Magnetic multilayers: oscillatory interlayer exchange and giant magnetoresistance

Journal of Magnetism and Magnetic Materials 104-107 (1992) 1712-1716 North-Holhmd

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Magnetic multilayers" oscillatory interlayer exchange and giant magnetoresistance A . F e r t ", A . B a r t h 6 1 6 m y ", P. E t i e n n e t,, S. L e q u i e n b, R . L o l o e e c, D . K . L o t t i s a, D . H . M o s c a ", F. P e t r o f f ~', W . P . P r a t t c a n d P . A . S c h r o e d e r c "Laboratoire de Physique des Solides. Universitd Paris-Sud, 91405 Orsay, France t, LCR Thomson CSF, 91404 Orsay, Francz, '" Physics Department, Michigan State University, East Lansing, Mi 48824, USA

We illustrate our presentation and discussion of the interlayer exchange and magnetoresistance properties in magnetic multilayers with experimental data on Fe/Cr, Co/Cu and Fe/Cu.

1. Introduction Interlayer exchange was first observed clearly in rare-earth multilayered structures [1,2]. In G d / Y , D y / Y , etc. the interlayer exchange is an oscillatory function of the Y thickness and this oscillatory bchaviour can be well explained by RKKY-like models [3]. Now strong interlayer exchange effects have also been found in many multilayered structures based on ferromagnetic transition metals, first in F e / C r / F e sandwiches [4,5] and Fe(001)/Cr(001) superlattices [6], then in systems such as C o / C r , C o / R u [7], C o / C u [8-12], C o / M o [13], F e / C u [ 14,15], N i / A g [ 16], C o / A g [17] and several other ferromagnetic 3d m e t a l / n o n magnetic metal structures [12]. A puzzling result, first found in Fe/Cr, C o / C r and C o / R u [7], is the observation that the interlayer exchange is an oscillatory function of the spacer thickness with a osurprisingly long period, generally between 10 and 20 A. A much shortcr pcriod is predicted by standard RKKY-likc modcls of indirect exchange and this has stimulated a large number of theoretical works. Another interesting property, partly related to the existence of antiferromagnetic interlayer exchange, is the giant magnetoresistance (GMR) or spin valve effect. The GMR was first observed in F e / C r [6,21]. In the Cr thickness range where the interlayer exchange is antiferromagnetic (AF), the resistivity drops steeply when an applied field wipes out the antiferromagnetic superstructure. The magnetoresistance ratio of Fe(001)/(Cr(001) superlattices can exceed 100%. MR effects have also been observed recently with the current perpendicular to the layers and they are even larger in this configuration [22]. Thc G M R of thc magnetic multilayers is very promising for applications to magnetic sensors. The spin-dcpcndent scattering of the conduction electrons in the magnetic layers or at their interfaces [6] is supposed to be at the origin of the GMR. However, the theoretical treatment of electron scattering by an inhomogeneous distribution of scattering centers is not a simple problem and several calculation models are in competition.

After a review of the experimental results on both the interlayer exchange and the magnetoresistance in section 2, we discuss the interpretation of the exchange oscillations in section 3 and the calculation of the GMR in section 4.

2. Review of experimental results on Fe/Cr, C o / C u and F e / C u multilayers The interlayer exchange in multilayered structures can be studied by several experimental methods: magnetization and torque measurements, neutron scattering, Brillouin scattering, FMR, SPLEED, magnetoresistance .... We show in fig. 1 typical features of the magnetization curves in a superlattiee with AF interlaycr exchange: (a) a relatively high field is necessary to overcome the AF exchange and saturate the magnetization and (b) the rcmancnt magnctization is very small. In fig. 2 wc show a typical magnctorcsistancc (MR) curvc of a Co fcc/Cu fcc multilaycrs ([111] tcxturc) with AF interlayer exchange [10]. The resistivity drops when one goes from AF to F (ferromagnetic) arrangement. This is the GMR or spin valve effect. ii

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MAGNETIC FIELD ( K O e ) Fig. 2. Magnetoresistance curves of a (Co 15 ,~,/Cu 9 ,~)x 30 multilayer at 4.2 K (preparation by sputtering). The Co and Cu layers are fcc with a well pronounced [111] texture• The magnetic field is in-plane along the current direction [10]. In fig~,3 we show the variation of the M R ratio of (Co 15 A / C u t c , ) multilaycrs as a function of thc thickness of Cu, tc,. The oscillations of the M R are due to the oscillatory behaviour of the interlayer cxchange, the M R peaks corresponding to the A F halfperiods. Similar oscillations are also observed in thc saturation field of the magnctization curvcs [10,11]. For C o / C u the period of the oscillations in fig. 3 is approximately 12.5 A (after averaging ovcr thc four oscillations of fig. 3) and similar valucs have bccn found in many systems. For F c / C u , scc fig. 4, thc pcriod is also around 12.5 but, puzzlingly, thc oscillations for C o / C u and F c / C u havc oppositc phascs. Thc interlayer exchange cncrgy bctwccn magnetic layers is generally written as Eex~h = -JP, i "/~2//xl tz 2, 8

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% ' " " ¢ , ~ ' .... ¢0"" .,¢'" 4 . s0 . o . . . . 7~ Cu T H I C K N E S S (,~) Fig. 4. Oscillations compared of the MR ratio as a function of the oCu thickness for (Fe 15 ~,/Cu)×50 (diamonds) and (Co 15 A / C u ) x 3 0 (dots) multilayers, in Cu/Fe, Fe is bcc with a [I |0] texture. Cu layers thinner than about 20 ,A "~re bcc with a [110] texture [15]. Above 20 ,~ the Cu structure becomes fcc [111] progressively. In Co/Cu, Co and Cu are fcc with a [111] texture. w h e r e / ~ l and ,u,2 are the layer magnetic moments and J is the exchange constant per unit surface. In the A F half-periods the exchange constant J can be straightforwardly derived from the saturation field of the magnetization or magnetoresistance curves. For measurements with in-plane fields and when the in-planc anisotropy is ncglcctcd, J is rclated to the saturation field H., by

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where M, is thc saturation magnetization and t M is the thic;mcss of the magnetic iaycrs [23]. In the F halfpcr~:~ds, J can be derived from Brillouin scattering m e a s u r e m e n t s [24], but also fronm nlagnetization or magnctorcsistancc data on specially dcsigncd multilaycrcd structurcs [25]. Thcsc structurcs combinc A F and F interlayer cxchanges in such a way that, during the m a g n e t i z a t i o , process, the applied field has first to overcome the F exchange couplings. An examplc of the preliminary results obtained in this way for C o / C u is shown in fig. 5. Now wc consider the M R results in morc detail (fig. 3). The decrease of the amplitude of the M R peak at increasing coppcr tlmickncss is duc to two indepcndent cffccts. First, as prcdicted by the theoretical models based on spin-dependcnt clcctron scattcring [26-31], an incrcasc of the t h i c k n e s s / m c a n - f r c c - p a t h ratio dccouples thc spin-dependent scattering processes occurring A ; .f v. ... . . .. ... .t . .,-,.., • In " ,., . . g ,~,~,io . . . . . . layers .,,,_.""Areduces ,I,..... . . .....,...;,:. tivity diffcrcncc betwccn thc A F and F structures. Secondly, as the interlayer exchange becomes smaller than the cocrclvity forces, the MR is rcduccd bccausc one gocs from the strong coupling limit (at the first M R peak in fig. 3, with a 100% A F arrangemcnt) to the uncoupled limit (for tc, >_.50 .~, in fig. 3) for which there is a random a r r a n g e m e n t of the magnetic moments at low field whatever the sign of the interlayer

1714

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Fig. 5. Thickness dependence of the interlayer exchange in Co/Cu multilayers (preliminary results). exchange. In the uncoupled limit, the MR corresponds to thc resistivity difference between random and F arrangemcnts, the oscillations disappear and the thickness dependence of the MR is due only to the variation of the thickness/mean-free-path ratio. Besides the thicknesses, the other important parameters for thc GMR are the temperature, the interface roughness and the concentration of impurities or defects. The GMR ratio decreases as the temperature increases, rather rapidly in systems such as F e / C r or F e / C u [15,23], much more slowly in C o / C u [10,11]. The dependence of the MR on the interface roughness has been clearly established for the F c / C r system. When one starts with Fe(001)/Cr(001) supcrlatticcs having sharp interfaces, annealing treatments can roughen the interfaces and enhance the MR [34]. In the same way, the MR can be enhanced by intentionally mixing Fc and Cr within a few ML at the interfaces during the epitaxiai growth (however, for a mixed layer thickcr than 4 A, AF cxchangc and GMR disappcar) [34]. In the same way, studies on sputtered F e / C r have shown that the MR is larger when the interfaces are rougher [35]. It thus turns out that, for F e / C r , the spin-dependent scattering giving rise to the MR certainly takes place at the interfaces and is related to their roughness or microstructure. However, this has been shown only for F e / C r and, in systems such as C o / C u or Fe/Cu, the spin-dependent scattering centers have not been identified yet. We finally point out that AF exchange is not required absolutely to obtain a MR of the spin valve type. MR effects can be obtained in the uncoupled ..... ,,

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arrangement at low fields (the limit above 50 ~, in fig. 3). Otherwise AF arrangements at low field without AF exchange can also be obtained with specially designed structures [18-20]. 3. Interlayer exchange (i) Long-period oscillations havc bccn obscrvcd in F c / C r (= 20 ,~,), C o / C u (~- 12.5 ,~,), F c / C u ( = 12.5

J,) and for many systems. Up to now there is no dcfinitc result on the dependence of the oscillations on the crystal structure and the orientation of the crystal axes. Co(l l l ) / C u ( l l l ) [10] and Co(001)/Cu(001) [8] present approximately the same period (12.5 and 10.5 At but their oscillations have different phases. For F e / C u the oscillations are not very different for fcc and bcc Cu [14,15]. For Fe b c c / C u [15] and Co f c c / C u fcc [10], the period is the same (12.5 A) but the phases are opposite (fig. 4). In addition recent measurements [36-39] have revealed that the oscillations also depend on the interface roughness. For sharper interfaces, short-period oscillations are superimposed on the long-period ones (see notc added in proof). (ii) The amplitude of the oscillations decreases rapidly with the thickness of the non-magnetic layer, generally more rapidly than t-2 (see fig. 5). (iii) Accordingly to Parkin et al. [18], the amplitude of the interlayer exchange increases as one goes from 5d to 4d and 3d, and from the left to the right of the transition-metal series. As one goes further to the right, the exchange becomes definitely smaller for noble metals. This goes with the tendency to magnetism of the conduction band of the non-magnetic layer and is consistent with an indirect exchange mechanism. Examples: J - - 2 . 8 crg cm -2 for ( F e / C r 9 ,~) [23], J = - 0 . 2 4 crg cm -2 for ( C o / C u 9 ,~) [10], J = - 0 . 1 6 erg cm -2 for (Co/Ag 9 A) [17]. I J I is smaller for Ni [16] than for Fc or Co. Simple extensions of the RKKY theory predict that the interlayer exchange should vary with the spacer thickness t as cos(q0t + & ) / t 2 where q0 is related to the size of the Fermi surface (q = 2 k i: for free elcctrons) or to specific nesting properties (example: Y, Cr) [3]. For F e / C r , Co/Cu, F e / C u and most systems, this leads to short periods Ca few Ak However, it begins to be clear that, for the spccific geometry of a superlattice, realistic RKKY-like calculations can yield very different results. For F e / C r , Wang et al. [40] have shown that a RKKY-likc model based on a realistic band structure of Cr, assuming an s-d mixing interaction (more relevant than s- S) and taking into account the interface roughness, can account for the observed long period. Removing the roughness restores the short period related to the major nesting properties of the Cr Fermi surface. This is in agrecmcnt with the recent experimental results mentioned abovc [36-38] and shows the probable role of roughness as a filter favouring the long periods. Other recent models [32,41] have emphasizcd the role of the aliasing (or vernicr) effects and, more generally, have dcscribcd the selection rules giving the q-vcctor of the oscillations for each specific orientation of the crystal axes. The theoretical predictions about the influence of the orientation and the role of the roughncss have now to bc tcstcd on well characterized supcrlatticcs. We finally mention the second important theoretical approach based on ab initio

A. Fert et al. / Magm'tic multihtyers i O0

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4. Interpretation of the magnetoresistance

The G M R has been ascribed to spin-dependent scattering in the magnetic layers [6,26]. In ferromagnetic metals, if the temperature is relatively low with respect to the Curie temperature, the conduction electron spin is conserved for distances much longer than the momentum mean free path (MFP), so that the current is carried by spin-up and spin-down electrons in two independent channels. The often large difference between the spin-up ana spin-down scattering rates is due to the difference between the spin-up and spin-down densities of states at the Fermi level and also to the local spin structure of the scattering centers [44]. In multilayers, both the interface and "'bulk" scattcrings can be spin dependent. The mechanism of the GMR can bc dcscribcd in simple terms. When, for H > H~, the magnetic moments of all the layers are parallel, the scattering is weak in one of the spin channels and strong in the other. There is a short circuit by the weak scattering channel and the resistivity is low. In contrast, with an AF arrangement, the scattering is alternately weak and strong in each channel and the resistivity is higher. This scheme holds when the MFP is much largcr than the thickness. If the MFP/thickncss ratio dccreascs below one thcrc is a dccoupling of the scattcrings in successive layers and the GMR progressively vanishcs. There are two types of theoretical model for the GMR. The scmiclassical approach was first dcvclopcd by Camlcy and Barnas [26]. Thc bulk and interface scattcring arc expressed phcnomcnologically by introducing spin-dependent MFP and boundary conditions with spin-dependent transmission coefficients. Numerical treatments have been worked out by Camley and Barnas [26], and Trigui ct al. [27]. Approximate analytical expressions have been derived by Barthelemy and Fcrt [30] and by Mosca et al. [31]. The calculations of Mathon et ai. [32] and Inoue ct al. [33] arc also based on a scmiclassical approach. However, they arc restricted to the limit of thickness much shorter than the MFP and, consequently, they cannot describe thc progrcssivc decoupling of the scattering in different layers that gives rise to the thickness dependence (rcf. [33] is rather focussed on the microscopic mechanisms). The quantum model of Levy et ai. [28,29] introduces spin-dependent scattering potentials to express the interface and bulk scattcrings. The model treats the scattering of electron wave packets by the resulting non-homogeneous distribution of scattering centers. The MR is expressed as a fimction of the interface roughness and impurity concentrations. Both types of models have been applied to the case of C o / C u [29,31] and the respective fits are shown in

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Cu. Symbols: experimental data of Mosca et al. [10] (at 4.2 K): Solid lines, semiclassical model [31]; Dashed lines: quantum model of Zhang and Lew [29]. fig. 6. The MR at the first peak (strong coupling limit, see section 2), is related to the full difference between the resistivities of the AF and F arrangements, MR = (PAv--Pv)/PF. In the uncoupled limit at large Cu thickness, the low-field resistivity is that of a multilaycr with a random arrangement of the magnetic moments. According to :he calculations of Zhang and Lcvy [29], this reduces the MR by a factor of around I).6 with respect to the case of the AF ariangcmcnt. The same reduction factor has also bccn introduced in the semiclassical calculation of Mosca ct al. [31]. In fig. 6 wc show the curves calculated for the strong coupling and uncoupled limits in the scmiclassical (solid lines, rcf. [31]) and quantum (dashed lines, rcf. [29]) models. The parameters of the fits have bccn chooscr~ to obtain the MR at the first peak on the strong coupling curves and the MR at large thickness tending to the uncoupled limit curves. Both models are able to account correctly for the dccreasc of the M R as the Cu thickness increases. The more realistic character of the quantum model appears when the quantitative aspects are considcrcd. The quantum model is able to account with the same parameters for the MR ratio and the absolute values of the rcsistivities [29]. In contrast, in thc scmiclassical model, fitting the MR leads to absolute values of the resistivity that are too small by a factor of six [31]. This is probably related to the drawbacks of the semiclassical approach that have already bccn emphasized by Tesanovic ct al. [45]. Finally, for the temperature dependence ol the MR, wc rclcr to rcI. L341. 5. Conclusions

There is currently an intensive research on the interlayer exchange and magnctorcsistancc properties of the magnetic multilaycrs. The experimental results on the interlayer show that the RKKY problem is less simple than usually admitted and rcvcal exciting new aspects. It is now necessary to test the recently dcvcl-

1716

A. Fert et al. / Magnetic multilayer~

opcd models by comparing the oscillations for diffcrcnt directions of growth and also by separating the intrinsic effects of perfcct supcrlatticcs from what is due to impcrfcct intcrfaccs. The giant magnctorcsistancc begins to bc fairly well understood. Howcvcr, a bcttcr understanding of the scattering mechanisms at the microscopic scale (interfaces, impurities) would be very useful for a better control of the magnetoresistance. An extension to various m ultilaycred structures containing soft ferromagnet layers is also necessary if one looks for applications to magnetic recording technology.

Acknowledgements

This work was partially supportcd by the Science Program fo the European Economic Community (Contract SCI-0387-CTT of the GP2M3 Consortium). Note added in proof

Short-period oscillations supcrimposed to long ones havc now bccn observed in F c / C r [36-38], F c / A u by Griinbcrg ct al. [46], C o / C u and F e / C u by J o h n s o n ct

al. [47].

References [!] R.W. Erwiv, J.J. Rhyne, M.B. Salamon, J. Borchers, S. Sinha, J.E. Cunningham and C.P. Flyn, Phys. Rev. B 35 (1987) 680',4. [2] C.F. Majkrzak, D. Gibbs, P. B6ni, A.I. Goldman, J. Kwo, M. Hong, T.C. Hsieh, R.M. Fleming, D.B. McWhan, Y. Yafet, J W. Cable, J. Bohr, H. Grimm and C.L. Chien, J. Appl. Phys. 63 (19881 3447. [3] Y. Yaf't, J. Appl. Phys. 61 (19871 4(158; Phys. Rev. B 36 ( 19871 3948. [4] J. Grimberg, R. Schreibcr, Y. Pang, IVI.B. Brodsky and II. Sowers, Phys. Rev. Lett. 57 (1986) 2442. [5] C. Carbone and S.F. Alvarado, Phys. Rev. B 36 (19871 2433. [6] M N. Baibich, J.M. Broto, A. Fert, F. Nguyen Van Dau, F Petroff, P. Etienne, G. Creuzet, A. Friederich and J. Chazelas, Phys. Rev. Lett. 61 (19881 2472. [7] S.S.P. Parkin, N. More and K.P. Roche, Phys. Rev. Lett. 64 (1990) 2304. [81 A. Cebollada, J.L Martinez, J.M. Gallego, J.J. de Miguel, R. Miranda, S. Ferrer, F. Batallan, G. Fillion and J.P. Rebouillat, Phys. Rev B 39 (19891 9726. A. Cebollada et al, preprint. [91 D. Pescia, D. Kerkmann, F. Shumann and W. Gudat, Z. Phys. B 78 (19~;~1}475. [lii] D.tI. Mosca, F. Pctroff, A. Fert, P.A. Schroeder, W.P. Pratt and R. Loloee, J. Magn. Magn. Mater. 94 (1991) LI. [11] S.S.P. Parkin, R. Bhadra and K.P. R~:.che, Phys. Rev. Lett. 6 (1991) 2152. [~21 S.S.P. Parkin, MRS Spring Meeting (19911. [131 M.E. Brubaker, J.E. Mattson, C.It. Sowers and S.D. Bader, prcprint. [za] W.R. Bennet, W. Schwarzacher and W.F. Egelhoff Jr, Phys. Rcv. Lett. 65 (19901 3169. B. lteinrich, Z. Celinski, J.F. Cochran, W.B. Mair, A.S. Arrot and K. Myrtle, Phys. Rev. Lett. 64 (199(I) 673.

[15] F. Petroff, A. Barth61t~my, D,H. Mosca, D.K. Lottis, A. Feet, P.A. Schroeder, W.P. Pratt, R. Loioee and S, Lequien, Phys. Rev. B 44 (19911 5355. [16] C.A. dos Santos and B. Rodmaq, to be published. [17] S. Araki, K, Yasui and Y. Narumiya, preprint. [18] C. Dupas, J. Appl. Phys. 67 (19901 5680. [19] B. Dieny, V.S. Speriosu, S.S.P. Parkin and B.A. Gurney, Phys. Rev. B 43 (19911 1297. [20] T. Shinjo and H. Yamamoto, J. Phys. Soc. Japan 59 (19911) 3061. [21] G. Binash, P. Griinberg, F. Saurenbach and W. Zinn, Phys. Rev. B 39 (1989) 4828. N. Hosoito, S. Araki, K. Mibu and T. Shinjo, J. Phys. Soc. Japan 59 (19901 1925. [22] W.P. Pratt, S.F. Lee, J.M. Slaughter, R. Loloee, P.A. Schroeder and J. Bass, Phys. Rev. Lett. 66 (19911 3060. [23] A. Barthelemy, A. Fert, M.N. Baibich, F. Petroff, P. Etienne, R, Cabanel and S. Lequien, J. Appl. Phys. 67 (1990) 5908. [24] P. Griinberg, J. Barnas and F. Saurenbach, J. Magn. Magn. Mater. 93 (1991) 58. [25] F. Petroff et al., to be published, S.S.P. Parkin and R. Mauri, preprint. [26] R.E. Camley and J. Barnas, Phys. Rev. Lett. 63 (19891 664. [27] F. Trigui, E. Velu and C. Dupas, J. Magn. Magn. Mater. 93 (19911 421. [28] P.M. Levy, S. Zhang and A. Fert, Phys. Rev. Lett. 65 (1990) 1643. [29] S. Zhang and P.M. Levy, to be published. [311] A. Barthelemy and A. Feet, Phys. Rev. B 43 (19911 13124. [31] D.H. Mosca, D.K. Lottis, P.A. Schroeder and A. Fert, to be published. [32] J. Mathon, D.M. Edwards, R.B. Muniz and M.S. Phan. J. Magn. Magn. Mater. 104-108 (19921 paper 3354A. [33] J. Inoue, A. Oguri and S. Maekawa, preprint. [34] F. Pctroff, A. Barthdlemy. A. Fert, P. Etienne and S. Lequienn, J. Magn. ?£agn. Mater. 93 (19911 95. [35] E.E. Fullerton, D.M. Kelly, Y.K. Schuller and Y. Bl'yunseraede, preprint. [36] S. Demokritov, J.A. Wolf and P. Grfinberg, preprint. [37] S.T. Purcell, W. Folkerts, M.T. Johnson, N.W.E. McGee, W.B. Zepen and W. Hoving, preprint. [38] J. Ungaris, R.J. Celotta and D.T. Pierce, Phys. Rev. Lett. 67 (19911 140. [39] B. Heinrich, private communication. [40] Y. Wang, P.M. Levy and J.L. Fry,, Phys. Rev. Lett. 65 ( 19901 2732. [41] Co Chappert and J.P. Renard, Europhys. l_,ett. 15 (19911 553. P. Bruno, C. Chappert, preprint. R. Coehoorn, preprint. [42] P.M. Lex'y, K. Ounadjela, Y. Wang and C.B. Sommers, J. Appl. Phys. 67 (19901 5914. K. Ounadjela, C.B. Sommers, A, Fert, D. Stoeffler. F. Gautier and V.L. Moruggi, Europhys. Left. 15 (1991) 875. [43] D. Stoeffer and F. Gautier, Prog. Theor. Phys. Suppl. 101 (1990) 134. [44] A. Fert and I.A. Campbell, J. Phys. F 6 (1976) 849. I.A. Campbell and A. Fert, Ferromagnetic Materials, ed. E.P. Wohlfarth (North-Holland, Amsterdam, 1982)p. 769. [45] Z. Tesanovic, M. Jaric and S. Maekawa, Phys. Rev. Lett. 57 (1986) 276{). [46] P. Griinberg, J. Magn. Magn. Mater. 104-107 (1992) 1734. [47] M. Johnson et al., private communication.