Detecting magnetic flux distributions in superconductors with polarized x rays

The magnetic flux distribution arising from a high-$T_c$ superconductor is detected and visualized using polarized x rays. Therefore, we introduce a sensor layer, namely, an amorphous, soft-magnetic ${\mathrm{Co}}_{40}{\mathrm{Fe}}_{40}{\mathrm{B}}_{20}$ cover layer, providing a large x-ray magnetic circular dichroism (XMCD). Temperature-dependent XMCD spectroscopy on the magnetic layer has been performed. Exploiting the temperature dependence of the critical current density of the superconductor we find a quantitative correlation between the XMCD signal and the in-plane stray field of the superconductor. Magneto-optical Kerr effect experiments on the sensor layer can simulate the stray field of the superconductor and hence verify the correlation. We show that the XMCD contrast in the sensor layer corresponds to the in-plane magnetic flux distribution of the superconductor and can hence be used to image magnetic structures in superconductors.

Figure 1

Magneto-optical images of the critical state of a YBCO thin film. The gray scale represents (a) the absolute value of the critical current density $j_c$ and (b) the magnetic flux distribution in the plane $B_x$, which is proportional to $j_c$. The orange point marks the spot for the in-plane x-ray spectroscopy measurements which are always performed in the critical state.

Figure 2

(a) SQUID and MOKE hysteresis loops of 30 nm CoFeB on YBCO, in plane (dark and light blue) and out of plane (green). The coercivity is ${\mu }_0{H}_c=(2\pm 0.4)\mathrm{mT}$ and when saturation of the in-plane component is reached the magnetization is a factor of 10 larger compared to the out-of-plane part. The inset displays a wider range of magnetic field. N.B. Kerr rotation can be converted into absolute values of the magnetization by comparing the curves from the two measurement methods. (b) Sketch of the measurement configuration in the reflectometry end station: The magnet is oriented along the sample's normal; the incoming beam is under an angle of $\Theta ={70}^{\circ }$ towards the film surface. The magnet is only used to induce current into the superconductor and is switched off during measurement. The magnetic fields for all measurements originate from the superconductor. (c) and (d) Absorption spectra at the Fe and Co $L_{2,3}\mathrm{edges}$ at $T=38$ K and $H_{\mathrm{ext}}=0$. The source of the magnetic field is the in-plane stray fields of the superconductor.

Figure 3

(a) XMCD signal from the Fe $L_{2,3}\mathrm{edges}$ shown in Fig. 2. (b) XMCD signal of the Fe $L_3\mathrm{edge}$ at various temperatures. (c) XMCD $L_3\mathrm{edge}$ of Co (red triangles) and Fe (black squares) in percentage of the XAS value versus temperature. At $T>T_c$ both XMCD signals vanish, in region 2 $\left(55\text{K}<T<T_c\right)$ there is an increase with decreasing temperature, and at $T<55\text{K}$ the signals saturate (area 1).

Figure 4

(a) SQUID measurement of the magnetic moment of YBCO (green circles) converted to the in-plane component of the magnetic flux distribution. The fit curve obtained by using the model for the temperature dependence of the critical current density [Eq. (1)] is shown as a red line. (b) XMCD $L_3\mathrm{edge}$ of Co (red triangles) and Fe (black squares) in percentage of the XAS value versus the in-plane field component of the stray field of the superconductor. With the correlation $B\left(T\right)$ obtained from Fig. 4 temperature can be converted into the magnetic flux density which the superconductor provides at this temperature. The graph shows the correlation between the measured XMCD signal in the sensor layer and the magnetic flux density of the superconductor. The data is modeled by Eq. (2).

Figure 5

MOKE minor loops obtained by the method of FORC [32]. The graph contains hysteresis loops each starting at a different field $H_{\mathrm{start}}$. Consequently the minor loops go from $H_x=H_{\mathrm{start}}$ to $H_x=H_{\mathrm{end}}$ indicated by the red dots on each loop. The resulting magnetization $\Delta M$ of the minor loops is the difference between the magnetization at each end point $\Delta M=M\left(H_{\mathrm{end}}\right)-M\left(H_{\mathrm{start}}\right)$. Measurements were taken on the same sample as the XMCD spectroscopy at $T=300$ K in order to simulate the in-plane magnetic stray field component of the superconductor by an external in-plane field.

Figure 6

$\Delta M$ extracted from the MOKE measurements versus the external in-plane field and XMCD $L_3\mathrm{edge}$ of Co (red triangles) and Fe (black squares) in percentage of the XAS value versus the in-plane component of the magnetic stray field of the superconductor. Since all three data sets collapse on one curve we conclude that the variable $\Delta M$ is proportional to the XMCD results.

Figure 7

Images of the horizontal in-plane magnetic flux distribution $B_x$ of the critical state of a YBCO thin film covered with a CoFeB sensor layer. The left image pictures the critical state at $T=12$ K taken by magneto-optical imaging (equivalent to Fig. 1). The right image is taken by scanning x-ray microscopy. The magnetic contrast is provided by the XMCD effect of the $L_3\mathrm{edge}$ of Co within the sensor layer CoFeB normalized to the XAS signal. The image has been taken at room temperature in absence of an external magnetic field after having prepared the superconductor in the critical state at $T=12$ K as shown on the left. The magnetic domains of the superconductor are persistent within the sensor layer above the critical temperature and closely represent the superconducting state at low temperatures. The image shows that qualitative mapping of the flux distribution is possible via the novel sensor layer.