Perpendicular giant magnetoresistance in magnetic multilayered nanowires

~

ELSEVIER

Journalof magnetism and magnetic materials

Journal of Magnetism and Magnetic Materials 159 (1996) L287-L292

Letter to the Editor

Perpendicular giant magnetoresistance in magnetic multilayered nanowires L. P i r a u x a S. D u b o i s a A. F e r t b,c,, a Unitg de Physico-Chimie et de Physique des Mat£riaux, UniversitC, Catholique de Loucain, B-1348 Louvain-la-Neuve, Belgium b Unit~ Mixte de Recherche du Centre National de la Recherche Scienti~que et de Thomson, Laboratoire Central de Recherches Thomson, 91404 Orsay, France c Unit'ersit~ Paris-Sud, Bat. 510, 91405 Orsay, France Received 4 April 1996

Abstract

We present giant magnetoresistance (GMR) measurements performed on electrodeposited Co/Cu multilayered nanowires. The variation of the GMR with the thicknesses of the Cu and Co layers over wide ranges is discussed in the framework of the Valet-Fert model for perpendicular GMR. The interface and bulk spin-dependent scattering parameters as well as the spin diffusion lengths in the nonmagnetic and ferromagnetic layers are extracted from this analysis. PACS: 72.15 Gd; 72.10 Fk; 75.50 Rr

Since the discovery of giant magnetoresistance (GMR) in antiferromagnetically coupled F e / C r in 1988 [1,2], a considerable number of experimental observations have been reported in various magnetic multilayers. Most data have been obtained with Current In the Plane of the layers (CIP), which is the most convenient geometry for experiments. Some measurements have also been done in the CPP (Current Perpendicular to the Planes) geometry, with conventional multilayers [3-10], and more recently with multilayered nanowires [11-13]. The physics of the CPP-GMR turns out to be essentially different from that of the CIP-GMR, with spin accumulation and relaxation effects coming into the game and

* Corresponding author. Fax: + 33-1-6933-0740.

playing an important role in the CPP geometry. The main consequence, as described by the Valet-Fert (VF) model [14,15] is that the scaling length of the CPP-GMR is the relatively long spin diffusion length (SDL) whereas the scaling length of the CIP problem is the much shorter electron mean free path. In most experimental results obtained up to now, the thicknesses of the nonmagnetic and magnetic layers, t N and t F respectively, are much shorter than the electron spin diffusion lengths l~ 1 and l~ ) and, in this limit, the CPP-GMR is expressed by very simple expressions that have been derived from a phenomenological approach [4,5] or, alternatively, can be demonstrated from the VF model. This simple behavior has been confirmed by extensive sets of experimental data obtained by the Michigan State University (MSU) group [4,5].

0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S 0 3 0 4 - 8 8 5 3 ( 9 6 ) 0 0 3 7 3 - 3

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L. Piraux et al. / Journal t~f Magnetism and Magnetic Materials 159 (1996) L287-L292

On the other hand, very few measurements have been performed out of the long SDL limit, especially in the opposite limit where the layers are much thicker than the SDL and the GMR is controlled by the spin relaxation processes [14,15]. As the SDL should generally exceed 100 nm in the usual metallic layers, this regime is expected for individual layer thicknesses approaching the Ixm range, a thickness range that has not been explored up to now. There do not exist measurements of the SDL in magnetic layers. Measurements of the SDL in non-magnetic layers have been performed by doping Cu or Ag layers with impurities having a strong spin-orbit interaction or paramagnetic impurities in order to shorten the spin diffusion length of the nonmagnetic metal in the nanometer range [10]. Recently, a value of 50 nm for Cu at 20 K has been obtained [12] in C o / C u multilayered nanowires (however, this value has been derived from measurements in a thickness range, below 70 rim, where the MR is still weakly affected by the SDL). In this article, we present measurements of the CPP-GMR in C o / C u multilayered nanowires electrodeposited in the pores of a polymer membrane. These multilayered nanowires are similar to those we have described in a previous publication [11] but we have now explored a very wide thickness range of the Cu and Co layers in order to study the CPP-GMR in both regimes, that is for layer thicknesses smaller and larger than the SDL (for both Cu and Co). In the long SDL regime, our results are in good agreement with the simple variation as a function of the thickness predicted by the theory and already found in many experiments by the MSU group. The n e w r e s u l t s are those obtained for Co (Cu) layers thicker than ~sf/(c°) (l~cu)). Our results in this regime are consistent with the predictions of the VF model and allow us to estimate the SDL in the Cu and Co layers. Electrodeposited C o / C u multilayered filaments were made from a single sulfate bath using a pulse deposition technique [16]. The multilayer sample shows an uniform cross section along the length of the filament and the dispersion in wire diameter is small (@ ~ 90 _+ 5 nm). Magnetoresistance (MR) measurements were performed using the method described elsewhere [11]. A typical example of an experimental curve obtained at T = 77 K for Co(4

nm)/Cu(10 nm) is shown in Fig. 1. The MR ratio amounts to about 47% (virgin state) and 42% (peak), which is very close to the values obtained for a sputtered Co(1.5 nm)/Cu(10 nm) multilayer [4] and confirms the quality of the electrodeposited samples. The difference we observe between virgin state and peak never exceeds ~ 10% of the total MR and has a negligible influence on the analysis of our results. We have used the values measured at the MR peak. We report and discuss data obtained on two series of samples: Co(8 nm and 25 nm)/Cu(10 n m < tcL, < 350 nm), that we call series 1, and Co(60 n m < tc, < 1 ;xm)/Cu(8 nm), that we call series 2. Magnetization measurements have also been performed to characterize the magnetic behavior. In series 1, the Co layers have the shape of discs (diameter = 90 nm, height = 8 or 25 nm) separated by thick Cu layers (10-350 nm). Throughout the series, the saturation field of the MR is smaller when the applied field is in the plane of the discs (in other words, the plane perpendicular to the wire axis is an easy plane) and all the results we present for series 1 have been obtained with this field orientation. EXAFS measurements on Co nanowires prepared in the same conditions have shown a preferential growth with c-axis perpendicular to the wires [17]. This suggests that the relatively high field of about 5 kG always required to saturate the MR is primarily the field needed to move the magnetization away from the local easy c-direction (approximately in the plane of the discs and pointing in random directions). We have also found that, throughout the series, the amplitude of the MR was practically the same in fields 5O 40

30 11

N

2o

~

10

0-8

T

-6

I

-4

-2

0

2

4

6

H (kOe) Fig. 1. Magnetoresistance vs applied field parallel to the Co layers at T = 77 K for Co(4 n m ) / C u ( 1 0 nm) multilayered nanowires.

L Piraux et al./Journal of Magnetism and Magnetic Materials 159 (1996) L287-L292

perpendicular and parallel to the wire, which shows that the contribution from anisotropic MR (AMR) is negligible. In series 2, a typical sample is composed of Co rods (diameter = 90 nm, lengths up to 1 Izm) separated by thin Cu layers (tcu = 8 nm << diameter of the rods). As expected from magnetostatic arguments, the saturation field is very large ( ~ 10 kG) when the field is applied in the plane perpendicular to the wire and the axis of the wire is now an easy axis. A detailed discussion will be presented in a further publication [18]. The MR measurements we report have been obtained with the field applied along the axis of the wire. MR measurements in pure Co nanowires have been used to determine the AMR effect and correct our results from its contribution. In previous studies, the experimental data and the theoretical prediction of the VF model were compared by plotting [(R AP - R P ) R A P ] 1/2 as a function of the number of bilayers for a constant total thickness [4,5]. We have found it more convenient to express the inverse of the square root of the magnetoresistance as a function of the thickness of the nonmagnetic layer. In the limit where t N, t v << ~sf I(N), l~ ), the MR is given by the following simple expression that is strictly equivalent to Eqs. (44)-(46) of Ref. [14], or to the similar equations used by the MSU group [4,5].

( AR~

,/2

PvtF +2rb

PNtN

I

-RZ-F]

/3P~ tv + 2yrb + /3pv tv + 2yrb

(l) This thickness dependence was first theoretically established in the simple case where R P and R AP represent the resistances of the parallel and antiparallel configurations. It has been later shown that the resistance R AP is the same for a strict antiparallel arrangement and when, less drastically, AP refers to a state with a zero magnetization for the set of magnetic layers included in a thickness range of the order of the SDL [15] i. Consequently, Eq. (1) holds

The equivalence of antiparallel and random configurations has also been demonstrated in Ref. [19] for the simple case of infinite spin diffusion length.

L289

also when the AP configuration is a random one. We use the same notations as in Ref. [14], i.e. p ¢(+)= 2p~ in Cu, p ~ + ) = 2 p ~ [ 1 - ( + ) f l ] in Co and p ~( ~ ~ = 2 r b [ 1 - ( + )y ] at the interfaces where /3 and 7 are the bulk and interfacial spin asymmetry coefficients, respectively. The resistivities p ~( + I in Cu and Co include a contribution from scattering at the surface of the wire in addition to that from scattering inside the wire. The proportion of the surface contribution is expected to depend on the diameter, that is to be small for Q ~ 90 nm, larger for smaller diameters. All our experiments have been performed with the same diameter, so that we can assume that the parameters PN, flF and /3 are the same for all the samples. Eq. (1) means that in the limit t N, t v << l~fN), I f ) and at constant thickness of the magnetic layers, (AR/RAP) - t/2 increases linearly with the thickness of the nonmagnetic layers. Such a linear variation is observed in our samples for t N (i.e. tcu) smaller than about 100 nm, as illustrated in Fig. 2 with data obtained at 77 K. Our results thus confirm the behavior systematically found by the MSU group in the long SDL limit [4,5]. The range of linear variation in Fig. 2, up to about 100 nm or a little more, indicates that l~cu) exceeds 100 nm at 77 K. For Cu layer thicknesses approaching 100 nm, the dipolar interactions between the Co discs turn out to be negligible, so that the magnetizations in successive discs along a current line should be randomly oriented at low field (MR peak). The continuation of the linear variation down to 10 nm suggests that, at the MR peak, throughout the series, there is the same sort of magnetic configuration with zero mean magnetization over the range of the SDL. As predicted from Eq. (1), the slope of this linear variation decreases as t v (i.e. tco) increases. In addition, for y >/3, the straight lines corresponding to different values of t v are expected to pass through a single point having t~ = [ 2 ( 3 , - / 3 ) r b ]//3p~ and /3- ~ for coordinates. On the contrary, for 7 / 3 and also allows us a direct determination of fl (/3 ~ 0.36). The determination of all the other parameters, PN, PF, Pb and Y involved in Eq. (1) can be achieved in the following way. First, we can deter-

L. Piraux et al. / Journal of Magnetism and Magnetic Materials 159 (1996) L287 L292

L290

10

, L i , , ~ i , , ~ i , , , i ~ , , i * ~ ~ l , , ~ I ,

l

8

fco = 8 n 6 4

2

t

20

40

60

Co

25

= 25 nm

80

100

120

140

160

tc. (nm) Fig. 2. Plot o f ( A R / R Ap)- i/2 vs tc. at T= 77 K for two series of Co/Cu multilatered nanowires with different Co layer thicknesses too. as indicated. Corresponding MR values (in percent) are also given on the right-hand side scale. (We had already found the same value o f / 3 from the intercept of the two lines in Fig. 2.) Out of the long SDL limit, deviations from the linear variation of Eq. (1) are expected by the VF model [14], with, for t N > > / ~ ), an exponential decrease of the GMR ratio as e x p [ - - t N / l ~ ) ] . The expected change in the plot of (A R / R AP) t/2 vs t N appears clearly in Fig. 3 where we have plotted our experimental results over a larger thickness range of tcu than in Fig. 2. The solid line in Fig. 3 has been calculated from the general expression of the G M R in the VF model [14] with the values of Pcu, Pco, rco/Cu, /3, Y derived from the long SDL regime (see above) and l~cu) = 140 nm. We estimate the uncertainty on this value of l~cu) to _+ 15 rim. In Fig. 3, we also show

mine p~] (Pcu). For copper layers much thicker than the cobalt ones, say for tcu ~ 300 nm with t c o ~ 8 nm, the total measured resistance is almost completely due to copper. By measuring the resistance at two temperatures, say 77 K and 300 K, we derive [PCu(300 K ) ] / [ pcu(77 K)] ~ 1.47. On the other hand, we know that [ p~u(300 K) - pcu(77 K)] equals 1.45 × 10 -8 t i m so that we straightforwardly derive Pcu(300 K) = 4.55 × 10 -8 lqm and pcu(77 K) = 3.1 × 10 -8 O m . Then, by identifying the equations of the straight lines in Fig. 2 for two different thicknesses of Co with Eq. (1), we derive: Pco=(18_+2)×

10-8~m,

/3=0.36+0.04,

r c o / c u = (3 _+ 0.5) × 10-16 ~ m 2,

T = 0.85 _+ 0.1.

30

I

J

~

i

I

i

/e

25

/ I

~

-

/ ,~

c

20

0.25

..o i ~ a.t~e_...~ " ~ ' ' f °

5

T=77K 4

o 0

I 50

0

~

""

25 r 100

I 150

~ 200

I 250

P 300

350

tcu (nrn) Fig.

3. Plot

line

is calculated

of (A

R/R apl- ]/2 by

using

the

as a function full

of

expressions

tCu f o r C o ( 8 of the

VF

nm)/Cu(tcu) model

multilayered

(expressions

40-42

Corresponding MR values (in percent) are also given on the right-hand side scale.

nanowires of I14]).

at two The

different

dashed

line

temperatures. is a guide

tbr

The

solid

the

eyes.

L Pirauxet al./Journalof MagnetismandMagneticMaterials159(1996)L287-L292 our experimental data at room temperature. It turns out that the GMR is not strongly reduced as temperature increases, in agreement with previous experimental results of Gijs et al. [20] on Co/Cu. For a rigorous interpretation of the data at 300 K, it would be necessary to use the extension of the VF model taking into account the phonon and magnon scatterings that become important around and above room temperature [15]. This is not in the scope of this paper and will be presented elsewhere [18]. Now, we present our results for series 2, with tcu = 8 nm and tco varying between 60 and 950 nm. For tF>> Vsf t(F) with t s <
RP

/3 2/~fF)

(1 - / 3 2 ) t F '

(2)

where A R is the resistivity change between random and parallel configuration (in the limit we are considering, A R would be twice for a perfectly antiparallel configuration [21]). In Fig. 4, we have plotted RP/A R vs tco for series 2. The linear variation we find agrees with Eq. (2). This agreement probably indicates that all the samples of series 2 present a similar random magnetic arrangement at the MR peak (more precisely, the condition for Eq. (2) is that the relative orientation of the magnetizations at the two interfaces of Cu layers is randomly distributed [21]). At T--- 77 K, by introducing /3 = 0.36 in Eq. i

150

T=

i

i

295K~/U

L291

(2), we derive 1~sf( C o ) = 4 4 + 4 nm. At 300 K, the slope is approximately twice that at 77 K. This could be due to some shortening of t(co) -se at 300 K but also to some reduction of the spin asymmetry coefficient fl as the temperature increases. For a precise interpretation of the results at room temperature, it would be necessary to use the extension of the VF model taking into account phonon and magnon scattering [ 15] and, as stressed above, this is not in the scope of this paper. Nevertheless, we can state that our results at room temperature suggest that the SDL is more reduced by temperature effects in the cobalt than in the copper layers. In summary, we have measured the CPP-GMR of C o / C u multilayered nanowires with layer thicknesses varying between the nanometer and micrometer ranges. Our results in series 1 for Cu layers thinner than 100 nm and at T = 77 K confirm the simple variation as a function of the nonmagnetic thickness already found for the long SDL limit by the MSU group [5]. They can be accounted for with /3 ~ 0.36 _+ 0.04 and y ,-, 0.85 _+ 0.1 for the spin asymmetry coefficient in the Co layers and at the C o / C u interfaces. The deviation from linearity for thicker Cu layers can be accounted for by a SDL in Cu of about 140 nm. As a function of Co thickness, in series 2, we have been able to explore the variation of the CPP-GMR up to the micrometer range. A new result is the variation of GMR as l/tco out of the long SDL limit. Our results are consistent with the predictions of the VF model and allow an estimation of t%f(c°) ~ 44 nm. Our results at 300 K will be analysed using a further publication in a model taking into account phonons and magnons [18].

7////~ Acknowledgements = 77K

0

2;0

4;0

6()0

8(10

1000

tco ( n r n ) Fig. 4. Linear variation of the inverse magnetoresistancevs tco for Co(tco)/Cu(8 nm) multilayered nanowires at two different temperatures.

We thank J.M. Beuken, C. Marchal, L. Filipozzi and J.F. Despres for contributions in the experimental part of this work and Whatman s.a. (Belgium) for providing the polycarbonate membrane used in this study. Collaboration between PCPM and LPS is supported by the 'Human Capital and Mobility Network CHRX-CT93-0139'. L.P. is a Research Associate of the National Fund for Scientific Research (Belgium). The work performed in Louvain-la-Neuve was carried out under the financial support of the

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L. Piraux et al. / Journal of Magnetism and Magnetic Materials 159 (1996) L287-L292

programme 'Action de Recherche Concert6e' sponsored by the 'DGESR de la Communaut6 Fran~aise de Belgique'.

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[8] N.J. List, W.P. Pratt, M.A. Howson, J. Xu, M.J. Walker, B.J. Hickey and D. Greig, 1995 MRS Proceedings (in press). [9] W. Vavra, S.F. Cheng, A. Fink, J.J. Krebs, G.A. Prinz, Appl. Phys. Lett. 66 (1995) 2579. [10] Q. Yang, P. Holody, S.F. Lee, L.L. Henry, R. Loloee, P.A. Schroeder, W.P. Pratt, Jr., and J. Bass, Phys. Rev. Lett. 72 (1994) 3274. [11] L. Piraux, J.M. George, J.F. Despres, C. Leroy, E. Ferain, R. Legras, K. Ounadjela and A. Fert, Appl. Phys. Lett. 65 (1994) 2484. [12] B. Voegeli, A. Blondel, B. Doudin, J.Ph. Ansermet, J. Magn. Magn. Mater. 151 (1995) 388. [13] K. Liu, K. Nagodawithana, P.C. Searson and C.L. Chien, Phys. Rev. B 51 (1995) 7381. [14] T. Valet and A. Fert, Phys. Rev. B 48 (1993) 7099. [15] A. Fert, J.L. Duvail, T. Valet, Phys. Rev. B 52 (1995) 6513. [16] D. Tench and J. White, Metall. Trans. 15A (1984) 2039. [17] D. Chandesris and L. Piraux, to be published. [18] L. Piraux, J.M. Beuken, S. Dubois, C. Marchal, K. Ounadjela and A. Fert, in preparation. [19] S. Zhang and P.M. Levy, Phys. Rev. B 47 (1993) 6776. [20] M.A.M. Gijs, S.K.J. Lenczowski, J.B. Giesberg, R.J.M. Vandeveerdonck, M.T. Johnson and J.B.F. aan de Stegge, Mater. Sci. and Eng. B 31 (1995) 85. [21] A. Fert and T. Valet, in preparation.