Master in NanoscienceNanostructural PropertiesLectures by A. Rubio, J. Aizpurua and A. Ayuela

Theory of spin-polarized STM : a short introduction

E. J. G. Santos

Master in NanoscienceDonostia – San Sebastian, April 9th 2008

Outline

Spin polarized tunneling

Spin-valve effect: in the light of Bardeen's theory

The Landauer formalism of tunneling problem- Concept and an elementary derivation

- Relation with Bardeen’s tunneling theory

Practical examples: How does it work?Conclusions References and acknowledgements

Spin Polarized Tunneling Formalism (I)

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

General formalism:

using spinors instead

of spatial wavefunctions

Spin Polarized Tunneling Formalism (II)

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

In a coordinate system the z-spin of electrode A is diagonized.

Starting with a spin-up state,

Starting with a spin-down state,

Following the procedure of deriving Bardeen’s theory…

Experimental configuration

Spinor in electrode A:

Spinor in electrode B, different z:

The most general

transformation:

through the Euler angles.

Spin-valve effect: in the light of Bardeen (I)

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

Spin-valve effect: in the light of Bardeen (II)

In the coordinate system of spin polarization of electrode A…

The total tunneling conductance is…

It can be simplified by introducing…

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

Finally, a familiar result of Slonczewski…

Further, by defining

We obtain

For SP-STM, the above results can be further simplified by using the Landauer formalism.

Master in NanoscienceDonostia – San Sebastian, April 9th 2008

Spin-valve effect: in the light of Bardeen (III)

J. S. Moodera and L. K. Kinder , J. Appl. Phys., 79, 4724 (1996).

Spin-valve effect: experimental verifications (I)

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

Spin-valve effect: experimental verifications (II)

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

MIT Database Patents, US 1998

The Landauer formalism of tunneling problem (I)

The tunneling conductance has an exponential dependence on z. What is the absolute value?

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

n-th wavefunction n-th energy eigenvalue

Local density of states at energy E, counting two spins,

Classical velocity

The Landauer formalism of tunneling problem (II)

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

Bias and Fermi levels Tunneling conductance

Impinging current

Finally…

The Landauer formalism of tunneling problem (III)

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

The Landauer formalism of tunneling problem (IV)

The tunneling conductance according to Landauer…

The tunneling conductance according to Bardeen…

Consequently,

Supriyo Datta made a connection between the Bardeen tunneling theory and the Landauer formalism (pp. 161-163 of Electronic Transport in Mesoscopic Systems ):

The spin-polarized tunneling conductance between two atoms is…

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

Conclusions

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

Simple model of SP-STM can already capture the essential features of atomic scale constant-current images of magnetic structures.

Understanding magnetic order and interactions on the atomic scale is an essential

prerequisite to achieve the ultimate goal of tailoring magnetic materials with desired

properties.

SP-STM is a topic of intense current research due to fundamental interest in the

dependence of magnetic interactions on chemical composition, structure, dimension,

and symmetry.

References and Acknowledgements

Master in Nanoscience

Donostia – San Sebastian, April 9th 2008

M. Bode, Spin-polarized scanning tunnelling microscopy Rep. Prog. Phys. 66(2003) 523-582.

C. Julian Chen, Introduction to Scanning Tunneling Microscopy Oxford Science

Publications, 2nd. Edition (2008).

S. Heinze, Simulation of spin-polarized scanning tunneling microscopy images of

nanoscale non-collinear magnetic structures, Appl. Phys. A 85 (2006) 407- 414.

Special thanks to Prof. A. Rubio for a nice Spin-STM review paper.

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Thanks for your attention