Effects of interface disorder on transmission probability in magnetic multilayer Julian Velev and William H. Butler Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee37831-6114, USA and Center for Materials for Information Technology, University of Alabama, Tuscaloosa, Alabama 35487, USA Received 8 August 2003; revised manuscript received 20 October 2003; published 13 January 2004 We present a study of conductance through disordered Fe-Cr100 and Co-Cu100 interfaces within a realistic tight-binding model. In our model, the specular and diffuse parts of the conductance are treated on an equal footing. We observe a substantial increase in conductance due to disorder in the channels that are strongly reflected by pure interfaces. We also show how this phenomenon affects the giant magnetoresistance. In addition, we find that the series resistor model may significantly overestimate the resistance if the thickness of the disordered layer is less than several times the electron mean free path. DOI: 10.1103/PhysRevB.69.024404 PACS numbers: 75.47.-m, 73.40.-c, 73.23.Ad I. INTRODUCTION The decade and a half following the discovery of the giant magnetoresistance GMR in Fe-Cr multilayers, 1,2 has wit- nessed a continuing growth of interest in spin-dependent electron transport. 3–7 There have been numerous calculations of GMR. Some of these have been based on a rigorous quan- tum treatment of transport. Some have also taken into ac- count the band structure of the materials comprising the multilayer. 8 Direct comparison between calculations and ex- periment, however, has been difficult because a number of factors that are important in determining the experimental resistance and magnetoresistance are difficult to take into account in model calculations. These factors may roughly be split in two groups: a finite temperature effects that lead to inelastic scattering, most importantly phonon and magnon scattering, and b effects of static disorder that lead to elas- tic scattering. In this paper, we are concerned with what we believe to be an important subset of these factors, those involved with substitutional disorder at the interfaces between different ma- terials in magnetic multilayers. The study of the interfaces is motivated by the fact that the effects of interfacial disorder have been particularly difficult to understand and the fact that interfaces can dramatically influence GMR. 9 In some cases, interfacial disorder is the primary source of electron scattering. The limitation to substitutional disorder is justi- fied as a first step by the fact that atomic scale studies 10 of interfaces of typical sputtered films produced for GMR de- vices often show sufficiently strong texture that over an elec- tron mean free path the films are well ordered crystals, the crystal structure being maintained across the interfaces be- tween the layers. We study the effect of interfacial disorder by calculating the effect of a random substitutional distribution of the atomic species on one or more atomic layers at the interface on transmission and reflection. We demonstrate that the su- percell can be made large enough to suppress artifacts asso- ciated with the artificial periodicity imposed by the supercell. We also demonstrate that one or only a few configurations are needed in order to represent the disorder. We report both the specular ( k  conserving and diffuse ( k  nonconserving parts of the transmission and reflectance because these help us to understand some novel effects caused by interfacial disorder. A similar approach, based on an ab initio LMTO code 11 was used in two recent papers. 12 In the first, the conductance of a Co-Cu-Co trilayer was studied in the presence of disorder in the bulk and close to the inter- faces. The second study attempted to recover the simple re- sistor model in order to compare with experiment. The au- thors postulated that the scattering from bulk is completely diffuse, and with this condition they were able to recover a series resistor model and an explicit expression for the inter- face resistance. In a very recent paper, 13 the same group cal- culated the specular and diffuse part of the conductance separately and managed to study the validity of the resistor model used earlier. The LMTO code however, scales poorly with the system size which limits their study to a few sys- tems in just one disorder configuration. Our code is based on a realistic tight-binding model fitted to ab initio band structures which gives us more flexibility with comparable precision. The fitting parameters consist of on-site energies and interatomic matrix elements. These are transferred to the alloy by assuming that the onsite energies are not changed by the local environment and that the inter- atomic matrix elements between species A and B is the av- erage of that between A and A and between B and B. Clearly this approach is limited to pairs of atoms of similar size and electronegativity such as Fe-Cr and Co-Cu. We believe, how- ever, that our approach is particularly well suited for explor- ing certain questions of principle that are more difficult to explore with fully ab initio techniques. We study the trans- mission through Fe-Cr100 and Co-Cu100 interfaces and GMR of Fe-Cr multilayers over the full range of substitu- tional disorder. II. MODEL In this paper we employ the two current model which neglects effects such as spin-orbit coupling or noncollinear moments that might mix the spin channels and electron- magnon scattering which may lead to spin-flip scattering. The method we use to calculate the conductance was origi- nally developed to study the conductance of nanowires. 14 For PHYSICAL REVIEW B 69, 024404 2004 0163-1829/2004/692/0244047/$22.50 ©2004 The American Physical Society 69 024404-1