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Spin-dependent Scattering and Giant Magnetoresistance and First-principles Calculations of Electrical Conductivity and Giant Magnetoresistance of Co|Cu|Co Spin Valves

Butler, et al (JMMM) Article Link

Butler, et al (PhRB) Article Link

Butler, W.H., Zhang, X.G., Nicholson, D.M.C. & MacLaren, J.M., 1995. Spin-dependent Scattering and Giant Magnetoresistance. Jour. Magn. Magn. Mater. 151, 354. and Butler, W.H., Zhang, X.G., Nicholson, D.M.C. & MacLaren, J.M., 1995. First-principles Calculations of Electrical Conductivity and Giant Magnetoresistance of Co|Cu|Co Spin Valves. Phys. Rev. B 52, 13339

Essay about these articles

Here I discuss ab-initio calculations of electron transport in metallic multilayers that combine calculations of the band structure and scattering, both in the bulk of the layers and at the interfaces. They are based on a quantum theory of electron conduction and derive the transport properties from the atomic parameters of the atoms constituting the multilayer, as well as the impurities and defects. One impediment to making correct predictions lies in our lack of knowledge of the details of the interface roughness and interdiffusion. A second arises from the use of the two-current model in which one calculates the scattering parameters in two spin channels. These two concerns are more critical in estimating the Current In Plane Magnetoresistance (CIP-MR) than the Current Perpendicular to the Plane Magnetoresitance (CPP-MR). At this time it is difficult to overcome our lack of precise knowledge of the roughness and interdiffusion, but an alternative exists for the second, i.e., to use a fully relativistic code to calculate the transport [1]. In a non-relativistic code the spin is uncoupled from orbital space, therefore all the channels of conduction with the same spin have a common set of parameters for characterizing the scattering. If as happens, for example, with copper impurities in cobalt, electrons are weakly scattered for one direction of spin relative to the other, then most of the current, which is limited by impurities, will be carried by this spin channel and one has a sort of short-circuit effect and a very large MR ratio. When one aligns the magnetic cobalt layers in a multilayer structure antiparallel to one another, the short-circuit is undone. However, in a relativistic code there are as many channels of conduction as there are states in the system; each orbital state is coupled to a spin and while there may be some states which have a short-circuit, there will not be enough of them to produce a macroscopic short-circuit. Therefore one obtains a more realistic estimate for CIP-MR using relativistic codes than from codes that fall into the two-current model [1].

Until recently ab-initio transport calculations calculated the current based on the band structure and scattering in the multilayer. This is in contradistinction to self-consistent calculations of steady state transport based on the Boltzmann equation, which takes account of spin accumulation induced by the current. This is particularly critical for CPP-MR [see Section 8]. Now ab-intio-like calculations, called Landauer-Keldysh [out-of-equilibrium, yet steady state] calculations, which were developed to determine the current induced torque in multilayers with non-collinear magnetic layers, have been developed to self consistently update the current and account for current induced spin accumulation; they should be extended to calculate CPP-MR [2].

One interesting point that has emerged is while the original ballistic band structure calculations are sensitive to details of the multilayers structure on the order of angstroms, the length scale of the spin accumulation, which is at least as large as the mean free path and can be considerably longer, is such as to produce final results by using the Landauer-Keldysh formalism for transport properties that resemble those found from semi-classical diffusive calculations [2].

[1] C. Blaas and P. Weinberger, L. Szunyogh, P. M. Levy and C. B. Sommers, Physical Review B, 492 (1999).

[2] P. M. Haney, D. Waldron, R. A. Duine, A. S. Núñez, H. Guo, and A. H. MacDonald, Physical Review B 76, 024404 (2007).

Discussion Question

Describe the differences between Butler et al.’s ab-initio calculations of transport in magnetic multilayers from those of Schep et al.?

The above article is reprinted with permission from the author(s) of Butler, W.H., Zhang, X.G., Nicholson, D.M.C. & MacLaren, J.M., 1995. Phys. Rev. B 52 . Copyright (1995) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.

Select articles citing these papers

Butler

Quan, J. J., X. W. Zhou, et al. (2006). "Low energy ion assisted atomic assembly of metallic superlattices." Surface Science 600(11): 2275-2287.

Brataas, A., G. E. W. Bauer, et al. (2006). "Non-collinear magnetoelectronics." Physics Reports-Review Section of Physics Letters 427(4): 157-255.

Brataas, A., G. E. W. Bauer, et al. (2006). "Non-collinear magnetoelectronics." Physics Reports-Review Section of Physics Letters 427(4): 157-255.

He, Y. D., S. J. Hu, et al. (2005). "Effect of Co ion implantation on GMR of [NiFeCo(10 nm)/Ag(10 nm)]x 20 multilayer film." Journal of Materials Science & Technology 21(4): 593-598.

Zhou, X. W., H. N. G. Wadley, et al. (2001). "Atomic scale structure of sputtered metal multilayers." Acta Materialia 49(19): 4005-4015.

Tsymbal, E. Y. and D. G. Pettifor (2001). Perspectives of giant magnetoresistance. Solid State Physics. 56: 113-237.

Steenwyk, S. D., S. Y. Hsu, et al. (1997). "Perpendicular-current exchange-biased spin-valve evidence for a short spin-diffusion length in permalloy." Journal of Magnetism and Magnetic Materials 170(1-2): L1-L6.

Kulikov, N. I. and C. Demangeat (1997). "Spin polarization of disordered Fe-Cr and Fe-Mn alloys." Physical Review B 55(6): 3533-3542.

Gijs, M. A. M. and G. E. W. Bauer (1997). "Perpendicular giant magnetoresistance of magnetic multilayers." Advances in Physics 46(3-4): 285-445.

Coehoorn, R. (1995). Relation between interfacial magnetism and spin-dependent scattering at non-ideal Fe/Cr and Fe/V interfaces.

Dieny

Noh, E. S., H. M. Lee, et al. (2008). "A theoretical study of a spin polarized transport and giant magnetoresistance: The effect of the number of layers in a magnetic multilayer." Journal of Applied Physics 103(8).

Waldron, D., L. Liu, et al. (2007). Ab initio simulation of magnetic tunnel junctions.

Brataas, A., G. E. W. Bauer, et al. (2006). "Non-collinear magnetoelectronics." Physics Reports-Review Section of Physics Letters 427(4): 157-255.

Tsymbal, E. Y. and D. G. Pettifor (2001). Perspectives of giant magnetoresistance. Solid State Physics. 56: 113-237.

Kudrnovsky, J., V. Drchal, et al. (2000). "Ab initio theory of perpendicular magnetotransport in metallic multilayers." Physical Review B 62(22): 15084-15095.

Sanvito, S., C. J. Lambert, et al. (1999). "General Green's-function formalism for transport calculations with spd Hamiltonians and giant magnetoresistance in Co- and Ni-based magnetic multilayers." Physical Review B 59(18): 11936-11948.

MacLaren, J. M., X. G. Zhang, et al. (1999). "Layer KKR approach to Bloch-wave transmission and reflection: Application to spin-dependent tunneling." Physical Review B 59(8): 5470-5478.

Zhou, X. W. and H. N. G. Wadley (1998). "Atomistic simulations of the vapor deposition of Ni/Cu/Ni multilayers: The effects of adatom incident energy." Journal of Applied Physics 84(4): 2301-2315.

Weinberger, P., P. M. Levy, et al. (1996). "'Band structure' and electrical conductivity of disordered layered systems." Journal of Physics-Condensed Matter 8(41): 7677-7688.

Tsymbal, E. Y. and D. G. Pettifor (1996). "Effects of band structure and spin-independent disorder on conductivity and giant magnetoresistance in Co/Cu and Fe/Cr multilayers." Physical Review B 54(21): 15314-15329.