Title: Quantum Paramagnet and Frustrated Quantum Criticality in a Spin-One Diamond Lattice Antiferromagnet,
Abstract: Motivated by the proposal of topological quantum paramagnet in the diamond
lattice antiferromagnet NiRh$_2$O$_4$, we propose a minimal model to describe
the magnetic interaction and properties of the diamond material with the
spin-one local moments. Our model includes the first and second neighbor
Heisenberg interactions as well as a local single-ion spin anisotropy that is
allowed by the spin-one nature of the local moment and the tetragonal symmetry
of the system. We point out that there exists a quantum phase transition from a
trivial quantum paramagnet when the single-ion spin anisotropy is dominant to
the magnetic ordered states when the exchange is dominant. Due to the
frustrated spin interaction, the magnetic excitation in the quantum
paramagnetic state supports extensively degenerate band minima in the spectra.
As the system approaches the transition, extensively degenerate bosonic modes
become critical at the criticality, giving rise to unusual magnetic properties.
Our phase diagram and experimental predictions for different phases provide a
guildeline for the identification of the ground state for NiRh$_2$O$_4$.
Although our results are fundamentally different from the proposal of
topological quantum paramagnet, it represents interesting possibilities for
spin-one diamond lattice antiferromagnets.