Electric Octupole Order in Bilayer Ruthenate Sr₃Ru₂O₇

Abstract

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 Sr 3 Ru 2 O 7 , 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 Sr 3 Ru 2 O 7 is discussed. It is proposed that the asymmetric band structure is a signature of the electric octupole order in Sr 3 Ru 2 O 7 . The odd-parity multipole order in other strongly correlated electron systems is discussed.

Magnetic hexadecapole order and magnetopiezoelectric metal state in Ba1−xKxMn2As2

“…Electric multipole moment is invariant under the TR operation, and therefore, the odd-parity electric multipole order parameter in k-space has "spin-dependent" form consistent with Fermi liquid theory by Fu [30]. For instance, the electric octapole order is regarded as spin nematic order in k-space [2]. This is in sharp contrast to the spin-independent form of odd-parity magnetic multipole order in k-space.…”

“…For example, basis functions of B 1u and B 2u IRs in real space represent the electric octapole order, which has been studied in Sr 3 Ru 2 O 7 and a bilayer Rashba system [2,7]. On the other hand, A 2u and E u IRs correspond to the ferroelectric order, and A 1u IR shows electric dotriacontapole order.…”

Electric Octupole Order in Bilayer Rashba System

“…Then, the order parameter is identified as the EO moment with T (x 2 −y 2 ) z symmetry in real space. 9) The electric charge distribution actually shows asymmetry of the (x 2 − y 2 ) z-type from the inversion center at the center of bilayers. The EO moment is viewed as magnetic a quadrupole moment 33) (or equivalently spin-nematicity 9) ) in momentum space.…”

“…9) The electric charge distribution actually shows asymmetry of the (x 2 − y 2 ) z-type from the inversion center at the center of bilayers. The EO moment is viewed as magnetic a quadrupole moment 33) (or equivalently spin-nematicity 9) ) in momentum space. In theoretical studies on the dPI in bilayer systems, 26,27) the EO state is not thermodynamically stable in the weak forward scattering region.…”

“…A sublattice-dependent antisymmetric spin-orbit coupling (ASOC) arises from the local parity violation in crystal structures. Previous studies of superconductivity in multilayers, [1][2][3][4] magnetic quadrupole order in zigzag chains, 5,6) toroidal order in a honeycomb lattice, 7,8) and electric octupole (EO) order in bilayer systems 9) have revealed exotic quantum states of matter induced by the ASOC. On the basis of the generalized multipole expansion, 10) some of them are classified into odd-parity multipole states beyond the paradigm of even-parity multipole order studied in d-and f -electron systems.…”