Fig. 1. Lattice and electric-quadrupolar coupling and ordering.

a–c The lattice deformations (d_θ) and charge quadrupoles (q_θ) with symmetry θ = x²−y², z² and xy, respectively. The blue and orange lobes of q_θ correspond to regions with excess and reduced electronic charge, respectively. d, e Below T_q, BMRO develops a simultaneous long-range order of the local distortion $d_{\theta }^{\mathbf{k}}$ and electric quadrupoles $q_{\theta }^{\mathbf{k}}$. d The θ = x²−y² component exhibits an antiferroic order with a k = [001] propagation vector. e The θ = z² component displays ferroic, k = [000] arrangement.