Element-specific magnetic properties of Co${}_2$(Mn${}_{1-x}$Fe${}_x$)Si films probed by x-ray magnetic circular/linear dichroism

Element-specific magnetic properties of epitaxial Co${}_2$Fe${}_x$Mn${}_{1-x}$Si/MgO(100) Heusler films prepared by laser ablation are measured by circular dichroism in x-ray absorption spectroscopy (XMCD). Surface and bulk magnetization of the 100-nm-thick films are equal as tested by comparing the total electron yield and transmission measurements and follow the generalized Slater-Pauling rule. For Co${}_2$FeSi, the large magnetization of 6 ${\mu }_B$ per formula unit indicates half-metallic behavior. Calculations using the local spin density approximation (LDA) result in a half-metallic band structure for this compound when an additional electron-electron-correlation correction ($\text{LDA}+U$) is considered. Simulated XMCD spectra using the LDA and $\text{LDA}+U$ approaches are compared to the experimental spectra. While the electron-electron Coulomb correlation has only a small effect on the observable XMCD spectra, the calculations predict that it will cause a significant change in the x-ray magnetic linear dichroism (XMLD).

Figure 1

(a) Absorption coefficient at the Mn $L_2$ and $L_3$ edges for magnetization direction parallel (antiparallel) to the x-ray polarization, ${\mu }^{+}\propto -\ln (I^{+}/I_{\mathrm{ref}})$ [${\mu }^{-}\propto -\ln (I^{-}/I_{\mathrm{ref}})$], for a Co${}_2$MnSi film on MgO. The XMCD spectrum ${\mu }^{+}-{\mu }^{-}$ is shown on the same scale. (b) Simultaneously measured total electron yield spectra $I_{\mathrm{TEY}}^{+}$ ($I_{\mathrm{TEY}}^{-}$) for the same sample. (c), (d) Corresponding data measured at the Co $L_2$ and $L_3$ edges.

Figure 2

(a) Absorption coefficient at the Mn $L_2$ and $L_3$ edges for magnetization direction parallel (antiparallel) to the x-ray polarization, ${\mu }^{+}\propto -\ln (I^{+}/I_{\mathrm{ref}})$ [${\mu }^{-}\propto -\ln (I^{-}/I_{\mathrm{ref}})$], for a Co${}_2$(Fe${}_{0.5}$Mn${}_{0.5}$)Si film on MgO. The XMCD spectrum ${\mu }^{+}-{\mu }^{-}$ is shown on the same scale. (b) Simultaneously measured total electron yield spectra $I_{\mathrm{TEY}}^{+}$ ($I_{\mathrm{TEY}}^{-}$) for the same sample. (c), (d) Corresponding data measured at the Fe $L_2$ and $L_3$ edges. (e), (f) Corresponding data measured at the Co $L_2$ and $L_3$ edges.

Figure 3

(a) Absorption coefficient at the Fe $L_2$ and $L_3$ edges for magnetization direction parallel (antiparallel) to the x-ray polarization, ${\mu }^{+}\propto -\ln (I^{+}/I_{\mathrm{ref}})$ [${\mu }^{-}\propto -\ln (I^{-}/I_{\mathrm{ref}})$], for a Co${}_2$FeSi film on MgO. The XMCD spectrum ${\mu }^{+}-{\mu }^{-}$ is shown on the same scale. (b) Simultaneously measured total electron yield spectra $I_{\mathrm{TEY}}^{+}$ ($I_{\mathrm{TEY}}^{-}$) for the same sample. (c), (d) Corresponding data measured at the Co $L_2$ and $L_3$ edges.

Figure 4

(a) Total magnetic moments (circles) and element-specific spin moments for Co${}_2$(Fe${}_{0.5}$Mn${}_{0.5}$)Si as a function of Fe concentration. Full symbols refer to transmission (TM) data and open symbols to TEY data (i.e., surface-sensitive data). The error bar for the statistical error not including the error of the common factors of x-ray polarization and number of $d$ holes for the spin and total moment corresponds to the symbol size. The solid line indicates the Slater-Pauling rule. (b) Ratio of the orbital magnetic moment to the spin magnetic moment for the transition-metal atoms. Error bars are estimated by varying the integration boundaries for the sum-rule analysis.

Figure 5

Spin-resolved density of states of Co${}_2$FeSi calculated with (top) the LDA and (bottom) the $\text{LDA}+U$. Majority (minority) DOS contributions are depicted by the up-pointing (down-pointing) arrows.

Figure 6

X-ray spectra at the $L_3$ edge along the $\mathbf{M}=\left(001\right)$ direction for the Co atom of Co${}_2$FeSi. (a) X-ray absorption spectra (XAS) of Co calculated using the LDA (dotted, green) and $\text{LDA}+U$ (full line, red) are compared to experimental data (open circles, black). Thin lines indicate calculated data with a Lorentzian broadening of 0.1 eV (note that these are not shown on the same scale). (b) Corresponding x-ray circular magnetic dichroism (XMCD) spectra calculated using the LDA (dotted, green), $\text{LDA}+U$ (full line, red), and experimental data (open circles, black). A Hubbard $U$ of 4.8 eV for the Co atom and a Lorentzian broadening of 0.3 eV were used.

Figure 7

The same as in Fig. 6, but for the Fe atom in Co${}_2$FeSi. The Hubbard $U$ was set to 4.5 eV for the Fe atom.

Figure 8

X-ray magnetic linear dichroism predicted for the Co atom in Co${}_2$FeSi with the LDA (upper panel) and the $\text{LDA}+U$ approach (lower panel). XMLD spectra are given for three magnetization directions, (001), (110), and (111). The Coulomb $U$ and Lorentzian broadening used are the same as in Fig. 6.

Figure 9

As Fig. 8, but for the Fe atom in Co${}_2$FeSi. The Coulomb $U$ and Lorentzian broadening used are the same as in Fig. 7.