Spontaneous dimerization and moment formation in the Hida model of spin-1 kagom\'e antiferromagnet

The Hida model, defined on honeycomb lattice, is a spin-1/2 Heisenberg model of aniferromagnetic hexagons (with nearest-neighbor interaction, $J_A>0$) coupled via ferromagnetic bonds (with exchange interaction, $J_F <0$). It applies to the spin-gapped organic materials, m-MPYNN.X (for $\mathrm{X}=$I, BF4, ClO4), and for $|J_F|\gg J_A$, it reduces to the spin-$1$ kagom\'e Heisenberg antiferromagnet (KHA). Motivated by the recent finding of trimerized singlet (TS) ground state for spin-1 KHA, we investigate the evolution of the ground state of Hida model from weak to strong $J_F/J_A$ using mean-field triplon analysis and Schwinger boson mean-field theory. Our triplon analysis of Hida model shows that its uniform hexagonal singlet (HS) ground state (for weak $J_F/J_A$) gives way to the dimerized hexagonal singlet (D-HS) ground state for all $J_F$'s beyond a moderate $J_F/J_A$. From the Schwinger boson calculations, we find that the evolution from the uniform HS phase for spin-1/2 Hida model to the TS phase for spin-1 KHA happens through two quantum phase transitions: 1) the spontaneous dimerization transition at $J_F/J_A \sim -0.28$ from the uniform HS to D-HS phase, and 2) the moment formation transition at $J_F/J_A \sim -1.46$, across which the pair of spin-1/2's on every FM bond begin to express as a bound moment that tends to spin-1 for large negative $J_F$'s. The TS ground state of spin-1 KHA is thus adiabatically connected to the D-HS ground state of the Hida model. Our calculations clearly imply that the \ce{m-MPYNN.X} salts realize the D-HS phase at low temperatures, which can be ascertained through neutron diffraction.