Transport in Solids

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Transport in Solids

• Peter M Levy

Email levy_at_nyu.edu Room 625 Meyer
Phone[phone]
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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).
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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
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1900 Drude model of conductionbased on
kinetic theory of gases PVRT
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1928 Sommerfeld model of conduction in metals
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Phenomena
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While each atom scatters electrons, when they
form a periodic array the atomic background only
electrons from one state k to another with kK.
This is called Bragg scattering it is
responsible for dividing the continuous energy
vs. momentum curve into bands.
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1911 Superconductivity is discoveredby
Kammerlingh-Onnes
The resistance of metals increases with
temperature thats 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.
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Provides explanation for negligible contribution
of conduction electrons to specific heat of
metals.
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What distinguishes a metal from an insulator
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Intrinsic semiconductors
The number of carriers depends on temperature at
T0K there are none.
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Doping with donors and acceptorsmany more
carriers at lower temperatures
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Transistor a p-n junction
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Depletion layer at interface-transfer of charge
across interface
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Effect of bias-voltage on depletion layer
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1955 the transistor rectification action of
p-n junction
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Magnetoresistance
Lorentz force acting on trajectory of
electronlongitudinal magnetoresistance (MR).
A.D. Kent et al J. Phys. Cond. Mat. 13,
R461 (2001)
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Anisotropic MR
Role of spin-orbit coupling on electron scattering
A.D. Kent et al J. Phys. Cond. Mat. 13,
R461 (2001)
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Domain walls
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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).
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• 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.

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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).

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Spintronics- control of current through spin of
electron
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The two current model of conduction in
ferromagnetic metals
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1988 Giant magnetoresistance Albert Fert Peter
Grünberg
Parallel configuration
Antiparallel configuration
Two current model in magnetic multilayers
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Data on GMR
M.N. Baibich et al., Phys. Rev. Lett. 61, 2472
(1988).
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GMR in Multilayers and Spin-Valves
Co95Fe5/Cu 110
multi-layer

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

DR/R110 at RT Field 10,000 Oe
H(kOe) 011
Py/Co/Cu/Co/Py
NiFe Co nanolayer Cu Co nanolayer NiFe FeMn
spin-valve
H(Oe)
DR/R8-17 at RT Field 1 Oe
NiFe Co nanolayer
S.S.P. Parkin
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Oscillations in GMRPolycrystalline 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
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Current in the plane (CIP)-MR
vs
Current perpendicular to the plane (CPP)-MR
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1995 GMR heads
From IBM website 1.swf 2.swf
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Tunneling-MR
Two magnetic metallic electrodes separated by an
insulator transport controlled by tunneling
phenomena not by characteristics of conduction in
metallic electrodes
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2000 magnetic tunnel junctions used in magnetic
random access memory
From IBM website http//www.research.ibm. com/res
earch/gmr.html
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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
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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
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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
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Methodology
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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
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Prepared by Carsten Heide
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Lexicon of transport parameters
Spin independent transport
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Spin dependent transport parameters
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Ballistic transport see S. Datta Electronic
Transport in Mesoscopic Systems (Cambridge Univ.
Press, 1995).
Critique of the mantra of Landauers formula
see M.P. Das and F. Green, cond-mat/0304573 v1
25Apr 2003.
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Spin and charge accumulation in metallic systems
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Application to magnetic multilayers
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Semi-classical approaches to electron dynamics
Validity
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Diffusive transport
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Simple derivation
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Derivation of Landauer formula (see Datta)
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Landauer reasoned that when the conductor is not
perfectly ballistic, i.e., has a transmission
probability Tlt1 that
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Conclusion
The contact resistance is also known as the
Sharvin resistance.