We have observed two forms of scaling in magnetotransport properties of (111) Co/Cu superlattices: (1) the extraoridnary Hall coefficient Rs correlates with the resistivity xx(0) in the form Rsxx2(0), and (2) the magnetothermopower S(H) correlates with the magnetoresistivity xx(H) in the form S(H)/Txx(0)/xx(H). The first effect relates to quantum mechanical side jump while the other relates to interfacial spin-dependent density of states (DOS). These results revel the different roles of bulklike spin-dependent scattering in Co layers and spin-dependent DOS of interfacial layers in causing the observed large positive extraodinary Hall effect and giant longitudinal magnetotransport

Barlett, D.

Chen, B.

Clarke, R.

Tsui, F.

Uher, C.

Carolina Digital Repository

VOLUME 72, NUMBER 5 PHYSICAL REVIEW LETTERS 31 JANUARY 1994Scaling Behavior of Giant Magnetotransport Elfects in ColCu SnperlatticesF. Tsui, Baoxing Chen, D. Barlett, Roy Clarke, and C. UherDepartment of Physics, University of Michigan, 500 East University Street, Ann Arbor, Michigan 48109(Received 29 October 1993)We have observed two forms of scaling in magnetotransport properties of (111) Co/Cu superlattices:(I) the extraordinary Hall coeflicient R, correlates with the resistivity p,„(0) in the form R, -p „(0),and (2) the magnetotbermopower S(H) correlates with the magnetoresistivity p„(H) in the formS(H)/T —p»(0)/p„(H). The first effect relates to quantum mechanical side jump while the other re-lates to interfacial spin-dependent density of states (DOS). These results reveal the different roles ofbulklike spin-dependent scattering in Co layers and spin-dependent DOS of interfacial layers in causingthe observed large positive extraordinary Hall eff'ect and giant longitudinal magnetotransport.PACS numbers: 73.50.3t, 75.50.Rr, 75.70.CnThe discovery of high field giant magnetoresistance(GMR) effects in Co-based superlattices grown bymolecular beam epitaxy (MBE) techniques [1-3] sug-gests that the observed effects do not depend on the dom-inant spins in these materials since they occur at fieldswell in excess of the saturation of the Co magnetization.The result questions the generality of the conventionalspin-dependent scattering mechanisms based on antifer-romagnetic coupling of the neighboring magnetic layers[4,5]. Recent publications further demonstrate the im-portant role of interfacial magnetic states in determiningthe overall spin-dependent scattering in multilayers [6,7].Polarized states of noble metal interlayers have also beenobserved [8,9]. Taken together, these findings call for acareful examination of all of the magnetotransport prop-erties so that the effects of density of states, of spin-orbitcoupling, and of spin-dependent scattering potentials canbe assessed. In this paper we report scaling behavior inmagnetotransport properties of (111)Co/Cu superlatticesthrough a comprehensive study of the Hall effect and themagnetothermopower in addition to the magnetoresistivi-ty. This has made it possible to identify the specificspin-dependent processes in these materials from existingmodel predictions.The superlattices were prepared using MBE techniquesstarting from 500 A of (110) Ge buffer, then bcc (110)Co and (111) Au, grown on (110) GaAs substrates.Samples studied here each contain typically 30 bilayers of15 A Co layer and Cu spacer layer between 6 and 20 Athick. The growth methods and the high quality of theresulting crystals, particularly the smooth and abrupt na-ture of the interfaces, are documented elsewhere [2]. Inparticular, the crystal coherence length of the superlat-tice, measured by reflection high energy electron dif-fraction, cross-sectional high-resolution transmission elec-tron microscopy, x-ray diA'raction, and spin-echo NMRexperiments, is & 200 A [2]. Samples were further pro-cessed for transport measurements using conventionallithography techniques including inert Ar ion etching.Bridge shaped patterns with 0.5 mm wide current chan-nels and 0.2 mm wide voltage terminals were made forstandard dc four-terminal measurements. Care was tak-en to avoid contamination during post-growth procedures.Thermopower measurements were performed using cali-brated fine Cu wires as electrodes, and constantan-chromel differential thermocouples. The temperaturedifference was maintained at about 1 K by a resistiveheater attached to one end of the —10 mm long and -3mm wide GaAs substrate, with the other end thermallyanchored to the Cu block of the cryostat using Stycastadhesive. Experimental details will be provided in a morecomplete publication.We measured the resistivity p„„, the Hall resistivityp„~, and the thermopower S with field applied along the[111] growth direction [10]. Large magnetotransporteffects were observed, and their qualitative behaviors donot vary from sample to sample. Typical field depen-dences at 161 K are shown in Fig. 1 for a (Co~5'/Cusp)M superlattice and they are compared with themeasured magnetization [Fig. 1(b)].The Hall resistivity p,y shown in Fig. 1(a) strictly fol-lows the phenomenological form [11]pzy=ROH+ R&4xMco ~where the first term is the ordinary Hall effect and thesecond is the extraordinary Hall effect which is propor-tional to the Co magnetization Mc, . In contrast, the lon-gitudinal transport properties shown in Figs. 1(c) and1(d) exhibit a very different field dependence including amarkedly gradual saturation at high fields. Figure 1 es-tablishes unequivocally that, while the Hall effect de-pends on the Co magnetization, the MR ratio [hp„„/p„„(0)],and the magnetothermopower [KS/S(0)] do not[12]. This leads to the conclusion that the Co magnetiza-tion cannot be the only field dependent state variable inthis superlattice system. %e note in particular that themagnetization of the superlattices is ferromagnetic incharacter so that the saturation behavior merely reAectsthe domain rotation in the bulk of the sample due to mag-netic anisotropy. Therefore, the scattering processes thatgive rise to the observed extraordinary Hall effect [Fig.l(a)] must occur within each Co layer and the observedgiant longitudinal magnetotransport effects [Figs. 1(c)and 1(d)] must arise from the scattering at the interfaces740 0031-9007/94/72(5)/740(4) $06.001994 The American Physical SocietyVOLUME 72, NUMBER 5 PHYSICAL REVIEW LETTERS 31 JANUARY 199440o 20IClO0-201.So1.0o.so.o '25H (kG)47TM R~ I ~I ~IPI ~IIIIM'(b)50 0(c) aeC)—5XXQ.—10 ~"O1025 50H (kG)C)(I)M0 OO~0~-~ ~ ~30-C)x 2040201O ~XXQ.X8 Q.OI12IOI10- 2FIG. 1. Field dependence of (a) Hall resistivity, (b) magne-tization, (c) magnetoresistivity, and (d) magnetothermopowerfor (Co~st/Cusp)30 at 161 K. Field was along the [111]growthdirection. The vertical dashed line indicates the perpendicularsaturation field of the Co layers. The linear portion of the Hallresistivity at high fields corresponds to the ordinary Hall eA'ect,and the low field magnetization-dependent behavior is the ex-traordinary Hall elect (a). The extraordinary Hall coefficientR, is obtained by extrapolating the high field linear behavior tozero field, as indicated by the dashed line in (a). Magnetizationwas measured separately using a commercial SQUID magne-tometer.C) —10100 2000300FIG. 2. Temperature dependences of (a) zero field resistivityin units of pAcm and magnetoresistivity at 5.7 T transversefield in %, (b) ordinary and extraordinary Hall coefficient inunits of IO " m3/C, and (c) zero field thermopower and mag-netothermopower at 5.7 T transverse field in units of pV/K for(CO15 x/C us x )30.where the spin states are not those of the ferromagneticCo. Any mechanism that describes the spin-dependentscattering processes in this system must include the spinstates of the interfaces.The presence of strong interfacial scattering is mademore evident by the temperature dependence of the resis-tivity p„(0) [Fig. 2(a)]. p„(0) of the superlattice ismore than twice the value of either Co or Cu at high tem-peratures where phonon scattering usually dominates theelectron relaxation. In the presence of relatively longstructural coherence length (& 200 A) [2] only interfa-cial scattering can put such a low limit on the electronmean free path, because diffusive scattering [13] from theinterfacial magnetic states reduces the overall mean freepath of the superlattice from those of the pure materials.This is completely consistent with the observed low resid-ual resistance ratio (-2), as shown in Fig. 2(a).The temperature dependences of the Hall coefficientsand thermopower are also sho~n in Fig. 2. Unlike theresistivity, they are more sensitive to the density of statesof the superlattice. Since pure Co possesses large densityof states at the Fermi level relative to those of the Cu[11] and of the interface [9], one would expect that thesebulk-sensitive eA'ects are Co-like. This is confirmed bythe measurements which show that both the ordinaryHall coefficient Ro [Fig. 2(b)] and the thermopower ofthe superlattice [Fig. 2(c)] are very close to the values ofbulk Co.The connection between the bulklike scattering, whichdepends on Co magnetization Mg„and the interfacialscattering is demonstrated by the strong correlation ex-hibited by the extraordinary Hall coefficient R, [Fig.2(b)] and resistivity p„(0) [Fig. 2(a)]. Experimentaland theoretical work establishes that this type of correla-tion depends on the specific electron scattering processesthrough spin-orbit interactions [14]. When the electronrelaxation is weak, plane wave states are present, and theclassical asymmetrical scattering is dominant, hence alinear correlation. On the other hand, when relaxation isstrong, the quantum mechanical side jump takes place forthe individual conduction electron wave packets and, inthis case a quadratic scaling is predicted, R, -gyp„(0)[14]. hy here is the transverse displacement of the other-wise linearly propagating wave packet. In the case ofCo/Cu superlattices studied here, with the short meanfree path resulting from strong interfacial scattering,plane wave states are suppressed and side jump mustdominate the bulk scattering even at low temperatures.This is observed experimentally (Fig. 3). All samplesstudied here, with the combined R, values varying overtwo decades, exhibit the same power Iaw behavior fortemperatures & 2 K. This result confirms that the elec-tron scattering in the bulk of the superlattice is dominat-ed by the quantum mechanical side jump. We note inpassing that the observation of this universal exponent isquite rare in superlattices, and generally much larger orsmaller exponents have been reported [1,15,16]. Such anagreement with existing theory is consistent with the highstructural quality and uniformity of the superlatticesstudied here.Can the side jump cause the observed GMR since itslow field MR is ——byHMc, [14]? The answer is no,simply because the hy inferred from our measurements isVOLUME 72, NUMBER 5 PHYSICAL REVIEW LETTERS 31 JANUARY 19940.09CL 3C23CV0.08iil o 78K113 K161 K«(» „„(o))FIG. 3. Scaling behavior between extraordinary Hall coeffi-cient and resistivity for (Coisx/Cus)t)3Q. The slope of the log-log plot is 2 indicating the relation R, -p„,(0).at least 10 times too small.While the MR shows no apparent dependence on theCo magnetization it does exhibit scaling with the thermo-power at temperatures where diffusion thermopower isdominant (T & 50 K) [see Figs. 1(c) and 1(d), and Figs.2(a) and 2(c)]. The scaling is of the form [17]S(H )/T —p,„(0)/p„„(H), (2)as illustrated in Fig. 4 for (Co~st/Cuing)M at threedifferent temperatures. Scattering of conduction elec-trons due to the spin-dependent density of states of theunfilled d bands at the Fermi level leads to precisely thisform of scaling [17]. Note that this mechanism does notrequire the presence of strong spin-orbit interaction orspin-wave excitation [17,18].At a paramagnetic-ferromagnetic interface, MR due todifferences in the spin-dependent density of states, bysymmetry, should depend on the superposition of thequadratic terms of the two magnetizations, namely, theinterfacial magnetization M;(H) and Mc, (H). To thelowest order, the three possible terms are [M~(H)],[Mc,(H)], and [M;(H)Mc, (H)]. The lack of depen-dence on [Mc,(H)] is apparent from the above discus-sions, and a dependence on [M;(H)] must also be weakowing to the following observations: the anisotropy be-tween the longitudinal and transverse MR effects [Figs.5(a) and 5(b)] at low fields requires that, if MR dependson [M~(H)], M;(H) is comparable to that of a Co filmowing to shape demagnetizing anisotropy and this cer-tainly is not consistent with the observed small Cu polar-ization [9,19]. It is not difficult to show that in the limitof strong relaxation at the interfaces, i.e., when the meanfree path along the [111]direction is comparable to thelayer thickness, the MR ratio [Ap„„/p„„(0)]only dependson [M;(H)MC, (H)]. Since direct evidence of polarizedinterfacial Cu states and the associated interfacial spin-dependent density of states is now available [8,9], we canprobe the behavior of the interfacial magnetizationM;(H), particularly its field dependence, through the ob-served MR. By assuming a paramagnetic interface, wefit the measured MR to the product of measured Co mag-0.071.00 1.05» „„(o)/» „„(H)I1.10FIG. 4. Scaling behavior of magnetothermopower andmagnetoresistance at various temperatures and fields for(Cois x/Cuiox)so.netization and a Langevin function in place of M; [2], asillustrated in Fig. 5. The usual small positive MR contri-bution, which is quadratic in H [13], is also included inthe fit. The quality of the fit is excellent for both fielddirections.The size of the MR in this picture depends on thedifferences in the interfacial spin-dependent density ofstates at the Fermi level, rather than those of the conven-tional anti-aligned Co layers. The observed small differ-ences of interfacial spin-dependent density of states [9]would result in a somewhat smaller MR relative to thoseobserved in the antiferromagnetically coupled Co-basedmultilayers.In summary, we have investigated magnetotransportproperties of M BE grown (111) Co/Cu superlattices.The results reveal that the quantum mechanical sidejump in the bulk of the superlattice is responsible for theobserved large extraordinary Hall effect with the scalingR, -p„„(0)for temperatures & 2 K, and that the effectof spin-dependent density of states of the interfacial lay-ers causes the observed high field GMR and leads to theassociated scaling between MR and thermopower. Thelatter effect requires the polarization of the interfacialCu, and this has now been confirmed by recent spin0O —5XXQ.XX—10Q.25 50 0I25F'1Q. 5. lvlR at 50 K for sample (Cois»t/Cu6x)so (a) for fieldalong the current direction and (h) for field along the It t tlgrowth direction perpendicular to the current. Closed circlesare experimental points and lines are fits discussed in the text.742VOLUME 72, NUMBER 5 PHYSICAL REVIEW LETTERS 31 JANUARY 1994resolved photoemission experiments [9]. From a broaderperspective, GMR can arise from a variety of spin-dependent scattering mechanisms not only limited to anti-ferromagnetically coupled systems and granular films.All of the magnetotransport properties must be studiedon an equal footing both experimentally and theoreticallyso that a better understanding of the microscopic originsof GMR effects can be obtained.This work was supported by ONR Grant No.N00014-92-J-1335. F.T. thanks M. B. Salamon and J.Shi for discussions, and acknowledges Margaret and Her-man Sokol for fellowship support.[1] W. Vavra, C. H. Lee, F. J. Lamelas, H. He, R. Clarke,and C. Uher, Phys. Rev. B 42, 4889 (1990).[2] D. Barlett, F. Tsui, D. Glick, L. Lauhon, T. Mandrekar,C. Uher, and R. Clarke, Phys. Rev. B 49, 1521 (1994); D.Barlett, F. Tsui, L. Lauhon, T. Mandrekar, C. Uher, andR. Clarke, in Magnetic Ultrathin Films, edited by B. T.Jonker et al. , MRS Symposia Proceedings No. 313 (Ma-terials Research Society, Pittsburgh, PA, 1993), p. 35.[3] D. Greig, M. J. Hall, C. Hammond, B. J. Hickey, H. P.Ho, M. A. Howson, J. J. Walker, N. Wiser, and D. G.Wright, J. Magn. Magn. Mater. 110, L239 (1992); M. J.Hall, B. J. Hickey, M. A. Howson, M. J. Walker, J. Xu,D. Greig, and N. Wiser, J. Phys. Condens. Matter 4,L495 (1992).[4] P. M. Levy, S. Zhang, and A. Fert, Phys. Rev. Lett. 65,1643 (1990); Phys. Rev. B 45, 8689 (1992); S. Zhangand P. M. Levy, Phys. Rev. B 43, 11048 (1991).[5] Y. Wang, P. M. Levy, and J. L. Fry, Phys. Rev. Lett. 65,2732 (1990); D. M. Edwards, J. Mathon, R. B. Muniz,and M. S. Phan, ibid 67, 493 (.1991); P. Bruno and C.Chappert, ibid 67, 1602 (. 1991).[6] S. S. P. Parkin, Phys. Rev. Lett. 71, 1641 (1993).[7] F. Tsui, C. Uher, and C. P. Flynn (to be published).[8] S. Pizzini, C. Giogetti, A. Fontaine, E. Dartyge, G. Krill,J. F. Bobo, and M. Piecuch, in Magnetic Ultrathin Films(Ref. [2]), p. 625.[9] K. Garrison, Y. Chang, and P. D. Johnson, Phys. Rev.Lett. 71, 2801 (1993);C. Carbone, E. Vescovo, O. Rader,W. Gudat, and W. Eberhardt, ibid 71., 2805 (1993).[10] We have observed weak anisotropy in the high field mag-netotransport properties for fields applied along variousorientations with respect to the current. In MR the formof the anisotropy in high fields is -dcos28 about thecurrent direction with d about 1%. The twofold symme-try evidently arises from the effect of spin-orbit coupling[see B. E. Miller, E. Y. Chen, and E. D. Dahlberg, J.Appl. Phys. 73, 6384 (1993)].[11]C. M. Hurd, The Hall Egect in Metals and Alloys (Ple-num, New York, 1972).[12] The absence of correlation between the MR and the Comagnetization is even more evident for applied fields inthe growth plane, where the saturation field of the fer-romagnetic Co layers is at least 100 times smaller thanthat of the MR [2l.[13]J. M. Ziman, Electrons and Phonons (Oxford Univ.Press, Oxford, 1960), Chap. 11.[14] L. Berger, Phys. Rev. B 2, 4559 (1970).[15] P. Xiong, G. Xiao, J. Q. Wang, J. Q. Xiao, J. S. Jiang,and C. L. Chien, Phys. Rev. Lett. 69, 3220 (1992).[16] S. N. Song, C. Sellers, and J. B. Ketterson, Appl. Phys.Lett. 59, 479 (1991).[17] L. Xing, Y. C. Chang, M. B. Salamon, D. M. Frenkel, J.Shi, and J. P. Lu, Phys. Rev. B 4$, 6728 (1993);J. Shi, S.S. P. Parkin, L. Xing, and M. B. Salamon, J. Magn.Magn. Mater. 125, L251 (1993).[18] l. A. Cambell, A. Fert, and A. R. Pomeroy, Philos. Mag.15, 977 (1967); A. Fert, J. Phys. C 2, 1784 (1969); A.Fert and l. A. Cambell, J. Phys. F 6, 849 (1976).[19]The observed total moment for a 15 A thick Co layer iswithin 5% of the pure Co value. This sets an upper limitfor the interfacial magnetization of ( 1/5 of the Co mo-ment.743

Scaling behavior of giant magnetotransport effects in Co/Cu superlattices

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Scaling behavior of giant magnetotransport effects in Co/Cu superlattices

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