lnterlayer exchange coupling in epitaxial Fe/Cr/Fe/Ag/GaAs(lOO) structures R. J. Hicken, C. Daboo, M. Gester,a) A. J. R. Ives, S. J. Gray, and J. A. C. Bland The Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 OHE, United Kingdom (Received 9 June 1995; accepted for publication 10 August 1995) The interlayer exchange coupling has been investigated in epitaxial Fe(20 &P3'Fe(20 ,&)/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 measurements have been combined to determine values for the relevant anisotropy constants and both the bilinear and biquadratic coupling strengths. The phase and period of the oscillations in the interlayer coupling are found to agree well with those reported by other researchers while the total coupling strength is found to be reduced. This reduction is presumably due to the presence of structural imperfections in our samples, and our results may therefore be of use in testing some of the recently proposed extrinsic biquadratic coupling mechanisms. Specifically. we find that for the Cr thicknesses studied the biquadratic coupling strength in our samples varies as dz:.`" where d,, is the thickness of the Cr layer. We also present results that show how the ultrathin Cr limit may be investigated. We show that the coercivity of the easy axis MOKE loops is sensitive to submonolayer coverages of Cr and that polar MOKE is sensitive to the strong ferromagnetic coupling found in the O-4 w Cr thickness range. 0 1995 Amen'can Institute of Physics. 1. INTRODUCTION surprising then that Cr spacer layers of different orientations should yield identical coupling periods.12 We should consider Antiferromagnetic (AFM) interlayer exchange coupling also that the magnetic structure of thin films of Cr may be through a transition-metal spacer layer was first observed in different to that of bulk Cr and indeed an enhanced N6el Fe/Cr/Fe trilayer structures.' The subsequent discovery of a temperature has already been observed" in the former. Re- giant magnetoresistance (GMR) effect" in Fe/Cr multilayers, cent studies using Fe whisker substrates13*`4 have provided which is of potential technological significance, has lead to information concerning the phase of the short period cou- great interest in this field and interlayer exchange coupling pling oscillations. One surprising result was that AFM cou- and GMR have subsequently been observed in a number of pling was obtained after 5 monolayers of Cr growth. A pos- other multilayered materials.3 The Fe/Cr system has, how- sible explanation may be that the first 2 monolayers of Cr ever, been particularly important in the development of our have ferromagnetic (FM) rather than AFM alignment.15 understanding of the interlayer coupling mechanism, since it was in the Fe/Cr system that it was first demonstrated that: Clearly trilayers containing Cr layers of a few monolayers the interlayer coupling energy is of the Heisenberg or bilin- thickness are of considerable interest but it is expected that ear form, being proportional to the scalar product of the Iayer roughness and pinhole coupling will affect both the strength magnetizations;4 the sign of the interlayer coupling oscillates of the coupling and the magnetic ordering of the Cr.16 as a function of the spacer thicknes$ the bilinear energy The biquadratic coupling strength in Fe/Cr/Fe structures term may be augmented by a higher-order term, the so called has been observed to be of similar magnitude to the bilinear biquadratic coupling term.6 In fact Cr is a particularly coupling strength14.17 and a nu'mber of mechanisms has been interesting choice of spacer material because bulk Cr is proposed to explain the origin of the biquadratic coupling. known to exhibit incommensurate spin density wave Those that apply to ideal structures with flat interfaces,`8-22 antiferromagnetism.' Structures grown on Fe( 100) whiskers the so-called intrinsic mechanisms, are found to predict only are believed to have the flattest interfaces that can be cur- very small values for the biquadratic coupling strength. The rently obtained and it was in such structures that the inter- so-called extrinsic mechanisms take into account the effects layer coupling was first observed to,oscillate with a period of of roughened interfaces,23'24 loose spins in the spacer approximately two atomic monolayers.`,' It was subse- material,= and pinholes through the spacer layer."6327 Re- quently demonstrated that these short period coupling oscil- searchers have examined the temperature dependence of the lations are correlated with the AFM ordering of the Cr." biquadratic coupling in order to differentiate between the While attempts are being made to unite the various theories mechanisms listed above (see Ref. 25 and the references of interlayer coupling,l' there is general agreement that the therein) and on this basis for Fe/Cr structures grown on Fe period of the coupling oscillations is determined by the ge- whiskers it was concluded that there must be a strong con- ometry of the Fermi surface of the spacer material, which tribution from an intrinsic mechanism.28 In order to explore also determines the AFM ordering of the Cr. It is somewhat the relevance of the various proposed extrinsic mechanisms there is clearly a need for studies of relatively structurally "Present address: I.P.C.M.S., Bitiment 69, 23 rue du Loess, 67037 Stras- imperfect samples in which both coupling constants are ac- bourg, France. curately determined. 6670 J. Appl. Phys. 78 (Ii), 1 December 1995 002l-8979J95/78(1l)l6670/9/$6.00 Q 1995 American Institute of Physics Downloaded 17 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp In this work we present a study of the interlayer coupling Fe(OO1) axes, which are found to propagate through the rest in Fe/Q/Fe trilayer structures, containing wedge-shaped Cr of the structure. The Cr wedge layer is grown by moving the layers, grown on Ag/GaAs(lOO) substrates. We have com- substrate behind a fixed shutter through a distance of 12 mm bined in-plane magneto-optical Kerr-effect (MOKE), polar in steps of 0.2 mm. The completed structure is capped with MOKE, and Brillouin light-scattering (BLS) measurements about 20 A of Cr that has been shown by electron-energy- in order to investigate how the bilinear and biquadratic cou- loss spectroscopy34 to be sufficient to prevent oxidation of pling strengths depend upon the value of the Cr thickness. the underlying Fe layers. The thicknesses of the various lay- Although short period coupling oscillations can be obtained ers were obtained by monitoring the deposition rate with for such structures grown at elevated temperatures,29 our quartz crystal oscillators which were calibrated by profilo- samples were grown at lower temperatures where rougher meter measurements made on specially grown thicker films. interfaces are expected to result. We discuss how our de- duced values of the bilinear coupling strength compare with those of other researchers and present our results for the Cr 111. EXPERIMENTAL CONSIDERATION thickness dependence of the biquadratic coupling strength. BLS and polar MOKE are sensitive to the perpendicular an- In-plane MOKE measurements were made using an ap- isotropy of the constituent Fe layers and interlayer coupling paratus developed for vector magnetometry.s5 Hysteresis of either sign. We discuss how this allows us to characterise loops were recorded with the field applied parallel to both the magnetic behavior for Cr thicknesses in the monolayer the in-plane easy, Fe(OOl), and hard, Fe(Oll), axes. The regime and we show how the coercivity of the easy axis HeNe laser beam was focused to a spot of about 0.2 mm MOKE loop changes in this same region. diameter and scanned along the wedge by moving the sample with a linear translation stage that is capable of a 1 pm II. SAMPLE GROWTH positioning accuracy. Let us assume the interlayer coupling energy to be a surface energy of the form The Fe/Cr/Fe structures described in this article were grown on %-doped GaAs(100) substrates capped with thick E coupling= -2A,2~*`~E2-2B12(~,.~~)2, (1) Ag(100) buffer layers. While direct growth on to an insulat- in which M, and M, are the magnetization vectors of the two ing substrate would be preferable for transport measure- Fe layers and Al2 and B,, are the bilinear and biquadratic ments, it is well known that the chemistry of the Fe/GaAs coupling constants, respectively. By considering the condi- interface is complicated by interdiffusion. The Ag buffer tion for the saturated state to become unstable one finds an layer therefore provides a flat substrate that will not interdif- expression for the saturation field of the form fuse with the deposited film. The surface of the GaAs sub- strate initially has an oxidized surface layer that is removed 2K, 4(A12+2B,,) ff,at=f~- Md , (2) by annealing at a temperature of 620 "C for 30 min.31 Cycles of sputtering and annealing at 600 "C are then employed to in which K,, M, and d are the cubic anisotropy constant, remove any carbon present and to smooth the surface. The magnetization, and thickness of the Fe layers (assumed to be observation of a p(4 X 6) reconstruction by low-energy elec- equal), respectively. The positive and negative signs refer to tron diffraction (LEED) then indicates that the surface is pe- the hard and easy axis directions, respectively. As we see riodic over distances in excess of 100 A. Reflection high- later, Eq. (2) may be inapplicable when the demagnetization energy electron diffraction has also been used to confirm the process occurs by domain-wall motion. These expressions flatness of the GaAs at this point.32 Next it is necessary to also apply only when the coupling field is antiferromagnetic grow an Fe seed layer in order to force the following Ag in nature, i.e., the second term in Eq. (2) is greater than zero. layer into the (100) orientation.33 An Fe layer of thickness 15 If the coupling field is ferromagnetic then we simply have A is grown at a substrate temperature of 150 "C before the Hsat= 2 2K,lM, where the negative case refers to the coer- Ag layer of approximately 1000 A thickness is grown at cive field of a square easy axis hysteresis loop. Although the ambient temperature at a rate of about 5 A per minute. The saturation field in Eq. (2) gives the total coupling strength the Ag layer is annealed at 300 "C for I h so that sharp LEED individual values of A,, and B i2 can sometimes be deduced spots are obtained. The (011) axes of the Ag(100) layer lie by considering other features in the hysteresis 10op.~~*~ Since parallel to the (001) axes of the Fe(100) seed layer. We a hysteresis loop may be obtained within a matter of seconds should point out that the Fe seed layer is at best weakly and since theoretical loops are readily generated ferromagnetic. The thick Ag buffer layer ensures that the Fe numerically36 in-plane MOKE is a very convenient tech- seed layer is not sensed by any of our magneto-optical mea- nique for the determination of interlayer coupling constants. surements and so we do not discuss it further when consid- Polar MOKE measurements have been made inside a 7 T ering the magnetic properties of the sample. superconducting magnet in steps of about 0.1 mm along the The trilayer structure is grown at ambient temperature. length of the sample, as has been described previously.37 Let During the deposition of the Iirst Fe layer LEED patterns us consider now a trilayer structure in which the two mag- taken between Bragg conditions show considerable spot netic layers are identical apart from their interface anisotro- broadening which indicates imperfect wetting of the Ag by pies. Let us define the quantity the Fe. After deposition of the first 20 A layer of Fe the sample is annealed at 150 "C for 30 min. Cross-shaped 2K1 4K,i H,,i=4~~- M- Md, LEED spots then indicate the presence of steps parallel to the (3) J. Appl. Phys., Vol. 78, No. 11, 1 December 1995 Hicken et al. 8671 Downloaded 17 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp in which K,.i is the interface anisotropy constant averaged over the two interfaces of layer i, where i= 1 or 2. We may 34 -is-- BLS assume that close to saturation the magnetisation vectors and 3 z 32 ' the surface normal are coplanar, and then we obtain the fol- s2 lowing expression for the saturation field: I- 5 3o M&f&at- Ha,&.Hsat- g 28 A,2+2Bi2= Ha.21 Es 2(&,1+&,2-2H,,l ' (4) 8 26 , - which reduces to the simple form H=5kOe 4iA,,+2BlJ Polar MOKE Hsat= Ha - &,d for the case of antiferromagnetic coupling only -when we assume that H,,, = Ha,2= H, . This was one of the approxi- mations made in Ref. 37. However, we shall see that in fact for the samples to be described here Ha,, # H,,,, and then Eq. (4) predicts that the polar MOKE saturation field has a 17.0 I. nonlinear dependence upon the coupling field and is sensi- tive to both FM and AFM coupling. 2.5 The apparatus used to perform BLS measurements has G 2.0 been described previously.38 The focused spot was scanned & 1.5 along the wedge by moving the sample with a translation 2 1.0 stage capable of 0.1 mm positioning accuracy. The magnetic field was applied parallel to the short side of the sample, an z? 0.5 Fe (110) direction, due to the limited pole piece separation of 0.0 our magnet. In order to analyze our results, the theory that -0.5 we used in Ref. 38 has been extended to include biquadratic 0 5 10 15 20 25 30 35 40 coupling and to allow for the effect of the layer magnetiza- Cr thickness (A) tions canting away from the applied field direction. This canting behavior is most reliably calculated for the case that FIG. 1. The following quantities are plotted as a function of Cr thickness for the field is applied along a hard axis direction as in our sample I: (a) BLS mode tkequencies, where the open and solid symbols experimental arrangement. The full theory requires evalua- denote the acoustic and optical modes, respectively; (b) the polar MOKE loop saturation field; (c) the in-plane easy axis MOKE saturation field (solid tion of large complex determinants, so we have also em- symbols), or the coercive field plotted as a negative quantity if the loop is ployed a simplified theory in which the dynamical magneti- square (open symbols). The inset in panel (c) is an expanded view of the zation is assumed to be independent of the coordinate that data for small Cr thicknesses. describes the position along the film normal.39 This reduced theory is then essentially a uniform mode Ferromagnetic resonance (FMR) calculation but with additional effective many of the polar MOKE loops showed a gentle approach to fields included to describe the dipolar fields that result from saturation, the saturation field was taken to be the field at the in-plane wave-vector component of the spin wave mode. which the polar Kerr intensity reached 96% of its maximum The algebraic expressions that are obtained are sufficiently value.37 BLS measurements were made at various points simple that they may be combined with standard optimisa- along the wedge with a field of 5 kOe applied parallel to the tion routines to obtain a chi square fit to the BLS data. In this Fe hard axis. This field value was chosen to be sufficiently article all fits to the BLS data have been performed with the large as to saturate the sample at all points along the wedge. reduced theory although each of the best fits was recalculated The spin wave frequencies that were obtained are plotted in with the full theory in order to investigate the magnitude of Fig. 1 (a), while the polar MOKE and in-plane easy axis satu- the error associated with the use of the reduced theory. ration fields are plotted in Fig. l(b) and l(c), respectively. Since the wedge sample must be repositioned for the Where the in-plane easy axis MOKE loop was found to be in-plane MOKE, polar MOKE, and BLS experiments we es- square we have plotted the coercive field as a negative field timate that positions on the wedge correspond to within value in Fig. l(c) and used an open rather than a solid sym- about 0;2 mm which implies a systematic error of up to 0.7 bol. A in the Cr thickness between the various experiments. The in-plane easy axis saturation field immediately re- veals the oscillatory nature of the coupling. Two regions of IV. RESULTS AFM coupling exist, in the first the Cr thickness varies be- tween 4 and 15 A, while the second begins at a Cr thickness We now describe in detail the results obtained for an of 20 k and continues to the end of the Cr wedge where the Fe(20 .&)/Cr(O-38 &/Fe(20 A) trilayer structure (sample I). Cr layer is 38 A thick. For Cr thicknesses less than 4 A and In-plane easy and hard axis MOKE loops and polar MOKE for Cr thicknesses between 16 and 20 A, the easy axis loops loops were taken at various points aIong the wedge. Since are square, indicating that the sample is either FM coupled or 6672 J. Appl. Phys., Vol. 78, No. 11, 1 December 1995 Hicken et al. Downloaded 17 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp simply uncoupled. While the Cr gradient was determined to be 3.3 &mm from the thickness calibration, the point at which the Cr wedge begins is not known exactly beforehand. However, we are able to identify 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, as shown in the inset in Fig. l(c). We suggest that the inclusion of a partial Cr layer in the middle of a 40 fi Fe layer provides new sites for domain nucleation that reduce the coercive field. It is interesting to compare the easy axis loop saturation field scan with the polar MOKE saturation field scan. The first AFM region, with maximum coupling field at a Cr thick- ness of about 8 A, is clearly visible in the polar MOKE scan 0 1 2 3 4 5 6 7 8 but the second AFM region is less well defined. Both in- plane and polar MOKE loops are subject to optical effects so H (kOe) that the Kerr intensity may not vary exactly linearly with the magnetization component parallel to the applied field. Also FIG. 1 BLS mode frequencies are plotted as a function of the applied field the curvature of the loops depends upon the relative amounts strength for the point on sample I at which the value of the Cr layer thick- ness is equal to 16 A. The field was applied parallel to one of the Fe (011) of bilinear and biquadratic coupling present and so our hard `axes. The curves have been fitfed to the data. The inset shows the method of determining the polar MOKE saturation field is corresponding polar MOKE loop which exhibits two clear kinks at the subject to an error that may vary as we scan along the wedge. points at which the two Fe layers saturate. From Eq. (4) we saw that the polar MOKE saturation field does not in general have a linear dependence upon the cou- the region between the first and second AFM regions where pling strength and therefore we do not expect an exact cor- the in-plane MOKE loops are square (Fig. 1) and here the respondence between the in-plane and polar MOKE satura- mode with higher frequency is always the more intense. This tion field scans. The polar MOKE does, however, give an means that the exchange coupling can only be very weakly excellent qualitative impression of the nature of the coupling. FM and is insufficient to overcome the dipolar coupling Particularly in the region where the Cr thickness varies from which is weakly AFM. In fact, from a detailed calculation we 0 to 4 A we see a sharp reduction of the polar MOKE satu- have determined that the quantity A, z + 2 B r 2 must lie in the ration field which we believe is due to strong ferromagnetic range of 0.0-0.034 erg/cm". At the thin end of the wedge we coupling of the two Fe layers. As a partial layer of Cr is see that there is a small jump in the acoustic mode frequency introduced into the middle of the 40 A Fe layer the saturation at a Cr thickness of about 2 A, which corresponds roughly to field decreases because of the additional perpendicular an- the minimum in the polar MOKE saturation field. As the Cr isotropy associated with the Cr layer. The saturation field thickness is decreased to zero we expect the acoustic mode to decreases until full Cr coverage is obtained. It is known that correspond to the surface mode of the 40 A Fe layer, while a monolayer of Cr orders antiferromagnetically with a neigh- the optical mode observed in the trilayer must evolve into the boring Fe layer'5P0 so that at this point we expect to have first volume mode of the 40 A layer. This volume mode lies two 20 A Fe layers that are strongly FM coupled. As the Cr at a much higher frequency bec~ause of the large associated thickness increases further the FM coupling decreases and exchange energy. We therefore expect that in the 0- 10 A Cr the polar MOKE saturation field increases. When the Cr region the optical mode frequency must change rapidly from thickness reaches a value of about 4 A the coupling becomes a small value in the AFM region to a large value in the limit antiferromagnetic and the saturation field increases further in of zero Cr thickness and that the acoustic and optical modes a manner similar to the in-plane MOKE saturation field. For must cross over at some intermediate point. The precise a Cr thickness of 16 A the two Fe layers are essentially variation of the mode frequencies in this region is difficult to uncoupled, as is discussed below, and then the polar MOKE predict since it depends upon the Cr thickness dependence of saturation field is seen to lie about half-way between the two both the interface anisotropy and interlayer coupling energies extremal values observed for small Cr thicknesses. and these are strongly affected by the initial growth mode of Two spin wave modes are expected in the BLS experi- the Cr. While we cannot conclude very much about the ul- ment which correspond to an in-phase and out-of-phase pre- trathin Cr limit from the BLS data presented here, this does cession of the magnetizations in the two Fe layers. These are suggest how BLS might be useful when both acoustic and referred to as the acoustic and optical spin wave modes, re- optical spin wave modes are observable. spectively. For the case that the sample is magnetically satu- In order to determine the values of the interface and rated, the acoustic mode is the more intense of the two cubic anisotropy fields for the two Fe layers for larger Cr modes but it is the optical spin wave mode frequency which thicknesses, we have made BLS measurements at a number is most sensitive to the inter-layer coupling and indeed we see of field values for the point on the wedge at which the Cr from Fig. 1 (a) that it is the frequency of the optical mode that thickness has a value of 16 A (Fig. 2). The interlayer ex- varies strongly as a function of Cr thickness. The optical change coupling field, which appears in Eqs. (2) and (5), mode was only sufficiently intense so as to be observable for changes sign at this point and so can be assumed to be neg- Cr thicknesses between 11 and 30 A. We see two modes in ligible. Indeed the polar MOKE curve shown in the inset in J. Appt. Phys., Vol. 78, No. 11, 1 December 1995 Hicken et a/. 6673 Downloaded 17 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp Fig. 2 shows a well defined kink which suggests that the inter-layer exchange coupling is small. Any exchange cou- pling, either FM or AFM, would be expected to make the curve more rounded. At lower fields the curve has a small positive curvature (d2MldH2>0) which is due to the posi- tive cubic anisotropy of the Fe and which may be exagger- 5 10 15 20 ated by a small quadratic dependence of the polar Kerr in- tensity upon the value of the magnetization component parallel to the polar axis. We have assumed that the two Fe layers are identical apart from their interface anisotropy con- stants. We assume the bulk Fe values of 1710 emu/cm3 for the Fe layer magnetization and 2.09 for the g factor. The fit -I in Fig. 2 was obtained with the reduced calculation described 0 1 2 3 4 5 6 7 8 in the previous section. From the best fit we deduce a value H (kOe) for the cubic anisotropy constant K1 of 3.1 X lo5 erg/cm3 and values of 0.30 and 0.60 erg/cm2 for the surface anisotropy constants of the two layers. These surface anisotropy con- FIG. 3. The BLS mode frequency is plotted as a function of the applied field strength at the point just before the Cr wedge begins in sample L The field stants are averaged over the two interfaces of each Fe layer was applied parallel to one of the Fe (011) hard axes and the curve is a fit to and the larger value applies to the Fe layer with one Cr and the data. The inset shows the corresponding polar MOKE loop. one Ag interface while the smaller value applies to that with two Cr interfaces. The fact that these two constants are not K, are identical since the Fe layers are of identical thickness equal means that the quantity H, defined in Eq. (3) is differ- and because we have no evidence to the contrary. If this ent for the two layers and so Eq. (4) rather than Eq. (5) must assumption were in fact incorrect then the values of A r2 and be used in considering the polar MOKE saturation fields. B12 estimated below for other points on the sample would be Also we may infer values of 0.30 and 0.90 erg/cm2 for the modified although this modification is only expected to be surface anisotropy constants of the FelCr and FelAg inter- significant for the case of weak coupling when the anisotropy faces, the latter comparing well with previously reported and coupling fields are of similar magnitude. values.4' The value deduced for the cubic anisotropy con- A BLS field scan was also performed for a point just stant is smaller than the bulk value of 4.5X105 erg/cm3 but before the beginning of the Cr wedge. The measured fre- we note that other recent studies42 have provided evidence quencies and the corresponding polar MOKE curve are that the magnetocrystalline volume anisotropy of an epitaxial shown in Fig. 3. Only one spin wave mode is observed and ultrathin film may not obtain its bulk value until the film is the polar MOKE curve shows a smooth approach to satura- some tens of angstroms thick. tion, with a little positive curvature induced by the cubic We should at this point comment upon some of the un- anisotropy, as expected for a single 40 A Fe layer. The best derlying assumptions that have been made in the fitting pro- fit value for the cubic anisotropy constant is now 4.3X lo5 cedure that we have just described. If the magnetizations of erg/cm3, close to the bulk value, while the best fit value for the two Fe layers were significantly different then this would the surface anisotropy constant is 0.72 erg/cm2. This latter greatly complicate the analysis; however, we have no reason value compares with the value of 0.60 erg/cm' obtained pre- to believe that this is the case. If, contrary to our assumption, viously for a 20 A layer with similar interfaces and the the Fe layer magnetizations were equal but reduced from the agreement can be seen to be quite good when we bear in bulk value then the deduced anisotropy and coupling param- mind that we have not included other possible contributions eters would need to be resealed. This resealing is, however, a to the perpendicular anisotropy such as magnetoelastic an- simple procedure since the effective demagnetizing fields, isotropy. The values of the anisotropy constants determined 4~M-4K,,ilMd, and the cubic anisotropy fields 2K,.ilM for the various Fe layers in this study are shown in Table 1. of the two layers, and the coupling fields, A 12/M and In the first AFM coupling peak it was possible to fit the B,2/M, should be unchanged by the assumption of a differ- easy axis in-plane MOKE loops by assuming that the system ent magnetization value. For the 16 A Cr point we neglected occupies the minimum energy state. The parameter values the effects of coupling although we knew only that the quan- obtained from the BLS fit to the 16 A Cr point were assumed tity A,,+2B12 was approximately equal to zero. In fact in and the coupling parameters A r 2 and B,, were varied to this case it can be shown that the individual values of A,, and B,, do not affect the calculation of the BLS frequencies so long as the static magnetizations of the two layers remain TABLE I. The parameter values determined by BLS for the Fe layers in approximately collinear. This is certainly the case for the sample I are shown. In addition, values of 1710 emu/cm3 and 2.09 were high-field BLS data which were used to obtain the values of assumed for the magnetization and g factor of the Fe layers. the surface anisotropy constants. However, when a small Layer K, (X105 erg/cm3) K,s (erg/cm') field is applied parallel to the in-plane hard axis the magne- tizations remain collinear only if, in addition to the magne- CdFe(20 A)/Ag 3.1 0.60 CdFe(20 A)/Cr 3.1 0.30 tization, the cubic anisotropy constant K, is also the same for Cr/Fe(40 A)/Ag 4.3 0.12 the two Fe layers. We have assumed that these two values of 6674 J. Appt. Phys., Vol. 78, No. 11, 1 December 1995 Hicken et al. Downloaded 17 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp -2 -1 0 1 2 -2 -1 0 1 2 H We) H We) H We) H (kOe) 50 ,---*__ 1 4 0 1 2 3 4 5; 6 7 8 012345678; H (kOe) H (kOe) FIG. 4. The in-plane easy and hard axis MOKE loops and BLS mode FIG. 5. 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 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 on sample I at which the Cr layer thickness has a value of 25 A. The field was applied parallel to one of the Fe (011) hard axes in (c) and the cmves was applied parallel to one of the Fe (011) hard axes in (c) and the curves are fits to the data. The best-tit parameters from (c) were used to generate are fits to the data. The best-fit parameters from (c) were used to generate the dashed curves in (a) and (b). the theory curves in (a) and (b). In the case of (a), branches representing all the local energy minima have been plotted. obtain the best fit. BLS field scans have been used previously to investigate interlayer coupling'4743-45 and we have per- tween the two theories is acceptably small for the data points formed a BLS field scan at the point at which the Cr thick- that we have used in our tits. Values of -0.14 and -0.010 ness has a value of 10 A for comparison with the MOKE erg/cm2 were obtained for A r 2 and B r *, respectively, from data. The measured frequencies and the in-plane hard and the fit to the BLS field scan shown in Fig. 4(c). These values easy MOKE loops are shown in Fig. 4. For the BLS scan we were used to calculate the expected MOKE loops and these see that for large field values only one mode is observed but are plotted with the experimental data in Fig. 4(a) and (b). as the field is reduced from the saturation value the magne- The saturation and switching fields of both the easy and hard tizations in the two layers cant apart and two modes are axis loops are well reproduced by the theoretical curves al- again observed. At a smaller field of approximately 0.4 kOe though the curvature of the experimental loops is found to be the magnetizations jump to an almost antiparallel alignment slightly different. Indeed, the fit of the easy axis MOKE loop and then the Stokes and anti-Stokes modes are observed to yielded values of -0.11 and -0.022 erg/cm" for A, z and have slightly different frequencies. This is due to the nonre- B,,, respectively. A simulation using these parameters pro- ciprocal nature of the spin wave modes which leads to dif- duced a very poor fit to the BLS data. This illustrates how ferent dipolar interactions for spin waves travelling in oppo- the coupling parameters determined by MOKE may depend site directions as has been previously noted.' It has been upon the curvature of the MOKE loops which is not neces- reported45 that the mode frequencies in this region are very sarily the same as that of the true magnetization curve. We sensitive to the exact values of the layer thicknesses and so should of course bear in mind that contrary to our assump- we have not included these points in our tit. Consequently tion the two Fe layers may have slightly different thick- the agreement between the theory curve and the data is good nesses, magnetizations, or cubic anisotropy constants and except in the low-field region. We have recalculated all the that this may also influence the curvature of the observed theory curves in this article using the full BLS theory de- loops. The layer magnetizations might also possess some scribed previously. The difference between the frequencies spatial nonuniformity which has not been accounted for in obtained from the full and reduced theories is found to be the modeling of either the BLS or the MOKE data. small except in the vicinity of the saturation field. At this In the second AFM coupling region it became difficult to point differences of up to 3 CiHz occur for the low- reliably determine the values of A r 2 and B r 2 from the in- frequency-mode calculation. We have not been able to ob- plane MOKE loops. The easy and hard axis loops for the serve the low-frequency mode close to the saturation field in point at which the Cr thickness has a value of 25 A are our measurements and we believe that the difference be- plotted in Figs. 5(a) and 5(b), respectively. At remenance the J. Appt. Phys., Vol. 78, No. 11, 1 December 1995 Hicken et al. 6675 Downloaded 17 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp sample is observed to occupy a state in which the layer mag- netizations lie 90' apart along different cubic easy axis di- 37, . 1 . , , rections, suggesting that the biquadratic coupling is signifi- $j 35. (a> BLS cant. For the hard axis loop the applied field causes the magnetizations to rotate gradually toward the field direction. We find that if the quantity A I 2 + 2B 1 2 is fixed so as to keep p;;:w the saturation field constant, the effect of varying the ratio of Br2 to A ,2 is to only slightly modify the curvature of the g 29 - loop. For the easy axis loop, once the remenant 90" state is & H=5kOe established, the saturation field is the only feature that we might attempt to fit. However, if the coupling field is small compared to the cubic anisotropy field, as in this case, this is unfortunately not possible. A coherent rotation calculation [Eq. (3)] would predict that the loop should be square while the assumption that the system must reside in the minimum energy state may be flawed since the reversal process is not known. In fact, for a pair of candidate values of A 12 and B Izr we may only establish which states exist at a given field value and then check that the experimental data corresponds to one of these states. The BLS field scan obtained at this point is shown in Fig. 5(c). The best fit to the data yields values of -0.0099 and -0.0079 erg/cm2 for A r2 and B,,, respectively, which implies a value of 0.80 for the ratio of B r2 to A ,2. In fact we find that a 90" state with one of the layer magnetizations parallel to the field direction only exists at the observed easy axis saturation field if this ratio has a __-l.. I I _.-L .__.. -.._1----. value less than about 0.9. It may seem odd that this is an 0 5 10 15 20 upper rather than a lower limit, but there is a simple physical Cr thickness (A) interpretation. When the coupling field is small and of the same order as the cubic anisotropy field then a close to 90" state exists at remenance. The biquadratic coupling exerts FIG. 6. The following quantities are plotted as a function of Cr thickness for sample II: (a) the BLS acoustic mode frequency; (bj the polar MOKE loop only a small torque between the two magnetizations in this saturation field; (c) the in-plane hard axis MOKE saturation field. case. As the applied field is increased it is the bilinear cou- pling that provides the torque to counteract that due to the applied field and so it is the bilinear coupling that is effective bounds on its value so the best lit value of the ratio of A, z to in stabilizing the 90" state at higher applied field values. The B,, may be subject to a large error. values of A, 2 and B , 2 determined by BLS are therefore fully A second sample (sample II) was studied which was consistent with the observed MOKE loops. The theory identical to sample I except that the Cr layer thickness was curves in Fig. 5(a) and S(b) assume the BLS best fit param- intended to be in the range of O-20 A. The in-plane and eter values. The hard axis theory curve was calculated as- polar MOKE saturation fields and the BLS frequencies for suming that the system resides in a local energy minimum various points on the wedge are shown in Fig. 6. Unfortu- until that minimum becomes unstable. For the easy axis we nately this sample has since deteriorated and only the origi- have shown the magnetization component associated with nal course scale data is available; however, this is still useful each local energy minimum to demonstrate that the observed in investigating the repeatability of the observed coupling loop is feasible even if we do not know exactly how the strengths. For the in-plane MOKE scan in Fig. 6(c) we have system moves between the different local minima. The plotted the hard axis saturation field as opposed to the easy agreement between theory and experiment for the hard axis axis saturation field that was plotted in Fig. l(c). We notice loop is reasonable given that the experimental loop is asym- here that a drop in the hard axis saturation field has been metric and does not exhibit a clear saturation field. Again the used to identify the beginning of the Cr wedge. The satura- presence of optical effects means that the experimental loop tion field of the 40 A Fe layer is approximately 0.5 kOe may not be a true magnetization curve. A BLS field scan was while this value drops to about 0.3 kOe when the Cr layer is also performed for the point at which the Cr thickness is introduced, just as for the first sample. The peak hard axis equal to 30 A. Here the total coupling field is even smaller saturation field of 3.75 kOe in Fig. 6(c) corresponds to an and it is consequently even more difficult to separate the easy axis saturation field of about 3 kOe which is in good values of A, z and B, 2. The best fit to the BLS scan yielded agreement with that observed in Fig. 1 (cj and hence suggests values of -0.0080 and -0.0045 erg/cm' for A, 2 and B,,, that the total coupling strength in the two samples is similar. respectively, which implies a value of 0.57 for the ratio of The polar MOKE saturation fields in Fig. 6(b) are somewhat B12 to Ar2. Unfortunately the fit is not very sensitive to this larger than those in Fig. l(bj and only one mode was ob- ratio and the MOKE loops did not permit us to put narrow served in the BLS measurements even at small applied fields. 6676 J. Appl. Phys., Vol. 78, No. 11, 1 December 1995 Hicken et a/. Downloaded 17 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp other samples grown on Ag/GaAs(lOO) for which short pe- 0::: 0: riod oscillations were not observed,46 the maximum coupling a : ~-Sample I - BLS . strength was found to be at least three times as large as that * -Sample I.1 - BLS - I shown in Fig. 7. This cannot be explained by the fact that thicker Fe layers were used by other researchers since the 0.06- i 0 -Sample I - MOKE . i coupling strength is actually expected to increase with de- creasing Fe layer thickness.47 We therefore believe that it is 0.04- 1 i likely that some structural imperfection is responsible for attenuating the total (bilinear plus biquadraticj coupling 0.02 - `VI .a+/ , strength in our samples. A -------II ___.___ O~:::::::::::::l::::j::::- From Fig. 7 we see that the biquadratic coupling con- stant B,, is largest for small Cr thicknesses. Dominant bi- quadratic coupling at small Cr thicknesses has also been ob- C-G- served for Samples grown on Fe whisker substrates13 while g 0.15; lb) *;i&;/Q@- : l the form of the curves for A 12 and B I2 in the first AFM coupling region are similar to those presented in Ref. 17. We bD have explained that it is difficult to accurately determine the 0.1 - ,i `$ 5 values of A 1 2 and B , 2 in the second AFM coupling region : c $9 because the coupling field is of similar size to the cubic 0.05: / `a $:" ;* anisotropy field. However, our best fits indicate that the ratio ;+ i of B, 2 to A, 2 in the center of this region is of the order of 0.8 O[.. ,,,,,, i ,,,,, ,(,, ,:J>,..,<: ,,,,,..,,,,,,, -a---.------ . ..I which is larger than the value of 0.26 obtained previously6 0 5 10 15 20 25 30 35 40 for samples grown on Ag/GaAs(lOO) substrates. In the latter case it was found that the biquadratic coupling became domi- Cr thickness (A> nant at somewhat larger Cr thicknesses," in the third AFM coupling region. By fitting a straight line to a log plot of the FIG. 7. The values of the coupling constants B,, and A,, for samples I and data in Fig. 7(a) we find that RI2 varies approximately as II are plotted as a km&ion of Cr thickness in panels (a) and (b), respectively. dGJ.4 over the full range of Cr thicknesses studied. The thick- The meaning of the various symbols is indicated in panel (a). The curve in ness dependence of B 12 panel (a) has been fitted to the data while the curve in panel (b) is a scaled can in principle be predicted from version of the curve in Fig. l(c) that serves only to guide the eye. the various extrinsic models of biquadratic coupling but in order to do this one must determine how the relevant struc- tural imperfection varies with the thickness of the Cr spacer Despite this it was found to be possible to fit BLS field scans layer. If we assume that the interfacial roughness, the distri- with, the same parameters for the Fe layers as for the first bution of loose spins, and the density of pinholes are all sample. We note that the acoustic mode is in fact sensitive to independent of the Ci- thickness then both the loose spins the values of the coupling parameters in the low-field regime mechanism and the mechanisms depending upon interfacial where canting of the Fe layer magnetizations occurs, The roughness predict that the biquadratic coupling should de- values of A,, and B,, deduced from BLS and MOKE mea- crease monotonically with Cr thickness as we indeed ob- surements for both samples I and II are displayed in Fig. 7. serve. The power-law behavior of B,, and the reduced val- ues of A,, observed in our data may therefore provide a V. DISCUSSION quantitative test of extrinsic coupling theories. In conclusion, MOKE and BLS measurements have been We begin by comparing our values for the coupling combined in order to determine the dependence of the inter- strengths in the Fe/Cr/Fe system with those obtained by other layer coupling constants upon the Cr thickness in Fe/CrPe researchers. From the separation of the maxima of the first trilayer samples. While short period coupling oscillations and second peaks in the easy axis saturation field in Fig. l(c) have not been observed we find that the phase and period of we obtain a value of about 18 8, for the long period of os- the long period oscillations agree well with those reported by cillation in the coupling strength. Taking the lattice param- other researchers. The coupling is however weaker in our eter of Cr to be 2.87 A we see that this agrees well with the samples which we attribute to the presence of structural im- value of 1251 monolayers (17.221.4 &) deduced for perfections. We observe a large value for the ratio of the samples grown on Fe whisker substrates.13 The position of hiquadratic to bilinear coupling strengths at the beginning of our first coupling maximum at 8 w of Cr lies close to the the first AFM coupling region and also in the second AFM observed position of the first short period AFM coupling coupling region, the thickness dependence of the biquadratic maximum at 5 monolayers (7.2 A) of Cr.14 We observe the coupling constant being well described by a dEi;`.4 power law. coupling strength to be offset in the AFM direction as has In view of the suspected structural imperfections in our been observed by other researchers.`4*29.46 After taking into samples we believe that this data may be useful in testing the account the different definitions of the coupling energy used extrinsic models that have been proposed for the biquadratic by different authors we note that in studies for which short coupling mechanism. 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