Spontaneous dimerization and moment formation in the Hida model of the spin-1 kagome antiferromagnet

Abstract

The Hida model, defined on honeycomb lattice, is a spin-1/2 Heisenberg model of aniferromagnetic hexagons (with nearest-neighbor interaction, JA > 0) coupled via ferromagnetic bonds (with exchange interaction, JF < 0). It applies to the spin-gapped organic materials, m−MPYNN · X (for X =I, BF 4 , ClO 4 ), and for |JF | JA, it reduces to the spin-1 kagomé 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 JF /JA 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 JF /JA) gives way to the dimerized hexagonal singlet (D-HS) ground state for |JF |/JA 1.26 (which for strong JF /JA approaches the TS state). 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 JF /JA ∼ −0.28 from the uniform HS to D-HS phase, and 2) the moment formation transition at JF /JA ∼ −1.46, across which the pair of spin-1/2's on every FM bond begins to express as a bound moment that tends to spin-1 for large negative JF '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 imply that the m−MPYNN · X salts realize the D-HS phase at low temperatures, which can be ascertained through neutron diffraction.

Effective spin-1 breathing kagome Hamiltonian induced by the exchange hierarchy in the maple leaf mineral bluebellite

“…[43][44][45]). This method has been successful in describing the ground state as well as thermodynamic properties of several magnetic materials [46][47][48][49][50]. The results from this bosonic theory agree well with the DMRG calculations.…”

Quantum paramagnetism and magnetization plateaus in a kagome-honeycomb Heisenberg antiferromagnet

“…It can also be viewed as a system of hexagons formed by two types of bonds (say, J B and J C ) and coupled via the third (say, J A ). This is exactly like a model for some spin-1 kagome materials with a ferromagnetic J A , but antiferromagnetic J B and J C [19][20][21][22]. An early example of a frustrated spin-1/2 Heisenberg model with an exact dimer ground state on kagome-honeycomb lattice occurs in Ref.…”

“…The basic framework of triplon analysis is to first identify such building-blocks of the system which in some limiting case realise singlet ground state locally independently, and then formulate an effective theory in terms of the low-energy triplet excitations of these building-blocks to describe the full system [22,[25][26][27]. In this spirit, our ABC model can be viewed either as a system of coupled dimers, or coupled hexagons.…”

“…Like the bond-operators employed for the dimer case, we now introduce the bosonic operators, ŝ R and tmν, R , corresponding to the hexagonal singlet and triplet states at position R [22]. Next we replace the singlet operator on every hexagon by a mean amplitude s that accounts for the hexagonal singlet background.…”

Competing orders in a frustrated Heisenberg model on the Fisher lattice

“…Hence, an effective Hamiltonian of interacting singlet or triplet bonds between neighboring dimers can be constructed within this approach. This procedure is known to be effective in explaining the low energy physics of interacting spin systems [47][48][49][50][51][52][53][54][55]. We now discuss the different VBS phases which are found to be realized as variational quantum ground states of the J 1 -J 2 -J 3 model.…”