Transport in Solids Introduction

1. Transport in SolidsIntroduction Peter M Levy New York University

2. A general review of the history of GMR can be found in:http://wiki.nsdl.org/index.php/PALE:ClassicArticles/GMR

3. Material I cover can be found in General: Solid State Physics, N.W. Ashcroft and N.D. Mermin (Holt, Rinehardt and Winston, 1976) Electronic Transport in Mesoscopic Systems, S. Datta (Cambridge University Press, 1995). Transport Phenomena, H. Smith and H.H. Jensen ( Clarendon Press, Oxford, 1989). J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986). Ab-initio theories of electric transport in solid systems with reduced dimensions, P. Weinberger, Phys. Reports 377, 281-387 (2003).

4. Electrical conduction in magnetic media How we got from 19th century concepts to applications in computer storage and memories. 1897- The electron is discovered by J.J. Thomson

5. ~1900 Drude model of conductionbased on kinetic theory of gases {PV=RT}

6. ~1928 Sommerfeld model of conduction in metals

9. Phenomena

10. While each atom scatters electrons, when they form a periodic array the atomic background only electrons from one state k to another with k+K. This is called Bragg scattering; it is responsible for dividing the continuous energy vs. momentum curve into bands.

11. Provides explanation for negligible contribution of conduction electrons to specific heat of metals.

12. What distinguishes a metal from an insulator

13. Magnetoresistance Lorentz force acting on trajectory of electron;longitudinal magnetoresistance (MR). A.D. Kent et al J. Phys. Cond. Mat. 13, R461 (2001)

14. Anisotropic MR Role of spin-orbit coupling on electron scattering A.D. Kent et al J. Phys. Cond. Mat. 13, R461 (2001)

15. Domainwalls

17. References Spin transport: Transport properties of dilute alloys, I. Mertig, Rep. Prog. Phys. 62, 123-142 (1999). Spin Dependent Transport in Magnetic Nanostructures, edited by S. Maekawa and T. Shinjo ( Taylor and Francis, 2002).

18. GMR: Giant Magnetoresistance in Magnetic Layered and Granular Materials, by P.M. Levy, in Solid State PhysicsVol. 47, eds. H. Ehrenreich and D. Turnbull (Academic Press, Cambridge, MA, 1994) pp. 367-462. Giant Magnetoresistance in Magnetic Multilayers, by A. Barthélémy, A.Fert and F. Petroff, Handbook of Ferromagnetic Materials, Vol.12, ed. K.H.J. Buschow (Elsevier Science, Amsterdam, The Netherlands, 1999) Chap. 1. Perspectives of Giant Magnetoresistance, by E.Y. Tsymbal and D,G. Pettifor, in Solid State PhysicsVol. 56, eds. H. Ehrenreich and F. Spaepen (Academic Press, Cambridge, MA, 2001) pp. 113-237.

19. CPP-MR: M.A.M. Gijs and G.E.W. Bauer, Adv. in Phys. 46, 285 (1997). J. Bass, W.P. Pratt and P.A. Schroeder, Comments Cond. Mater. Phys. 18, 223 (1998). J. Bass and W.P. Pratt Jr., J.Mag. Mag. Mater. 200, 274 (1999). Spin transfer: Brataas, G.E.W. Bauer and P. Kelly, Physics Reports 427, 157 (2006).

20. Spintronics-control of current through spin of electron

21. The two current model of conduction in ferromagnetic metals

23. 1988 Giant magnetoresistance Albert Fert & Peter Grünberg Parallel configuration Antiparallel configuration Two current model in magnetic multilayers

24. Data on GMR M.N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988).

25. GMR in Multilayers and Spin-Valves Co95Fe5/Cu [110] multi-layer • GMR • metallic spacer between magnetic layers • current flows in-plane of layers H(kOe) [011] DR/R~110% at RT Field ~10,000 Oe Py/Co/Cu/Co/Py NiFe Co nanolayer Cu Co nanolayer NiFe FeMn spin-valve H(Oe) DR/R~8-17% at RT Field ~1 Oe NiFe + Co nanolayer S.S.P. Parkin

26. Current in the plane (CIP)-MR vs Current perpendicular to the plane (CPP)-MR

28. 1995 GMR heads From IBM website; 1.swf2.swf

29. Tunneling-MR Two magnetic metallic electrodes separated by an insulator; transport controlled by tunneling phenomena not by characteristics of conduction in metallic electrodes

30. 2000 magnetic tunnel junctions used in magnetic random access memory From IBM website; http://www.research.ibm. com/research/gmr.html

31. PHYSICAL REVIEW LETTERS VOLUME 84, 3149 (2000) Current-Driven Magnetization Reversal and Spin-Wave Excitations in CoCuCo Pillars J. A. Katine, F. J. Albert, and R. A. Buhrman School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853 E. B. Myers and D. C. Ralph Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853

34. Spin Accumulation-left layer-current reversed Spin Accumulation from left layer z z j j How reversal in current directions changes alignment of layers

35. How can one rotate a magnetic layer with a spin polarized current? By spin torques: Slonczewski-1996 Berger -1996 Waintal et al-2000 Brataas et al-2000 By current induced interlayer coupling: Heide- 2001

36. Current induced switching of magnetic layers by spin polarized currents can be divided in two parts: Creation of torque on background by the electric current, and reaction of background to torque. Latter epitomized by Landau-Lifschitz equation; micromagnetics Former is current focus article in PRL: Mechanisms of spin-polarized current-driven magnetization switching by S. Zhang, P.M. Levy and A. Fert. Phys. Rev. Lett.88, 236601 (2002). Extension of Valet-Fert to noncollinear multilayers

37. Methodology

38. To discuss transport two calculations are necessary: • Electronic structure, and • Transport equations; out of equilibrium collective electron • phenomena. • Structures • Metallic multilayers • Magnetic tunnel junctions • Insulating barriers • Semiconducting barriers • Half-metallic electrodes • Semiconducting electrodes different length scales

39. Prepared by Carsten Heide

40. Lexicon of transport parameters Spin independent transport

41. Spin dependent transport parameters

43. Spin and charge accumulation in metallic systems

45. Derivation of Landauer formula (see Datta)

46. Landauer reasoned that when the conductor is not perfectly ballistic, i.e., has a transmission probability T<1 that