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Magnetotransport in nanostructures, José d’Albuquerque e Castro, Universidade Federal do Rio de JaneiroInstituto de Física
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Magnetotransport in nanostructures
Universidade Federal do Rio de Janeiro Instituto de Física
José d’Albuquerque e Castro
PAN AMERICAN ADVANCED STUDIES INSTITUTE Ultrafast and Ultrasmall; New Frontiers and AMO Physics
March 30 - April 11, 2008
Nanostructures
• Structure and composition: nanometer scale ⇒ ultra fine films and multilayered structures ⇒ quantum wires and dots ⇒ granular systems etc.
• Main interest
⇒ distinct physical properties ⇒ confinement effects (quantum interference) ⇒ possibility of controlling their physical properties ⇒ technological applications
Giant magnetoresistance
• Source of the effect: spin dependent scattering
• It may occur in both regimes: ⇒ diffusive ⇒ ballistic
• Diffusive regime: the usual approach is based on the Boltzmann formalism
⇒ R. E. Camley and J. Barnás, PRL 63, 664 (1989) ⇒ R. Q. Hood and L. M. Falicov, PRB 46, 8287 (1992)
Boltzmann theory
Semiclassical theory of transport
⇒ Bloch states
• crystalline system: H0
translational symmetry ⇒
Boltzmann theory
Semiclassical theory of transport
⇒ Bloch states
• Wannier states
• crystalline system: H0
translational symmetry ⇒
• for slowly varying potential V
• external potential V( r )
Wannier ⇒
⇒ fn( r ,t) = envelope function
NB: interband transitions n → n’ have been neglected
• semiclassical approximation (correspondence principle)
• semiclassical equations of motion
with
the wave packet follows the classical trajectory determined by the corresponding classical Hamiltonian
• distribution function:
density of occupied states in the phase space at time t
⇒ equilibrium (V=0) distribution:
⇒ electric current:
• equation for the distribution function
• Boltzmann equation
⇒ Liouville theorem
• relaxation time approximation
τ = relaxation time
Giant magnetoresistance
• Boltzmann formalism: distribution function
I II
z
• Important point: no interference between and
Giant magnetoresistance
• Ballistic regime (λ >> L): Landauer formalism
€
ε = (µ1−µ2) /evoltage drop
M = # channels between µ1 and µ2
T
I1+ I2
+
ε I1- €
I1+ =
2eh
M µ1−µ2[ ]
€
I2+ =
2eh
MT µ1−µ2[ ]
⇒
€
G =I
µ1−µ2( ) /e=2e2
h
MT
€
I1− =
2eh
M (1−T) µ1−µ2[ ]
Giant magnetoresistance
two current model
€
Rα = Gα↑ + Gα
↓( )−1
translational symmetry
α = FM, AF
Magnetotransport in multilayers
Magnetotransport in multilayers
• How could the magnetoresistance ratio be enhanced?
• Would it be possible to have in such systems an insulating antiferromagnetic configuration ( )?
• Could interference effects lead to such situation?
Transmission coefficients
“Enhanced magnetoresistance effect in layered systems” M. S. Ferreira, J. dA.C., R. B. Muniz and Murielle Villeret,
Appl. Phys. Lett. 75, 2307 (1999)
Modulated spacer
Interesting features:
⇒ huge magnetoresitance ratio
⇒ spin filtering effect
⇒ Could be used as a logical gate
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