Magnetic Friedel Oscillation at the Fe(001) Surface: Direct Observation by Atomic-Layer-Resolved Synchrotron Radiation ${}^{57}\mathrm{Fe}$ Mössbauer Spectroscopy

The surface magnetism of Fe(001) was studied in an atomic layer-by-layer fashion by using the in situ iron-57 probe layer method with a synchrotron Mössbauer source. The observed internal hyperfine field $H_{\mathrm{int}}$ exhibits a marked decrease at the surface and an oscillatory behavior with increasing depth in the individual upper four layers below the surface. The calculated layer-depth dependencies of the effective hyperfine field $|H_{\mathrm{eff}}|$, isomer shift $\delta$, and quadrupole shift $2ϵ$ agree well with the observed experimental parameters. These results provide the first experimental evidence for the magnetic Friedel oscillations, which penetrate several layers from the Fe(001) surface.

Figure 1

(a) Experimental setup. $e_{\pi }$, electric field vector of the incident beam; $H_{\mathrm{ex}}$, external magnetic field (300 Oe); detector, NaI(Tl) scintillation detector. (b) Mössbauer spectra of the $N$th probe layer samples measured at 300 K. Black solid lines represent the fitted curves. Red, blue, and green lines represent three different magnetic components. $M(i)$ represents the magnetic component assigned to the iron-57 atoms located in the $i$th layer below the surface.

Figure 2

Plots of the experimental and theoretical layer-by-layer hyperfine parameters. (a) Experimental $H_{\mathrm{int}}$ values and experimental $H_{\mathrm{int}}$ vs theoretical $|H_{\mathrm{eff}}|$ values. (b) Experimental $\delta$, $2ϵ$, and $\mathrm{\Delta }{H}_{\mathrm{int}}$ values. (c) Theoretical $M_{\mathrm{Fe}}$, $|H_{\mathrm{eff}}|$, $H_{\mathrm{core}}$, $H_{\mathrm{cond}}$, and $H_{\mathrm{orbit}}$ values. (d) Theoretical $\delta$ and $2ϵ$ values. Circles and symbols denote data points. Solid and dashed lines connect data points. In (a) and (b), some uncertainties are less than the size of the data points.

Figure 3

Band structures and surface states of a 30-ML-thick Fe(001) film. (a) Layer-resolved electron density of states. (b) Spin density map in units of ${10}^{-4}\mathrm{electrons}/a_0^3$ on the (110) plane. Each contour differs by a factor of 2. Dashed lines indicate a negative spin density. (c) Charge density map in units of ${10}^{-3}\mathrm{electrons}/a_0^3$ on the (110) plane. Each contour differs by a factor of $\sqrt{2}$. In (b), the dashed contours between the atoms exhibit a Friedel-type oscillation penetrating the surface.