Electric Octupole Order in Bilayer Ruthenate Sr$_3$Ru$_2$O$_7$

TL;DR

This paper proposes that electric octupole order, arising from local quadrupole stacking and symmetry breaking, can occur in bilayer Sr$_3$Ru$_2$O$_7$, leading to observable effects like asymmetric band structures and spin nematic order.

Contribution

It introduces the concept of electric octupole order in bilayer ruthenates and links it to observable electronic nematic states and asymmetric band structures.

Findings

Electric octupole order can be realized in Sr$_3$Ru$_2$O$_7$.

Spin nematic order is induced by spin-orbit coupling in this state.

Asymmetric band structure serves as a signature of the octupole order.

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.