The Curious Case of NiRh${}_2$O${}_4$: A Spin-Orbit Entangled Diamond Lattice Paramagnet

Abstract

Motivated by the interest in topological quantum paramagnets in candidate spin-$1$ magnets, we investigate the diamond lattice compound NiRh${}_2$O${}_4$ using {\it ab initio} theory and model Hamiltonian approaches. Our density functional study, taking into account the unquenched orbital degrees of freedom, shows stabilization of $S=1$ and $L=1$ state. We highlight the importance of spin-orbit coupling, in addition to Coulomb correlations, in driving the insulating gap, and uncover frustrating large second-neighbor exchange mediated by Ni-Rh covalency. A single-site model Hamiltonian incorporating the large tetragonal distortion is shown to give rise to a spin-orbit entangled non-magnetic ground state, largely accounting for the entropy, magnetic susceptibility, and inelastic neutron scattering results. Incorporating inter-site exchange within a slave-boson theory, we show that exchange frustration can suppress exciton condensation. We capture the dispersive gapped magnetic modes, uncover `dark states' invisible to neutrons, and make predictions for future experiments.

5 pages, 3 figures

References in corpus (12)

• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets
• Structural, orbital, and magnetic order in vanadium spinels
• A Spin-Orbital Singlet and Quantum Critical Point on the Diamond Lattice: FeSc2S4
• Orbital order in ZnV${}_2$O${}_4$
• Quantum spin liquids in frustrated spin-1 diamond antiferromagnets
• Effective magnetic interactions in spin-orbit coupled $d^4$ Mott insulators
• Quantum order by disorder in frustrated diamond lattice antiferromagnets
• Magnetic Excitations in Spin-Orbit Coupled $d^4$ Mott Insulator on Square Lattice
• Topological Paramagnetism in Frustrated Spin-One Mott Insulators
• Spin order and dynamics in the diamond-lattice Heisenberg antiferromagnets CuRh2O4 and CoRh2O4
• Emergent quantum criticality from spin-orbital entanglement in $d^8$ Mott insulators: the case of a diamond lattice antiferromagnet

Cited by in corpus (11)

• The Chemistry of Quantum Spin Liquids
• Octupolar order in d-orbital Mott insulators
• Generic Spiral Spin Liquids
• Experimental Evidence for the Spiral Spin Liquid in LiYbO${}_2$
• Featureless quantum paramagnet with frustrated criticality and competing spiral magnetism on spin-1 honeycomb lattice magnet
• Electronic structure of the frustrated diamond lattice magnet NiRh${}_2$O${}_4$
• Universal excitonic superexchange in spin-orbit-coupled Mott insulators
• Room Temperature Ferrimagnetism, Magnetodielectric and Exchange Bias Effect in CoFeRhO${}_4$
• Phase transitions in the spin-1/2 Heisenberg antiferromagnet on the dimerized diamond lattice
• Nematic correlations and nematic Berezinskii-Kosterlitz-Thouless transition in spin-1 kagome lattice antiferromagnets
• Magnetic ordering in the $J_{\mathrm{eff}}$ = 0 Nickelate NiRh${}_2$O${}_4$ prepared via a solid-state metathesis