops are well reproduced by the theory curves, although the curvature of the experimental loops is found to be slightly different. The fit to the easy axis MOKE loop yielded somewhat different values of - 0.11 and - 0.022 erg cmw2 for A 12 and B12 respectively. In the second AFM coupling region it became difficult to reliably determine the values ofAl and B12 from the in-plane MOKE loops. This is because when the coupling field is of the same order as the cubic anisotropy field, the magnetization reversal process is not well known. BLS field scans have been used to determine the values of A,, and B,, for two points in this region [ 121. A second sample (sample II) was studied which was identical to sample I except that the Cr layer thickness was intended to be in the range of 0 to 20 A. The deduced coupling strengths in samples I and II were found to be of similar magnitude and both are plotted in Fig. 3.
*-Sample
d
-2 -1
0
1
2
-2 -1 0
H (kOe)
0
1
I -
MOKE
2
H (kOe)
1..
012345678 H (kOe)
Fig. 2. The in-plane easy and hard axis MOKE loops and BLS mode frequencies are shown in panels (a), (b) and (c) respectively for the point on sample I at which the Cr layer thickness has a value of 10 A. The field was applied parallel to one of the Fe(Ol1) hard axes in (c) and the curves are fits to the theory as discussed in the text. The best fit parameters from (c) were used to generate the dashed curves in (a) and (b).
0 5 10 15 20 25 30 35 40 Cr thickness (A) Fig. 3. The values of the coupling constants B,, and A,2 for samples I and II are plotted as a function of Cr thickness in panels (a) and (b) respectively. The meaning of the various symbols is indicated in panel (a). The curve in panel (a) is a fit that is described in the main text while the curve in panel (b) is a scaled version of the curve in Fig. 1(c) that serves only to guide the eye.
202
R. J. Hicken et al. /Thin Solid Films 275 (I 996) 199-202
4. Discussion From the separation of the maxima of the first and second peaks in the easy axis saturation field in Fig. 1 (c) we obtain a value of about 18 8, for the long period of oscillation of the coupling strength which agrees well with the value of 12 + 1 monolayers (17.2_+ 1.4 A) deduced for samples grown on Fe whisker substrates [ 31. The position of our first coupling maximum at 8 8, of Cr is close to that observed for the first short period AFM coupling maximum at 5 monolayers (7.2 A) of Cr [4]. We observe the coupling strength to be offset in the AFM direction as has been observed by other researchers [ 4,11,17] but we observe smaller coupling strengths in the present study. We believe that some structural imperfection is responsible for attenuating the total (bilinear plus biquadratic) coupling strength in our samples. The form of the curves for Al2 and B,* in the first AFM coupling region are similar to those presented in Ref. [ 81, while we note that dominant biquadratic coupling at small Cr thicknesses has also been observed for samples grown on Fe-whisker substrates of high structural quality [ 31. Our best fits indicate that the ratio of B,, to Al2 in the centre of the second AIM region is of the order of 0.8 which is larger than the value of 0.26 obtained previously [7] for samples grown on Agl GaAs( 100) substrates. In the latter case it was found that the biquadratic coupling became dominant at somewhat larger Cr thicknesses [ 171, in the third AFM coupling region. By fitting a straight line to a log plot of the data in Fig. 3 (a) we find that B,, varies approximately as d&-4 (dashed curve) over the full range of Cr thicknesses studied. The thickness dependence of B12 can in principle be predicted from the various extrinsic models of biquadratic coupling [ lo] and so the power law behaviour of B,, and the reduced values ofA,, observed in our data may provide a quantitative test of extrinsic coupling theories. In conclusion, MOKE and BLS measurements have been combined in order to determine the dependence of the interlayer coupling strengths upon the Cr thickness in Fe/G/Fe trilayer samples. It has been demonstrated that polar MOKE may be particularly useful in obtaining a qualitative description of the coupling behaviour in the very thin Cr region where the coupling is strongly FM in nature and large changes in the polar saturation field are observed. We find that the phase and period of the long-period coupling oscillations agree well with those reported by other researchers while we
attribute the weaker coupling observed in our samples to the presence of structural imperfections. The biquadratic coupling constant is well described by a simple power law which we believe may be useful in testing the extrinsic models that have been proposed for the biquadratic coupling mechanism.
References [I] [2] [3] [4]
[5] [61 [7] [8] [9]
P. Grilnberg, R. Schreiber, Y. Pang, M.D. Brodsky, H. Sowers, Phys. Rev. Len., 57 (1986) 2442. J.A.C. Bland and B. Heimich (eds.), Ultrathin Magnetic Structures II, Chapter 2. Springer Verlag, New York, 1994. . D.T. Pierce, J.A. Stroscio, J. Unguris, R.J. Celotta, Phys. Rev., B49 (1994) 14564. B. Heinrich, M. From, J.F. Co&an, L.X. Liao, Z. Celinski, C.M. Schneider and K. Myrtle, Mater. Res. Sot. Symp. Proc., 313 (1993) 119. C. Turtur, G. Bayreuther, Phys. Rev. L.ett.. 72 (1994) 1557. A. Vega, L.C. Balbas, A. Chouairi, C. Demangeat and H. DreyssC, Phys. Rev., 849 (1994) 12797. ] M. Riihrig, R. Schiifer, A. Hubert, R. Mosler, J.A. Wolf, S. Demokritov and P. Griinberg, Phys. Starus Sofidi A, 125 (1991) 635. U. KGbler, K. Wagner, R. Wiechers, A. Fuss, W. Zinn, J. Magn. Magn. Mater., 103 (1992) 236. R.P. Erickson,
K.B. Hathaway
and J.R. Cullen, Phys. Rev., 847
( 1993) 2626; J. Barnas and P. Grunberg, J. Magn. Magn. Marer., 121 ( 1993) 326; J. Barnas, J. Magn. Magn. Mater., 223 ( 1993) L21; D.M. Edwards. J.M. Ward and J. Mathon, J. Magn. Magn. Mater., 126 (1993) 380; J.C. Slonczewski, J. Magn. Magn. Mater., 126 (1993) 374.
[ 101 J.C. Slonczewski, Phys. Rev. Lett.. 67 (1991) 3172; S. Demokritov, E. Tsymbal, P. Griinberg, W. Zinn, I.K. Schuller, Phys. Rev., 849 ( 1994) 720; J.C. Slonczewski, J. Appl. Phys., 73 (1993) 5957; J.-F.
Ill
I
[121
Bobo, M. Piecuch and E. Snoeck, J. Magn. Magn. Mater., 126 ( 1993) 440; D.B. Fulghum and R.E. Camley, Phys. Rev., 852 (1995) 13436. P. Griinberg, A.Fuss,Q. Leng, R. Schreiberand J.A. Wolf, Magnetism and Structure in Systems of Reduced Dimension, NATO ASI series, 1992.
. R.J. Hicken, C. Daboo, M. Gester, A.J.R. Ives, S.J. Gray and J.A.C. Bland, 3. Appl. Phys., 78 (1995) 6670.
[ 131 A.J.R. Ives, R.J. Hicken. J.A.C. Bland, C. Daboo, M. Gester and S.J. Gray, J. Appl. Phys., 75 (1994) 6458.
[ 141 R. Jungblut, C. Roth, F.U. Hillebrecht and E. Kisker, J. Appl. Phys.. 70 ( 1991) 5923; T.G. Walker, A.W. Pang and H. Hopster, Phys. Rev. Lett., 69 (1992) 1121. [ 151 R.J. Hicken, D.E.P. Eley, A.J.R. Ives, C. Daboo, J.A.C. Bland, J.R. Childress and A. Schuhl, Phys. Rev., BSO (1994) 6143. [ 161 B. Heinrich and J.F. Cochran, Adv. Phys., 42 (1993) 523. [171 S. Demokritov. J.A. Wolf and P. Griinberg, Europhys. L.ett., I5 (1991) 881.
Thin Solid Films 275 ( 1996) 199-202
Bilinear and biquadratic exchange coupling in epitaxial Fe/Cr/Fe/Ag/GaAs( 100) structures R.J. Hicken, C. Daboo, M. Gester, A.J.R. Ives, S.J. Gray, J.A.C. Bland The Cavendish Laboratory. University of Cambridge, Madingley Road. Cambridge CB3 OHE, UK
Abstract
The interlayer exchange coupling has been investigated in epitaxial Fe( 20 A) lCrlFe(20 A) /Ag/GaAs( 100) structures that contain a wedge-shaped (O-40 A) Cr layer. Longitudinal and polar magneto optical Kerr effect (MOKE) and Brillouin light scattering (BLS) measurements have been combined to determine values for the bilinear and biquadratic coupling strengths. While the phase and period of the oscillations in the interlayer coupling agree well with those reported by other researchers, the magnitude of the coupling strength is found to be reduced. The dependence of the biquadratic coupling strength upon the Cr thickness is well described by a simple power law and may provide a useful test of extrinsic biquadratic coupling models. We show that the combination of MOKE and BLS measurements are very effective in investigating the ultrathin Cr region and that ferromagnetic (FM) coupling produces large changes in the polar MOKE saturation field. Keywords: Epitaxy; Magnetic properties and measurements; Light scattering; Chromium
1. Introduction Antiferromagnetic (AFM) interlayer exchange coupling through a transition metal spacer layer was first observed in Fe/Cr/Fe trilayer structures [ I]. Although interlayer coupling has now been observed in many different materials [ 21 there are a number of reasons why Fe/Cr remains one of the most interesting systems to study. Firstly the antiferromagnetism of the Cr may be modified in an ultrathin film, with phase slips occurring in the magnetic order [ 3-51 and frustration effects resulting from interfacial roughness [ 61. Secondly, Fe/Cr structures are known to exhibit biquadratic coupling [ 4,7,8]. A number of intrinsic mechanisms [ 91, that apply to ideal structures, and extrinsic mechanisms [ lo] , that depend upon some form of structural defect, have been proposed to explain the existence of the biquadratic coupling. In this paper we present a study of the interlayer coupling in Fe/Cr/Fe trilayer structures, containing wedge-shaped Cr layers, grown on Ag/GaAs( 100) substrates. Although shortperiod coupling oscillations can be obtained for such structures grown at elevated temperatures [ 111, our samples were grown at lower temperatures. We therefore expect our samples to contain structural defects that may favour extrinsic biquadratic coupling. We have combined in-plane magneto optical Kerr effect (MOKE), polar MOKE and Brillouin light scattering (BLS) measurements in order to determine 0040-6090/96/$15.00
0 1996 Elsevier Science S.A. All rights reserved
SSDlOO40-6090(95)07042-7
how the bilinear and biquadratic coupling strengths depend upon the value of the Cr thickness. Both BLS and polar MOKE are sensitive to the perpendicular anisotropy of the constituent Fe layers and interlayer coupling of either sign. We will show how this allows us to observe the nature of the coupling in the ultrathin Cr limit.
2. Experimental consideration The epitaxial Fe/Cr/Fe structures described in this paper were grown on GaAs( 100) substrates capped with thick Ag( 100) buffer layers. In-situ structural characterisation was performed by means of low-energy electron diffraction (LEED) and reflection high-energy electron diffraction (RHEED) . Further details of both the growth and the structural characterisation will be given elsewhere [ 121. The samples were capped with a protective Cr layer approximately 20 w thick before being removed from the growth chamber for ex-situ magnetic characterisation. In-plane MOKE measurements were recorded with the field applied parallel to both the in-plane easy, Fe(OOl), and hard, Fe(Ol1) axes. Let us assume the interlayer coupling energy to be a surface energy of the form E coupling= -2A,2~,.~~-2B,2(~,.~*)2
(1)
200
R.J. Hicken et al. / Thin Solid Films 275 (I 996) 199-202
in which M, and M2 are the magnetization vectors of the two Fe layers and Al2 and B,, are the bilinear and biquadratic coupling constants respectively. By considering the condition for the saturated state to become unstable we find that for the case of antiferromagnetic coupling the in-plane saturation field has the form H
sat
= +2K, --IV
4(~,,+2~,~) Md
(2)
in which K,, M and d are the cubic anisotropy constant, magnetization and thickness of the Fe layers (assumed to be equal) respectively. The positive and negative signs refer to the hard and easy axis directions respectively. Although the saturation field in Eq. (2) gives the total coupling strength the individual values of A,, and B,, can sometimes be deduced by considering other features in the hysteresis loop -0.5u
[7,81.
0
Let us consider a trilayer structure in which the two magnetic layers are identical apart from their interface anisotropies. We define the quantity H,,,=~TM---~
2K1
4K,i
M
Md
(3)
in which KS,; is the interface anisotropy constant averaged over the two interfaces of layer i, where i = 1 or 2. We may assume that close to saturation the magnetisation vectors and the surface normal are coplanar, and then we obtain the following expression for the polar saturation field A
=Md(H,,,-H,,,)(H,,,-H,,2)
+2B
12
12 2(%,
+X,2
-
(4)
=LA
For the samples to be described here Ha,, f Ha,*, (contrary to the assumption made in Ref. [ 131) and then Eq. (4) predicts that the polar saturation field has a non-linear dependence upon the coupling field and is sensitive to both ferromagnetic (FM) and AFM coupling. Since the polar curves are generally rounded near the saturation point, the polar MOKE saturation field was taken to be that at which the polar Kerr intensity reached 96% of its maximum value [ 131. Further details of the MORE and BLS experiments will be given elsewhere [ 121. We note however that since the sample must be repositioned for each of the three experiments, the Cr thickness scale in these experiments are subject to a systematic error of up to 0.7 A.
3. Results In-plane and polar MORE and BLS measurements were made at various points on a Fe( 20 A) /Cr( O-38 A) /Fe( 20 A) wedge structure (Sample I). BLS measurements were made with a field of 5 kOe applied parallel to the Fe hard axis which was sufficient to saturate the sample at all points along the wedge. The spin wave frequencies and the MOKE saturation fields are plotted in Fig. 1. The in-plane easy axis
5 10 15 20 25 30 35 Cr thickness (A)
Fig. 1, The following quantities are plotted as a function of Cr thickness for sample I: (a) BLS mode frequencies, where the open and closed symbols denote the acoustic and optical spin wave modes respectively; (b) the polar MOKE loop saturation field; (c) the in-plane easy axis MOKE saturation field (closed symbols), or the coercive field, plotted as a negative quantity, if the loop is square (open symbols). The inset in panel (c) is an expanded view of the data for small Cr thicknesses
saturation field (Fig. 1 (c) ) reveals the oscillatory nature of the coupling. Where an open symbol has been used in Fig. 1 (c) the easy axis loops are square, indicating that the sample is either FM coupled or simply uncoupled. We have identified the beginning of the wedge as the point at which the coercivity of the easy axis loop decreases abruptly to about half its previous value (see inset in Fig. 1 (c)). This change may occur because the inclusion of a partial Cr layer provides new sites for domain nucleation. The first AFM region (4-15 A> is also clearly visible in the polar MOKE scan but the second AFM (20-38 A) region is less we11 defined. In the region where the Cr thickness varies from 0 to 4 A we see a sharp reduction of the polar MOKE saturation field which we believe is due to strong ferromagnetic coupling of the two Fe layers. As Cr is introduced into the middle of the 40 A Fe layer the saturation field decreases, because of the additional perpendicular anisotropy associated with the Cr layer, until a full monolayer of Cr is present. It is known that a monolayer of Cr orders antiferromagnetically with a neighbouring Fe layer [5,14], so we expect the two 20 A Fe layers to be strongly FM coupled through the Cr monolayer. As the Cr thickness is increased the FM coupling decreases and the polar MORE saturation field increases. When the Cr thickness reaches a value of about 4 A the coupling becomes antiferromagnetic and the saturation field increases further in a manner similar to the in-plane MORE saturation field. For a Cr thickness of 16 A the two Fe layers are essentially uncoupled and then the polar MOKE saturation field is seen to lie about half way between the two extremal values observed for smaller Cr thicknesses.
R. J. Hicken et al. /Thin Solid Films 275 (1996) 199-202
The two spin wave modes observed in the BLS experiment correspond to an in-phase and out-of-phase precession of the magnetizations in the two Fe layers and are referred to as the acoustic and optical spin wave modes respectively [ 151. We see from Fig. 1 (a) that the frequency of the optical mode varies strongly as a function of Cr thickness although it was only sufficiently intense as to be observable for Cr thicknesses between 11 and 30 A. The optical mode is seen to lie lower than the acoustic mode for Cr thicknesses between 16 A and 20 A where the easy axis MOKE loops are square. This means that the exchange coupling can only be very weakly FM in this region and is insufficient to overcome the dipolar coupling which is weakly AFM. In fact from a detailed calculation we have determined that the quantity A,* + 2B,, must lie in the range of 0.0 to 0.034 erg cm-*. In order to determine the values of the interface and cubic anisotropy fields for the Fe layers in the structure we have performed BLS field scans at appropriate positions on the wedge [ 121. The parameter values obtained from the fitting procedure are shown in Table 1. The value of the cubic anisotropy constant, K,, for the 20 %, Fe layers is found to be reduced relative to the value of 4.5 X lo5 erg cm-3 for bulk Fe. We note however that reduced values of K, have been observed previously for the Fe/Ag( 100) system [ 161. In the first AFM coupling peak it was possible to fit the easy axis Table 1 The parameter
values determined
Layer
K, (
Cr/Fe(20 A)/Ag Cr/Fe( 20 A)/Cr Cr/Fe(40 A)/Ag
3.1 3.1 4.3
by BLS for the Fe layers in sample X
I
K, (erg cm-‘)
lo5 erg cmm3)
0.60 0.30 0.72
Values of 1710 emu cm-j and 2.09 were assumed for the magnetization and R factor of the Fe layers.,
201
in-plane MOKE loops by assuming that the system occupies the minimum energy state. The parameter values in Table 1 were assumed and the coupling parameters A,, and B12 were varied to obtain the best fit. BLS field scans were also used to investigate the interlayer coupling. The easy and hard axis MOE loops and the BLS field scan for a Cr thickness of 10 A are shown in Fig. 2. For the BLS scan both spin wave modes are observed only when the layer magnetizations begin to cant apart from the applied field direction. At a smaller field of approximately 0.4 kOe the magnetizations jump to an almost antiparallel alignment and then the Stokes and antiStokes modes are observed to have slightly different frequencies as has been observed previously [ 11. The procedure for fitting the BLS data will be described elsewhere [ 121. Values of - 0.14 and - 0.010 erg cm-* were obtained for A,, and B,* respectively from the fit to the BLS field scan. These values were used to calculate the theory curves plotted with the experimental data in Fig. 2(a) and 2(b) . The saturation and switching fields of both the easy and hard axis loops are well reproduced by the theory curves, although the curvature of the experimental loops is found to be slightly different. The fit to the easy axis MOKE loop yielded somewhat different values of - 0.11 and - 0.022 erg cmw2 for A 12 and B12 respectively. In the second AFM coupling region it became difficult to reliably determine the values ofAl and B12 from the in-plane MOKE loops. This is because when the coupling field is of the same order as the cubic anisotropy field, the magnetization reversal process is not well known. BLS field scans have been used to determine the values of A,, and B,, for two points in this region [ 121. A second sample (sample II) was studied which was identical to sample I except that the Cr layer thickness was intended to be in the range of 0 to 20 A. The deduced coupling strengths in samples I and II were found to be of similar magnitude and both are plotted in Fig. 3.
*-Sample
d
-2 -1
0
1
2
-2 -1 0
H (kOe)
0
1
I -
MOKE
2
H (kOe)
1..
012345678 H (kOe)
Fig. 2. The in-plane easy and hard axis MOKE loops and BLS mode frequencies are shown in panels (a), (b) and (c) respectively for the point on sample I at which the Cr layer thickness has a value of 10 A. The field was applied parallel to one of the Fe(Ol1) hard axes in (c) and the curves are fits to the theory as discussed in the text. The best fit parameters from (c) were used to generate the dashed curves in (a) and (b).
0 5 10 15 20 25 30 35 40 Cr thickness (A) Fig. 3. The values of the coupling constants B,, and A,2 for samples I and II are plotted as a function of Cr thickness in panels (a) and (b) respectively. The meaning of the various symbols is indicated in panel (a). The curve in panel (a) is a fit that is described in the main text while the curve in panel (b) is a scaled version of the curve in Fig. 1(c) that serves only to guide the eye.
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4. Discussion From the separation of the maxima of the first and second peaks in the easy axis saturation field in Fig. 1 (c) we obtain a value of about 18 8, for the long period of oscillation of the coupling strength which agrees well with the value of 12 + 1 monolayers (17.2_+ 1.4 A) deduced for samples grown on Fe whisker substrates [ 31. The position of our first coupling maximum at 8 8, of Cr is close to that observed for the first short period AFM coupling maximum at 5 monolayers (7.2 A) of Cr [4]. We observe the coupling strength to be offset in the AFM direction as has been observed by other researchers [ 4,11,17] but we observe smaller coupling strengths in the present study. We believe that some structural imperfection is responsible for attenuating the total (bilinear plus biquadratic) coupling strength in our samples. The form of the curves for Al2 and B,* in the first AFM coupling region are similar to those presented in Ref. [ 81, while we note that dominant biquadratic coupling at small Cr thicknesses has also been observed for samples grown on Fe-whisker substrates of high structural quality [ 31. Our best fits indicate that the ratio of B,, to Al2 in the centre of the second AIM region is of the order of 0.8 which is larger than the value of 0.26 obtained previously [7] for samples grown on Agl GaAs( 100) substrates. In the latter case it was found that the biquadratic coupling became dominant at somewhat larger Cr thicknesses [ 171, in the third AFM coupling region. By fitting a straight line to a log plot of the data in Fig. 3 (a) we find that B,, varies approximately as d&-4 (dashed curve) over the full range of Cr thicknesses studied. The thickness dependence of B12 can in principle be predicted from the various extrinsic models of biquadratic coupling [ lo] and so the power law behaviour of B,, and the reduced values ofA,, observed in our data may provide a quantitative test of extrinsic coupling theories. In conclusion, MOKE and BLS measurements have been combined in order to determine the dependence of the interlayer coupling strengths upon the Cr thickness in Fe/G/Fe trilayer samples. It has been demonstrated that polar MOKE may be particularly useful in obtaining a qualitative description of the coupling behaviour in the very thin Cr region where the coupling is strongly FM in nature and large changes in the polar saturation field are observed. We find that the phase and period of the long-period coupling oscillations agree well with those reported by other researchers while we
attribute the weaker coupling observed in our samples to the presence of structural imperfections. The biquadratic coupling constant is well described by a simple power law which we believe may be useful in testing the extrinsic models that have been proposed for the biquadratic coupling mechanism.
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