Probing magnetic ordering in multilayers using soft x-ray resonant magnetic scattering

We have carried out resonant magnetic x-ray scattering from $\mathrm{Co}∕\mathrm{Ru}$ multilayers with weak antiferromagnetic coupling. We have measured hysteresis loops at different points in reciprocal space (specular or diffuse, integer or half-order peaks), which reveal a rich variety of different shapes. These arise from different degrees of mixing of the scattering arising from the field dependence of the order parameters describing the degree of ferromagnetic, antiferromagnetic correlations in the sample, with the off-specular measurements giving information about their lateral extent. We make a comparison with macroscopic measurements that give information about the degree of different forms of magnetic order averaged over the whole sample in real space.

Figure 1

Specular x-ray reflectivity spectrum of the $\mathrm{Co}∕\mathrm{Ru}$ multilayer measured with Cu $K_{\alpha }$ radiation. The points are experimental data while the solid line is a best fit using a dynamical model. The inset shows the room temperature hysteresis loop measured using the Kerr effect.

Figure 2

(Color online) A sketch of the experimental geometry used. The $x$ and $z$ directions are defined with respect to the sample, and the magnetic field is applied along the $x$ axis. The point in reciprocal space probed is determined by the settings of the sample angle $\omega$ and the detector angle $2\theta$.

Figure 3

Difference in specularly reflected intensity $I_{+}-I_{-}$ for a fixed detector angle of 15° for the sample in two oppositely magnetized directions $(H=\pm 300\mathrm{Oe}$ as a function of photon energy. The tabulated positions of the Co $L_3$ and $L_2$ edges (Ref. 32)are marked by the vertical dashed lines. The open circles show experimental data, while the solid line is a simulation using the model described in the text. The simulated curve is displaced vertically from the data. There is no particular significance to the choice of $2\theta =15°$. We measured this curve for several different detector angles at the specular condition. Although differing slightly in the details, this curve is representative of them all.

Figure 4

Narrow rocking curves through the specular position for an integer $(n=2)$ and half $(n=\frac{5}{2})$ order Bragg peak position. On the left curves for four different fields are shown, $\pm 300\mathrm{Oe}$, a saturating field; and $\pm 120\mathrm{Oe}$, roughly the coercive field. On the right the average and difference plots are shown for the two different field values, normalized to the specular reflectivity. Higher levels of diffuse scatter are evident at $120\mathrm{Oe}$, in particular at the $n=\frac{5}{2}$ position, where the sensitivity to AF ordering in the multilayer is highest. The arrows indicate the off-specular positions where hysteresis loops shown in Fig. 5 were recorded, measurements were also made at the specular position $Q_x=0$. It is worth making a comment here about the accuracy of our data, since the difference signal is a small difference of two large numbers. The level of noise in the various scans gives an indication of the degree of uncertainty in the data, visible only when the signal is close to the background. The uncertainty in the difference signal on the specular ridge is less than one part in ${10}^3$ and is at least one part in ${10}^2$ over most of the diffuse part of the scan as well.

Figure 5

Hysteresis loops of x-ray intensity measured with the apparatus set to be sensitive to scatter at different points in reciprocal space. Loops with offsets in $\omega$ of 0° (엯), and $-0.5°$ (◻) are shown. The data for the specular position $(\Delta \omega =0)$, $n=2$ loop appears rather compressed on this scale, but is reproduced in Fig. 6 more clearly.

Figure 6

A superposition of the normalized Kerr hysteresis loop (solid line) and the $n=2$ specular loop measured by XRMS (엯). Although there are distortions in the loop shape due to the dynamical variations in the scattered intensity with field, the broad agreement is evident.

Figure 7

(a) Magnetoresistance measurements of the sample in the longitudinal ($R_{\Vert }$, ●) and transverse ($R_{\perp }$, 엯) geometries. The results are dominated by the AMR. (b) The average of the two transport data sets, $(R_{\Vert }+R_{\perp })∕2$, showing hysteretic peaks at $\pm 90\mathrm{Oe}$. (c) The XRMS data at an offset angle of $\Delta \omega =-0.5°$ for $n=\frac{3}{2}$ and $n=2$. Only the peaks measured at the half-order positions align with the data in panel (b).