Between Mott and cluster Mott: spin-orbit entangled dimer singlets in Ba3CeRu2O9

Abstract The hexagonal 4 d ruthenates Ba 3 M Ru 2 O 9 host structural dimers and exhibit a delicate balance of competing interactions. Hund’s coupling, trigonal crystal-field splitting, and hopping for a 1 g and $${e}_{g}^{\pi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> orbitals all fall within a narrow energy window. This yields a series of possible ground states, ranging from the localized Mott limit with (anti-)ferromagnetic exchange coupling via orbital-selective behavior to the cluster Mott limit with quasimolecular orbitals that are delocalized over the two dimer sites. Using resonant inelastic x-ray scattering, we show that Ba 3 CeRu 2 O 9 with four holes per dimer resides in the intricate crossover regime between the localized Mott case and the quasimolecular limit. The spin-orbit entangled singlet ground state predominantly shows a Mott-like charge distribution with two holes per Ru site, but at the same time a dominant fraction of the holes occupies bonding orbitals. Furthermore, spin and orbital occupation contradict an exchange-based Mott scenario but agree with a cluster Mott approach. A quasimolecular trial wave function describes more than 70 % of the ground state. In this crossover regime, small changes of, e.g., the crystal field may strongly affect the character of electronic states. In Ba 3 CeRu 2 O 9 , both the crystal field and hopping lower the a 1 g orbitals. For spin-orbit coupling ζ = 0, Hund’s coupling favors an S = 0 ground state for small hopping but S = 1 for realistic larger hopping. Finite ζ , even though small, finally yields a non-magnetic J = 0 state.