The tri-layered perovskite Sr4Rh3O10 is reported for the first time. High-pressure and high-temperature heating (6 GPa and 1500 C) brought about successful preparation of a polycrystalline sample of the expected member at n=3 of Srn+1RhnO3n+1. Neutron-diffraction studies revealed the orthorhombic crystal structure (Pbam) at room temperature and 3.4 K. Local structure distortions rotationally tilt the RhO6 octahedra ~12 degrees in the perovskite-based blocks along the c-axis, and approximately a 20 % disorder was found in sequence of the alternating rotational tilt. The sample was also investigated by measurements of specific heat, thermopower, magnetic susceptibility, and electrical resistivity. The data clearly revealed enhanced paramagnetism and electrically conducting character, which reflected nature of the correlated 4d5-electrons of Rh4+. However, no clear signs of magnetic and electrical transitions were observed above 2 K and below 70 kOe, providing a remarkable contrast to the rich electronic phenomena for the significantly relevant ruthenate, Sr4Ru3O10.
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