1. Transport in Solids Peter M Levy Email: levy@nyu.edu Room 625 Meyer Phone:212-998-7737

2. 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).

3. 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

4. ~1900 Drude model of conduction based on kinetic theory of gases {PV=RT}

5. ~1928 Sommerfeld model of conduction in metals

8. Phenomena

9. 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.

10. 1911 Superconductivity is discovered by Kammerlingh-Onnes The resistance of metals increases with temperature; that’s sort of intuitive: the greater the thermal agitation the greater the scattering. What was completely unanticipated was the lose of all resistance at a finite temperature. When mercury was cooled to 4.18K above absolute zero it lost all resistance; once a current was started one could remove the battery and it would continue to flow as if there were no collisions any more. An understanding of this phenomenon was not fully enunciated till 1958 with the theory of Bardeen-Cooper and Schreiffer. A key ingredient in understanding superconductivity is the coupling of motion of the background to that of the electrons. While this is largely responsible for resistance when the two are not coupled, those electrons that are responsible for superconductivity are no longer scattered.

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

12. What distinguishes a metal from an insulator

13. Intrinsic semiconductors The number of carriers depends on temperature; at T=0K there are none.

14. Doping with donors and acceptors many more carriers at lower temperatures

15. Transistor: a p-n junction

16. Depletion layer at interface-transfer of charge across interface

17. Effect of bias-voltage on depletion layer

18. ~1955 the transistor; rectification action of p-n junction

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

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

21. Domain walls

23. 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).

24. GMR: Giant Magnetoresistance in Magnetic Layered and Granular Materials, by P.M. Levy, in Solid State Physics Vol. 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 Physics Vol. 56, eds. H. Ehrenreich and F. Spaepen (Academic Press, Cambridge, MA, 2001) pp. 113-237.

25. 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: A.Brataas, G.E.W. Bauer and P. Kelly, Physics Reports 427, 157 (2006).

26. Spintronics- control of current through spin of electron

27. The two current model of conduction in ferromagnetic metals

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

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

31. spin-valve multi-layer GMR -metallic spacer between magnetic layers -current flows in- plane of layers Co 95 Fe 5 /Cu [110]  R/R~110% at RT Field ~10,000 Oe Py/Co/Cu/Co/Py  R/R~8-17% at RT Field ~1 Oe NiFe + Co nanolayer NiFe Co nanolayer Cu Co nanolayer NiFe FeMn H(Oe) H(kOe) [011] S.S.P. Parkin GMR in Multilayers and Spin-Valves

32. Oscillations in GMR: Polycrystalline vs. Single Crystal Co/Cu Multilayers S.S.P. Parkin et al, Phys. Rev. Lett. 66, 2152 (1991) Polycrystalline Single crystalline S.S.P. Parkin Sputter deposited on MgO(100), MgO(110) and Al 2 O 3 (0001) substrates using Fe/Pt seed layers deposited at 500C and Co/Cu at ~40C

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

36. 1995 GMR heads From IBM website; 1.swf 2.swf1.swf2.swf

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

38. 2000 magnetic tunnel junctions used in magnetic random access memory From IBM website; http://www.research.ibmhttp://www.research.ibm. com/research/gmr.html

39. 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

42. 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

43. 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

44. Methodology

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

46. Prepared by Carsten Heide

47. Lexicon of transport parameters Spin independent transport

48. Spin dependent transport parameters

49. Ballistic transport: see S. Datta Electronic Transport in Mesoscopic Systems (Cambridge Univ. Press, 1995). Critique of the “mantra” of Landauer’s formula; see M.P. Das and F. Green, cond-mat/0304573 v1 25Apr 2003.

51. Spin and charge accumulation in metallic systems

53. Application to magnetic multilayers

58. Semi-classical approaches to electron dynamics Validity

59. Diffusive transport

60. Simple derivation

62. Derivation of Landauer formula (see Datta)

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

68. Conclusion The contact resistance is also known as the Sharvin resistance.