Space-Group Determination of Superlattice Structure Due to Electric Toroidal Ordering in Ca5Ir3O12

Synchrotron X-ray diffraction measurements on a single crystal of Ca5Ir3O12 were performed to clarify the details of the superlattice reflections characterized by q = (1/3, 1/3, 1/3). A search for superlattice reflections in a wide reciprocal space was performed using an imaging plate, and it was confirmed that there were no superlattice reflections at other than q = (1/3, 1/3, 1/3). From the extinction rule of the superlattice reflections, the space group of the crystal structure below 105 K was found to be R3. The details of the superlattice reflections at specific q were investigated using a four-circle diffractometer. The temperature dependence of the integrated intensity at several q confirms that the order parameter of the phase transition of Ca5Ir3O12 at 105 K belongs to an A2 irreducible representation in the point group C3, from the discussion based on the Landau theory of phase transitions. The basis function of the A2 irreducible representation, which is a rotation around the c-axis, corresponds to an electric toroidal dipole.