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Lecture Notes in Physics Editorial Board R Beig, Wien, Austria J Ehlers, Potsdam, Germany U Frisch, Nice, France K Hepp, Zăurich, Switzerland W Hillebrandt, Garching, Germany D Imboden, Zăurich, Switzerland R L Jaffe, Cambridge, MA, USA R Kippenhahn, Găottingen, Germany R Lipowsky, Golm, Germany H v Lăohneysen, Karlsruhe, Germany I Ojima, Kyoto, Japan H A Weidenmăuller, Heidelberg, Germany J Wess, Măunchen, Germany J Zittartz, Kăoln, Germany Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo Editorial Policy The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teaching quickly, informally but with a high quality Manuscripts to be considered for publication are topical volumes consisting of a limited number of contributions, carefully edited and closely related to each other Each contribution should contain at least partly original and previously unpublished material, be written in a clear, pedagogical style and aimed at a broader readership, especially graduate students and nonspecialist researchers wishing to familiarize themselves with the topic concerned For this reason, traditional proceedings cannot be considered for this series though volumes to appear in this series are often based on material presented at conferences, workshops and schools (in exceptional cases the original papers and/or those not included in the printed book may be added on an accompanying CD ROM, together with the abstracts of posters and other material suitable for publication, e.g large tables, colour pictures, program codes, etc.) Acceptance A project can only be accepted tentatively for publication, by both the editorial board and the publisher, following thorough examination of the material submitted The book proposal sent to the publisher should consist at least of a preliminary table of contents outlining the structure of the book together with abstracts of all contributions to be included Final acceptance is issued by the series editor in charge, in consultation with the publisher, only after receiving the complete manuscript Final acceptance, possibly requiring minor corrections, usually follows the tentative acceptance unless the final manuscript differs significantly from expectations (project outline) In particular, the series editors are entitled to reject individual contributions if they not meet the high quality standards of this series The final manuscript must be camera-ready, and should include both an informative introduction and a sufficiently detailed subject index Contractual Aspects Publication in LNP is free of charge There is no formal contract, no royalties are paid, and no bulk orders are required, although special discounts are offered in this case The volume editors receive jointly 30 free copies for their personal use and are entitled, as are the contributing authors, to purchase Springer books at a reduced rate The publisher secures the copyright for each volume As a rule, no reprints of individual contributions can be supplied Manuscript Submission The manuscript in its final and approved version must be submitted in camera-ready form The corresponding electronic source files are also required for the production process, in particular the online version Technical assistance in compiling the final manuscript can be provided by the publisher’s production editor(s), especially with regard to the publisher’s own Latex macro package which has been specially designed for this series Online Version/ LNP Homepage LNP homepage (list of available titles, aims and scope, editorial contacts etc.): http://www.springer.de/phys/books/lnpp/ LNP online (abstracts, full-texts, subscriptions etc.): http://link.springer.de/series/lnpp/ Michael Ziese Martin J Thornton (Eds.) Spin Electronics 13 Editors Michael Ziese Dept of Superconductivity and Magnetism University of Leipzig Linnestrasse 04103 Leipzig, Germany Martin J Thornton Clarendon Laboratory Oxford University Parks Road Oxford 3PU OX1, UK Cover picture: Schematic illustration of the passage of an electron through a spin field The field was calculated using the OOMMF micromagnetic solver developed by Mike Donahue and Don Porter Library of Congress Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Spin electronics / Michael Ziese ; Martin J Thornton (ed.) - Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo : Springer, 2001 (Lecture notes in physics ; 569) (Physics and astronomy online library) ISBN 3-540-41804-0 ISSN 0075-8450 ISBN 3-540-41804-0 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Violations are liable for prosecution under the German Copyright Law Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de c Springer-Verlag Berlin Heidelberg 2001 Printed in Germany The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Typesetting: Camera-ready by the authors/editor Cover design: design & production, Heidelberg Printed on acid-free paper SPIN: 10783210 57/3141/du - Contents Part I Introduction Introduction to Spin Electronics J F Gregg Part II Basic Concepts An Introduction to the Theory of Normal and Ferromagnetic Metals G A Gehring 35 Basic Electron Transport B J Hickey, G J Morgan and M A Howson 52 Phenomenological Theory of Giant Magnetoresistance J Mathon 71 Electronic Structure, Exchange and Magnetism in Oxides D Khomskii 89 Transport Properties of Mixed-Valence Manganites M Viret 117 Spin Dependent Tunneling F Guinea, M J Calder´ on and L Brey 159 Basic Semiconductor Physics H J Jenniches 172 Metal–Semiconductor Contacts D I Pugh 199 10 Micromagnetic Spin Structure R Skomski 204 11 Electronic Noise in Magnetic Materials and Devices B Raquet 232 XIV Contents Part III Materials, Techniques and Devices 12 Materials for Spin Electronics J M D Coey 277 13 Thin Film Deposition Techniques (PVD) E Steinbeiss 298 14 Magnetic Imaging A K Petford–Long 316 15 Observation of Micromagnetic Conﬁgurations in Mesoscopic Magnetic Elements K Ounadjela, I L Prejbeanu, L D Buda, U Ebels, and M Hehn 332 16 Micro– and Nanofabrication Techniques C Fermon 379 17 Spin Transport in Semiconductors M Ziese 396 18 Circuit Theory for the Electrically Declined J F Gregg and M J Thornton 416 19 Spin–Valve and Spin–Tunneling Devices: Read Heads, MRAMs, Field Sensors P P Freitas 464 Index 489 Introduction to Spin Electronics J F Gregg Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, U.K 1.1 Coey’s Lemma The driving force behind Spin Electronics is neatly summarized in J M D Coey’s incisive observation  that “Conventional Electronics has ignored the spin of the electron” In every hi-ﬁ and radio set, 50% of the conducting electrons tend to be spin-up and the remainder are spin down (where up and down relate to some locally induced quantisation axis in the relevant wires and devices) Yet, although electron spin was known about for most of the 20th Century, no technical use is made of this fact 1.2 The Two Spin Channel Model The mechanistic basis for Spin Electronics is almost as old as the concept of electron spin itself In the mid-thirties, Mott postulated  that certain electrical transport anomalies in the behaviour of metallic ferromagnets arose from the ability to consider the spin-up and spin-down conduction electrons as two independent families of charge carriers, each with its own distinct transport properties Mott’s hypothesis essentially is that spin-ﬂip scattering is suﬃciently rare on the timescale of all the other scattering processes canonical to the problem that defections from one spin channel to the other may be ignored, hence the relative independence of the two channels [3,4,5] 1.2.1 Spin Asymmetry The other necessary ingredient of this model is that the two spin families contribute very diﬀerently to the electrical transport processes This may be because the number densities of each carrier type are diﬀerent, or it may because they have diﬀerent mobilities – in other words that the same momentum or energy scattering mechanisms treat them very diﬀerently In either case, the asymmetry which makes spin-up electrons behave diﬀerently to spin-down electrons arises because the ferromagnetic exchange ﬁeld splits the spin-up and spin-down conduction bands, leaving diﬀerent bandstructures evident at the Fermi surface If the densities of electron states diﬀers at the Fermi surface, then clearly the number of electrons participating in the conduction process is diﬀerent for each spin channel However, more subtly, diﬀerent densities of states for spin-up and spin-down implies that the susceptibility to scattering of the two spin types is diﬀerent, and this in turn leads to their having diﬀerent mobilities M.J Thornton and M Ziese (Eds.): LNP 569, pp 3–31, 2001 c Springer-Verlag Berlin Heidelberg 2001 J F Gregg 1.2.2 Spin Accumulation Let us consider two spin channels of diﬀerent mobility (Fig 1.1) When an electric ﬁeld is applied to the metal, there is a shift, ∆k, in momentum space of the spin-up and spin-down Fermi surfaces in accordance with the equation: ∆k dk = (1.1) τ dt where F is force on carrier, E is electric ﬁeld, e is electronic charge, τ is electron scattering time given by µ = eτ /m∗ , µ being the electron mobility and m∗ the electron eﬀective mass Since the channels have diﬀerent mobilities, this shift is diﬀerent for the spin-up and spin-down Fermi surfaces as illustrated F = eE = displaced Fermi spheres ∆k + Electric Field k=0 Brillouin zone Fig 1.1 The shift of the Fermi surface when an electric ﬁeld is applied to a ferromagnet is shown The solid circles represents the Fermi sphere of up and down spin electrons in a ﬁeld, the dashed circle represents the Fermi sphere in zero external ﬁeld From Fig 1.1, it is evident that the spin-up electrons are performing the lion’s share of the electrical conducting, and, moreover, that if a current is passed from such a spin-asymmetric material – for example cobalt – into a paramagnet like silver (where there is no asymmetry between spin channels ), there is a net inﬂux into the silver of up-spins over down-spins Thus a surplus of up-spins appears in the silver and with it a small associated magnetic moment per volume This surplus is known as a “spin accumulation” Evidently, for constant current ﬂow, the spin accumulation cannot increase indeﬁnitely; this is because as fast as the spins are injected into the silver across the cobalt-silver interface, they are converted into down-spins by the slow spin-ﬂip processes which we have hitherto ignored This spin-ﬂipping goes on throughout all parts of the silver which have been invaded by the spin accumulation So now we have a dynamic equilibrium between inﬂux of up-spins and their death by spin-ﬂipping This in turn deﬁnes a Introduction to Spin Electronics characteristic lengthscale which describes how far the spin accumulation extends into the silver Incidentally, to establish the concept of spin accumulation, we have assumed that both spin-up and spin-down electrons were present in the ferromagnet in equal numbers but that their mobilities are diﬀerent The same result could have been achieved by assuming a half-metallic ferromagnet in which one spin channel is entirely absent and no assumption need be made about the mobility of its spins In other words, we can produce a spin accumulation as a direct consequence of an asymmetric density of states or as an indirect consequence via asymmetry in electron mobility 1.2.3 Spin Diﬀusion Length It follows from the above discussion that the spin accumulation decays exponentially away from the interface on a lengthscale called the “spin diﬀusion length” It is instructive to a rough “back of the envelope” calculation to see how large is this spin diﬀusion length, λsd , and on what parameters it depends The estimate proceeds as follows Consider a newly injected up-spin arriving across the interface into the nonmagnetic material It undergoes a number N of momentumchanging collisions before being ﬂipped (on average after time τ↑↓ ) The average distance between momentum scattering collisions is λ, the mean free path We can now make two relations By analogy with the progress of a drunken sailor leaving a bar and executing a random walk up and down the street, we can say (remembering to include a factor of since, unlike the sailor, our spin can move in dimensions) that the average distance which the spin penetrates into the nonmagnetic material (perpendicular to the interface) is λ N/3 This distance is λsd , the spin diﬀusion length which we wish to estimate Moreover, the total distance walked by the spin is N λ which in turn equals its velocity (the Fermi velocity, vF ) times the spin-ﬂip time τ↑↓ Eliminating the number N of collisions gives λvF τ↑↓ λsd = (1.2) 1.2.4 The Role of Impurities in Spin Electronics This relation is interesting because it highlights the critical importance of impurity concentration in determining spin diﬀusion length If the impurity levels are increased in the silver, not only does the spin diﬀusion length drop because of the shortened mean free path, it also drops because the impurities reduce the spin-ﬂip time by introducing more spin-orbit scattering  1.2.5 How Long is the Spin Diﬀusion Length? The relation also allows us to estimate values for the size of the spin diﬀusion length Again taking silver as an example, the spin diﬀusion length can vary between microns for very pure silver to of order 10 nm for silver with 1% gold impurity Yang etc [8,9,10,11] have made elegant measurements of this parameter in J F Gregg other materials For a mathematically rigorous analysis of the spin-accumulation in terms of the respective electrochemical potential of the spin channels, the reader is referred to Valet and Fert  from which it can be seen, numerical factors apart, that the crude “drunken sailor” model gives a remarkably accurate insight into the physics of this problem 1.2.6 How Large is a Typical Spin Accumulation? It is also of interest to estimate how large is the spin accumulation for typical current densities The calculation is done by balancing the net spin injection across the interface: dn Aαj = (1.3) dt e with the total decay rate of spins due to spin ﬂipping in the entire volume inﬂuenced by the spin accumulation: A τ↑↓ ∞ ndx = n0 A τ↑↓ ∞ exp −x λsd dx = An0 λsd τ↑↓ (1.4) A is sectional area, j is current density, n is number density of excess spins, x is distance from the interface, α is ferromagnet spin polarization This in turn gives a spin accumulation just inside the interface of n0 = αjτ↑↓ 3αjλsd = eλsd evF λ (1.5) Putting in typical numbers of j = 1000 Amps/cm2 , α = 1, vF = 106 m/s, λ = nm, λsd = 100 nm, gives n0 = × 1022 m−3 Thus, given an electron density of × 1028 m−3 , it is seen that only one part in 106 of the electrons are spin polarized The signiﬁcance of this will be discussed below Incidentally the magnetic ﬁeld B associated with this spin accumulation is: B = µ0 M = µ0 µB n0 = 10−6 × 10−24 × 1022 = 10 nTesla!! (1.6) (1.7) This is experimentally very hard to detect, especially considering the magnetic ﬁelds caused by the current which generates the spin accumulation in the ﬁrst place 1.3 Two Terminal Spin Electronics The next step in the Spin Electronic story is to make a simple device and this is realized by making a sandwich in which the “bread” is two thin ﬁlm layers of ferromagnet and the “ﬁlling” is a thin ﬁlm layer of paramagnetic metal (Fig 1.2) This is the simplest Spin Electronic device possible It is a two-terminal passive device which in some realizations is known as a “spin valve” and it passes muster in the world of commerce as a Giant Magnetoresistive hard-disk read-head ... between in ux of up-spins and their death by spin- ﬂipping This in turn deﬁnes a Introduction to Spin Electronics characteristic lengthscale which describes how far the spin accumulation extends into... done by balancing the net spin injection across the interface: dn Aαj = (1.3) dt e with the total decay rate of spins due to spin ﬂipping in the entire volume in uenced by the spin accumulation:... the initial spin polarized current 1.6.5 How to Improve Direct Spin- Injection Eﬃciency With this problem in mind it is interesting to examine the results of an experiment which injects spin polarized
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