Field-induced spin reorientation in ${\left[\mathrm{Fe}/\mathrm{Cr}\right]}_n$ multilayers studied by nuclear resonance reflectivity

We present depth-resolved nuclear resonance reflectivity studies of the magnetization evolution in ${[{}^{57}\mathrm{Fe}\left(3\mathrm{nm}\right)/\mathrm{Cr}\left(1.2\mathrm{nm}\right)]}_{10}$ multilayer under applied external field. The measurements have been performed at the station BL09XU of SPring-8 at different values of the external field (0–1500 Oe). We apply the joint fit of the delayed reflectivity curves and the time spectra of the nuclear resonance reflectivity measured at different grazing angles for enhancement of the depth resolution and reliability of results. We show that the azimuth angle, which is used in all papers devoted to the magnetization profile determination, has a more complicated physical sense due to the partially coherent averaging of the scattering amplitudes from magnetic lateral domains. We describe how to select the true azimuth angle from the determined “effective azimuth angle.” Finally we obtain the noncollinear twisted magnetization depth profiles where the spin-flop state appears sequentially in different ${}^{57}\mathrm{Fe}$ layers at increasing applied field.

Figure 1

The used coordinate system.

Figure 2

The illustration of the partially coherent interference of waves reflected by different domains.

Figure 3

Experimental CEMS (dots) and fit result by three magnetic subspectra (dotted lines) corresponding to ${\vec{B}}_{hf}^{\left(1\right)}=33.1\mathrm{T},{\vec{B}}_{hf}^{\left(2\right)}=30.8\mathrm{T},{\vec{B}}_{hf}^{\left(3\right)}=24.5\mathrm{T}$ for the ${[{}^{57}\mathrm{Fe}\left(3.0\mathrm{nm}\right)/\mathrm{Cr}\left(1.2\mathrm{nm}\right)]}_{10}$ sample.

Figure 4

Magnetization curve for ${[{}^{57}\mathrm{Fe}\left(3.0\mathrm{nm}\right)/\mathrm{Cr}\left(1.2\mathrm{nm}\right)]}_{10}$ sample, measured by magneto-optical Kerr effect. The steps and small hysteresis are hardly seen.

Figure 5

Prompt and delayed reflectivity measured without external field for the sample ${[{}^{57}\mathrm{Fe}\left(3.0\mathrm{nm}\right)/\mathrm{Cr}\left(1.2\mathrm{nm}\right)]}_{10}$. The angles at which the time spectra of the NRR were measured are marked by the dashed vertical lines.

Figure 6

Depth profile of the electron density and of the absorption obtained by the fit of the prompt reflectivity curves.

Figure 7

NRR time spectra, measured at the angles, marked by vertical lines in Fig. 5 (left panel), and their Fourier transform (right panel). The spectra are normalized and vertically shifted.

Figure 8

Time spectra of NRR measured at four grazing angles in logarithm scale and vertically shifted. Symbols represent the experimental data, lines—the fit results.

Figure 9

The depth distribution of the ${}^{57}\mathrm{Fe}$ nuclei, characterizing by one of the three kinds of $B_{hf}$, obtained by the fit of CEM spectrum in Fig. 3.

Figure 10

Delayed reflectivity curves measured at different magnitude of the ascending external field in $L$ geometry. Symbols represent the experimental data, lines—the fit results.

Figure 11

The same as in Fig. 10 but for $T$ geometry.

Figure 12

Time spectra of NRR reflectivity, measured at three incidence angles of SR for different magnitude of the ascending external field in $L$ geometry. Symbols represent the experimental data, lines—the fit results.

Figure 13

The same as in Fig. 12, but for $T$ geometry.

Figure 14

The layer-by-layer variations of the effective azimuth angle in our ML as a function of the ascending applied field; these are the results of the joint fit of the delayed reflectivity curves (Figs. 10 and 11) and time spectra of NRR reflectivity (Figs. 12 and 13).

Figure 15

The same as in Fig. 14 (e.g., the magnetization directions in azimuth plane for ten ${}^{57}\mathrm{Fe}$ layers of our ML) for the selected values of the external field, presented as polar graphs.

Figure 16

Time spectrum, measured at the half-order Bragg peak from our sample with 450-Oe field applied along the beam (symbols) and theoretical curves for two models (being results of the best fit of all the data for this field): for the model of collinear magnetization in two “magnetic sublattices”—$5^{\circ }/156.7^{\circ }$—(thin blue line) and the model of twisted magnetization (thick red line), presented in the inset (thin dashed vertical lines and lines with square symbols, respectively).

Figure 17

The layer-by-layer variations of the effective azimuth angle in our ML for the applied field of 50 Oe obtained from the fit of data for $L$ geometry (filled squares) and $T$ geometry (empty squares). The direction of the external field is drawn by a thick vertical line for the $L$ geometry and by a thick dashed vertical line for the $T$ geometry. Note that the effective azimuth angle ${\gamma }^{\mathrm{eff}}$ is determined in the axis, connected with beam direction (Fig. 1).

Figure 18

Two models of the depth profile of the ${}^{57}\mathrm{Fe}$ layer magnetizations under the 350-Oe applied field obtained by the all-data joint fit.