Electric Octupole Order in Bilayer Ruthenate Sr3Ru2O7

Although the odd-parity multipole order barely occurs in crystals with high symmetry, it can be formed in locally noncentrosymmetric crystals. We illustrate the odd-parity electric octupole order generated in a bilayer structure. When the local electric quadrupole is alternatively stacked between layers, it is regarded as an electric octupole order from the viewpoint of symmetry. We show that the p(y)s(x) + p(x)s(y) spin nematic order is induced by the spin-orbit coupling in the electric octupole state, and it results from the spontaneous inversion symmetry breaking leading to the D-2d point group symmetry. We investigate the possible realization of the electric octupole order in the bilayer ruthenate Sr3Ru2O7, assuming a local electric quadrupole arising from the Pomeranchuk instability and/or the orbital order. Effects of the lattice distortion and magnetic field are also clarified, and the nature of the "electronic nematic state" of Sr3Ru2O7 is discussed. It is proposed that the asymmetric band structure is a signature of the electric octupole order in Sr3Ru2O7. The odd-parity multipole order in other strongly correlated electron systems is discussed.