pss basic solid state physics b status solidi www.pss-b.com physica REPRINT Electric transport perpendicular to the planes H. C. Herper 1, 2 1 Theoretische Tieftemperaturphysik, Universität Duisburg – Essen, Duisburg Campus, 47048 Duisburg, Germany 2 Center for Computational Materials Science, TU Vienna, 1060 Vienna, Austria Received 8 March 2006, revised 15 May 2006, accepted 11 July 2006 Published online 23 August 2006 PACS 71.15.– m, 75.47.De, 75.70.Cn Since the discovery of the giant magnetoresistance (GMR) in magnetic multilayers, several theoretical de- scriptions have been used to determine the resistivity of such layered structures. The resistance for the current in direction of the planes of layers can easily be measured, and has been intensively studied theo- retically. However, the investigation of the GMR for the current perpendicular to the planes (CPP) is slightly more difficult. Here, a microscopic formalism for the study of the CPP GMR is reported by mak- ing use of the Kubo – Greenwood equation. Within this method perturbations of the interfaces like inter- diffusion, alloy formation, or impurities can easily be included, which is of importance, because the dis- cussion of the GMR is always related to the structure of the interfaces. The presentation of the Kubo – Greenwood formalism for CPP transport is complemented by a brief discussion of some exemplary results. phys. stat. sol. (b) 243, No. 11, 2632 – 2642 (2006) / DOI 10.1002/pssb.200642107
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Electric transport perpendicular to the planes
H. C. Herper1, 2
1
Theoretische Tieftemperaturphysik, Universität Duisburg–Essen, Duisburg Campus,
47048 Duisburg, Germany
2
Center for Computational Materials Science, TU Vienna, 1060 Vienna, Austria
Received 8 March 2006, revised 15 May 2006, accepted 11 July 2006
Published online 23 August 2006
PACS 71.15.–m, 75.47.De, 75.70.Cn
Since the discovery of the giant magnetoresistance (GMR) in magnetic multilayers, several theoretical de-
scriptions have been used to determine the resistivity of such layered structures. The resistance for the
current in direction of the planes of layers can easily be measured, and has been intensively studied theo-
retically. However, the investigation of the GMR for the current perpendicular to the planes (CPP) is
slightly more difficult. Here, a microscopic formalism for the study of the CPP GMR is reported by mak-
ing use of the Kubo–Greenwood equation. Within this method perturbations of the interfaces like inter-
diffusion, alloy formation, or impurities can easily be included, which is of importance, because the dis-
cussion of the GMR is always related to the structure of the interfaces. The presentation of the Kubo–
Greenwood formalism for CPP transport is complemented by a brief discussion of some exemplary results.
fore in a good agreement with the experimental findings, which allows the conclusion that the small
GMR of Fe/Si multi- or trilayers is related to the formation of Fe/Si alloys at the interfaces.
The GMR obtained from Eqs. (25) and (27) only provides information for the whole trilayer. In order
to check which layers or parts contribute mostly to the GMR, it is helpful to use sheet resistance frac-
tions. These fractions can be obtained from Eq. (28) by investigating the differences of the layer-resolved
sheet resistances. Therefore, the system is split into characteristic regions s: The leads (region I and V),
the spacer (III), and the interfaces (II and IV). The sheet resistance fraction is then defined by
tot
1
( (AF, ) (FM, ) )( )
, .( )
(AF, ) (FM, )
s s
ss
n
p p
p
r n r n
r n
s n
r n
r n r n
=
-D
= <D
-
Â
 (29)
A typical example is shown in Fig. 6 for the case of 12 6 12
Fe Si Fe/ / . It turns out that the main contribution
of the sheet resistance fraction, and therefore of the GMR, stems from the interfaces. Even for c = 0 there
still exists a reasonably large contribution (20%) from the spacer. With increasing interdiffusion, the
latter becomes smaller and vanishes for c = 0.2. The contributions from the leads are negligible.
5 Summary
In this work I have shown that the GMR values for CPP geometry can reliably be calculated using the
Kubo–Greenwood formalism instead of the Landauer–Büttiker method. Although we use equilibrium
Green’s functions and steady state conditions, we expect that aspects of charge accumulation are mini-
mized by allowing for smooth transition from the spacer layer region to the lead (bulk) region. The width
of the transition region, in which changes of magnetization are taken into account by electronic structure
calculations, may be considered as an additional parameter. A condition for the number of layers belong-
ing to this region is the dependence of the sheet resistance on the number of buffer layers. For a suffi-
ciently large transition region the sheet resistance becomes constant.
Acknowledgment This work has been partially funded by the RT-Network Computational Magnetoelectronics and the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 491 Magnetic Heterostructures: Structure and Electronic Transport. The author would like to thank P. Weinberger for his kind support.
Fig. 6 Normalized fractions of the layer-resolved sheet resistance differences
prD for characteristic regions p of
12 6 12Fe /Si /Fe . In the upper panel, the results for the system with ideal interfaces are shown. The results for interface alloying are displayed in the middle and bottom panel. Roman numbers mark particular regions of the system: I left lead, II left lead interface, III spacer, IV right interface, and V right lead.
2642 H. C. Herper: Electric transport perpendicular to the planes
[1] J. Mathon, in: Spin-electronics (Springer, Berlin, 2001), p. 71. [2] C. Blaas, P. Weinberger, L. Szunyogh, P. M. Levy, and C. B. Sommers, Phys. Rev. B 60, 492 (1999). [3] W. H. Butler, Phys. Rev. B 31, 3260 (1985). [4] G. Binash, P. Grünberg, F. Saurenbach, and W. Zinn, Phys. Rev. B 39, 4828 (1989). [5] A. Fert, P. Grünberg, A. Berthélémy, F. Petroff, and W. Zinn, J. Magn. Magn. Mater. 140–144, 1 (1995). [6] Spin dependent transport in magnetic nanostructures, edited by S. Maekawa and T. Shinjo (Taylor & Francis,
London, 2002). [7] N. W. Ashcroft and N. D. Mermin, Solid State Phys. (Harcourt, USA, 1976). [8] P. M. Levy, Solid State Phys., Vol. 47 (Academic Press, Cambridge, 1994). [9] C. Tsang, M. Chin, T. Togi, and K. Ju, IEEE Trans. Magn. 26, 1689 (1990). [10] R. E. Matick, Computer storage systems and technology (Wiley & Sons, New York, 1976). [11] S. S. P. Parkin et al., J. Appl. Phys. 85, 5828 (1999). [12] J. Bass and W. P. Pratt Jr., J. Magn. Magn. Mater. 200, 274 (1999). [13] A. Muñoz-Martin, C. Prieto, C. Ocal, J. L. Martínez, and J. Colino, Surf. Sci. 482–485, 1095 (2001). [14] K. Nagasaki, A. Jogo, T. Ibusuki, H. Oshima, Y. Shimizu, and T. Uzumaki, FUJITSU Sci. Tech. J. 42, 1
(2006). [15] M. Takagishi, K. Koi, M. Yoshikawa, T. Funayama, H. Iwasaki, and M. Sahashi, IEEE Trans. Magn. 38, 2277
(2002). [16] M. A. M. Gijs, S. K. J. Lenczowski, and J. B. Giesbers, Phys. Rev. Lett. 70, 3343 (1993). [17] J. W. P. Pratt, S.-F. Lee, J. M. Slaughter, R. Loloee, P. A. Schroeder, and J. Bass, Phys. Rev. Lett. 66, 3060
(1990). [18] P. Weinberger, P. M. Levy, J. Banhart, L. Szunyogh, and B. Újfalussy, J. Phys: Condens. Matter 8, 7677
(1996) [19] R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957). [20] H. E. Camblong, S. Zhang, and P. M. Levy, Phys. Rev. B 47, 4735 (1993). [21] J. Mathon, Phys. Rev. B 56, 11810 (1997). [22] P. Mavropoulos, N. Papanikolaou, and P. H. Dederichs, Phys. Rev. Lett. 85, 1088 (2000). [23] J. Kudrnovsky, V. Drchal, I. Turek, P. Weinberger, and P. Bruno, Comput. Mater. Sci. 25, 584 (2002) [24] G. Bauer, K. Schep, K. Xia, and J. Kelly, J. Phys. D. Appl. Phys. 35, 2410 (2002). [25] D. H. Mosca, F. Petroff, A. Fert, P. A. Schroeder, W. P. Pratt, and Laloee, J. Magn. Magn. Mater. 94, L1
(1991). [26] M. C. Cyrille, S. Kim, M. E. Gomez, J. Santamaria, K. M. Krishnan, and I. K. Schuller, Phys. Rev. B 62, 3361
(2000). [27] D. A. Greenwood, Proc. Phys. Soc. 71, 585 (1958). [28] G. D. Mahan, Many-particle Physics, Physics of Solids and Liquids, 2nd ed. (Plenum, New York, 1990). [29] H. E. Camblong, P. M. Levy, and S. Zhang, Phys. Rev. B 51, 16052 (1995). [30] A. Braatas, Y. V. Nazarov, J. Inoue, and G. E. Bauer, Phys. Rev. B 59, 93 (1999). [31] P. Weinberger, L. Szunyogh, C. Blaas, and C. Sommers, Phys. Rev. B 64, 184429 (2001). [32] E. Y. Tsymbal, Phys. Rev. B 63, R3608 (2000). [33] H. C. Herper, P. Weinberger, A. Vernes, L. Szunyogh, and C. Sommers, Phys. Rev. B 64, 184442 (2001). [34] H. C. Herper, P. Entel, L. Szunyogh, and P. Weinberger, Mater. Res. Soc. Proc. 746, 101 (2003). [35] P. Weinberger and L. Szunyogh, Comput. Mater. Sci. 17, 414 (2000) [36] L. Szunyogh, B. Újfalussy, and P. Weinberger, Phys. Rev. B 51, 9552 (1995). [37] H. C. Herper, P. Weinberger, L. Szunyogh, and C. Sommers, Phys. Rev. B 66, 064426 (2002). [38] G. J. Strijkers, J. T. Kohlhepp, H. J. M. Swagten, and W. J. M. de Jonge, Phys. Rev. B 60, 9583 (1999). [39] J. L. de Vries, J Kohlhepp, F. J. A. de Broeder, R. Coehoorn, R. Jungblut, A. Reinders, and W. J. M. de Jonge,
Phys. Rev. Lett. 78, 3023 (1997). [40] K. Inomata, K. Yusu, and Y. Saito, Phys. Rev. Lett. 74, 1863 (1995). [41] R. J. Highmore, K. Yusu, S. N. Okuno, Y. Saito, and K. Inomata, J. Magn. Magn. Mater. 151, 95 (1995).