Magnetization plateaus, spin-canted orders and field-induced transitions in a spin-1/2 Heisenberg antiferromagnet on a distorted diamond-decorated honeycomb lattice

Abstract

We investigate the spin-1/2 Heisenberg antiferromagnet on a distorted diamond-decorated honeycomb lattice in an external magnetic field. By combining density-matrix renormalization group, sign-problem-free quantum Monte Carlo in a mixed dimer-monomer basis, exact diagonalization, and an effective lattice-gas approach, we determine the ground-state phase diagram and analyze the finite-temperature magnetization process. The model hosts a rich variety of frustration-induced quantum phases including a quantum ferrimagnetic phase of Lieb-Mattis type, a quantum ferromagnetic phase, a spin-canted phase, a monomer-dimer phase, a dimer-tetramer liquid, a dimer-tetramer solid, and two distinct one-dimensional-crossover phases of ferromagnetic and ferrimagnetic character. Depending on the lattice distortion, we identify robust magnetization plateaus at 0, 1/4, 1/2, and 3/4 of the saturation magnetization originating from competing local dimer and tetramer singlets. Finite-temperature QMC data reveal how thermal fluctuations progressively smear the plateau structure, while the effective lattice-gas description reliably captures the corresponding low-temperature behavior.

Figures (8)

• Figure 1: A schematic illustration of the spin-1/2 Heisenberg model on a distorted diamond-decorated honeycomb lattice. The coupling constants $J_1$, $J_1'$ and $J_2$ are indicated by lines of distinct colors. styles, and thicknesses. A single unit cell is highlighted by the pink rhombus. The right panel shows an enlarged view of the eight-spin cluster forming the unit cell including the site-numbering convention.
• Figure 2: Finite-size cluster of a distorted diamond-decorated honeycomb lattice with linear system size $L=4$ (16 unit cells) used for DMRG and QMC simulations. The numbers in parentheses denote unit-cell coordinates (row, column), whereas toroidal boundary conditions were applied.
• Figure 3: Ground-state phase diagrams of the spin-1/2 Heisenberg model on the diamond-decorated honeycomb lattice in the $J_{2}/J_{1}$–$h/J_{1}$ plane for two representative values of the distortion parameter $\delta_{1}=-0.5$ (a) and $1.0$ (c) as obtained from DMRG simulations for a linear system size $L=4$ (128 spins). Panels (b) and (d) illustrate zero-temperature magnetization curves for two selected values of the coupling ratio $J_2/J_1$ as obtained from DMRG simulations for $L=4$ and cross-validated by ED using the Lanczos algorithm for $L=2$.
• Figure 4: Ground states of the spin-1/2 Heisenberg model on the diamond-decorated honeycomb lattice. Singlet dimers and singlet tetramers are shown by small and large yellow ovals, while red (blue) circles denote sites with positive (negative) local magnetization. The radius of each circle is proportional to the magnitude of the local magnetization with $m = \pm 0.5$ representing the extremal on-site values. Numbers shown in the panels indicate specific numerical values of the local magnetizations rounded to two decimal places as obtained from DMRG simulations for a finite system of linear size $L=4$ ($N=128$ spins). The notation of individual ground states: 2d quantum ferrimagnetic (2d-QFI) phase, 2d quantum ferromagnetic (2d-QFM) phase, 1d classical ferromagnetic (1d-CFM) phase, 1d quantum ferrimagnetic (1d-QFI) phase, 0d monomer-dimer (0d-MD) phase, 0d dimer-tetramer solid (0d-DTS) phase, and 0d dimer-tetramer liquid (0d-DTL) phase.
• Figure 5: Field dependence of the total magnetization $m$ is plotted together with the local magnetizations of the monomer spins ($m_{1\text{--}2}$), the dimer spins on the vertical diamonds ($m_{3\text{--}4}$), and the dimer spins on the zigzag diamonds ($m_{5\text{--}8}$) for $J_{2}/J_{1}=0$ and $\delta_{1}=-0.5$. For better clarity, there is a break on the horizontal field axis within the low-field region, where all depicted magnetizations remain constant.