Figure 1

(a) Schematic illustration of the atomically controlled tricolor SL. The SL consists of 10 repeated sequences of ${\mathrm{LaMnO}}_3/{\mathrm{SrMnO}}_3/{\mathrm{LaAlO}}_3$ in such a manner as ABCABC…, which can break the space-inversion symmetry along the stacking direction. (b) ${\mathrm{LaMnO}}_3$ and ${\mathrm{SrMnO}}_3$ are $A$-type and $G$-type AF insulators, respectively, while the interface layer is expected to be FM. The anticipated orbital characters at the ${\mathrm{Mn}}^{3+}$-containing sites are shown schematically. (c) The in-plane magnetization $M_{\mathrm{interface}}$ measured in the field-cooling (FC) and zero field-cooling (ZFC) runs of the SL increase below 150 K in the magnetic field of 2 kOe, indicating the presence of the spontaneous magnetization or equivalently the breaking of the time-reversal symmetry at ${\mathrm{LaMnO}}_3/{\mathrm{SrMnO}}_3$ interfaces. The inset shows the anisotropy of in-plane (solid line) and out-of-plane (dotted line) magnetization measured at 100 K, indicating that the magnetic easy axis lies in the plane. The magnetic fields of $\pm 2\mathrm{kOe}$ that we used here are represented by vertical dotted lines.Reuse & Permissions

Figure 2

(a) Photograph, (b) optical microscopy image, and (c) atomic force microscope profile of the prepared patterned tricolor oxide superlattice.Reuse & Permissions

Figure 3

The temperature dependence of the relative change of the diffracted light intensity $\Delta I/I_n$ (circles and squares) for Bragg spots of the order $n=\pm 1$ by reversals of the magnetic field $H$ (2 kOe) in (a) reflection and (b) transmission geometries. The temperature dependence of the magnetization $M_{\mathrm{interface}}$ of the tricolor SL is also shown for comparison with solid lines. Solid lines for $n=-1$ are just inversed in sign for clarity of comparison. (c) Schematics of Bragg diffractions from the grating of the tricolor SL in transmission and reflection geometries with the intensities affected by an application of $H$. The relationships among the directions of the effective electric polarization $P_{\mathrm{ABC}}$ induced by asymmetric stacking sequences of different oxides, the interface magnetization $M_{\mathrm{interface}}$ induced at ${\mathrm{LaMnO}}_3/{\mathrm{SrMnO}}_3$ interfaces, and the toroidal moment $T$ defined as $P_{\mathrm{ABC}}\times M_{\mathrm{interface}}$. $T$ is parallel or antiparallel to the reciprocal lattice vector $G$ of the grating. The light polarization $E^{\omega }$ is fixed to the direction of $H$. The temperature dependence of $\Delta I/I_{n=\pm 1}$ in (d) reflection and (e) transmission geometries when the sample was rotated by 180° [(f)].Reuse & Permissions