Spin Polarization of the Split Kondo State

Spin-resolved scanning tunneling microscopy is employed to quantitatively determine the spin polarization of the magnetic field-split Kondo state. Tunneling conductance spectra of a Kondo-screened magnetic atom are evaluated within a simple model taking into account inelastic tunneling due to spin excitations and two Kondo peaks positioned symmetrically around the Fermi energy. We fit the spin state of the Kondo-screened atom with a spin Hamiltonian independent of the Kondo effect and account for Zeeman splitting of the Kondo peak in the magnetic field. We find that the width and the height of the Kondo peaks scales with the Zeeman energy. Our observations are consistent with full spin polarization of the Kondo peaks, i.e., a majority spin peak below the Fermi energy and a minority spin peak above.

Figure 1

(a) Setup of the spin-resolved STM experiment on individual Co atoms on ${\mathrm{Cu}}_2\mathrm{N}/\mathrm{Cu}(001)$ in an in-plane magnetic field, STM topography image ($10\mathrm{nm}\times 10\mathrm{nm}$, $V=+10\mathrm{mV}$, $I=0.1\mathrm{nA}$); white lines denote the different uniaxial hard anisotropy axes perpendicular to each other; the right inset shows a $dI/dV$ spectrum of a Co atom at $B=0$. (b),(c) Spin-averaged (gray) and spin-resolved (color) tunnel spectra of Co atoms with magnetic field of 7 T applied along (CoV) and perpendicular (CoN) to the hard anisotropy axis, respectively (stabilization set point $\sigma =80\mathrm{nS}$, $V=+25\mathrm{mV}$, $I=2\mathrm{nA}$). Insets sketch the two relevant spin-flip excitations as a function of magnetic field. (d) The tip’s spin polarization, deduced from measurements of a Mn atom on ${\mathrm{Cu}}_2\mathrm{N}$, as a function of applied magnetic field; the solid line is a fit accounting for the paramagnetic behavior of the Mn atoms on tip and sample by Brillouin functions for spins with $S=5/2,g=2,T=0.5\mathrm{K}$, ${\eta }_{\text{sample}}=1$, ${\eta }_{\text{tip}}^{\max }=0.5$.

Figure 2

Decomposition of the $dI/dV$ spectra into spin-flip excitation and Kondo related contributions. (a),(b) Experimental data (circles) measured on a CoV and a CoN atom at $B=5\mathrm{T}$ (stabilization set point $\sigma =80\mathrm{nS}$, $V=+25\mathrm{mV}$, $I=2\mathrm{nA}$). Upper solid line: best fit using the sum of an asymmetric double step function (dashed line) and two Frota functions (lower solid lines), according to Eq. (1) of the main text. (c),(d) Energies ${ϵ}_{i,o}$, (e),(f) ratio of the intensities $(h_i^{+}+h_i^{-})/(h_o^{+}+h_o^{-})$, and (g),(h) effective asymmetries of the two steps at different magnetic field. Symbols are fits to the data [25]. Lines are calculated with the model spin Hamiltonian using $D=2.6\pm 0.1$ $(2.5\pm 0.1)\mathrm{meV}$, $E=0.45\pm 0.05$ $(0.40\pm 0.05)\mathrm{meV}$, and $g=2.1\pm 0.1$ ($2.4\pm 0.1$) for the CoV (CoN) atom.

Figure 3

The splitting and the polarization of the Kondo peak. (a),(b) Kondo-related experimental data (circles) and fit with two Frota functions (solid lines) for CoV and CoN (curves in magnetic field are shifted vertically for better visualization). Fit results for (c) the width ${\mathrm{\Gamma }}_K$, (d) the peak height $h_K$, (e) the area ${\mathrm{\Gamma }}_K{h}_K$, and (f) the experimental peak asymmetry ${\eta }_K^{\text{eff}}$ plotted against the splitting energy ${ϵ}_K$ [25]. The horizontal and vertical dashed lines in (c)–(f) mark the characteristic Kondo energy.

Figure 4

(a) The spin polarization of the Kondo state ${\eta }_K$ is approximately one for both CoV and CoN independent of ${ϵ}_K$. (b) Simulated spectra with ${\eta }_K=1$ and a magnetic field which splits the Kondo state by ${ϵ}_K=2{\mathrm{\Gamma }}_K$ for different tip spin polarizations; gray is the sum of the majority and minority states, i.e., the experimentally measured spectrum. The dashed line in the lower panel shows the peak-dip structure expected for an apparent ${\eta }_K=1.2$.