Transport Properties of Dilute Alloys
Mertig, I., 1999. Transport properties of Dilute Alloys Rep. Prog. Phys. 62, 237.
Essay about this article
Defects in solids scatter electrons and produce resistance to the flow of charge. In ferromagnetic metals electrons scatter differently depending on the direction of their spin relative to the background magnetization; this is called “spin dependent scattering”. It should be distinguished from spin-flip scattering in which the spin of the electron is reversed in the scattering, which is inherently inelastic in ferromagnetic metals and less probable than just spin dependent scattering at least at low temperatures.
In magnetic multilayers there are two sources of spin dependent scattering: in the bulk of the layers, and due to roughness and interdiffusion of adjacent metal ions at the interfaces. Before the advent of ab-initio calculations, estimates of the scattering cross-section [probability] for the first were derived from the relation between the measured resistivity and the time between collisions given in the introduction. Starting in the late eighties Ingrid Mertig, while at Institut fur Theoretische Physik in Dresden, Germany, started to calculate the spin dependent scattering cross sections for 3d transition-metal impurities in copper, and 3d impurities in the ferromagnetic transition-metals; see Section 4 of her 1999 review article. By using these scattering parameters she estimated the resistivity induced by defects by using the Boltzmann equation and compared her results to resistivity data. Her calculations were excellent and produced a faithful rendering of the variation of the resistivity across the entire series of 3d impurities. This was one of the outstanding successes in the ab-intio calculation of transport properties in ferromagnetic metals.
The key to Professor Mertig’s success was her use of fully self-consistent impurity calculations in which the effect of embedding the impurity on the metal matrix is determined. This is particularly crucial for magnetic impurities where it induces a magnetic polarization in the surrounding matrix; when the matrix is ferromagnetic, the induced polarization by the impurity depends on the orientation of its magnetic moment relative to the magnetization of the matrix and one obtains a realistic evaluation of the spin dependent scattering.
Interface roughness and interdiffusion are other sources of scattering in multilayers. They are more difficult to calculate because of the extended nature of these types of defects, i.e., details about the form of the roughness and extent of the interdiffusion are not well known. When the interfaces are flat the scattering is specular, i.e., one can predict the scattered trajectory of the scattering by knowing the incoming path. There is no uncertainty so that this type of scattering does not produce resistance, although it does produce multiple reflections that can alter the resistivity by causing electrons to multiply sample defects in the bulk of a layer before losing track of their initial momentum [this is known as channeling in the context of the CIP geometry].
There are basically two different ways of growing multilayers: sputtering, which usually produces more granular layers, with columnar growth and irregular roughness, and molecular beam epitaxy (MBE), which deposits the atoms monolayer by monolayer and has the potential of creating flat interfaces except for steps and interdiffusion of atoms between layers, which is controlled by the temperature during the deposition. Whereas the first multilayers that demonstrated GMR were grown by MBE, this is a slow process. And though it afforded proof of the existence of GMR, it proved unrealistic for the mass production of these multilayers for applications.
In the period just after the discovery of GMR there was apprehension about the poor quality of multilayer growth by sputtering and that the high-defect scattering would produce high resistivity and low GMR. However, sputtering techniques were refined in the late eighties-early nineties, in particular by Stuart Parkin at IBM, to the point where he was able to grow multilayers that displayed GMR ratios comparable to MBE samples. In fact, it was found that the right kind of interface roughness that produced more spin-dependent than ordinary scattering enhanced the GMR ratio by increasing the difference in resistivity between the parallel and antiparallel configurations, more than the increase of either configuration. The lesson was that the right kind of roughness would be beneficial for GMR, and Parkin applied this knowledge to “dusting” the interfaces between the magnetic and nonmagnetic layers to produce spin-dependent scattering, and thereby enhance the GMR ratio of the spin valves developed by IBM.
A group in Holland, including Kees Schep, Gerrit Bauer, Paul Kelly and Ke Xia, spearheaded ab-initio calculations of the role of roughness in producing spin dependent scattering resitivity at interfaces.1 They calculated the scattering matrices of heterointerfaces and showed how they can be used to compute interface resistances of dirty magnetic multilayers. Their “first principles” calculations of these interface resistances agreed well with data on CPP-MR ratios. This was achieved by calculating the resistances for several kinds of alloying at the interfaces and finding which alloying fit the data best. Nonetheless, the lack of detailed knowledge of the interface roughness and alloying there has hindered true ab-initio predictions of the GMR produced by interfaces.
1 See, for example, GEW Bauer, KM Schep, K Xia and PJ Kelly, Bauer J Phys D Appl. Phys. 35, 2410 (2002).
What differentiates Mertig’s calculation of spin-dependent scattering by impurities in metals from those calculations that use the Born approximation for the scattering?
The full text of Mertig 1999 was provided with kind permission of the Institute of Physics and IOP Publishing Limited.
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