We consider a SU(3) model with antiferromagnetic three-site ring exchanges, in addition to two-site exchanges, on the triangular lattice. We first present numerical site-factorized state studies on the magnetic ordered states, which shows two different three-sublattice-ordered states, the antiferro-quadrupolar phase and the standard 120^o anti-ferromagnetic phase, along the axis of the strength of the three-site ring exchanges. We further study the model using slave-fermion mean field approaches in which we rewrite the exchange operators in terms of three flavors of fermions. At the mean-field level, we find the main competing trial states are the trimer state (triangular plaquette state), gapped uniform π/3-flux chiral spin liquid, and gapped uniform 2π/3-flux chiral spin liquid. The filled band of the π/3-flux chiral spin liquid has Chern number +1, and that of the 2π/3-flux chiral spin liquid has Chern number +2. We also give the effective Chern-Simons theory for each chiral spin liquid at the mean-field level.
A novel doubly chiral magnetic order is found out in the structurally chiral langasite compound Ba$_3$NbFe$_3$Si$_2$O$_{14}$. The magnetic moments are distributed over planar frustrated triangular lattices of triangle units. On each of these they form the same triangular configuration. This ferro-chiral arrangement is helically modulated from plane to plane. Unpolarized neutron scattering on a single crystal associated with spherical neutron polarimetry proved that a single triangular chirality together with a single helicity is stabilized in an enantiopure crystal. A mean field analysis allow…
We study the double-exchange model at half-filling with competing superexchange interactions on a triangular lattice, combining exact diagonalization and Monte-Carlo methods. We find that in between the expected itinerant ferromagnetic and $120^{\circ}$ Yafet-Kittel phases a robust scalar-chiral, insulating spin state emerges. At finite temperatures the ferromagnet - scalar-chiral quantum critical point is characterized by anomalous bad-metal behavior in charge transport as observed in frustrated itinerant magnets R$_2$Mo$_{2}$O$_7$.
We discuss the possibility of finding n-type nematic order in the vicinity of a FM phase in the multiple--spin exchange model on the triangular lattice. We study this problem both from S=\infty (classical) and S=1/2 (quantum) limits.
We report on a topological Hall effect possibly induced by scalar spin chirality in a quasi-two- dimensional helimagnet Fe$_{1+x}$Sb. In the low-temperature region where the spins on interstitial- Fe (concentration $x=0.3$) intervening the $120^\circ$ spin-ordered triangular planes tend to freeze, a non-trivial component of Hall resistivity with opposite sign of the conventional anomalous Hall term is observed under magnetic field applied perpendicular to the triangular-lattice plane. The observed unconventional Hall effect is ascribed to the scalar spin chirality arising from the heptamer spi…
We propose a variant of the antiferromagnetic XY model on the triangular lattice to study the interplay between the chiral and nematic orders in addition to the magnetic order. The model has a significant bi-quadratic interaction of the planar spins. When the bi-quadratic exchange energy dominates, a large temperature window is shown to exist over which the nematic and the chiral orders co-exist without the magnetic order, thus defining a chiral-nematic state. The phase diagram of the model and some of its critical properties are derived by means of the Monte Carlo simulation.
We show how a gapless spin liquid with hidden octupolar order arises in an applied magnetic field, in a model applicable to thin films of 3He with competing ferromagnetic and antiferromagnetic (cyclic) exchange interactions. Evidence is also presented for nematic -- i.e., quadrupolar -- correlations bordering on ferromagnetism in the absence of a magnetic field.
Chiral fluctuations in triangular antiferromagnets (TAFs) at $T \ll T_N$ are studied theoretically. The case of a ferromagnetic interaction along c axis (which is directed perpendicular to the plane of the lattice), Dzyaloshinskii-Moriya interaction ${\bf D}\| c$ and a weak magnetic field ${\bf H}\| c$ is considered in detail. Previously, this model has been proposed to describe quantum TAF CsCuCl$_3$. Expressions for dynamical chirality (DC) are derived within the linear spin-wave approximation. In contrast to non-frustrated antiferromagnets, DC is found to be nonzero even at $D,H=0$ in a one…
Recent numerical simulations find a possible chiral spin liquid state in the intermediate coupling regime of the triangular lattice Hubbard model. Here we provide a simple picture for its origin in terms of a Bosonic RVB description. More specifically, we show that such a chiral spin liquid state can be understood as a quantum disordered tetrahedral spin state stabilized by the four spin ring exchange coupling, which suppresses the order-by-disorder effect toward a stripy spin state. Such a chiral spin liquid state features a spin Berry phase of $\fracπ{2}$ per triangle. However, we show that …
We investigate the $J_1$-$J_2$ Heisenberg model on the triangular lattice with an additional scalar chirality term and show that a chiral spin liquid is stabilized in a sizeable region of the phase diagram. This topological phase is situated in between a coplanar $120^\circ$ Néel ordered and a non-coplanar tetrahedrally ordered phase. Furthermore we discuss the nature of the spin-disordered intermediate phase in the $J_1$-$J_2$ model. We compare the groundstates from Exact Diagonalization with a Dirac spin liquid wavefunction and propose a scenario where this wavefunction describes the quantum…
We study a spin-1/2 system with Heisenberg plus ring exchanges on a four-leg triangular ladder using the density matrix renormalization group and Gutzwiller variational wave functions. Near an isotropic lattice regime, for moderate to large ring exchanges we find a spin Bose-metal phase with a spinon Fermi sea consisting of three partially filled bands. Going away from the triangular towards the square lattice regime, we find a staggered dimer phase with dimers in the transverse direction, while for small ring exchanges the system is in a featureless rung phase. We also discuss parent states a…
A semiclassical theory of a quantum spin$-S$ model with competing ring and Heisenberg exchange terms on the triangular lattice is obtained. A mechanism for the generation of $Z_2$ vortices is exhibited. The vortices are shown to carry a nontrivial geometric phase for the order parameter when $2S$ is odd, leading to a difference between the quantum disordered ground states and low energy spectra for half odd integer and half even integer spin systems, and a topological degeneracy on surfaces with nontrivial cycles. A connection to dimer models is discussed.
We model the newly predicted high-$T_c$ superconducting candidates constructed by corner-shared trigonal bipyramidal complexes with an effective three-orbital tight-banding Hamiltonian and investigate the pairing symmetry of their superconducting states driven by electron-electron interactions. Our combined weak and strong coupling based calculations consistently identify the chiral $d+id$ superconductivity as the leading pairing symmetry in a wide doping range with realistic interaction parameters. This pairing state has nontrivial topological Chern-number and can host gapless chiral edge mod…
The effects of the ring-exchange Hamiltonian H_3 = J_3 sum_{<ijk>} (S_i * S_j) (S_i * S_k) on the triangular lattice are studied using classical Monte Carlo simulations. Each spin $S_i$ is treated as a classical XY spin taking on Q equally spaced angles (Q-states clock model). For Q=6, a first-order transition into a stripe-ordered phase preempts the macroscopic classical degeneracy. For Q > 6, a finite window of critical phase exists, intervening between the low-temperature stripe phase and the high-temperature paramagnetic phase.
Ring-exchange interactions have been proposed as a possible mechanism for a Bose-liquid phase at zero temperature, a phase that is compressible with no superfluidity. Using the Stochastic Green Function algorithm (SGF), we study the effect of these interactions for bosons on a two-dimensional triangular lattice. We show that the supersolid phase, that is known to exist in the ground state for a wide range of densities, is rapidly destroyed as the ring-exchange interactions are turned on. We establish the ground-state phase diagram of the system, which is characterized by the absence of the exp…
We study the spin wave in the S=1/2 multiple-spin exchange model on a triangular lattice in a magnetic field within the linear spin-wave theory. We take only two-, three- and four-spin exchange interactions into account and restrict ourselves to the region where a coplanar three-sublattice state is the mean-field ground state. We found that the Y-shape ground state survives quantum fluctuations and the phase transition to a phase with a 6-sublattice structure occurs with softening of the spin wave. We estimated the quantum corrections to the ground state sublattice magnetizations due to zero-p…
Spin scalar chiral ordering gives rise to nontrivial topological characters and peculiar transport properties. We here examine how quantum spin fluctuations affect the spin scalar chiral ordering in itinerant electron systems. We take the Kondo lattice model on a triangular lattice, and perform the linear spin wave analysis in the Chern insulator phases with spin scalar chiral ordering obtained in the case that the localized spins are classical. We find that, although the quantum fluctuation destabilizes the spin scalar chiral phase at 3/4 filling that originates from the perfect nesting of Fe…
Ferroelectric properties in magnetic fields of varying magnitude and direction have been investigated for a triangular-lattice helimagnet CuFe1-xGaxO2 (x=0.035). The magnetoelectric phase diagrams were deduced for magnetic fields along [001], [110], and [1-10] direction, and the in-plane magnetic field was found to induce the rearrangement of six possible multiferroic domains. Upon every 60-degree rotation of in-plane magnetic field around the c-axis, unique 120-degree flop of electric polarization occurs as a result of the switch of helical magnetic q-vector. The chirality of spin helix is al…
While a quantum spin liquid (QSL) phase has been identified in the $J_1$-$J_2$ Heisenberg model on a triangular lattice via numerical calculations, debate persists about whether or not such a QSL is gapped or gapless, with contradictory conclusions from different techniques. Moreover, information about excitations and dynamics is crucial for the experimental detection of such a phase. In this work, we use exact diagonalization to characterize signatures of a QSL phase on the triangular lattice through the dynamical spin structure factor $\mathcal{S}(q,ω)$ and Raman susceptibility $\mathcalχ(ω)…
By using Gutzwiller projected fermionic wave functions and variational Monte Carlo technique, we study the spin-$1/2$ Heisenberg model with the first-neighbor ($J_1$), second-neighbor ($J_2$), and additional scalar chiral interaction $J_χ{\bf S}_i \cdot ({\bf S}_j \times {\bf S}_k)$ on the triangular lattice. In the non-magnetic phase of the $J_1-J_2$ triangular model with $0.08 \lesssim J_2/J_1 \lesssim 0.16$, recent density-matrix renormalization group (DMRG) studies [Zhu and White, Phys. Rev. B {\bf 92}, 041105 (2015); Hu, Gong, Zhu, and Sheng, Phys. Rev. B {\bf 92}, 140403 (2015)] find a p…
We performed an exact diagonalization study of the spin liquid phase of the Multiple-Spin Exchange model on the triangular lattice. It is characterized by no Neel Long Range Order (NLRO), short-ranged magnetic correlations and a spin gap. We found no LRO in any local order parameter we investigated (chiral, dimer,...). The probable asymptotic ground state degeneracy is discussed. We argue that it could be of topological origin and that the system is probably not a chiral spin liquid. A possible relation to the Affleck-Kennedy-Lieb-Tasaki (AKLT) phase is discussed.
By using a numerically exact diagonalization technique and a block-extended version of the finite-temperature Lanczos method, we study thermodynamic properties of an $S=1/2$ Heisenberg model on the triangular lattice with an antiferromagnetic nearest-neighbor interaction $J$ and a four-spin ring-exchange interaction $J_{\rm c}$. Calculations are performed on small clusters under the periodic-boundary conditions. In contrast to the purely triangular case with $J_{\rm c}=0$, the specific heat exhibits a characteristic double-peak structure for $J_{\rm c}/J \gtrsim 0.04$. From the calculation of …
We present the temperature dependence of the uniform susceptibility of spin-half quantum antiferromagnets on spatially anisotropic triangular-lattices, using high temperature series expansions. We consider a model with two exchange constants, $J_1$ and $J_2$ on a lattice that interpolates between the limits of a square-lattice ($J_1=0$), a triangular-lattice ($J_2=J_1$), and decoupled linear chains ($J_2=0$). In all cases, the susceptibility which has a Curie-Weiss behavior at high temperatures, rolls over and begins to decrease below a peak temperature, $T_p$. Scaling the exchange constants t…
The interplay between spin frustration and charge fluctuation gives rise to an exotic quantum state in the intermediate-interaction regime of the half-filled triangular-lattice Hubbard model, while the nature of the state is under debate. Using the density matrix renormalization group with SU(2)$_{\rm{spin}} \otimes $U(1)$_{\rm{charge}}$ symmetries implemented, we study the triangular-lattice Hubbard model defined on the long cylinder geometry up to circumference $W=6$. A gapped quantum spin liquid, with on-site interaction $9 \lesssim U / t \lesssim 10.75$, is identified between the metallic …
Using exact diagonalizations, we investigate the T=0 phase diagram of the Multi-Spin Exchange (MSE) model on the triangular lattice: we find a transition separating a ferromagnetic phase from a non-magnetic gapped Spin Liquid phase. Systems far enough from the ferromagnetic transition have a metamagnetic behavior with magnetization plateaus at m/m_sat=0 and 1/2. The MSE has been proposed to describe solid 3He films adsorbed onto graphite, thus we compute the MSE heat capacity for parameters in the low density range of the 2nd layer and find a double-peak structure.
We study the effects of quantum fluctuations on a non-coplanar tetrahedral spin structure, which has a scalar chiral order, in the spin-1/2 multiple-spin exchange model with up to the six-spin exchange interactions on a triangular lattice. We find that, in the linear spin-wave approximation, the tetrahedral structure survives the quantum fluctuations because spin waves do not soften in the whole parameter region of the tetrahedral-structure phase evaluated for the classical system. In the quantum corrections to the ground-state energy, sublattice magnetization, and scalar chirality, the effect…
The Heisenberg model on a triangular lattice is a prime example for a geometrically frustrated spin system. However most experimentally accessible compounds have spatially anisotropic exchange interactions. As a function of this anisotropy, ground states with different magnetic properties can be realized. Motivated by recent experimental findings on Cs$_{2}$CuCl$_{4-x}$Br$_{x}$, we discuss the full phase diagram of the anisotropic model with two exchange constants $J_{1}$ and $J_{2}$, including possible ferromagnetic exchange. Furthermore a comparison with the related square lattice model is c…
The existence of a gapped chiral spin liquid has been recently suggested in the vicinity of the metal-insulator transition of the Hubbard model on the triangular lattice, by intensive density-matrix renormalization group (DMRG) simulations [A. Szasz, J. Motruk, M.P. Zaletel, and J.E. Moore, Phys. Rev. X {\bf 10}, 021042 (2020)]. Here, we report the results obtained within the variational Monte Carlo technique based upon Jastrow-Slater wave functions, implemented with backflow correlations. As in DMRG calculations, we consider $N$-leg cylinders. For $N=4$ and in the presence of a next-nearest n…
We investigate the ground-state phase diagram for the ferromagnetic Kondo lattice model on a triangular lattice by a variational calculation for various spin orderings up to a four-site unit cell. We find that a noncoplanar four-sublattice ordering with a finite scalar spin chirality emerges at and around 1/4 filling, in addition to the 3/4-filled case, which was predicted to be induced by the perfect nesting of the Fermi surface [I. Martin and C. D. Batista: Phys. Rev. Lett. {\bf 101} (2008) 156402]. The 1/4-filling phase is stable in a wider range of parameters than the 3/4-filling one, and …
The ground state of the multiple-spin exchange model with up to the six-spin exchange interactions on a triangular lattice in the magnetic field is investigated within the mean-field approximation. By comparing the phase diagrams of systems with and without the five- and six-spin interactions, we find that the five- and six-spin interactions expand the ferromagnetic phase. In contrast, the antiferromagnetic-like phases are contracted. A phase with a 1/2 plateau is also contracted by the five- and six-spin interactions. In addition to the results that have not yet been reported for systems with…
We investigate the effect of ring-exchange on the ground-state properties and magnetic excitations of the $S = 1/2$ Heisenberg model on the anisotropic triangular lattice with ring-exchange at $T = 0$ using linear spin-wave theory. Classically, we find stable Néel, spiral and collinear magnetically ordered phases. Upon including quantum fluctuations to the model, linear spin-wave theory shows that ring exchange induces a large quantum disordered region in the phase diagram, completely wiping out the classically stable collinear phase. Analysis of the spin-wave spectra for each of these three m…
We study the interplay of competing interactions in spin-$1/2$ triangular Heisenberg model through tuning the first- ($J_1$), second- ($J_2$), and third-neighbor ($J_3$) couplings. Based on large-scale density matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a new {\it gapless} chiral spin liquid (CSL) phase in the intermediate $J_2$ and $J_3$ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge…
We consider a SU(3) ring-exchange model on a triangular lattice. Unlike the SU(2) case, under perturbation expansion of the SU(3) Hubbard model, the three-site ring exchange is present as well as the usual four-site ring exchange. Interestingly, the three-site ring exchange differs from the usual two-site and four-site exchanges by a minus sign and is ferromagnetic. We first present numerical site-factorized state studies on this model which shows a three-sublatticed order phase and a ferromagnetic phase. We further study the model using slave-fermion mean field in which we rewrite the exchang…
At strong repulsion, the triangular-lattice Hubbard model is described by $s=1/2$ spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120$^\circ$ order. Using the infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that at physically rel…
The entire magnetic phase diagram of the quasi two dimensional (2D) magnet on a distorted triangular lattice KFe(MoO4)2 is outlined by means of magnetization, specific heat, and neutron diffraction measurements. It is found that the spin network breaks down into two almost independent magnetic subsystems. One subsystem is a collinear antiferromagnet that shows a simple spin-flop behavior in applied fields. The other is a helimagnet that instead goes through a series of exotic commensurate-incommensurate phase transformations. In the various phases one observes either true 3D order or quasi-2D …
Thermodynamic properties of the twisted three-leg spin tube under magnetic field are studied by the finite-$T$ density-matrix renormalization group method. The specific heat, spin, and chiral susceptibilities of the infinite system are calculated for both the original and its low-energy effective models. The obtained results show that the presence of the chirality is observed as a clear peak in the specific heat at low temperature and the contribution of the chirality dominates the low-temperature part of the specific heat as the exchange coupling along the spin tube decreases. The peak struct…
We investigate the nature of a $Z_2$-invariant XY ring-exchange interaction with a frustrated Ising coupling on the triangular lattice. In the limit of pure XY ring-exchange interaction, we show that the classical ground state is degenerate resulting from the $Z_2$-invariance of the Hamiltonian. Quantum fluctuations lift these classical degenerate ground states and produce an unusual state whose excitation spectrum exhibits a gapped maximum quadratic dispersion near ${\bf k}=0$ and vanishes at the midpoints of each side of the Brillouin zone. This result is in contrast to a gapless quadratic d…
Triangular Heisenberg antiferromagnets are prototypes of geometric frustration, even if for nearest-neighbor interactions quantum fluctuations are not usually strong enough to destroy magnetic ordering: stronger frustration is required to stabilize a spin-liquid phase. On the basis of static magnetization and electron spin resonance measurements, we demonstrate the emergence of ${\tilde{j}_{\text{eff}}=\frac12}$ moments in the triangular-lattice magnet Na$_2$BaCo(PO$_4$)$_2$. These moments are subject to an extra source of frustration that causes magnetic correlations to set in far above both …
Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study the Hubbard model on this lattice at half filling using the infinite-system density matrix renormalization group (iDMRG) method. On infinite cylinders with finite circumference, we identify an intermediate phase between observed metallic behavior at low interaction strength and Mott insulating spin-ordered behavior at strong interactions. Chiral ordering from spontaneous breaking of time-reversal sy…
We study the Kondo Lattice and Hubbard models on a triangular lattice for band filling factor 3/4. We show that a simple non-coplanar chiral spin ordering (scalar spin chirality) is naturally realized in both models due to perfect nesting of the Fermi surface. The resulting triple-Q magnetic ordering is a natural counterpart of the collinear Neel ordering of the half-filled square lattice Hubbard model. We show that the obtained chiral phase exhibits a spontaneous quantum Hall-effect with sigma_{xy}= e^2/h.
Ground state magnetic properties of the spin-dependent Falicov-Kimball model (FKM) are studied by incorporating the intrasite exchange correlation J (between itinerant $d$- and localized $f$- electrons) and intersite (superexchange) correlation $J_{se}$ (between localized $f$- electrons) on a triangular lattice for two different fillings. Numerical diagonalization and Monte-Carlo techniques are used to determine the ground state magnetic properties. Transitions from antiferromagnetic to ferromagnetic and again to re-entrant antiferromagnetic phase is observed in a wide range of parameter space…
The mechanism of the unconventional topological superconductivity (TSC) remains a long-standing issue. We investigate the quantum phase diagram of the extended $t$-$J$-$J_χ$ model including spin chiral interactions on triangular lattice based on the state-of-the-art density matrix renormalization group simulations. We identify distinct classes of superconducting phases characterized by nonzero topological Chern numbers $C=1$ and $2$, and a nematic d-wave superconducting phase with a zero Chern number. The TSC states are shown to emerge from doping either a magnetic insulator or chiral spin liq…
We investigate the interplay between spatial anisotropy and further exchange interactions in the spin-$\frac{1}{2}$ Heisenberg antiferromagnetic model on a triangular lattice. We use the Schwinger boson theory by including Gaussian fluctuations above the mean-field approach. The phase diagram exhibits a strong reduction of the long range collinear and incommensurate spirals regions with respect to the mean-field ones. This reduction is accompanied by the emergence of its short range order counterparts, leaving an ample room for $0$-flux and nematic spin liquid regions. Remarkably, within the n…
Chiral enhancement of two-magnon bound states in an $S=1/2$ triangular-lattice magnet
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；HUN-REN Wigner Research Centre for Physics, Institute for Solid State Physics and Optics（匈牙利研究网络维格纳物理研究中心固体物理与光学研究所）
Single helicity of the triple-$q$ triangular skyrmion lattice state in cubic chiral helimagnet EuPtSi
Hiroshima University（广岛大学）；Japan Atomic Energy Agency（日本原子能机构）；Institute of Materials Structure Science, High Energy Accelerator Research Organization（高能加速器研究机构物质结构研究所）；University of the Ryukyus（琉球大学）；RIKEN Center for Emergent Matter Science（理化学研究所 新兴物质科学中心）
Skyrmions, topologically-protected nanometric spin vortices, are being investigated extensively in various magnets. Among them, many of structurally-chiral cubic magnets host the triangular-lattice skyrmion crystal (SkX) as the thermodynamic equilibrium state. However, this state exists only in a narrow temperature and magnetic-field region just below the magnetic transition temperature $T_\mathrm{c}$, while a helical or conical magnetic state prevails at lower temperatures. Here we describe that for a room-temperature skyrmion material, $β$-Mn-type Co$_8$Zn$_8$Mn$_4$, a field-cooling via the …
We study ring-exchange models for bosons or XY-spins on the triangular lattice. A four-spin exchange leads to a manifold of ground states with gapless excitations and critical power-law correlations. With a nearest-neighbour exchange, fluctuations select a four-fold ferrimagnetically ordered ground state with a small spin/superfluid stiffness which breaks the global U(1) and translational symmetry. We explore consequences for phase transitions at finite temperature and in an in-plane magnetic field.
We investigate the ground-state phase diagram of the Kondo lattice model with classical localized spins on triangular-to-kagome lattices by using a variational calculation. We identify the parameter regions where a four-sublattice noncoplanar order is stable with a finite spin scalar chirality while changing the lattice structure from triangular to kagome continuously. Although the noncoplanar spin states appear in a wide range of parameters, the spin configurations on the kagome network become coplanar as approaching the kagome lattice; eventually, the scalar chirality vanishes for the kagome…
We study the ground state properties of the Hubbard model on three-leg triangular cylinders using large-scale density-matrix renormalization group simulations. At half-filling, we identify an intermediate gapless spin liquid phase between a metallic phase at weak coupling and Mott insulating dimer phase at strong interaction, which has one gapless spin mode and algebraic spin-spin correlations but exponential decay scalar chiral-chiral correlations. Upon light doping the gapless spin liquid, the system exhibits power-law charge-density-wave (CDW) correlations but short-range single-particle, s…
Chiral Spin Liquid and Quantum Phase Transition in the Triangular Lattice Hofstadter-Hubbard Model
University of California, Berkeley（加州大学伯克利分校）；Center for Computational Quantum Physics, Flatiron Institute（Flatiron Institute计算量子物理中心）；Harvard University（哈佛大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Columbia University（哥伦比亚大学）
The effects of pressure on a quantum spin liquid are investigated in an organic Mott insulator $κ$-(ET)$_2$Ag$_2$(CN)$_3$ with a spin-1/2 triangular lattice. The application of negative chemical pressure to $κ$-(ET)$_2$Cu$_2$(CN)$_3$, which is a well-known sister Mott insulator, allows for extensive tuning of antiferromagnetic exchange coupling, with $J/k_{\rm B} = 175 - 310$ K, under hydrostatic pressure. Based on $^{13}$C nuclear magnetic resonance measurements under pressure, we uncover universal scaling in the static and dynamic spin susceptibilities down to low temperatures $\sim 0.1k_{\r…
In order to study effects of frustration in an itinerant electron system, we investigate ground states of the antiferromagnetic double-exchange model on a triangular lattice. In this model, pseudo-spins are coupled to electron transfer integrals in such a way that antiparallel configurations of pseudo-spins gain kinetic energies. Although the antiferromagnetic Ising model on a triangular lattice shows macroscopic dengenerate ground states, the present model shows that the degeneracy is lifted due to long-range natures of the double exchange interactions. Spin ordering at the ground state is al…
We investigate thermodynamic properties like specific heat $c_{V}$ and susceptibility $χ$ in anisotropic $J_1$-$J_2$ triangular quantum spin systems ($S=1/2$). As a universal tool we apply the finite temperature Lanczos method (FTLM) based on exact diagonalization of finite clusters with periodic boundary conditions. We use clusters up to $N=28$ sites where the thermodynamic limit behavior is already stably reproduced. As a reference we also present the full diagonalization of a small eight-site cluster. After introducing model and method we discuss our main results on $c_V(T)$ and $χ(T)$. We …
Magnetic exchange couplings can be tuned by coupling to periodic light, where the frequency and amplitude are typically varied: a process known as Floquet engineering. The polarization of the light is also important, and in this paper, we show how different polarizations, including several types of unpolarized light, can tune the exchange couplings in distinct ways. Using unpolarized light, for example, it is possible to tune the material without breaking either time-reversal or any lattice symmetries. To illustrate these effects generically, we consider single-band Hubbard models at half-fill…
Through Variational Monte Carlo simulation we show the d-wave RVB pairing in the Heisenberg model on triangular lattice can be better described in terms of a two component order parameter. The fully gapped chiral d-wave RVB state, which is predicted by the mean field theory to be the unique minimum of variational energy in the two dimensional representation space of d-wave pairing, is found to be actually a local maximum and the true minimum of energy is reached by the non-chiral $d_{xy}$ state with line nodes. We also find that the usual Gutzwiller approximation, which enjoys great success fo…
Recent experiments on triangular lattice organic Mott insulators have found evidence for a 2D spin liquid in proximity to the metal-insulator transition. A Gutzwiller wavefunction study of the triangular lattice Heisenberg model with appropriate four-spin ring exchanges has found that the projected spinon Fermi sea state has a low variational energy. This wavefunction, together with a slave particle gauge theory, suggests that such spin liquid possesses spin correlations that are singular along surfaces in momentum space ("Bose surfaces"). Signatures of this state, which we refer to as a "Spin…
Inhomogeneity in the ground state is an intriguing, emergent phenomenon in magnetism. Recently, it has been observed in the magnetostructural channel of the geometrically frustrated $α$-NaMnO$_2$, for the first time in the absence of active charge degrees of freedom. Here we report an in-depth numerical and local-probe experimental study of the isostructural sister compound CuMnO$_2$ that emphasizes and provides an explanation for the crucial differences between the two systems. The experimentally verified, much more homogeneous, ground state of the stoichiometric CuMnO$_2$ is attributed to th…
