Magnetocrystalline anisotropy and Gilbert damping in iron-rich Fe${}_{1-x}$Si${}_x$ thin films

The magnetocrystalline anisotropy of Fe${}_{1-x}$Si${}_x$ ($0\le x\le 0.4$) epitaxial thin films on MgO(001) was studied by ferromagnetic resonance. The experimental results are in good agreement with theoretical predictions of ab initio electronic structure calculations using the fully relativistic Korringa-Kohn-Rostoker Green's function method within spin-density-functional theory. The Gilbert damping $\alpha$ is found to be isotropic by theory and experiment with a minimum at the composition $x=0.2$.

Figure 1

Polar plot of the resonance fields of the sample with 10$\%$ Si at room temperature at 9.8 GHz as a function of the in-plane angle of the external field. Black dots: Experimental data with error bar smaller than the symbol size. Red (gray) line: Fit according to Eqs. (1) and (2).

Figure 2

(a) Cubic MCA constant $K_4$ as a function of the Si concentration in Fe${}_{1-x}$Si${}_x$. Red (gray) dots: Experimental data (error bar $\le$10$\%$, uncertainty of Si content $<$1$\%$) obtained from FMR on thin films at room temperature. Black squares: Theoretical data from ab initio DFT calculations. Experimental data for $x=0$ are taken from Ref. 28. (b) Gilbert parameter $\alpha$. The dashed line represents the theoretical data shifted by an offset of $+1.5\times {10}^{-3}$. (c) Density of states $n\left(E_F\right)$ at the Fermi level and the average spin magnetic moment ${\mu }_S$.

Figure 3

Bloch spectral function for pure Fe [calculated for an imaginary part of the energy $\text{Im}\left(E\right)={10}^{-5}$ Ry] (a) and for the random alloy Fe${}_{0.75}$Si${}_{0.25}$ (b).