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Transport in Solids. Peter M Levy. Email: levy@nyu.edu 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

Email: levy@nyu.edu

Room 625 Meyer

Phone:212-998-7737

material i cover can be found in
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).

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

slide9

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.

slide11

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.

slide19

Magnetoresistance

Lorentz force acting

on trajectory of

electron;longitudinal

magnetoresistance

(MR).

A.D. Kent et al

J. Phys. Cond.

Mat. 13, R461

(2001)

slide20

Anisotropic MR

Role of spin-orbit coupling on electron scattering

A.D. Kent et al

J. Phys. Cond.

Mat. 13, R461

(2001)

slide23

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).

slide24

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.

slide25

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).

slide29

1988 Giant magnetoresistance

Albert Fert & Peter Grünberg

Parallel configuration

Antiparallel configuration

Two current model in magnetic multilayers

slide30

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

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

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

Polycrystalline

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

slide33

Current in the plane (CIP)-MR

vs

Current perpendicular to the

plane (CPP)-MR

slide36

1995 GMR heads

From IBM website; 1.swf2.swf

slide37

Tunneling-MR

Two magnetic metallic electrodes separated by an insulator; transport

controlled by tunneling phenomena not by characteristics of conduction

in metallic electrodes

slide38

2000 magnetic tunnel junctions used in magnetic random access memory

From IBM website;

http://www.research.ibm.

com/research/gmr.html

slide39

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

slide42

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

slide43

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

slide45

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

slide47

Lexicon of transport parameters

Spin independent transport

slide49

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.

slide63

Landauer reasoned that when the conductor is not perfectly

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

slide68

Conclusion

The contact resistance is also known as the Sharvin resistance.