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Transport in Solids. Peter M Levy. Email: Room 625 Meyer Phone:212-998-7737. 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

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transport in solids

Transport in Solids

Peter M Levy


Room 625 Meyer


material i cover can be found in
Material I cover can be found in


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).

electrical conduction in magnetic media
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


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.

1911 superconductivity is discovered by kammerlingh onnes
1911 Superconductivity is discoveredby 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.


Provides explanation for negligible contribution of conduction electrons to specific heat

of metals.

intrinsic semiconductors
Intrinsic semiconductors

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



Lorentz force acting

on trajectory of




A.D. Kent et al

J. Phys. Cond.

Mat. 13, R461



Anisotropic MR

Role of spin-orbit coupling on electron scattering

A.D. Kent et al

J. Phys. Cond.

Mat. 13, R461




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).



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.



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).


1988 Giant magnetoresistance

Albert Fert & Peter Grünberg

Parallel configuration

Antiparallel configuration

Two current model in magnetic multilayers


Data on GMR

M.N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988).

gmr in multilayers and spin valves
GMR in Multilayers and Spin-Valves




  • GMR
  • metallic spacer between magnetic layers
  • current flows in-plane of layers



DR/R~110% at RT

Field ~10,000 Oe



Co nanolayer


Co nanolayer





DR/R~8-17% at RT

Field ~1 Oe

NiFe + Co nanolayer

S.S.P. Parkin

oscillations in gmr polycrystalline vs single crystal co cu multilayers
Oscillations in GMR:Polycrystalline vs. Single Crystal Co/Cu Multilayers


S.S.P. Parkin et al,

Phys. Rev. Lett. 66, 2152 (1991)

Single crystalline

S.S.P. Parkin

Sputter deposited on MgO(100), MgO(110) and Al2O3 (0001) substrates using Fe/Pt seed layers deposited at 500C and Co/Cu at ~40C


Current in the plane (CIP)-MR


Current perpendicular to the

plane (CPP)-MR


1995 GMR heads

From IBM website; 1.swf2.swf



Two magnetic metallic electrodes separated by an insulator; transport

controlled by tunneling phenomena not by characteristics of conduction

in metallic electrodes


2000 magnetic tunnel junctions used in magnetic random access memory

From IBM website;




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


How can one rotate a magnetic layer with a spin polarized current?

By spin torques:


Berger -1996

Waintal et al-2000

Brataas et al-2000

By current induced interlayer coupling:

Heide- 2001


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


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


Lexicon of transport parameters

Spin independent transport


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.


Landauer reasoned that when the conductor is not perfectly

ballistic, i.e., has a transmission probability T<1 that



The contact resistance is also known as the Sharvin resistance.