Molecule-decorated pyrochlore lattice

In search of exotic quantum magnetism on a frustrated pyrochlore lattice, scientists from the Max Planck Institute discovered an unexpected valence bond state arising from unique quenching of bond degree of freedom.

Complex ruthenium compounds are a platform for a plethora of exotic electronic phases produced by the interplay of not only Coulomb repulsion, bandwidth or crystal field, but also sizeable spin-orbit coupling. The intricate balance between those interactions can be controlled and tuned by selecting an appropriate type of material, or, in other words, constructing the desired lattice with an appropriate building block. The common building block in ruthenates is an octahedrally coordinated Ru⁴⁺ ion, which locally hosts a spin-orbit-entangled J_eff = 0 singlet. While this singlet is in principle a non-magnetic state, the situation may become interesting once the inter-site interaction is switched on. If the exchange interaction is strong enough, a quantum phase transition to a magnetic order through a condensation of excited states, dubbed excitonic magnetism, may occur.

In a layered perovskite with corner-sharing octahedra featuring 180^o Ru-O-Ru bonds, the magnetic exchange is reasonably large, and indeed an excitonic magnet state is realised. One may be tempted to weaken this magnetic exchange to reach a quantum critical point where magnetic exchange and spin-orbit coupling become comparable and exotic magnetism may emerge. A promising type of structure to finely tune the strength of magnetic exchange is a pyrochlore lattice. Pyrochlore ruthenates A₂Ru₂O₇ (A = Y, rare earth) feature a Ru-O-Ru angle of ∼130◦ with corner-sharing RuO₆, resulting in a reduced exchange. Furthermore, pyrochlore lattice is characterized by strong geometrical frustration, which further suppresses long-range magnetic order. Yet A₂Ru₂O₇ display long-range magnetic order, albeit at relatively low temperatures, likely representing “marginal” excitonic magnets in vicinity of a quantum critical point.

To approach the quantum critical point of an excitonic magnet, the research team tried to drive a pyrochlore ruthenate to the limit by utilising “spectator” A-ion. Introducing a small A ion reduces the Ru-O-Ru bond angle, which weakens the exchange interaction. In addition, covalent A-O bond can further weaken the exchange interaction due to suppressed Ru-O hybridisation. For this purpose, with high pressure synthesis, the scientists synthesised new pyrochlore ruthenate In₂Ru₂O₇. While at high temperatures it hosts a J_eff = 0 singlet, it does not exhibit excitonic magnetism on cooling. Instead, the compound undergoes a series of first-order phase transitions in a narrow temperature range. At low temperatures, covalent In-O bonds disproportionate and trigger a modulation of the Ru-O-Ru bonds and Ru-O bonds lengths, generating a non-magnetic state: semi-isolated Ru₂O “molecules” decorating the original pyrochlore lattice.

The disproportionation of covalent In-O bonds reveals an instability towards formation of nearly linear Ru-O-Ru molecules likely arising from the degree of freedom of bond deformation in a pyrochlore lattice with a bonding geometry of ∼130◦. Furthermore, the presence of multiple first order phase transitions imply proximity of competing states, including potential excitonic magnetism and various “molecule” patterns. The covalent In-O bonds therefore uncover a previously concealed rich phase competition in pyrochlore ruthenates.

The research opens new avenues for using covalent “filler” or “spectator” bonds as a tuning parameter in quantum materials, transcending the traditional phase diagrams of systems constrained by energy scales associated with d-electrons or lattice geometries.