PHYSICAL REVIEW B VOLUME 56, NUMBER 5 1 AUGUST 1997-I Strong temperature dependence of the interlayer exchange coupling strength in Co/Cu/Co sandwiches N. Persat and A. Dinia IPCMS-Gemme, UMR 46 CNRS-ULP, 23, rue du Loess, 67 037 Strasbourg, France Received 29 October 1996; revised manuscript received 15 April 1997 We present a study of the temperature dependence of the interlayer coupling strength in Co hcp /Cu sand- wiches. The thermal variation of the coupling has been studied between 20 and 300 K by superconducting quantum interference device magnetometry for the samples corresponding to the first and second maxima in the oscillation of the exchange coupling of a series of Co/Cu(tCu /Co trilayers. We find a very strong decrease of the exchange coupling strength between 20 and 300 K. We show that the existing theoretical models cannot explain this unusual strong decrease. However, we believe that this behavior could be due to the confinement of carriers of one spin orientation in the spacer layer. S0163-1829 97 07830-2 I. INTRODUCTION predicted by one-band model6 and the free-electron model.3 The characteristic temperature is given by Since the discovery of the exchange coupling between ferromagnetic layers separated by a nonmagnetic layer,1 vF various models2 have been proposed to explain its mecha- T0 2 kSL , nism. As recently shown by Bruno,3 in agreement with Stiles,4 these various approaches such as total-energy calcu- where vF is the Fermi velocity and L the spacer thickness. lations, RKKY model, free-electron model, hole- Although the above-mentioned model had to be somewhat confinement model, or Anderson model can be considered modified, the variation of J(T) could be well reproduced by as particular cases of the quantum well theory of the ex- only considering the features of the spacer Fermi surface. change coupling. In this general description, the interlayer The Fermi velocity of Ru, of the order of 107 cm s 1, is magnetic coupling consists of quantum interferences due to about an order of magnitude smaller than most nonmagnetic spin-dependent reflections of Bloch waves at the metals and this leads to a characteristic temperature T0 of the paramagnet-ferromagnet interfaces. order of 100 K. Such a value of T0 is well suited to explain The RKKY theory, considering the Fermi surface of the the strong variations of J with the temperature in Co/Ru spacer layer, succeeded very early in predicting the oscilla- structures. tion periods of the coupling. In the general frame of the It has been nevertheless found in other structures, such as quantum well theory, the oscillation periods are related to the Fe/Pd/Fe or Fe/Cu/Fe trilayers,10 that the exchange coupling oscillation of the reflection coefficient at the magnetic/ can also be very sensitive to temperature. The strong varia- nonmagnetic interface and the results are the same as within tion of the coupling with the temperature is unexpected the RKKY theory. within the models taking only into account the features of the The various models have shown that the coupling strength Fermi surface of the spacer metal. J is governed essentially by the degree of band matching However, within the quantum well theory,11 the thermal between the nonmagnetic and ferromagnetic metals. In the variation of J depends not only on the spacer Fermi surface, quantum well state model, this is expressed in terms of the but also on the degree of confinement of magnetic carriers in spin asymmetry of the reflection of the electrons at the the spacer quantum well, which is governed by the mismatch magnetic/nonmagnetic interfaces. However, a realistic evalu- between the spacer and ferromagnet bands. It is demon- ation of the exchange coupling strength requires accurate strated that the temperature dependence of J is very strong knowledge of the features of the interfaces.5 when the Fermi level lies near the top of the confining well. Several theoretical studies have focused on the tempera- In this paper we present experimental results on the ex- ture dependence of the interlayer exchange coupling.6­8 A change coupling in Co hcp /Cu sandwiches grown by UHV general trend is that the velocity of the electrons at the ex- evaporation. We find a decrease of the order of 73% of the tremal points of the Fermi surface governs the temperature antiferromagnetic exchange coupling between 20 and 300 K dependence. for samples corresponding to the first and second maxima in Using ferromagnetic resonance between 10 and 300 K in the exchange coupling oscillation. We compare our results to the case of Co/Ru/Co trilayers, Zhang et al.9 could recently the behavior expected from theories. confirm that the thermal variation of the exchange coupling strength roughly follows the relationship II. STRUCTURE AND MAGNETORESISTANCE A series of Co 24 Å /Cu(t T Cu /Co 24 Å) sandwiches with J T J t 0 Cu ranging from 3.2 to 29.6 Å was prepared by UHV evapo- T sinh T 0 T0 ration on freshly cleaved mica substrates. A 112-Å-thick Ru 0163-1829/97/56 5 /2676 4 /$10.00 56 2676 © 1997 The American Physical Society 56 STRONG TEMPERATURE DEPENDENCE OF THE . . . 2677 FIG. 1. Magnetoresistance of the Co hcp /Cu sandwiches as a function of the Cu interlayer thickness at room temperature. The field is applied along the film plane with the current parallel to the FIG. 2. Magnetization loops obtained by SQUID magnetometry field. The line is only a guide to the eye. for the Co 24 Å /Cu 8 Å /Co 24 Å sandwich at a 20 K, b 150 K, c 200 K, and d 250 K. buffer layer was grown at 700 °C in order to provide a flat and single-crystalline surface. After cooling down the sub- strate to 14 °C, a thin Cu layer was grown prior to the Å /Cu 22 Å /Co 24 Å has been carried out between 20 K deposition of the Co/Cu sandwich. The latter was then cov- and room temperature by use of superconducting quantum ered with a thin Cu layer and finally a thin Ru cap layer. interference device SQUID magnetometry with fields up to Reflection high-energy electron diffraction RHEED per- 80 kOe. The qualitative evolution of the exchange coupling formed in situ has shown a close-packed structure with a strength can be seen in Fig. 2, which presents the magneti- sixfold symmetry in plane.12 NMR has clearly evidenced the zation loops measured at 20, 150, 200, and 250 K for the 00.1 hcp structure with good crystallographic quality of sandwich with tCu 8 Å. The important decrease of the satu- both Co layers for samples with spacer thickness from 3.2 to ration field and also of the area between the M(H) and the 25 Å.13 Although hcp growth of Co on a Cu 111 surface is M Msat lines with increasing temperature evidences the in fact expected, as shown by Hochstrasser et al.14 Co has strong sensitivity of the coupling strength to temperature. until now always been obtained with a fcc 111 structure in Using the relationship JAF HsatMsattCo/2, holding for sand- molecular-beam-epitaxy- MBE- grown superlattices or wiches where Hsat is the saturation field, Msat the saturation sandwiches, even when using a Cu 111 single-crystal magnetization, and tCo the magnetic layer thickness , the ex- substrate.15,16 We believe that the thin Cu seed layer has change coupling strength has been evaluated as a function of allowed the occurrence of the hcp phase by providing a very temperature as shown in Fig. 3. The decrease of 73% of J flat surface with a small lattice mismatch for the first Co layer. Although the growth of the second Co layer occurs on a rougher surface than for the first one, the hcp stacking remains of good quality as can be seen from the main line shape no fcc or stacking faults contribution of the NMR spectra.13 Magnetoresistance MR measurements have been first performed at room temperature for all samples using the classical four-point method with the applied field in plane and parallel to the current. Figure 1 shows the variation of the MR ratio as a function of the Cu thickness. The oscilla- tion period about 13 Å and the position of the first maxi- mum about 9 Å are quiet close to the values usually ob- served on 111 Co/Cu multilayers. This shows that the hcp structure of the Co layers has no significant effect on both period and phase of the MR oscillation. The sandwiches with tCu 8 Å and tCu 22 Å have been chosen to study the tem- perature dependence of the coupling strength since they cor- respond to the maxima in the exchange coupling oscillation. III. TEMPERATURE DEPENDENCE FIG. 3. Evolution with temperature of the antiferromagnetic OF THE EXCHANGE COUPLING coupling strength for the Co 24 Å /Cu 8 Å /Co 24 Å squares and the Co 24 Å /Cu 22 Å /Co 24 Å circles sandwich. The lines cor- The temperature study of the interlayer exchange cou- respond to the fit with the relevant expression in the Edwards pling of the samples Co 24 Å /Cu 8 Å /Co 24 Å and Co 24 model. 2678 N. PERSAT AND A. DINIA 56 between 20 and 300 K for the sandwiches with tCu 8 Å and tCu 22 Å is huge compared to the values observed by other groups17,18 in 111 Co/Cu systems. The strong sensitivity of the antiferromagnetic coupling strength to temperature may be due to the nature of the Co hcp /Cu interfaces in our sandwiches. However, one cannot exclude that the effec- tive anisotropy contributes significantly to the observed temperature dependence of the energy of these Co/Cu sandwiches. Indeed, in these sandwiches the Co layers have a hcp structure with a large magnetocrystalline anisotropy 5.5 erg/cm2 for bulk Co and are temperature dependent. For this reason we have performed torque measurements for sev- eral temperatures between 20 and 300 K on Co/Cu sand- wich with the same Co thickness as the sample presented in this study, but with the Cu thickness of 1.6 nm correspond- ing to the minimum of the coupling to get rid of the ex- change coupling.19 The results show that the effective anisot- ropy is strong at 300 K with the value Keff 1.2 erg/cm2, indicating that the magnetization lies in the film plane. The Keff decreases with decreasing the temperature and reaches the value Keff 0.65 erg/cm2 at T 20 K, which is still strong enough to maintain the magnetization in the film plane. This result is in agreement with the well-known varia- tion of the magnetocrystalline anisotropy of the bulk Co FIG. 4. Magnetoresistance curves for the Co 24 Å / from 5.5 106 erg/cm3 at room temperature to approxi- Cu 8 Å /Co 24 Å sandwich at a 300 K and b 4.2 K. The satu- mately 9 106 erg/cm3 at low temperature,20 which is ration fields of respectively 2.5 and 8 kOe confirm the strong tem- strong, but not sufficient to counterbalance the shape anisot- perature dependence of the antiferromagnetic coupling strength. ropy (13 106 erg/cm3) and to switch the magnetization out of the film plane. On the basis of these results, the anisotropy T term has been neglected in the calculation and the whole sinh T , temperature effect has been attributed to the change of the T0 T0 exchange coupling. with T0 vF/2 kBL, where vF (1/ ) E/ kz at the neck To confirm such a strong temperature dependence of the and belly of the Fermi surface and L is the spacer thickness. coupling, magnetoresistance measurements have been per- For Cu, vF is of the order of 1.57 108 cm s 1 free-electron formed on the sample with tCu 8 Å at 4.2 and 300 K. The model , leading to a theoretical characteristic temperature MR curves reported in Fig. 4 support the strong temperature T0th of about 2400 K. This value is in fact well above the dependence of the interlayer coupling strength, with satura- characteristic temperature T0 exp 99 K first antiferromag- tion fields of, respectively, 8 and 2.5 kOe. The MR value at netic AF maximum or T0 exp 85 K second AF maxi- room temperature reaches 4%, indicating a good crystallo- mum we find, by fitting the experimental results with the graphic quality of the samples. However, the unexpected function small MR value observed at 4.2 K about 1% can be ex- plained by the shunting effect in the relatively thick Ru T buffer layer. J T J0 T sinh TT The calculated J 0 0 AF represent the maximum coupling val- ues that can be reached in our samples. Indeed, the shape of see Fig. 3. Even when using the precise Fermi velocity at the the magnetization curves Fig. 2 suggests that the coupling neck, vF* 0.67 108 cm s 1 determined by the de Haas­ is not homogeneous in the samples and a biquadratic com- van Alphen effect,22 which leads to T0t*h 1020 K, the model ponent in the coupling can be expected. Thus we have used a is still unable to reproduce the strong decrease of the ex- magnetization model presented elsewhere21 to fit magneti- change coupling strength with increasing temperature. zation loops, adding a biquadratic coupling to the classical The huge difference between experimental and theoretical bilinear term. The magnetization loops have never been well T0 values clearly shows that the observed decrease of the reproduced by combining bilinear and biquadratic coupling coupling strength is much stronger than expected from this terms. We conclude the presence of a distribution of inde- theory. While in this model only the spacer Fermi surface is pendent magnetic behaviors from areas larger than the lateral relevant, Cullen and Hathaway8 assumed that the tempera- magnetic coherence length (LCo) of the Co layers. ture dependence is due to the disordering of the ferromagnet As already mentioned in the Introduction, the theoretical moments. However, for sandwiches with 12 monolayers in models7,6 predict that the temperature dependence of the cou- one ferromagnet like in our case, the decease is weak, with a pling is governed by the velocity of carriers at the stationary T3/2 behavior at low temperatures, followed by a quasilinear points of the spacer Fermi surface. The dominant tempera- decrease at higher temperatures. To explain what happens in ture factor is indeed our samples, it is likely that both spacer and ferromagnet 56 STRONG TEMPERATURE DEPENDENCE OF THE . . . 2679 lated to the magnetic nature of the Co/Cu interfaces. We have measured the magnetization loops for a series of Co(tCo)/Cu 15.2 Å /Co(tCo) sandwiches. Figure 5 shows the variation in saturation magnetization per unit surface of Co, MstCo , versus the cobalt thickness (tCo). The linear decrease in magnetization with decreasing tCo is expressed by a linear function which intercepts the abscissa at a thickness of about 4 Å. This indicates that about 2 Å of Co at each interface are magnetically dead at room temperature, due to intermixing. Such a dead layer would round off the potential well giving it a profile. When the temperature is decreasing, the dead layer is expected to become thinner, making consequently the well sharper than at room temperature. The evolution of the potential well shape with temperature could modify the confinement of the carriers and thus lead to a strong tempera- ture dependence of the coupling. FIG. 5. Variation of the measured saturation magnetization per IV. CONCLUSION unit surface of Co, MStCo , with Co layer thickness tCo for the Co(tCo)/Cu 15.2 Å /Co(tCo) sandwiches. In conclusion, we have found an unexpected strong de- crease of the interlayer coupling strength in Co hcp /Cu layers have to be considered. A recent model of temperature sandwiches. We expect this behavior to be due to the change dependence of J which depends on matching of ferromagnet of the potential well with temperature at the Co hcp /Cu in- and spacer bands in direction perpendicular to the layers11 terfaces. The theories existing up to now are not able to seems to concur with this hypothesis. The calculation per- explain such a behavior. However, a model where the tem- formed on 001 Co/Cu predicts a strong temperature depen- perature dependence is not only governed by the spacer dence when magnetic carriers of one spin orientation are Fermi surface, but also by the ferromagnet, seems likely to fully confined in spacer potential well of finite depth. They explain our results. also show that this temperature dependence is relatively ACKNOWLEDGMENTS stronger for thicker Cu spacer layers. Such results agree very well with our experimental measurements. We thank R. Poinsot and A. 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