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Perpendicular magnetoresistance of magnetic multilayers: theory and experiments
Journal of Magnetism and Magnetic Materials 126 (1993) 454-456 North-Holland
Perpendicular magnetoresistance of magnetic multilayers: theory and experiments Gerrit E.W. Bauer ~, Martin A.M. Gijs b, Staszek K.J. L e n c z o w s k i c and J. Ben Giesbers " Faculty of Applied Physics and DIMES, Delft Unit,ersity of Technolo.gy, 2628 CJ Delft, The Netherlands Philips Research Laboratories, 5600 JA Eindho~,en, The Netherlands ' Department of Physics, Eindhocen Unit,ersity of Technology, 5600 MB Eindhocen, The Netherlands
A theory on the perpendicular magnetoresistance of antiferromagnetically coupled magnetic multilayers is discussed. which is based on the Landauer-Biittiker scattering formalism. New experimental results on the perpendicular magnetorcsistance of microstructured Fe/Cr magnetic multilayers are presented and compared with the theory. The 'giant magnetoresistance' (MR) or 'spin-valve' effect in antiferromagnetically coupled magnetic multilayers [1] has great potential for magnetic recording applications [2]. The effect is caused by the switching of the magnetizations of the magnetic layers by an applied magnetic field from an antiferromagnetic to a ferromagnetic configuration. The sample geometry for most electric transport experiments is chosen such that the current flows in the plane of the multilayer (the so-called CIP-geometry) [1-5]. The most complete theoretical description so far for this situation is the linear response (Kubo) formalism by Levy et al. [3,4]. The experimental results for the parallel configuration arc well described by this theory if a number of disposable parameters are introduced [5]. The configuration, where the current is perpendicular to the multilayer plane (the so-called CPP-geometry), has been under scrutiny since only recently [6-11]. For infinite superlattices Zhang et al. [6] predicted an increase of the spin-valve effect in the perpendicular as compared to the parallel geometry, which was subsequently verified by experiment [7,11]. Moreover, the perpendicular transport experiments through microstructured samples by Gijs et al. [11] in principle allow investigation of just a few numbers of layers, which cannot be treated by theory so far. The present paper addresses theory [9] and experiments [11] of the perpendicular transport in metallic magnetic multilayers. It is shown that the LandauerBiittiker (LB) scattering formalism [12], established mainly for the transport properties of semiconductor
Correspondence to: Gerrit E.W. Bauer, Faculty of Applied
Physics, Delft University of Technology, 2628 CJ Delft, The Netherlands. Fax: +31 15 612156; E-mail: bauerfa' duttnto.tn.tudelft.nl.
nanostructures [13], is well suited for this problem (see [14] for the CIP configuration) since finite size effects are included naturally and internal charge and magnetization redistributions are implicitly integrated out [15]. Spin-flip scattering processes arc not included, which limits the validity of the theory in its present form to the low temperature regime [10,11]. In addition we present first experimental results [11] on thc perpendicular giant magnetoresistance effect of pillar structures made from F c / C r multilayers using microlithographic technique. Our results arc interpreted by the new theory and compared with the experimental data for the current-in-plane configuration [5]. For low temperatures and a parabolic band model the Landaucr conductance formula for a non-magnetic multilayer consisting of N bilayer of equal thickness and in the perpendicular configuration can bc evaluated in a semiclassical approximation to be [9]
G~G~I"vl_ GGII ....
2N=N~/GGo .....
N(
in I + ~ V
(;,, j.
(1)
is the mean-free-number of traversed interfaces, (;~ is the intrinsic (Sharvin) conductance of a perfect pillar consisting of one metal of the multilayer only, and G ..... is the contact conductance of an ideal hereto-interface. The conductance of a non-magnetic multilayer (fig. 1) is determined by N and G~.,,,,. Note that the Drudc result, derived earlier in ref. [6], is approached rather slowly and only when the contact term can be disregarded. The relative magnetoconductance of an antiferromagnetically coupled magnetic multilaycr is defined by A G / G AF, where AG = G v - G AF and G v
0304-8853/93/$06.00 ~3 1993 - Elsevier Science Publishers B.V. (North-Holland)
455
G.E.W. Bauer et al. / Perpendicular magnetoresistance a r e straightforward generalizations of eq. (1) for the ferromagnetic and antiferromagnetic configuration of the magnetic layers, respectively. The mean number of traversed interfaces in the A F configuration / ~ A F is defined by 1 / / ~ AF= 1 / 2 ( 1 / N ~ + 1/ffI~) and GcAF = (;AF
min{Qro,, G~o.}. A description of the fabrication process of the pillar structure can be found in ref. [11]. Briefly, classical photolithography and reactive ion etching techniques are used to fabricate pillar structures in 100 x (3 nm Fe + tcr Cr) multilayers with tc,, the Cr thickness, as a variable. The F e / C r multilayers are deposited using dc sputtering for the Fe and rf sputtering tbr the Cr, followed by an in situ dc sputter deposition of a 0.3 ~ m thick Au layer. After covering with an insulating polyimid layer and structuring of Au contacts, a few hundred pillars with a cross section S ranging between 6 and 130 I~m 2 are obtained on one substrate. Pillar resistances (typically a few m O ) are measured using an ac bridge technique in the 4-300 K temperature range and in fields up to 1600 k A / m (2 T). The resistance of the multilayer is of the same order of magnitude as the extrinsic contact resistance, which is determined by comparing different multilayer thicknesses. Also the pillar height is relatively small compared to the width w, which gives rise to a non-uniform current distribution in the pillar. Q u o t e d M R values are extrapolations for w ~ 0 and typically are a
10 o
% '"",.L L . o 1 0 -~
CD
10.2 !
10-~
I I !1~11 I
10o
I
\ I I i l:lt
101
N/N Fig. 1. Conductance of a spin-less multilayer as a function of the contact conductance Gcon and the number of layers N relative to the mean free number F/. The dashed line is the Drude result [6].
40 E
E 8O
rr-
120
2
-I
0
1
2
B (T)
Fig. 2. Giant magnetoresistance effect of a microstructured pillar in a 100x(3 nm F e + l nm Cr) multilayer with the current perpendicular to the multilayer plane (CPP) and for different temperatures.
factor 1.1-1.2 higher than the directly measured value for the smallest pillar in each series. Fig. 2 shows C P P - M R curves at different temperatures for a pillar with a cross section S = 90 ~ m 2 structured in a 100 x (3 nm Fe + 1 nm Cr) multilayer. At 9.3 K we observe a M R effect of 108%, more than four times higher than the corresponding C I P - M R effect in unstructured films [5]. The saturation field B S (~-tz0H s) is defined by the crossing point of the low field resistance decrease with the horizontal line of constant resistance at higher fields. W e find that B s = 0.54 T. The rather high Bs-value is characteristic for the strong AF-coupling in the F e / C r system, which makes it very suitable for comparison with M R theories [5]. The M R effect is weakly temperature dependent below about T = 60 K (fig. 2); above that temperature the decrease with temperature is much stronger. At room temperature a 14% C P P - M R remains, two times larger than the corresponding CIP-MR. We now compare our low temperature M R with eq. (1), disregarding the effects of the intrinsic interface resistance which is estimated to be small for F e / C r [9]. For the sample of fig. 2 with /cr = 1 nm and a low temperature M R of 108%, we find that N t / N + = 6.4. This number reflects an 'effective' spin-dependent asymmetry of the mean free path, which is consistent with asymmetry coefficients found in CIP-experiments [5]. F r o m the resistances the electronic mean free paths are estimated to be 1 r = 1 ~ = 2 . 2 nm in the antiferromagnetic configuration and l t = 5.9 nm and 1 ~ = 1.1 nm in the ferromagnetic configuration. In conclusion, we present a theory of the low temperature magnetoconductance as well as experiments on the temperature dependence of the C P P - M R effect in F e / C r multilayers. By comparing experiments and
456
G.E.W. Bauer et al. / Perpendicular magnetoresistance
theory we have b e e n able to estimate the s p i n - d e p e n dence of the m e a n free p a t h s in a straightforward and t r a n s p a r a n t way. Acknowledgements: W e would like to t h a n k H.T. Munsters, H.C. Donkersloot, J.F.M. Janssen, M.M. den Dekker, H.M.M. B a k e r m a n s and O.J.A. Buyk for their contributions to the sample p r e p a r a t i o n , and A. Brataas, H.H.J.M. Janssen, R. C o e h o o r n , A. Fert, H. van H o u t e n , M.T. J o h n s o n , a n d W.J.M. de J o n g e for valuable discussions. This work is part of the research p r o g r a m m e of the " S t i c h t i n g voor F u n d a m e n t e e l Onderzoek d e r M a t e r i e ( F O M ) " , which is financially supp o r t e d by the " N e d e r l a n d s e O r g a n i s a t i e voor W e t e n schappelijk O n d e r z o e k ( N W O ) " .
References [1] 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 (1988) 2472; P.M. Levy, Science 256 (19921 972; L.M. Falicov, Physics Today, Oct. 1992, p. 46. [2] L.M. Falicov, D.T. Pierce, S.D. Bader, R. Gronsky, K.B.
Hathaway, H.J. Hopster, D.N. Lambeth, S.S.P. Parkin, G. Prinz, M. Salamon, 1.K. Schuller and R.H. Victoria, J. Material Res. 5 (1990) 1299. [3] P.M. Levy, S. Zhang and A. Fert, Phys. Rev. Lett. 65 (1990) 1643. [4] S. Zhang, P.M. Levy and A. Fert, Phys. Rev. B45 (1992) 8689. [5] M. Gijs and M. Okada, Phys. Rev. B46 (19921 29118. [6] S. Zhang and P.M. Levy, J. Appl. Phys. B69 (1991) 4786. [7] W.P. Pratt, S.-F. Lee, R. Loloee, P.A. Schroeder and J. Bass, Phys. Rev. Lett. 66 (1991) 3060. [8] M. Johnson, Phys. Rev. Lett. 67 (1991) 3594. [9] G.E.W. Bauer, Phys. Rev. Lett. 69 (1992) 1676; A. Brataas and G.E.W. Bauer, to be published. [10] T. Valet and A. Fert, unpublished; S.-F. Lee, W.P. Pratt Jr., Q. Yang, P. Holody, R. Loloee, P.A. Schroeder and J. Bass, J. Magn. Magn. Mater. 118 (1991) LI. [11] M.A.M. Gijs, S.K.J. Lenczowski and J.B. Giesbers, Phys. Rev. Lett. 7(I (1993) 3343. [12] M. Bfittiker, IBM J. Res. Dev. 32 (1988) 317. [13] C.W.J. Beenakker and H. van Houten, Solid State Physics 44 (1991) 1. [14] A. Oguri, Y. Asano and S. Maekawa, J. Phys. Soc. Japan 61 (1992) 2652. [15] H.U. Baranger and A.D. Stone, Phys. Rev. B89 (19891 8169.
Perpendicular magnetoresistance of magnetic multilayers: theory and experiments Gerrit E.W. Bauer ~, Martin A.M. Gijs b, Staszek K.J. L e n c z o w s k i c and J. Ben Giesbers " Faculty of Applied Physics and DIMES, Delft Unit,ersity of Technolo.gy, 2628 CJ Delft, The Netherlands Philips Research Laboratories, 5600 JA Eindho~,en, The Netherlands ' Department of Physics, Eindhocen Unit,ersity of Technology, 5600 MB Eindhocen, The Netherlands
A theory on the perpendicular magnetoresistance of antiferromagnetically coupled magnetic multilayers is discussed. which is based on the Landauer-Biittiker scattering formalism. New experimental results on the perpendicular magnetorcsistance of microstructured Fe/Cr magnetic multilayers are presented and compared with the theory. The 'giant magnetoresistance' (MR) or 'spin-valve' effect in antiferromagnetically coupled magnetic multilayers [1] has great potential for magnetic recording applications [2]. The effect is caused by the switching of the magnetizations of the magnetic layers by an applied magnetic field from an antiferromagnetic to a ferromagnetic configuration. The sample geometry for most electric transport experiments is chosen such that the current flows in the plane of the multilayer (the so-called CIP-geometry) [1-5]. The most complete theoretical description so far for this situation is the linear response (Kubo) formalism by Levy et al. [3,4]. The experimental results for the parallel configuration arc well described by this theory if a number of disposable parameters are introduced [5]. The configuration, where the current is perpendicular to the multilayer plane (the so-called CPP-geometry), has been under scrutiny since only recently [6-11]. For infinite superlattices Zhang et al. [6] predicted an increase of the spin-valve effect in the perpendicular as compared to the parallel geometry, which was subsequently verified by experiment [7,11]. Moreover, the perpendicular transport experiments through microstructured samples by Gijs et al. [11] in principle allow investigation of just a few numbers of layers, which cannot be treated by theory so far. The present paper addresses theory [9] and experiments [11] of the perpendicular transport in metallic magnetic multilayers. It is shown that the LandauerBiittiker (LB) scattering formalism [12], established mainly for the transport properties of semiconductor
Correspondence to: Gerrit E.W. Bauer, Faculty of Applied
Physics, Delft University of Technology, 2628 CJ Delft, The Netherlands. Fax: +31 15 612156; E-mail: bauerfa' duttnto.tn.tudelft.nl.
nanostructures [13], is well suited for this problem (see [14] for the CIP configuration) since finite size effects are included naturally and internal charge and magnetization redistributions are implicitly integrated out [15]. Spin-flip scattering processes arc not included, which limits the validity of the theory in its present form to the low temperature regime [10,11]. In addition we present first experimental results [11] on thc perpendicular giant magnetoresistance effect of pillar structures made from F c / C r multilayers using microlithographic technique. Our results arc interpreted by the new theory and compared with the experimental data for the current-in-plane configuration [5]. For low temperatures and a parabolic band model the Landaucr conductance formula for a non-magnetic multilayer consisting of N bilayer of equal thickness and in the perpendicular configuration can bc evaluated in a semiclassical approximation to be [9]
G~G~I"vl_ GGII ....
2N=N~/GGo .....
N(
in I + ~ V
(;,, j.
(1)
is the mean-free-number of traversed interfaces, (;~ is the intrinsic (Sharvin) conductance of a perfect pillar consisting of one metal of the multilayer only, and G ..... is the contact conductance of an ideal hereto-interface. The conductance of a non-magnetic multilayer (fig. 1) is determined by N and G~.,,,,. Note that the Drudc result, derived earlier in ref. [6], is approached rather slowly and only when the contact term can be disregarded. The relative magnetoconductance of an antiferromagnetically coupled magnetic multilaycr is defined by A G / G AF, where AG = G v - G AF and G v
0304-8853/93/$06.00 ~3 1993 - Elsevier Science Publishers B.V. (North-Holland)
455
G.E.W. Bauer et al. / Perpendicular magnetoresistance a r e straightforward generalizations of eq. (1) for the ferromagnetic and antiferromagnetic configuration of the magnetic layers, respectively. The mean number of traversed interfaces in the A F configuration / ~ A F is defined by 1 / / ~ AF= 1 / 2 ( 1 / N ~ + 1/ffI~) and GcAF = (;AF
min{Qro,, G~o.}. A description of the fabrication process of the pillar structure can be found in ref. [11]. Briefly, classical photolithography and reactive ion etching techniques are used to fabricate pillar structures in 100 x (3 nm Fe + tcr Cr) multilayers with tc,, the Cr thickness, as a variable. The F e / C r multilayers are deposited using dc sputtering for the Fe and rf sputtering tbr the Cr, followed by an in situ dc sputter deposition of a 0.3 ~ m thick Au layer. After covering with an insulating polyimid layer and structuring of Au contacts, a few hundred pillars with a cross section S ranging between 6 and 130 I~m 2 are obtained on one substrate. Pillar resistances (typically a few m O ) are measured using an ac bridge technique in the 4-300 K temperature range and in fields up to 1600 k A / m (2 T). The resistance of the multilayer is of the same order of magnitude as the extrinsic contact resistance, which is determined by comparing different multilayer thicknesses. Also the pillar height is relatively small compared to the width w, which gives rise to a non-uniform current distribution in the pillar. Q u o t e d M R values are extrapolations for w ~ 0 and typically are a
10 o
% '"",.L L . o 1 0 -~
CD
10.2 !
10-~
I I !1~11 I
10o
I
\ I I i l:lt
101
N/N Fig. 1. Conductance of a spin-less multilayer as a function of the contact conductance Gcon and the number of layers N relative to the mean free number F/. The dashed line is the Drude result [6].
40 E
E 8O
rr-
120
2
-I
0
1
2
B (T)
Fig. 2. Giant magnetoresistance effect of a microstructured pillar in a 100x(3 nm F e + l nm Cr) multilayer with the current perpendicular to the multilayer plane (CPP) and for different temperatures.
factor 1.1-1.2 higher than the directly measured value for the smallest pillar in each series. Fig. 2 shows C P P - M R curves at different temperatures for a pillar with a cross section S = 90 ~ m 2 structured in a 100 x (3 nm Fe + 1 nm Cr) multilayer. At 9.3 K we observe a M R effect of 108%, more than four times higher than the corresponding C I P - M R effect in unstructured films [5]. The saturation field B S (~-tz0H s) is defined by the crossing point of the low field resistance decrease with the horizontal line of constant resistance at higher fields. W e find that B s = 0.54 T. The rather high Bs-value is characteristic for the strong AF-coupling in the F e / C r system, which makes it very suitable for comparison with M R theories [5]. The M R effect is weakly temperature dependent below about T = 60 K (fig. 2); above that temperature the decrease with temperature is much stronger. At room temperature a 14% C P P - M R remains, two times larger than the corresponding CIP-MR. We now compare our low temperature M R with eq. (1), disregarding the effects of the intrinsic interface resistance which is estimated to be small for F e / C r [9]. For the sample of fig. 2 with /cr = 1 nm and a low temperature M R of 108%, we find that N t / N + = 6.4. This number reflects an 'effective' spin-dependent asymmetry of the mean free path, which is consistent with asymmetry coefficients found in CIP-experiments [5]. F r o m the resistances the electronic mean free paths are estimated to be 1 r = 1 ~ = 2 . 2 nm in the antiferromagnetic configuration and l t = 5.9 nm and 1 ~ = 1.1 nm in the ferromagnetic configuration. In conclusion, we present a theory of the low temperature magnetoconductance as well as experiments on the temperature dependence of the C P P - M R effect in F e / C r multilayers. By comparing experiments and
456
G.E.W. Bauer et al. / Perpendicular magnetoresistance
theory we have b e e n able to estimate the s p i n - d e p e n dence of the m e a n free p a t h s in a straightforward and t r a n s p a r a n t way. Acknowledgements: W e would like to t h a n k H.T. Munsters, H.C. Donkersloot, J.F.M. Janssen, M.M. den Dekker, H.M.M. B a k e r m a n s and O.J.A. Buyk for their contributions to the sample p r e p a r a t i o n , and A. Brataas, H.H.J.M. Janssen, R. C o e h o o r n , A. Fert, H. van H o u t e n , M.T. J o h n s o n , a n d W.J.M. de J o n g e for valuable discussions. This work is part of the research p r o g r a m m e of the " S t i c h t i n g voor F u n d a m e n t e e l Onderzoek d e r M a t e r i e ( F O M ) " , which is financially supp o r t e d by the " N e d e r l a n d s e O r g a n i s a t i e voor W e t e n schappelijk O n d e r z o e k ( N W O ) " .
References [1] 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 (1988) 2472; P.M. Levy, Science 256 (19921 972; L.M. Falicov, Physics Today, Oct. 1992, p. 46. [2] L.M. Falicov, D.T. Pierce, S.D. Bader, R. Gronsky, K.B.
Hathaway, H.J. Hopster, D.N. Lambeth, S.S.P. Parkin, G. Prinz, M. Salamon, 1.K. Schuller and R.H. Victoria, J. Material Res. 5 (1990) 1299. [3] P.M. Levy, S. Zhang and A. Fert, Phys. Rev. Lett. 65 (1990) 1643. [4] S. Zhang, P.M. Levy and A. Fert, Phys. Rev. B45 (1992) 8689. [5] M. Gijs and M. Okada, Phys. Rev. B46 (19921 29118. [6] S. Zhang and P.M. Levy, J. Appl. Phys. B69 (1991) 4786. [7] W.P. Pratt, S.-F. Lee, R. Loloee, P.A. Schroeder and J. Bass, Phys. Rev. Lett. 66 (1991) 3060. [8] M. Johnson, Phys. Rev. Lett. 67 (1991) 3594. [9] G.E.W. Bauer, Phys. Rev. Lett. 69 (1992) 1676; A. Brataas and G.E.W. Bauer, to be published. [10] T. Valet and A. Fert, unpublished; S.-F. Lee, W.P. Pratt Jr., Q. Yang, P. Holody, R. Loloee, P.A. Schroeder and J. Bass, J. Magn. Magn. Mater. 118 (1991) LI. [11] M.A.M. Gijs, S.K.J. Lenczowski and J.B. Giesbers, Phys. Rev. Lett. 7(I (1993) 3343. [12] M. Bfittiker, IBM J. Res. Dev. 32 (1988) 317. [13] C.W.J. Beenakker and H. van Houten, Solid State Physics 44 (1991) 1. [14] A. Oguri, Y. Asano and S. Maekawa, J. Phys. Soc. Japan 61 (1992) 2652. [15] H.U. Baranger and A.D. Stone, Phys. Rev. B89 (19891 8169.