magnetic tunnel junctions. transfer hamiltonian tunneling magnetoresistance

G =(e2 /h) 16k1k2kb2 (exp−2kbd)

(k12 +kb

2)(k22 + kb

2 )k||,σ∑

k1,2 = 2m(εF −V1, 2) /h2 −k||

2

kb = 2m(U −εF )/ h2 + k||

2

GWKB =(e2 /h2) |t|2 k2k||,σ∑ / k1

t=k1k2

exp− kb(x)dx0

d

∫ ⎛

⎝ ⎜ ⎞

⎠ ⎟

G =(e2 /h) exp−2 kb(x)dx0

d

∫ ⎛

⎝ ⎜ ⎞

⎠ ⎟

k||,σ∑

Magnetic Tunnel Junctions

HT = TkqckσL ∗cqσ

R +h.c.[ ]kqσ∑

Tkq2 =

C2

ρL(Ek)ρR(Eq)

I =e dε |Tkqσ |2 AR(qσ ,ε)AL(kσ,ε +eV) nF (ε) −nF(ε +eV)[ ]∫kqσ∑

Ap ≡−ℑmGssp =2πZkσ

p δ(ε −Ekσp )

= ρL(Ekσ )ρR(Eqσ )dEkσdEqσ∫kq∑

I = 2πe2C2 ZLσ

σ∑ ZR

σV

Transfer HamiltonianTransfer Hamiltonian

Tunneling Magnetoresistance

Tunneling: see Phil. Mag. 83, 1255 (2003)

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k|| resolved (partial) DOS in units of states/atom. eV ofbcc(100) Fe plotted in the first 2DBZ. Left column is for the majority spin channeland right column is for theminority spin channel.

From top to bottom, DOSfor a bulk Fe layer, a freesurface Fe layer and the isolated electrode surface Fe layer.

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k|| resolved (partial) DOS in units of states/atom. eV of fcc(100) Co plotted in the first 2DBZ. Left column is for the majority spin channel and right column is for the minority spin channel.

From top to bottom, DOS for a bulk Co layer, a free surface Co layer and the isolated electrode surface Co layer.

Also see for resonant states: O.Wunnicke et al. PRB 65, 064425 (2002).

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k|| resolved (partial) tunneling conductance of bcc (100) Fe/vacuum(10)/Fe tunnel junction at an energy 0.05eV below the Fermi level (a) only for the barrier region, and (b) for the entire junction.

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zoomed-in view.

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k|| resolved (partial) tunneling conductance of the barrier region of a Co junction in the first 2DBZ when the magnetizations of the two electrodes are aligned in parallel(a) majority spin channel,(b) minority spin channel, and (c) antiparallelly aligned. The vacuum barrier is 6 atomic layers thick.

The need to diagonalize basis when more than one state transforms under same irreducible representation

C. Uiberacker and P.M. Levy, PRB 64, 193404 (2001);erratumPRB 65, 169904 (2002).

Fe/ZnSe/Fe

Bias dependence of TMR

Bias dependence of TMR-trapezoidal barrier

JMR ratio vs. bias for free electron trapezoidal barrier model tunnel junction with a Fermi sea depth of 16eV for majority and 3eV for minority spins; square barrier height at zero bias is 1eV measured from Fermi level

Oscillating TMR S.Yuasa et al. Science 297, 234 (2002)

Ab-initio calculation of JMR for Co/Vac(6)/Cu(p)Co junction; K. Wang private communication.

Tunneling with semiconducting electrodes

As there is little screening of electrons in semiconductors Isurmise that the SDT with 2-3ML of magnetic semiconductingelectrodes is very different from 20-30 ML.

Also, there will be hole as well as electron conduction; particularlyfor holes spin-orbit coupling plays an important role. The spin-orbit coupling can be detrimental to the polarization of spin currents.

For metallic electrodes it is sufficient to have 2-3ML of themagnetic electrode for spin dependent tunneling (SDT) ; therefore it is not the spin polarization of the current that produces SDT. What happens for semiconducting electrodes?

One can conceptualize spin dependent tunneling in two steps:

• Presenting spin polarized electrons at the interface of between the electrode and barrier. This is accounted for by the DOS.

• The decay of wavefunction inside the barrier. There are evanescent states inside the barrier whose decay is given by an imaginary k vector.

So what’s new?

The spin Hall effect: Hirsch (1999), Zhang (2000)*

In general the Hall effect is the current or voltage transverseto the applied electric field. This usually appears when oneapplies a magnetic field perpendicular to the electric field;however in systems that contain spin-orbit coupling one can have preferential scattering of spins to the left or right of thecurrent, so that one can produce a Hall voltage in the absenceof a magnetic field. This principle was first enunciated by Mottand has the formed the basis of Mott spin scattering detectors.

*

Then we were told there’s an intrinsic SHE

But can one detect the ISHE? It seems not!

What do the experimentalists say about the ISHE?

Molecular spintronics

Published online March 6, 2005 in Nature Materials

Conclusion