STM Differential Conductance of a Pair of Magnetic Adatoms

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-0312939

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) (ED)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
10-6
-10-6
-10-4
-10-8
10-8
10-4
eV/D
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. kFR
FM
AFM
IRKKY/TK(1-imp) measures the competition
between the two effects.
8
2-imp Tchi d-spectral function
Two-Impurity Thermodynamic and Spectral Results
Impurity Spectral Density vs. w/D
Tc vs. T/D
0.4
0.3
Tc
0.2
0.1
0.0
10-15
10-5
1
10-5
10-10
1
-10-5
-10-10
-1
10-10
T/D
w/D

• r(E) (ED)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
10-10
10-5
eV/D
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
• 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 R0).
• Compare more closely with experiment.

12

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