Interface-related magnetic and vibrational properties in Fe/MgO heterostructures from nuclear resonant spectroscopy and first-principles calculations

We combine ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopy and ${}^{57}\mathrm{Fe}$ nuclear resonant inelastic x-ray scattering (NRIXS) on nanoscale polycrystalline $[\mathrm{bcc}\text{−}{}^{57}\mathrm{Fe}/\mathrm{MgO}]$ multilayers with various Fe-layer thicknesses and layer-resolved density-functional-theory (DFT)-based first-principles calculations of a (001)-oriented [Fe(8 ML)/MgO(8 ML)](001) heterostructure (where ML denotes monolayer) to unravel the interface-related atomic vibrational properties of a multilayer system. Being consistent in theory and experiment, we observe enhanced hyperfine magnetic fields $B_{\text{hf}}$ in the multilayers as compared to $B_{\text{hf}}$ in bulk bcc Fe; this effect is associated with the Fe/MgO interface layers. NRIXS and DFT both reveal a strong reduction of the longitudinal acoustic phonon peak in combination with an enhancement of the low-energy vibrational density of states (VDOS) suggesting that the presence of interfaces and the associated increase in the layer-resolved magnetic moments results in drastic changes in the Fe-partial VDOS. From the experimental and calculated VDOS, vibrational thermodynamic properties have been determined as a function of Fe thickness and were found to be in excellent agreement.

Figure 1

Schematic representation of the heterostructure. For three studied multilayers we have varied the number of Fe monolayers ($t_{\text{Fe}}=55$, 28, and 10 MLs), while keeping the MgO thickness (effectively 19 MLs) constant. A fourth multilayer had the composition [Fe(7 MLs)/MgO(5 MLs)]${}_{15.5}$.

Figure 2

(a) Result of zero-field CEMS measurements at $T=80\mathrm{K}$ for bulk bcc Fe (top) and Fe/MgO multilayers with varying Fe thicknesses $t_{\text{Fe}}$ of 55, 28, and 10 monolayers (MLs) and a MgO thickness of 19 MLs and for a multilayer with $t_{\text{Fe}}=7$ MLs and $t_{\text{MgO}}\approx 5$ MLs. Black dots, experimental data; red lines, least-squares fitted curves using the corresponding hyperfine-field distributions $p\left(B_{\text{hf}}\right)$ obtained from the fittings and shown in (b). The sextet lines are numbered in (a) for bcc Fe as an example. In (a), a clear reorientation of the Fe spins from preferred in-plane to preferred out-of-plane direction with decreasing Fe thickness is evident from the reduction of the relative intensity of lines 2 and 5. In (b), a broadening of $p\left(B_{\text{hf}}\right)$ with decreasing Fe thickness is observed, which extends up to large values $B_{\text{hf}}$ of about 40 T.

Figure 3

Field-dependent magnetization curves measured for different Fe thicknesses for in-plane and out-of-plane geometry. Measurements have been performed at $T=80$ K. The MgO layer thickness was 19 MLs for the 55-, 28-, and 10-ML Fe samples and $\sim 5$ MLs for the 7-ML Fe sample.

Figure 4

Fe-partial VDOS obtained from NRIXS for a bcc Fe foil and Fe/MgO multilayer systems with varying Fe thicknesses $t_{\text{Fe}}$ of 55, 28, and 10 MLs and constant MgO layer thickness $t_{\text{MgO}}$ of 19 MLs. One can clearly observe a softening of the Fe-partial VDOS and a reduction of the longitudinal-acoustic phonon mode at 35 meV. The VDOS of the bcc Fe foil has been taken from Ref. [94]. All VDOS are area normalized to 3 (three vibrational degrees of freedom per Fe atom).

Figure 5

Layer-resolved Fe-projected phonon dispersion and VDOS obtained from our DFT calculations. The left panel shows the low-energy part of the phonon dispersion for reciprocal vectors lying in plane. The size of the symbols indicates the contribution of the symmetry-inequivalent Fe atoms (marked by different colors) to the eigenvectors corresponding to the respective $q$-vector. Contributions from Mg and O atoms are not shown. The rightmost three panels show the corresponding site-resolved VDOS (normalized to 1) for all inequivalent Fe, Mg, and O atoms in the respective energy window of the Fe phonons.

Figure 6

Extrapolation of the Fe-projected VDOS obtained from our DFT calculations (Fig. 5) to the layer thickness of the experimental sample corresponding to Fig. 4. To improve the comparison of the characteristic features with experiment, the Gaussian broadening has been increased to 4 meV. The calculations reproduce the significant loss of spectral weight below 18 meV for increasing slab thickness, which is accompanied by a moderate increase at the two peaks around 25 meV and the evolution of a sharp peak above 30 meV.