  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.
