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Register a new userInteger vs. half-integer spin on an approximate honeycomb lattice
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Recent interest in honeycomb lattice materials has focused on their potential to host quantum spin liquid (QSL) states. Variations in bond angles and spin allow a range of interesting behaviors on this lattice, from the predicted QSL ground state of the Kitaev model to exotic magnetic orders. Here we report the physical properties of two compounds with rare earths on an approximate honeycomb lattice. The isostructural compounds Nd$_2$S$_5$Sn (J = $frac{9}{2}$) and Pr$_2$S$_5$Sn (J = 4) permit a direct comparison of half-integer versus integer spins on this lattice. We find strikingly different magnetic properties for the two compounds. Nd$_2$S$_5$Sn orders antiferromagnetically at T$_N$ $approx$ 2.5 K, and undergoes several magnetic transitions to other ordered states under applied field. Pr$_2$S$_5$Sn displays no magnetic ordering transition above T = 0.41 K, and may be proximate to a spin liquid state.
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We study the thermodynamic properties of modified spin-$S$ Kitaev models introduced by Baskaran, Sen and Shankar (Phys. Rev. B 78, 115116 (2008)). These models have the property that for half-odd-integer spins their eigenstates map on to those of spin-1/2 Kitaev models, with well-known highly entangled quantum spin-liquid states and Majorana fermions. For integer spins, the Hamiltonian is made out of commuting local operators. Thus, the eigenstates can be chosen to be completely unentangled between different sites, though with a significant degeneracy for each eigenstate. For half-odd-integer spins, the thermodynamic properties can be related to the spin-1/2 Kitaev models apart from an additional degeneracy. Hence we focus here on the case of integer spins. We use transfer matrix methods, high temperature expansions and Monte Carlo simulations to study the thermodynamic properties of ferromagnetic and antiferromagnetic models with spin $S=1$ and $S=2$. Apart from large residual entropies, which all the models have, we find that they can have a variety of different behaviors. Transfer matrix calculations show that for the different models, the correlation lengths can be finite as $Tto 0$, become critical as $Tto 0$ or diverge exponentially as $Tto 0$. There is a conserved $Z_2$ flux variable associated with each hexagonal plaquette which saturates at the value $+1$ as $Trightarrow0$ in all models except the $S=1$ antiferromagnet where the mean flux remains zero as $Tto 0$. We provide qualitative explanations for these results.
Theoretical studies have predicted the existence of topological magnons in honeycomb compounds with zig-zag antiferromagnetic (AFM) order. Here we report the discovery of zig-zag AFM order in the layered and non-centrosymmetric honeycomb nickelate Ni$_2$Mo$_3$O$_8$ through a combination of magnetization, specific heat, x-ray and neutron diffraction and electron paramagnetic resonance measurements. It is the first example of such order in an integer-spin non-centrosymmetric structure ($P$$_6$3$mc$). Further, each of the two distinct sites of the bipartite honeycomb lattice has a unique crystal field environment, octahedral and tetrahedral Ni$^{2+}$ respectively, enabling independent substitution on each sublattice. Replacement of Ni by Mg on the octahedral site suppresses the long range magnetic order and results in a weakly ferromagnetic state. Conversely, substitution of Fe for Ni enhances the AFM ordering temperature. Thus Ni$_2$Mo$_3$O$_8$ provides a platform on which to explore the rich physics of $S = 1$ on the honeycomb in the presence of competing magnetic interactions with a non-centrosymmetric, formally piezeo-polar, crystal structure.
An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y-junctions, systems with three arms of $n$ sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to $N = 3n + 1 approx 500$ sites are studied with antiferromagnetic (AF) Heisenberg exchange $J$ between nearest-neighbor spins $S$ or electron transfer $t$ between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with $N_A e N_B$. The ground state (GS) and spin densities $ rho_r = <S^z_r >$ at site $r$ are quite different for junctions with $S$ = 1/2, 1, 3/2 and 2. The GS has finite total spin $S_G = 2S (S)$ for even (odd) $N$ and for $M_G =S_G$ in the $S_G$ spin manifold, $rho_r > 0 (< 0)$ at sites of the larger (smaller) sublattice. $S$ = 1/2 junctions have delocalized states and decreasing spin densities with increasing $N$. $S$ = 1 junctions have four localized $S_z = 1/2$ states at the end of each arm and centered on the junction, consistent with localized states in $S$ = 1 chains with finite Haldane gap. The GS of $S$ = 3/2 or 2 junctions of up to 500 spins is a spin density wave (SDW) with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in $S$ = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in $S$ = 3/2 or 2 junctions.
The quantum Hall effect (QHE) in two-dimensional (2D) electron gases, which is one of the most striking phenomena in condensed matter physics, involves the topologically protected dissipationless charge current flow along the edges of the sample. Integer or fractional electrical conductance are measured in units of $e^2/2pihbar$, which is associated with edge currents of electrons or quasiparticles with fractional charges, respectively. Here we discover a novel type of quantization of the Hall effect in an insulating 2D quantum magnet. In $alpha$-RuCl$_3$ with dominant Kitaev interaction on 2D honeycomb lattice, the application of a parallel magnetic field destroys the long-range magnetic order, leading to a field-induced quantum spin liquid (QSL) ground state with massive entanglement of local spins. In the low-temperature regime of the QSL state, we report that the 2D thermal Hall conductance $kappa_{xy}^{2D}$ reaches a quantum plateau as a function of applied magnetic field. $kappa_{xy}^{2D}/T$ attains a quantization value of $(pi/12)(k_B^2/hbar)$, which is exactly half of $kappa_{xy}^{2D}/T$ in the integer QHE. This half-integer thermal Hall conductance observed in a bulk material is a direct signature of topologically protected chiral edge currents of charge neutral Majorana fermions, particles that are their own antiparticles, which possess half degrees of freedom of conventional fermions. These signatures demonstrate the fractionalization of spins into itinerant Majorana fermions and $Z_2$ fluxes predicted in a Kitaev QSL. Above a critical magnetic field, the quantization disappears and $kappa_{xy}^{2D}/T$ goes to zero rapidly, indicating a topological quantum phase transition between the states with and without chiral Majorana edge modes. Emergent Majorana fermions in a quantum magnet are expected to have a major impact on strongly correlated topological quantum matter.
Tight binding models like the Hubbard Hamiltonian are most often explored in the context of uniform intersite hopping $t$. The electron-electron interactions, if sufficiently large compared to this translationally invariant $t$, can give rise to ordered magnetic phases and Mott insulator transitions, especially at commensurate filling. The more complex situation of non-uniform $t$ has been studied within a number of situations, perhaps most prominently in multi-band geometries where there is a natural distinction of hopping between orbitals of different degree of overlap. In this paper we explore related questions arising from the interplay of multiple kinetic energy scales and electron-phonon interactions. Specifically, we use Determinant Quantum Monte Carlo (DQMC) to solve the half-filled Holstein Hamiltonian on a `decorated honeycomb lattice, consisting of hexagons with internal hopping $t$ coupled together by $t^{,prime}$. This modulation of the hopping introduces a gap in the Dirac spectrum and affects the nature of the topological phases. We determine the range of $t/t^{,prime}$ values which support a charge density wave (CDW) phase about the Dirac point of uniform hopping $t=t^{,prime}$, as well as the critical transition temperature $T_c$. The QMC simulations are compared with the results of Mean Field Theory (MFT).
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