The formation of Heavy Magnetic Lanthanide Molecules*

The electronic structure of magnetic lanthanide atoms is fascinating from a fundamental perspective.

They have electrons in a submerged open 4f shell lying beneath a filled 6s shell with strong

relativistic correlations leading to a large magnetic moment and large electronic orbital angular

momentum. This large angular momentum leads to strong anisotropies, i. e. orientation

dependencies, in their mutual interactions. The long-ranged molecular anisotropies are crucial for

proposals to use ultracold lanthanide atoms in spin-based quantum computers, the realization of

exotic states in correlated matter, and the simulation of orbitronics found in magnetic

technologies. Short-ranged interactions and bond formation among these atomic species have thus far

not been well characterized. Efficient relativistic computations are required. Here, for the first

time we theoretically determine the electronic and ro-vibrational states of heavy homonuclear

lanthanide Er₂ and Tm₂ molecules by applying state-of-the-art relativistic methods. In spite

of the complexity of their internal structure, we were able to obtain reliable spin-orbit and

correlation-induced splittings between the 91  Er₂ and 36  Tm₂ electronic potentials

dissociating to two ground-state atoms. A tensor analysis allows us to expand the potentials between

the atoms in terms of a sum of seven spin-spin tensor operators simplifying future research.  The

strengths of the  tensor operators as functions of atom separation are presented and relationships

among the strengths, derived from the dispersive long-range interactions, are explained. Finally,

low-lying spectroscopically relevant ro-vibrational energy levels are computed with coupled-channels

calculations and analyzed.