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Exotic coupled spin-charge states in decorated honeycomb magnets: A hybrid-Monte Carlo study

Satyabrata Jana, Sahinur Reja

TL;DR

The study addresses how conduction electrons interacting with frustrated localized spins on a decorated honeycomb lattice yield emergent spin-charge orders. It employs a hybrid-MCMC approach that couples classical spin sampling with exact diagonalization of the itinerant electron problem across fillings $n_e$ in {1/3,1/2,2/3}. The main result is the identification of four coupled spin-charge ground states—S-AF, S-YK, FM-D, and FM-T—each linked to cluster-based magnetic textures and accompanied by flat electronic bands and large gaps that stabilize the states. This band-structure stabilization and the associated macroscopic degeneracy offer insights into electron-doped frustrated magnets and metal-organic frameworks, with potential relevance to MOF-based quantum materials.

Abstract

We uncover four exotic coupled spin-charge ground states in the strong coupling limit of the Kondo lattice model at various electronic fillings on a frustrated decorated honeycomb lattice, where each regular honeycomb sublattice point is occupied by three-site triangular units. We employ a hybrid Markov Chain Monte Carlo (hMCMC) simulation method which combines classical MCMC for localized spins and exact diagonalization of the electronic Hamiltonian. Two of the spin-charge ground states, respectively consists of three-site and six-site ferromagnetic (FM) clusters arranged in anti-FM and $120^{\circ}$ Yafet-Kittel (YK) phase which we label as S-AF (super-antiferromagnet) and S-YK (super-YK) respectively. Two even more interesting coupled spin-charge states, respectively accommodate FM dimers and trimers (as three-site line segment), which we label as FM-D and FM-T. In both cases, the anti-FM aligned dimers and trimers in respective phases, are arranged in stripes along one of three lattice directions: the spontaneously symmetry broken phases giving rise to non-trivial macroscopic degeneracy. These underlying magnetic textures (except S-YK state) restrict electrons in fragmented small regions (e.g, triangular units, two-site dimers, three-site line segments respectively in S-AF, FM-D and FM-T), resulting in flat bands by opening large gaps in electronic density of states, which in turn stabilize these coupled spin-charge states: a "band effect". These exotic spin-charge ground states could be relevant to electron-doped spin-systems resulting from various metal-organic frameworks (MOFs), which have attracted significant attention to condensed matter physics

Exotic coupled spin-charge states in decorated honeycomb magnets: A hybrid-Monte Carlo study

TL;DR

The study addresses how conduction electrons interacting with frustrated localized spins on a decorated honeycomb lattice yield emergent spin-charge orders. It employs a hybrid-MCMC approach that couples classical spin sampling with exact diagonalization of the itinerant electron problem across fillings in {1/3,1/2,2/3}. The main result is the identification of four coupled spin-charge ground states—S-AF, S-YK, FM-D, and FM-T—each linked to cluster-based magnetic textures and accompanied by flat electronic bands and large gaps that stabilize the states. This band-structure stabilization and the associated macroscopic degeneracy offer insights into electron-doped frustrated magnets and metal-organic frameworks, with potential relevance to MOF-based quantum materials.

Abstract

We uncover four exotic coupled spin-charge ground states in the strong coupling limit of the Kondo lattice model at various electronic fillings on a frustrated decorated honeycomb lattice, where each regular honeycomb sublattice point is occupied by three-site triangular units. We employ a hybrid Markov Chain Monte Carlo (hMCMC) simulation method which combines classical MCMC for localized spins and exact diagonalization of the electronic Hamiltonian. Two of the spin-charge ground states, respectively consists of three-site and six-site ferromagnetic (FM) clusters arranged in anti-FM and Yafet-Kittel (YK) phase which we label as S-AF (super-antiferromagnet) and S-YK (super-YK) respectively. Two even more interesting coupled spin-charge states, respectively accommodate FM dimers and trimers (as three-site line segment), which we label as FM-D and FM-T. In both cases, the anti-FM aligned dimers and trimers in respective phases, are arranged in stripes along one of three lattice directions: the spontaneously symmetry broken phases giving rise to non-trivial macroscopic degeneracy. These underlying magnetic textures (except S-YK state) restrict electrons in fragmented small regions (e.g, triangular units, two-site dimers, three-site line segments respectively in S-AF, FM-D and FM-T), resulting in flat bands by opening large gaps in electronic density of states, which in turn stabilize these coupled spin-charge states: a "band effect". These exotic spin-charge ground states could be relevant to electron-doped spin-systems resulting from various metal-organic frameworks (MOFs), which have attracted significant attention to condensed matter physics

Paper Structure

This paper contains 7 sections, 3 equations, 9 figures.

Table of Contents

  1. introduction
  2. Model and Method
  3. Numerical results
  4. Phases at n$_\text{e}$ = 2/3
  5. Phases at n$_\text{e}$ = 1/2
  6. Phases at n$_\text{e}$ = 1/3
  7. Conclusions

Figures (9)

  • Figure 1: (Color online) Schematic of unit cell of decorated honeycomb lattice consisting of 6-sites (filled circle) defined by lattice vectors $\vec{a_1}$ and $\vec{a_2}$. The electron hopping (Heisenberg exchange) $t_1 (J_1)$ and $t_2 (J_2)$ are on intra-triangular (blue) and inter-triangular (black) bonds respectively.
  • Figure 2: (Color online) (a) Ground state energy per site $E_0$ vs $J_1$ plot at $n_e=2/3$ obtained by hMCMC simulation (circles) at temperature $T=0.001t_1$. Straight lines are the energies of different phases as indicated. (b) Electron density of states corresponding to phases as mentioned.
  • Figure 3: (Color online) The real space spin configuration (arrows) and electron charge density profile (indicated by size of red circles) obtained from hMCMC simulation at $\text{n}_\text{e} = 2/3$ for (a) S-YK phase at $J_1 = 0.08$ and (b) AF-YK phase at $J_1 = 0.27$. (c) Six Possible configurations (A, B ...F) of two anti-aligned trimers (black and blue segments) within a unit cell to account for the degeneracy of FM-T phase, and (d) The hMCMC snapshot of FM-T phase at $J_1 = 0.14$ represents one of many degenerate configurations tiled with B and D types running along $(\vec{a_2}$-$\vec{a_1})$ lattice direction
  • Figure 4: (Color online) Structure factor of (a) S-YK, and (b) S-AF phase.
  • Figure 5: (Color online) (a) Energy per site Vs $\text{J}_\text{H}/\text{t}_0$ is plotted here for electron concentration $\text{n}_\text{e} = 1/2$ per site. Black circles are energies obtained from hMCMC simulation. The color lines are to indicate the energy of different phases mentioned. (b) Density of states of electron at the ground state for three different phases (FM, FM-D & AF-YK).
  • ...and 4 more figures