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

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)

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

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.

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

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.

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

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.

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

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

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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