Itinerant Nature of Atom-Magnetization Excitation by Tunneling Electrons

We have performed single-atom magnetization curve (SAMC) measurements and inelastic scanning tunneling spectroscopy (ISTS) on individual Fe atoms on a Cu(111) surface. The SAMCs show a broad distribution of magnetic moments with $3.5{\mu }_B$ being the mean value. ISTS reveals a magnetization excitation with a lifetime of 200 fsec which decreases by a factor of 2 upon application of a magnetic field of 12 T. The experimental observations are quantitatively explained by the decay of the magnetization excitation into Stoner modes of the itinerant electron system as shown by newly developed theoretical modeling.

Figure 1

(a) Topograph of a distribution of Fe atoms on Cu(111). The color bar spans 90 pm. (b) Spatially-resolved magnetic asymmetry map between saturation field values $B=\pm 0.4\mathrm{T}$ [$I_{\mathrm{stab}}=0.6\mathrm{nA}$, $V_{\mathrm{stab}}=-10\mathrm{mV}$, $V_{\mathrm{mod}}=5\mathrm{mV}$ (rms)]. Color bar from 0 a.u. to 0.025 a.u. (c) Dots: SAMC extracted from the $B$-dependent $dI/dV$ maps by averaging over the signal from an individual atom. Solid line: fit to the data using the continuum model. (d) Histogram of effective magnetic moments extracted from the fit to the SAMCs of Fe atoms with minimum distance 2 nm to other atoms or Co islands.

Figure 2

(a) ISTS at different $B$ as indicated [$I_{\mathrm{stab}}=1\mathrm{nA}$, $V_{\mathrm{stab}}=-10\mathrm{mV}$, $V_{\mathrm{mod}}=0.1\mathrm{mV}$ (rms)]. Top spectra were taken on an Fe atom. Bottom spectra were taken with the same tip on Cu (vertically shifted by $-14\mathrm{nS}$). (b) Numerical differentiation of spectra taken on another Fe atom using a different tip [$I_{\mathrm{stab}}=2\mathrm{nA}$, $V_{\mathrm{stab}}=-10\mathrm{mV}$, $V_{\mathrm{mod}}=0.05\mathrm{mV}$ (rms)]. (c) Energy and (d) averaged FWHM (high resolution data; error corresponds to the maximum and minimum value) of the excitation as a function of $B$ extracted from Gaussian fits to spectra (b). The inset in (c) shows a histogram of the measured $g$ factors determined from the slope of (c) divided by ${\mu }_B$. The values are extracted from spectra measured on 78 (c) and 16 (d) different atoms.

Figure 3

(a) Calculated density of magnetization excitations for an Fe atom on Cu(111) for various magnetic fields using the ETB approach. At zero field, spin-orbit induced anisotropy renders the excitation energy finite. (b) and (c) show magnetic field dependency of the peak energy and of the linewidth $\Delta E$ in the excitation spectrum (a).