Origin of the Spin-Orbital Liquid State in a Nearly J=0 Iridate Ba3ZnIr2O9

We show using detailed magnetic and thermodynamic studies and theoretical calculations that the ground state of Ba3ZnIr2O9 is a realization of a novel spin-orbital liquid state. Our results reveal that Ba3ZnIr2O9 with Ir5+ (5d(4)) ions and strong spin-orbit coupling (SOC) arrives very close to the elusive J = 0 state but each Ir ion still possesses a weak moment. Ab initio density functional calculations indicate that this moment is developed due to superexchange, mediated by a strong intradimer hopping mechanism. While the Ir spins within the structural Ir2O9 dimer are expected to form a spin-orbit singlet state (SOS) with no resultant moment, substantial frustration arising from interdimer exchange interactions induce quantum fluctuations in these possible SOS states favoring a spin-orbital liquid phase down to at least 100 mK

Room temperature magnetic order on zigzag edges of narrow graphene nanoribbons

Magnetic order emerging in otherwise non-magnetic materials as carbon is a paradigmatic example of a novel type of s-p electron magnetism predicted to be of exceptional high-temperature stability. It has been demonstrated that atomic scale structural defects of graphene can host unpaired spins. However, it is still unclear under which conditions long-range magnetic order can emerge from such defect-bound magnetic moments. Here we propose that in contrast to random defect distributions, atomic scale engineering of graphene edges with specific crystallographic orientation, comprising edge atoms only from one sub-lattice of the bipartite graphene lattice, can give rise to a robust magnetic order. We employ a nanofabrication technique based on Scanning Tunneling Microscopy to define graphene nanoribbons with nanometer precision and well-defined crystallographic edge orientations. While armchair ribbons display quantum confinement gap, zigzag ribbons narrower than 7 nm reveal a bandgap of about 0.2 - 0.3 eV, which can be identified as a signature of interaction induced spin ordering along their edges. Moreover, a semiconductor to metal transition is revealed upon increasing the ribbon width, indicating the switching of the magnetic coupling between opposite ribbon edges from antiferromagnetic to ferromagnetic configuration. We found that the magnetic order on graphene edges of controlled zigzag orientation can be stable even at room temperature, raising hope for graphene-based spintronic devices operating under ambient conditions

Acknowledgment to the Reviewers of Magnetism in 2022

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Equation of motion approach to the two-dimensional Hubbard model

Using a Green's-function equation of motion approach the Using a Green's-function equation of motion approach th