For the past decades, the low-temperature phase of Ca3Ru2O7 below the 48K first-order phase transition remains a puzzle with controversial suggestions involving metallic ferroelectric, orbital or magnetic ordering. Through analysis of experimental lattice structure, density functional theory calculation, and effective model analysis, we propose that the 48K phase transition is a bond formation transition promoted by the magnetism mediated orbital re-polarization. Most interestingly, this transition is accompanied by a switch of two metallic ferroelectric orders from a xy + y symmetry to xz + z. Our study not only resolves a long-standing puzzle of this phase transition in this material, but also demonstrates perhaps the first example of transition between multiple emergent ferroelectric orders in bad metals, resulting from interplay between multiferroic orders.

We introduce a cluster slave-particle theory for Hubbard models based on a density matrix expansion approach over overlapping real-space clusters. We improve on prior slave-particle approaches by extending the description of the slave operators to correctly describe particle hopping along bonds between sites in the system. The interacting lattice slave-particle problem is then turned into a set of overlapping real-space clusters which are solved self-consistently and with appropriate physical matching constraints at shared lattice sites between clusters. Our cluster expansion approach leads to an exact description for short-ranged correlations with the cluster radius and joins that smoothly to an approximated description of long-ranged correlations. Specifically, it avoids making large errors caused by cutting bonds at cluster boundaries. We test our theory in 1D and 2D d-p Hubbard model and compare it to exact ground-state benchmark results. Our method reproduces accurate total energies, site occupancies, and double occupancies with modest computational costs.