Kondo resonance lineshape of magnetic adatoms on decoupling layers

The zero-bias resonance in the $dI/dV$ tunneling spectrum recorded using a scanning tunneling microscope above a spin-1/2 magnetic adatom (such as Ti) adsorbed on a decoupling layer on a metal surface can be accurately fitted using the universal spectral function of the Kondo impurity model both at zero field and at finite external magnetic field. Excellent agreement is found both for the asymptotic low-energy part and for the high-energy logarithmic tails of the Kondo resonance. For finite magnetic field, the nonlinear fitting procedure consists of repeatedly solving the impurity model for different Zeeman energies in order to obtain accurate spectral functions which are compared with the experimental $dI/dV$ curves. The experimental results at zero field are sufficiently restraining to enable an unprecedented reliability in the determination of the Kondo temperature, while at finite fields the results are more ambiguous and two different interpretations are proposed.

Figure 1

Theoretical function (light line, red online) and experimental data (black symbols) for the Kondo resonance in the $dI/dV$ spectral function for a Ti magnetic impurity atom adsorbed on the Cu${}_2$N layer on Cu(100) surface. The theoretical function is given by Eq. (1), the parameters are explained in the main text. The experimental results have been extracted from Fig. 4 in Ref.23.

Figure 2

Comparison of the resonance line-shapes arising from Fano-like quantum interference in processes where the resonant channel is described by a Lorentzian (dashed line, red online) or by the Kondo resonance curve (full line, black online).

Figure 3

Theoretical function (light function, red online) and experimental data (black symbols) for the Kondo resonance splitting in the external magnetic field $B=7\mathrm{T}$. Upper panel: fixed parameter ${\Delta }_{\mathrm{HWHM}}$. Lower panel: unconstrained ${\Delta }_{\mathrm{HWHM}}$. The magnetic field strength is 7B. The experimental data have been extracted from Fig. 4 in Ref.23.

Figure 4

“Goodness of fit” ${\sigma }^2$ (sum of the residual squared errors) for the field splitting of the Kondo resonance assuming constant or unconstrained parameter ${\Delta }_{\mathrm{HWHM}}$ as a function of the Zeeman energy to Kondo temperature ratio.