Field-induced interplanar magnetic correlations in the high-temperature superconductor ${\text{La}}_{1.88}{\text{Sr}}_{0.12}{\text{CuO}}_4$

We present neutron-scattering studies of the interplanar magnetic correlations in the high-temperature superconductor ${\mathrm{La}}_{1.88}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_4$ ($T_c=27$ K). The correlations are studied both in a magnetic field applied perpendicular to the ${\mathrm{CuO}}_2$ planes, and in zero field under different cooling conditions. We find that the effect of the magnetic field is to increase the magnetic scattering signal at all values of the out-of-plane wave vector $L$, indicating an overall increase of the magnetic moments. In addition, weak correlations between the copper oxide planes develop in the presence of a magnetic field. This effect is not taken into account in previous reports on the field effect of magnetic scattering, since usually only $L\approx 0$ is probed. Interestingly, the results of quench-cooling the sample are similar to those obtained by applying a magnetic field. Finally, a small variation of the incommensurate peak position as a function of $L$ provides evidence that the incommensurate signal is twinned with the magnetic scattering from the dominant and subdominant structural twin displaying peaks at even and odd values of $L$, respectively, in our crystal.

Figure 1

(a) Illustration of the quartet of IC peaks around $\left(100\right)$ in orthorhombic notation. The scattering signal from the $\left(100\right)$ structural second-order peak belonging to the dominant domain is shown by the red circle. The crystal shows twinning into two subdominant domains of which we show the strongest by the blue circles. The red and blue lines show the Cu-O-Cu axes. Note that the IC peaks are shifted off these high-symmetry axes in agreement with earlier reports [4]. The black arrow shows the axis $\left(H0.14H0\right)$, which we probe in the scattering plane. (b) Illustration of the scattering plane spanned by $\left(H0.14H0\right)$ and $\left(00L\right)$. We show examples of a sample rotation scan through a signal rod with a proposed weak $L$ dependence of the signal shown for the two twins of the IC signal, with maximum signal visualized by red and minimum signal shown in yellow. The width of the signals along $\left(H0.14H0\right)$ is exaggerated for clarity. Note that one twin (red circle) displays peaks at even $L$ values and the twin shown by the blue circle exhibits peaks at odd $L$ values. The white points visualize how the nine analyzer blades of the monochromatic $\mathbf{q}$-dispersive mode (imaging mode) on RITA-II enable measurements at distinct values of $L$ for one sample rotation scan. For clarity, only every second analyzer blade has been shown. The solid lines show the trajectory of the reciprocal lattice vectors in a sample rotation scan. From the scan line centered at $L=0$, it is clear that a sample rotation scan is not applicable for small $L$ values. With increasing $L$, the change in $L$ during one sample rotation scan through the signal rod becomes smaller.

Figure 2

(a, b) Raw data for sample rotation scans through the IC position $\left(H0.14HL\right)$ for $L=3.0$ and $L=4.0$ in $H=6.8$ T (red data points) and zero (black data points) applied field along the $c$ direction, taken at $T=2$ K. These data were taken at RITA-II, PSI. For each scan the data of five blades were combined, leading to an uncertainty in $L$ of $0.1$ r.l.u. Error bars are smaller than the marker size. The field data are shifted upwards by a constant offset for clarity. The solid curves display fits to Gaussian functions on a sloping background. (c) The fitted peak position $H_{\mathrm{IC}}$ for $6.8$ T field data as a function of $L$. The dashed black line shows a fit to a straight line and the solid black line displays a fit to a sine function, which provides a better fit to the data. The color inset shows the intensity of the structural scattering signal around $\left(200\right)$.

Figure 3

Measured peak intensity at $T=2$ K for the IC position $\left(H0.14H2.0\right)$ in 6 T field (red data points) and zero field (black data points). Pointwise background subtraction has been performed, using 40-K data as background. The solid curves are Gaussian fits to the data. These data were taken at FLEXX, HZB. The field data are shifted upwards by a constant offset for clarity.

Figure 4

Background-subtracted elastic response at the IC position $\left(0.887\right(2),0.124(1),L)$ versus $L$ in zero field, a $6.0$-T field (FLEXX data), and a $6.8$-T field (RITA-II data). The $y$-axis label corresponds to the counting rate at the RITA-II experiment. To compare the two data sets, the FLEXX data have been scaled by a constant factor determined by the fraction of the signal intensities at the common data point $L=2.2$. The red solid line corresponds to a fit to three Lorentzian functions with the same width and fixed centers at $L=2$, 3, and 4. The three Lorentzian functions are shown separately by the red and blue dashed lines, belonging to the first and second IC twins, respectively. The color code is the same as in the cartoon drawing in Fig. 1.

Figure 5

Scans through $\left(H0.14HL\right)$ at $T=3$ K (blue open squares) and $T=40$ K (black points) in zero field for (a) $L=1$ and (b) $L=2$. In both panels, the solid blue line shows a fit to a Gaussian function on a sloping background. (c) $L$ dependence of the incommensurate magnetic signal above background in zero field measured at PANDA. The solid black line shows the fit to two Lorentzian functions with fixed centers at $L=0$ and $L=2$. The dashed lines show each of the Lorentzian functions separately.