Journal of Magnetism and Magnetic Materials 187 (1998) 1-11 Exchange coupling of Co/Cr(0 0 1) superlattices for in-plane and perpendicular anisotropy Th. Zeidler*, K. Theis-Brošhl, H. Zabel Fakulta(t fu(r Physik und Astronomie, Institut fu(r Experimentalphysik/Festko(rperphysik, Ruhr-Universita(t Bochum, D 44780 Bochum, Germany Received 2 January 1998 Abstract We have investigated the exchange coupling of Co/Cr(0 0 1) superlattices by polar and longitudinal magneto-optical Kerr effect measurements, by varying both the Co and Cr film thicknesses. At a Co thickness of +10 A> a nearly perpendicular anisotropy is found with antiferromagnetic order in the range of 5-15 A> of Cr thickness. For these superlattices the magnetization curve starting from remanence to saturation is characterized by a surface spin-flip transition at low field, followed by domain wall nucleation and motion, and finally by a coherent spin rotation with increasing field. Antiferromagnetic coupling is also observed for superlattices with thicker Co layers and with in-plane magnetic anisotropy. 1998 Elsevier Science B.V. All rights reserved. Keywords: Exchange coupling; Superlattices; Anisotropy - perpendicular; Anisotropy - in-plane 1. Introduction attention. Nevertheless, it would be of considerable interest to compare the coupling period, phase and There has been much interest in recent years in amplitude of the exchange coupling in Fe/Cr and the magnetic properties of Fe/Cr(0 0 1) superlat- Co/Cr superlattices. The somewhat lower interest tices. The most important discoveries include the in Co/Cr is, in part, due to the mismatched crystal observation of a magnetic exchange coupling [1], structures and the complex epitaxial relationship a long-period oscillatory exchange coupling as between Co and Cr. While both Fe and Cr have a function of the Cr layer thickness [2,3] super- a BCC structure with a lattice mismatch of less posed on a shorter two monolayer oscillation than 0.4%, the equilibrium crystal structure of Co period [4,5], a non-collinear contribution to the is HCP. The first few monolayers of Co grow with exchange coupling [6-8], and a giant mag- a pseudomorphic BCC structure on Cr(0 0 1) ro- netoresistance effect [9,10]. In comparison, Co/ tated by 45° with respect to the Cr[1 0 0] in-plane Cr(0 0 1) superlattices have received much less axis [11-13]. With increasing Co thickness the structure relaxes back continuously into the intrin- sic HCP structure with the c-axis in the plane * Corresponding author. parallel to Cr[1 1 0] [11,12]. This lattice relaxation 0304-8853/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 1 2 1 - 8 2 Th. Zeidler et al. / Journal of Magnetism and Magnetic Materials 187 (1998) 1-11 has a profound effect on the magnetic anisotropy strength of the exchange coupling, whereas the su- properties of Co/Cr superlattices [14]. For thicker perlattices with fixed layer thicknesses were used Co layers of 20 A> and more, the easy axis is in the for the study of spin structures and magnetization plane due to the shape anisotropy. For thinner Co processes. The Co thicknesses were chosen between layers the surface anisotropy contribution domin- t ates the magnetic properties of this system, which is ! +5-30 A> and in the wedged samples the Cr-thicknesses varied from t negative for HCP-Co but positive for BCC-Co. ! +5-25 A> and from +12-19 A>. Thus, with decreasing Co thickness first the easy We have studied the exchange coupling in axis turns up into the perpendicular direction Co/Cr(0 0 1) superlattices via the magneto-optical reaching a maximum at about 10-13 A>. However, Kerr effect (MOKE) using a set-up described in before reaching a complete out-of-plane orienta- more detail in Ref. [14]. With a Faraday modulator tion, the magnetization vector drops back into the and lock-in techniques we achieve angular resolu- plane. This re-orientation of the perpendicular tions of )10\ °. The plane of polarization of the anisotropy as a function of the magnetic layer He-Ne laser beam ( "632.8 nm, P"5 mW) was thickness has to be distinguished from re-orienta- aligned perpendicular to the plane of incidence (s tional transitions which can be observed as a func- state). In the polar configuration, used for samples tion of temperature, for instance, in Fe/Cu [15,16] with perpendicular anisotropy, the angle of inci- and Fe/Ag superlattices [17,18]. In contrast, dence was smaller than 2°. Co/Cr(0 0 1) superlattices offer the unique oppor- At room temperature, magnetic fields up to tunity to independently tune both, the perpendicu- 18 kOe are available. For low-temperature work lar anisotropy and the sign of the exchange down to č"4.2 K we used a cryostat as shown in coupling by varying either the ferromagnetic or Fig. 1 with a superconducting magnet providing the non-ferromagnetic metal layer thickness, fields up to 30 kOe. An experimental problem con- respectively. stitutes the optical windows for low temperature For more detailed information on the structure studies. Windows without changes of the optical and magnetic anisotropy, we refer to our previous birefringence exist only at room temperature. papers [11,12,14,19-22]. Here we present a detailed Therefore, we avoided any optical windows inside study of the exchange coupling in Co/Cr(0 0 1) su- of the cryostat and the sample was positioned out- perlattices. We have also extended our previous side of the inner cryostat, as indicated in Fig. 1. investigations of the magnetic anisotropy to lower Liquid He flow through the inner part guaranteed temperatures, which are reported in here. 2. Sample preparation and MOKE set-up High-quality single crystal Co/Cr(0 0 1) super- lattices were grown by molecular beam epitaxy (MBE) at 300-350°C on a buffer system consisting of a Nb(0 0 1) seed layer grown at 900°C on Al O (1 0 1 2)-substrates and an additional Cr(0 0 1) buffer layer grown at 450°C with thick- nesses t, , t! +500 A>. For the study of the ex- change coupling and anisotropy, we have grown Co/Cr(0 0 1) superlattices with specific thicknesses for the Co and the Cr layers as well as superlattices with a wedge-type Cr layer between the Co layers of constant thickness. The wedged superlattices are Fig. 1. Schematic outline of the He cryostat used for polar more convenient for comparative studies of the MOKE-measurements at low temperatures. Th. Zeidler et al. / Journal of Magnetism and Magnetic Materials 187 (1998) 1-11 3 satisfactory heat contact. The outside window also If all anisotropy contributions are known, a fit of causes problems since it produces a Faraday effect the calculated magnetization M(H) loop according proportional to the applied magnetic field yielding to Eq. (1) and an additional linear contribution to the MOKE signal. All measurements shown here have been M 1 , " cos corrected for these effects. M L (2) 1 N L to the experimental points is possible and produces 3. Phenomenological anisotropy energy model quantitative values for the coupling term J $. For the analysis of the magnetic anisotropy and the interlayer exchange coupling of Co/Cr(0 0 1) 4. Magnetic anisotropy properties of Co/Cr(0 0 1) superlattices we have performed absolute minima calculations of the phenomenological energy den- For the analysis of the interlayer exchange coup- sity E, including terms for the Zeeman energy, ling a knowledge of the anisotropy properties is shape anisotropy, crystal anisotropies of second indispensable. The room temperature results can be and forth order of HCP-Co, K summarized as follows [14,19,20]. An interface an- and K , respective- ly, and an interface anisotropy constant K isotropy constant K 1. For the 1+!0.65 mJ/m causes a polar configuration we use the expression: transition of the orientation of the magnetization vector from in-plane to the out-of-plane direction , E"! with decreasing Co thickness t M1H cos( L! &) ! . Extrapolation of L the anisotropy field as a function of the inverse Co layer thickness yields the critical thickness for the 1 , # reorientation of t 2 M 1 cos L ! +13.5 A>. The rotation of the L easy axis stops at an angle of +75°, and for , , t! (12 A> the easy axis turns back into the plane. # K This most remarkable effect is governed by the cos L# K cos L L L concomitant structural phase transition of the Co , 1 L layers from hcp to bcc with decreasing Co thick- # 2K1 cos L# K3 cos ( L! 3) ness, which, in turn, causes a sign change of the L t! L interface anisotropy constant K1. ,\ J By minimizing Eq. (1) and fitting to the mea- # $ cos( L! L> ), (1) sured MOKE hysteresis curves we find the other L t! crystal anisotropy constants: K here t +2.1;10 J/m ! is the thickness of the Co layer. The angle and K +1.1;10 J/m . The value for K is slight- L (n"1..N, N"number of Co layers) is defined as ly smaller than typical values reported in the litera- the angle between the sample normal and the ori- ture [23-25], but remains of the same order of entation of the magnetization vector in the layers of magnitude. the superlattice. The magnetic field H is applied In the Co layer thickness regime of the reorienta- perpendicular to the surface with &"0. The satu- tional transition an additional anisotropy constant ration magnetization M1 is assumed to be homo- K geneous in each Co layer. An additional uniaxial 3 is required, which defines a canted orientation for the magnetization vector anisotropy contribution is introduced via K 3 according to 3 with Eq. (1). Introducing this anisotropy constant is jus- an arbitrary orientation 3 with respect to the tified by the experimental results shown in Fig. 2, sample normal. The need for this anisotropy term which reveal a hard axis if the magnetic field is will be justified later. The AFM coupling term applied with an angle of 15° to the sample surface prefers an antiparallel orientation of adjacent Co (see inset of the figure). This indicates that a canted layers for J $(0. easy axis exists with an orientation of about 4 Th. Zeidler et al. / Journal of Magnetism and Magnetic Materials 187 (1998) 1-11 Fig. 2. Hard-and easy-axis hysteresis loops for a Co/Cr(0 0 1) superlattice with t Fig. 3. Polar MOKE measurements of Co/Cr(0 0 1) super- ! "12 A> and measured in the polare MOKE configuration at room temperature. The circles show a hyster- lattices for Co thicknesses t! *17 A> at č"4.2 K and near esis with the magnetic field applied along a direction 105° away room temperature. No significant temperature dependence of from the perpendicular direction as indicated in the inset. The the hysteresis loops is observable. solid line shows the appertaining MOKE curve along the easy axis at an angle of 15° with respect to the normal. change coupling is rather weak. The polar MOKE measurements are taken with the magnetic field 3"15° away from the normal direction and for applied along the hard axis. As shown in Fig. 3, t! "12 A>. By the shape of the hard axis loop in there is no significant change of the magnetization Fig. 2 it is clear that no sixth- or higher-order curve at high and low temperatures. This is a rather anisotropy term is required for the description of surprising result, which is clearly inconsistent with the magnetic anisotropy of this system. From the the temperature dependence known for bulk HCP observed saturation field of H +7.2 kOe and Co [23]. In bulk Co, the crystal anisotropy con- a slightly reduced value for the saturation magne- stant K tization M increases by about 40% between room 1"10 A/m , we determine the uniaxial temperature and 70 K, while K anisotropy constant to K remains nearly 3+2.8;10 J/m . The constant. One would expect a similar temperature origin of K3 is not clear at present. It may be dependence also to be present for Co/Cr(0 0 1) related to the substrate and buffer layer miscut in superlattices with thickner Co layers, which, how- the present superlattices. In any case, the K3 is ever, is clearly not the case. required for a phenomenological description of the For Co thicknesses in the range of the perpen- anisotropy and the coupling behavior for Co layer dicular anisotropy (t thicknesses smaller than 14 A>. ! (12 A>), the magnetic an- isotropy is also nearly temperature independent. We are now turning to our low-temperature The polar MOKE measurements reproduced in results. We were interested in the temperature Fig. 4 show that only the coercive fields and the dependence of the anisotropy constants K and K , remanent Kerr rotation increases slightly at and the question, whether at low temperatures an- č"4.2 K. other re-orientational transition of the anisotropy For both anisotropies, the MOKE data clearly occurs, as reported previously for the Fe/Cu show that no further reorientation of the easy axis [15,16], the Fe/Ag [17,18], and most recently also as a function of temperature takes place. Therefore, for the Co/Ho interfaces [26]. the reorientational transition is solely induced by First, we compare magnetic hysteresis curves re- the structural transition of the Co layer from HCP corded at high (250 K) and low temperatures to pseudo-BCC with decreasing thickness. (4.2 K) and for two different Co thicknesses of 17 It is well known that the magneto-crystalline and 35 A> for which the easy axis is in the plane. The anisotropy depends sensitively on crystal field and Cr thickness of 20 A> is chosen such that the ex- band structure properties. In particular, the Co Th. Zeidler et al. / Journal of Magnetism and Magnetic Materials 187 (1998) 1-11 5 Fig. 5. The polar MOKE hysteresis curve of Co/Cr(0 0 1) super- Fig. 4. Polar MOKE measurements of Co/Cr(0 0 1) superlatti- lattices with t ces with different Co thicknesses t ! )13 A> exhibits an AF coupling. The slope in the ! )14 A> at č"4.2 K and remnant regime is due to a uniaxial anisotropy with a canted near room temperature. Aside from slightly increased coercive easy axis with respect to the layer normal. fields at low temperatures, no significant temperature depend- ence of the hysteresis loops is observable. anisotropy constant K depends strongly on small changes of the c/a ratio for the HCP lattice con- stants. Due to epitaxial strains and pseudomorphic growth of the Co layers in Co/Cr(0 0 1) superlatti- ces, we expect the magneto-elastic contribution of the anisotropy to deviate from its bulk counterpart and, furthermore, to be temperature dependent. At present the temperature dependence of the c/a ratio for Co/Cr superlattices is not known. The temper- ature-independent hysteresis curves seem, however, to indicate that the c/a ratio remains constant with decreasing temperature. Fig. 6. Polar saturation field H as a function of Cr layer thickness. The superlattices are not saturated in the area around t! +6 A> in magnetic fields up to 18 kOe. The dashed line reproduces the position and shape of the saturation field in 5. Exchange coupling in Co/Cr(0 0 1) superlattices Fe/Cr(0 0 1) superlattices around the first AF maximum accord- ing to Ref. [22]. 5.1. Exchange coupling with perpendicular anisotropy be explained in detail further below. The saturation In the following we report room temperature field, which is a measure of the coupling strength, is results on the exchange coupling in Co/Cr(0 0 1) plotted as a function of the Cr layer thickness in superlattices and for Co thicknesses (t! +10 A>) Fig. 6. exhibiting perpendicular anisotropy. Hysteresis The first maximum of the AFM interlayer coup- loops were taken along a wedged superlattice with ling occurs at t Cr layer thickness increasing between 5 and 25 A>. ! +6 A>. Using Eq. (1) and the an- isotropy parameters as discussed in Section 4, A typical hysteresis loop is reproduced in Fig. 5 for a coupling strength of "J a Cr thickness of 13 A>. Here we clearly observe an $"'0.5 mJ/m is evalu- ated. We can provide only a lower limit for the antiferromagnetically (AFM) coupled superlattice coupling strength since we could not saturate the close to perpendicular anisotropy. The shape of the sample in the polar configuration with fields up to hysteresis curve and the resulting spin structure will 18 kOe. 6 Th. Zeidler et al. / Journal of Magnetism and Magnetic Materials 187 (1998) 1-11 Our results should be compared with earlier ex- periments by Parkin on polycrystalline Co/Cr multilayers [27]. In the latter case a first AFM maximum is observed at 7 A> with a coupling strength of 0.24 mJ/m . Both values are in fair agreement with our results, considering the differ- ent growth methods and structures. According to the earlier experiments, the second long period maximum occurs at 25 A> which is outside of the Fig. 7. Symmetric spin orientation of a magnetic sandwich sys- thickness range investigated here. The shape, posi- tem during the remagnetization process. In (a) coherent spin tion, and strength of the saturation field as a func- rotation is dominant wheras in (b) only spin flip transitions tion of the Cr layer thickness in Co/Cr(0 0 1) is also occur. in rather good agreement with the Fe/Cr(0 0 1) results for the long period exchange coupling (dashed line in Fig. 6) [3]. 5.2. Magnetic hysteresis of exchange coupled superlattices with perpendicular anisotropy Sandwich structures with a uniaxial anisotropy K3 and an interlayer antiferromagnetic coupling (J $(0) exhibit a spin structure as a function of an external field which is usually completely sym- metric. Therefore, the magnetic hysteresis is expected to be symmetric as well, as shown sche- Fig. 8. Polar MOKE measurement of an AF coupled matically in Fig. 7. If K Co/Cr(0 0 1) superlattice (open circles) and the theoretical mag- 3(J $/t , where t is the thickness of the magnetic layers, a coherent rota- netization curve using Eq. (1) (solid line). The theoretical tion of the spins occurs, as shown in Fig. 7a. In the MOKE curve is plotted by dashed lines. For more details see text. opposite case of K3'J $/t , a spin flip transition at the field H$"H1 dominates the magnetization process, as shown in Fig. 7b. analysis via a fit to the hysteresis curve, as discussed Fig. 8 reproduces the polar MOKE hysteresis below. measurement (open circles) of an antiferromagneti- Close to remanence a crossing of the magneti- cally coupled Co/Cr(0 0 1) superlattice with N" zation curves can be recognized. This is due to the 10 magnetic double layers. The wide range of fact that the top magnetic layer of the superlattice a nearly zero remanent magnetization and the high contributes mainly to the MOKE signal, whereas saturation field are characteristic of the strong for the inner layers the MOKE sensitivity decreases coupling in this superlattice. As mentioned above, exponentially. Neglecting depth-dependent MOKE at t! "12 A>, the easy axis is slightly slanted with sensitivity, our fit to the MOKE curve shown by respect to the perpendicular orientation. Because of the solid line in Fig. 8 is in excellent agreement with this, the MOKE curves in Fig. 8 and also in Fig. 5 the experimental data. exhibit a significant slope in the field range The model calculation is based on Eq. (1) and the between H"0 and H"H . Comparing the parameters are listed in Table 1. We have cal- schematics in Fig. 7 with the experimental results culated the hysteresis loop according to the classi- as shown in Fig. 8, we can qualitatively conclude cal Maxwell theory for magnetic multilayers with that the magnetic hysteresis is characterized by arbitrary orientation of the magnetization vector coherent spin rotation. Details of the spin structure will, however, follow from a more quantitative following the treatment of Moog et al. [28-31]. For the optical and magneto-optical constants of Th. Zeidler et al. / Journal of Magnetism and Magnetic Materials 187 (1998) 1-11 7 Table 1 Magnetic anisotropy and coupling parameters used to fit the magnetic hysteresis in Fig. 8 according to the model described in Eq. (1) M1 K K K1 K3 3 J $ t! (kA/m) (J/m ) (J/m ) (mJ/m ) (J/m ) (deg) (mJ/m ) (A>) 1000 2.1;10 1.1;10 !0.65 1.8;10 30 !0.33 12 Co and Cr we used literature values from Refs. [32,33]. According to our model calculation, the spin structure of the Co/Cr(0 0 1) superlattice with 10 double layers is highly asymmetric at low fields, explaining the rather complicated hysteresis loop in Fig. 8. In remanence the magnetic moments are oriented antiparallel along the easy-axis direction, as indicated schematically in Fig. 9a, including the canted easy axis. With increasing field, a surface spin flip transition with a domain wall nucleation takes place at H and leads to an asymmetric spin structure (Fig. 9b). At slightly higher fields, H , we observe a `domain wall' motion to a more stable state. The spins are now oriented symmetrically with respect to the center of the superlattice (Fig. 9c). For H'H , all spins switch into the field direction. Finally, a coherent rotation of the layer magnetization takes place until saturation is reach- ed. The two outermost Co layers differ slightly in their orientation from the inner layers, since they are coupled to only one neighbor each. In Fig. 10 we show another example for perpen- dicular anisotropy and spin rotation in exchange coupled Co/Cr superlattices as determined by polar MOKE measurements. Here the hysteresis is char- acterized by a spin flip transition, according to Fig. 7b. Again the MOKE curves cross close to remanence due to magneto-optical effects. In prin- ciple, the finite Kerr rotation in remanence could be Fig. 9. Spin structure of an AF coupled Co/Cr(0 0 1) super- explained by a non-collinear spin structure con- lattice for different magnetic fields. More details are provided in taining biquadratic coupling terms. However, addi- the text. tional investigations with polarized neutron reflectivity provided no evidence for this assump- tion occurs again at very low fields, which is, tion [34]. however, extremely unstable. With a slight increase The calculated magnetization curve using Eq. (1) of the field up to H is shown by a solid line in Fig. 10. The correspond- , the spin structure becomes symmetric with respect to the center of the super- ing layer magnetization vectors are schematically lattice (Fig. 11b). A second spin flip transition reproduced in Fig. 11. Starting from the remanent occurs at H magnetization (Fig. 11a), a surface spin flip transi- and leads to saturation without any further intermediate states (Fig. 11c). The fit 8 Th. Zeidler et al. / Journal of Magnetism and Magnetic Materials 187 (1998) 1-11 Fig. 10. Polar MOKE measurement of an AF coupled Fig. 12. Longitudinal MOKE hysteresis loop of an AFM Co/Cr(0 0 1) superlattice (open circles) and the theoretical mag- coupled superlattice with t netization curve using Eq. (1) (solid line). ! "12 A>. The superlattice comprises an odd number of periods, such that the magnetization is not completely cancelled in remanence. yields a rather weak AFM coupling constant of J $++!0.07 mJ/m . 5.3. Exchange coupling with in-plane anisotropy We have also investigated the exchange coupling for Co thicknesses with in-plane anisotropy. Longi- tudinal MOKE measurements were carried out using wedged sample with a constant Co thickness of 22 A> and with Cr thicknesses varying between 12-19 A>. In Fig. 12 we show a hysteresis loop taken with the longitudinal MOKE configuration and for a su- perlattice having five periods of thicknesses t! "22 and t! "12 A>, respectively. The odd num- ber of magnetic layers prevents the magnetization from complete cancellation at remanence even in the case of a perfect AFM coupling. The depend- ence of the saturation field as a function of the Cr thickness is plotted in Fig. 13. A very high satura- tion field is observed at about 12 A>. However, the maximum may occur at even smaller Cr thickness, in agreement with the out-of-plane coupling. From the saturation field and the known anisotropy con- stants we derive an exchange coupling constant J $+!0.3 mJ/m . 5.4. Temperature dependence of the exchange coupling Fig. 11. Spin structure of an AF coupled Co/Cr(0 0 1) super- lattice for different magnetic fields. More details are given in the We have also measured the low-temperature text. magnetic hysteresis of samples with perpendicular Th. Zeidler et al. / Journal of Magnetism and Magnetic Materials 187 (1998) 1-11 9 theories. The hysteresis changes shape between the flip fields !H (H(#H , which is caused by an increased number of pinning centers for domain wall motion. This stretches out and rounds off the descrete jumps in the hysteresis loops with decreas- ing temperature. 6. Discussion and summary One important result of the present investigation is the observation that the interlayer exchange Fig. 13. Saturation fields H coupling in Co/Cr(0 0 1) superlattices is in principal 1 from longitudinal MOKE measurements are plotted as a function of the Cr thickness. The agreement with the exchange coupling in Fe/ results are qualitatively in good agreement with exchange coup- Cr(0 0 1) superlattices respecting the amplitude and ling in the perpendicular orientation. the phase of the first AFM maximum. The mag- netic exchange splitting of bulk Co and Fe are comparable and, according to the theory of quantum well states (QWS), prefer similar phases for the interlayer coupling [35-38]. In contrast to Fe/Cr(0 0 1), so far we have not been able to observe a second AFM maximum nor a two ML oscillation period. Some indications for a 2 ML short period oscillation have been found in asymmetric trilayer structures of Co/Cr/Fe(0 0 1) [22]. Some information on the exchange coupling of Co/Cr(0 0 1) superlattices with in-plane anisotropy is also available from other groups. Harp and Parkin [39] observed AFM coupling for a super- Fig. 14. Polar MOKE measurements of AF coupled lattice with a Cr thickness of 10 A>, whereas for 12 A> Co/Cr(0 0 1) superlattices with different Cr layer thicknesses are compared for temperatures of 4.2 and 250 (290) K. The temper- Cr thickness they report ferromagnetic coupling. ature dependence is not dramatic, indicating that neither the However, their 12 A> sample shows a remanent anisotropy nor the exchange coupling depend strongly on the magnetization which is considerably reduced com- temperature. pared to the saturation magnetization, indicative of AFM or biquadratic contributions at this Cr anisotropy (Co thickness +10 A>). In Fig. 14 we thickness. Picconatto et al. [40] investigated compare polar MOKE curves taken at 4.2 K with a Co(20 A>)/Cr(10 A>) superlattice, exhibiting a hys- measurements at higher temperatures. For the teresis with a clear AFM coupling. They derive an sample with t! "10 A> we observe a coherent spin exchange coupling constant of "0.55" mJ/m , in rotation with very little temperature dependence good agreement with our results. Recently, Aliev (Fig. 14c and d). However, a strong temperature et al. [41] have investigated Co/(Cr/Ag)/Co super- dependence of the magnetization curve can be rec- lattices with Cr/Ag bilayers as non-ferromagnetic ognized for the sample with weak AFM coupling spacer layers. The Co thickness of 45 A> guarantees (t! "12 A>) as shown in Fig. 14a and b. Neverthe- an in-plane easy axis. Below 7 A> they observe less, the saturation field remains unchanged indic- ferromagnetic coupling, whereas AFM coupling ating no significant temperature dependence of the occurs between 10 !23 A> with a very broad max- coupling term J $+, in agreement with coupling imum. A second AFM peak was not observed. 10 Th. Zeidler et al. / Journal of Magnetism and Magnetic Materials 187 (1998) 1-11 Our polar MOKE measurements and the simu- Acknowledgements lations do not require a second-order biquadratic coupling term of the form J /t! cos ( L! L\ ), as We would like to thank W. Donner for the MBE for Fe/Cr(0 0 1). Using such a term in our simula- growth of the Co/Cr superlattices, and J. Pod- tion does not improve the fits to the experimental schwadek and W. Oswald for their technical assist- points. ance. The work in Bochum was supported by the Another important aspect of our investigations DFG through SFB 166 "Structural and magnetic concerns the magnetic hysteresis for perpendicular phase transitions." anisotropy in an external magnetic field. The two cases of magnetization curves known for trilayers can also be observed in the superlattices. In the References former case, saturation will be reached either via a coherent spin rotation or by spin flip processes [1] P. Grušnberg, R. Schreiber, Y. 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