STM Differential Conductance of a Pair of Magnetic Adatoms

Brian Lane, Kevin Ingersent, U. of Florida

Outline Review of one-impurity results Setup of two-impurity problem Two-impurity results

Thanks

Charles Taylor and the UF HPC staff.

Brent Nelson and the UF Physics Computer Support staff.

Supported by NSF Grant DMR-0312939

Investigate competition between Kondo screening and magnetic ordering, which occurs in systems such as heavy fermions, small magnetic devices, and quantum dots. This competition can be studied using scanning tunneling microscopy (STM).

W. Chen, et al, Phys. Rev. B 60, 12 (1999)

Motivation for Study

Review of the one-impurity problem

impurity

STM tip

tc

td

Vd = hybridization between impurity and conduction electrons

td = matrix element for tunneling into discrete impurity state

tc = matrix element for tunneling into continuous surface state

Vd

non-magnetic metal

One-Impurity STM Results

Energies measured in units of ½-bandwidth D.DOS: (E) ~ (E+D)½

Fano line shape develops due to interference between tunneling paths.

G(V) vs. VVd = 0.18

-10-8-10-6-10-4 10-8 10-6 10-4

0.2

0.4

0.6

5.0

0.0

G(V) vs. V

eV/D

G(V

) (a

rb. u

nits

)

One-Impurity STM Results

STM with two impurities

impurity 1

STM tip

tc

td

Impurities are identical and separated by a distance R.

No direct tunneling between impurities.

STM tip is directly over one of the impurities (no direct tunneling into the other).

Now we have a Kondo effect and an RKKY interaction.

Vd

impurity 2

Vd

R

non-magnetic surface

IRKKY(R) (arb. units) vs. kFR

FM

AFM

|IRKKY|/TK(1-imp) measures the competition between the two effects.

4

sin 2 2 cos 2~

F F F

RKKY

F

k R k R k RI

k R

2-imp T*chi & d-spectral functionT vs. T/D

T

T/D

(E) ~ (E+D)½, Vd = 0.18

Effective TK is dropping as R decreases for the FM cases.

Impurity Spectral Density vs. /D

/D

Two-Impurity Thermodynamic and Spectral Results

10-15 10-10 10-5 10.0

0.1

0.2

0.3

0.4

10-510-10 1-10-5 -10-10-1

Two-Impurity STM ConductanceG(V) vs. V

td/tc = 0.1

eV/D

G(V

) (a

rb. u

nits

)

-10-5 -10-10 10-10 10-5

0.2

0.0

0.4

Two-Impurity STM ConductanceG(V) vs. V

td/tc = 0.4

eV/D

G(V

) (a

rb. u

nits

)

-10-5 -10-10 10-10 10-5

0.4

0.0

0.2

0.6

0.8

1.0

Conclusions The competition between Kondo screening and the RKKY

interaction is clearly revealed in the STM spectrum. For FM RKKY, the effective TK drops and the lowest

energy scale of the STM line shape decreases with R. For AFM RKKY, the STM spectrum remains featureless.

Future Work Include direct-exchange interaction between impurities. Vary tip position and tunnel from tip into both impurities. Compare with predictions from other methods (e.g.,

DMRG for R=0). Compare more closely with experiment.

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