1. 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

2. Motivation for Study
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)

3. Review of the one-impurity problem
STM tip td
impurity tc Vd
non-magnetic metal
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

4. One-Impurity STM Results
G(V) vs. V
Vd = 0.18
Energies measured in units of ½-bandwidth D.
DOS: r(E) ~ (E+D)½
Fano line shape develops due to interference between tunneling paths.

5. One-Impurity STM Results
G(V) vs. V
0.6
5.0
0.4
G(V) (arb. units)
0.0
0.2
-10-4
-10-6
-10-8
eV/D
10-8
10-6
10-4

6. STM with two impurities
STM tip td tc
impurity 2
impurity 1 R Vd Vd
non-magnetic surface
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.

7. IRKKY(R) (arb. units) vs. kFRFM
AFM
|IRKKY|/TK(1-imp) measures the competition between the two effects.

8. 2-imp T*chi & d-spectral function
Two-Impurity Thermodynamic and Spectral Results
2-imp T*chi & d-spectral function
Tc vs. T/D
Impurity Spectral Density vs. w/D
0.4
0.3 Tc
0.2
0.1
0.0
10-15
10-10
10-5 1 -1
-10-5
-10-10
10-10
10-5 1
T/D
w/D
r(E) ~ (E+D)½, Vd = 0.18
Effective TK is dropping as R decreases for the FM cases.

9. Two-Impurity STM Conductance
G(V) vs. V
td/tc = 0.1
0.4
G(V) (arb. units)
0.2
0.0
-10-5
-10-10
eV/D
10-10
10-5

10. Two-Impurity STM Conductance
G(V) vs. V
td/tc = 0.4
1.0
0.8
0.6
G(V) (arb. units)
0.4
0.2
0.0
-10-5
-10-10
10-10
10-5
eV/D

11. Conclusions Future Work
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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References