Electric Octupole Order in Bilayer Ruthenate Sr₃Ru₂O₇

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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 py sₓ + pₓ sy 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 D₂d 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.