The classical Heisenberg antiferromagnet on a triangular lattice with the single-ion anisotropy of the easy-axis type is theoretically investigated. The mean-field phase diagram in an external magnetic field is constructed. Three finite-temperature Berezinskii-Kosterlitz-Thouless transitions are found by the Monte Carlo simulations in zero field. The two upper transitions are related to the breaking of the discrete ${\mathbb Z}_{6}$ symmetry group, while the lowest transition is associated with a quasi-long-range ordering of transverse components. The intermediate collinear phase between first and second transitions is the sliding phase predicted by J. V. José {\it et al}. [Phys. Rev. B {\bf 16}, 1217 (1977)].
We study multilayer triangular lattice Ising antiferromagnets with interlayer interactions that are weak and frustrated in an abc stacking. By analysing a coupled height model description of these systems, we show that they exhibit a classical spin liquid regime at low temperature, in which both intralayer and interlayer correlations are strong but there is no long range order. Diffuse scattering in this regime is concentrated on a helix in reciprocal space, as observed for charge-ordering in the materials LuFe$_2$O$_4$ and YbFe$_2$O$_4$.
We examine the optical conductivity σ(ω) and the chemical potential μ, together with the spin correlation, in the strong-coupling limit of a hole-doped two-dimensional triangular Hubbard model near half filling by using an exact diagonalization technique. In contrast to the case of a square lattice without frustration, the doping dependences of μand the Drude weight indicate that the charge degree of freedom is weakly coupled to the spin degree of freedom. However, we find that σ(ω) shows strong incoherent excitations extended to a higher energy region. This implies that geometrical frustratio…
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 …
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$_7$.
For magnets with a fully frustrated inter-layer interaction, we argue that the quantum phase transitions from a paramagnetic to an antiferromagnetic ground state, driven by pressure or magnetic field, are asymptotically three-dimensional, due to interaction-generated non-frustrated inter-layer couplings. However, the relevant crossover scale is tiny, such that two-dimensional behavior occurs in an experimentally relevant low-temperature regime. In the pressure-driven case the phase transition may split, in which case an Ising symmetry related to inter-layer bond order is broken before magnetis…
We present an exact diagonalization study on layered $J_{1}-J_{2}$ antiferromagnetic Heisenberg spin model to examine the role of frustration induced by inplane next-nearest neighbor coupling $J_{2}$, in presence of interlayer antiferromagnetic coupling $J_{\perp}$. A finite lattice of 24 spins in layered geometry of $(4\times 3)\oplus (4\times 3)$ is considered and the resulting Hamiltonian matrix diagonalized using Davidson iterative algorithm to obtain the ground and a few low-lying excited states. The lattice size ($24$ spins with Hilbert space dimensionality of $2704156$ in $S_{z}^{tot}=0…
Evolution of the magnetic response function in the triangular-lattice Hubbard model is studied with interaction strength within a systematic inverse-degeneracy expansion scheme which incorporates self-energy and vertex corrections and explicitly preserves the spin-rotation symmetry. It is shown that at half filling the response function goes through a nearly dispersionless regime around K for intermediate coupling strength, before undergoing an inversion at strong coupling, resulting in maximum response at the K point, consistent with the expected 120^o AF instability. Effects of finite hole/e…
Single-particle dynamics in the 120$^{\circ}$ ordered antiferromagnetic state of the triangular-lattice Hubbard model is studied using a physically transparent fluctuation approach in terms of multiple magnon emission and absorption processes within the noncrossing approximation. Hole and electron spectral features are evaluated at intermediate $U$, and analyzed in terms of a competition between the frustration-induced direct hopping and the virtual hopping terms. Finite $U$-induced competing interactions and frustration effects contributing through the magnon dispersion are also discussed. Fi…
We report high resolution neutron scattering measurements on the triangular lattice Mott insulator Na$_x$CrO$_2$ ($x$=1) which has recently been shown to exhibit an unusually broad fluctuating crossover regime extending far below the onset of spin freezing ($T_c\sim$41K). Our results show that below some crossover temperature ($T\sim0.75T_c$) a small incommensuration develops which helps resolve the spin frustration and drives three-dimensional magnetic order supporting coherent spin wave modes. This incommensuration assisted dimensional crossover suggests that inter-layer frustration is respo…
The $1/4$-filled organic compound, $δ$-(EDT-TTF-CONMe$_{2}$)$_{2}$AsF$_6$ is a frustrated two-dimensional triangular magnetic system as shown by high-frequency (111.2 and 222.4 GHz) electron spin resonance (ESR) and structural data in the literature. The material gradually orders antiferromagnetically below 40~K but some magnetically disordered domains persist down to 4 K. We propose that in defect free regions frustration prevents true magnetic order down to at least 4 K in spite of the large first- and second-neighbor exchange interactions along chains and between chains, respectively. The a…
Frustration-driven topological textures on the honeycomb lattice: antiferromagnetic meron-antimeron and skyrmion crystals emerging from spiral spin liquids
We synthesized a quasi-two-dimensional distorted triangular lattice antiferromagnet Ca$_3$CoNb$_2$O$_9$, in which the effective spin of Co$^{2+}$ is 1/2 at low temperatures, whose magnetic properties were studied by dc susceptibility and magnetization techniques. The x-ray diffraction confirms the quality of our powder samples. The large Weiss constant $θ_{CW}\sim$ $-55$ K and the low Neel temperature($T_N\sim$ 1.45 K) give a frustration factor $f$ ($=\midθ_{CW}/T_N \mid$) $\approx$ 38, suggesting that Ca$_3$CoNb$_2$O$_9$ resides in strong frustration regime. Slightly below $T_N$, deviation be…
We present single crystal inelastic neutron scattering measurements of the S=1 dimerized quasi-two-dimensional antiferromagnet Ba$_3$Mn$_2$O$_8$. The singlet-triplet dispersion reveals nearest-neighbor and next-nearest-neighbor ferromagnetic interactions between adjacent bilayers that compete against each other. Although the inter-bilayer exchange is comparable to the intra-bilayer exchange, this additional frustration reduces the effective coupling along the c-axis and leads to a quasi-two dimensional behavior. In addition, the obtained exchange values are able to reproduce the four critical …
Antiferromagnetically coupled moments on the frustrated triangular lattice typically order in a coplanar state at low temperature. Here, we demonstrate that the presence of not-very-large easy axis single ion anisotropy leads to an interesting orientationally ordered collinear state in triangular lattice antiferromagnets with moments $S \ge 3/2$. This ordered state breaks the symmetry of $π/3$ rotations about a lattice site, while leaving intact the translational symmetry of the lattice.
The $S=1/2$ kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.
The spectral properties of the spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice in a magnetic field are investigated using a weak-interchain-coupling approach combined with exact solutions of a chain. Dominant modes induced by interchain interactions in a magnetic field behave as quasiparticles which show distinctive features such as anomalous incommensurate ordering and high-energy modes. In terms of them, various unusual features observed in the anisotropic triangular antiferromagnet Cs_2CuCl_4 in a magnetic field are quantitatively explained in a unified manner.
We study the $S = 1$ triangular lattice Ising antiferromagnet by Monte Carlo simulations. Frustrations between a major antiferromagnetic third-neighbor interaction $J_3$ and a minor ferromagnetic nearest-neighbor interaction $J_1$ cause incommensurate short-range orders at intermediate temperatures. At low temperatures (below $T/J_3 \lesssim 0.2$ for $J_1/J_3 = -1/3$), the system exhibits fourfold periodic ordered state. In the short-range order phase, the system shows a glassy two-step relaxation. We demonstrate that the features of the short-range order are attributed to the cooperation betw…
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 the phase diagram of the anisotropic spin-1/2 triangular lattice antiferromagnet, with interchain diagonal exchange J' much weaker than the intrachain exchange J. We find that fluctuations lead to a competition between (commensurate) collinear antiferromagnetic and (zig-zag) dimer orders. Both states differ in symmetry from the spiral order known to occur for larger J', and are therefore separated by quantum phase transitions from it. The zero-field collinear antiferromagnet is succeeded in a magnetic field by magnetically-ordered spin-density-wave and cone phases, before reachi…
The effect of nonmagnetic impurities on the phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice is investigated. We present analytical arguments confirmed by numerical calculations that at zero temperature vacancies stabilize a conical state providing an example of "order by quenched disorder" effect. Competition between thermal fluctuations and the site disorder leads to a complicated H-T phase diagram, which is deduced from the classical Monte Carlo simulations for a representative vacancy concentration. For the XY triangular-lattice antiferromagnet with in-plan…
We show strong numerical evidence in favor of an unexpected virtually gapless spectrum, with edge states localized at the boundaries, in frustrated spin-1/2 antiferromagnetic ladders with an odd number of legs. These features can be accurately reproduced by using a projected BCS wave function with a non-trivial pairing, that mixes even and odd reflection symmetries. This approach gives the correct classification of the excitations and provides a simple and very appealing picture of an unconventional spin-liquid phase stabilized by frustration.
This paper discusses the ground state of quantum spins interacting via Heisenberg antiferromagnetic exchange, in two dimensional lattices having several different local environments. In unfrustrated lattices, when a Néel type order exists, quantum fluctuations lead to an inhomogeneous order parameter. I consider the effects of adding frustration to such a system by including next nearest neighbor antiferromagnetic interactions. Within linear spin wave theory, it is found that as the frustration parameter increases, the local order parameters decrease at a rate that depends on the type of sites…
We show that the introduction of frustration into the spin-1/2 two-dimensional (2D) antiferromagnetic Heisenberg model on a square lattice via a next-nearest neighbor exchange interaction can lead to a Peierls-like transition, from a tetragonal to an orthorhombic phase, when the spins are coupled to adiabatic phonons. The two different orthorhombic ground states define an Ising order parameter, which is expected to lead to a finite temperature transition. Implications for ${\rm Li_2VOSiO_4}$, the first realization of that model, will be discussed.
We consider the spin--orbital model for a magnetic system with singly occupied but triply degenerate $t_{2g}$ orbitals coupled into a planar, triangular lattice, as would be exemplified by NaTiO$_2$. We investigate the ground states of the model for interactions which interpolate between the limits of pure superexchange and purely direct exchange interactions. By considering ordered and dimerized states at the mean--field level, and by interpreting the results from exact diagonalization calculations on selected finite systems, we demonstrate that orbital interactions are always frustrated, and…
We investigate the effect of geometrical frustration on the $H$--$T$ phase diagrams of the classical Heisenberg antiferromagnets on triangular and kagome lattices. The phase diagrams for the two models are obtained from large scale Monte Carlo simulations. For the kagome antiferromagnet thermal fluctuations are unable to lift completely degeneracy and stabilize translationally disordered multipolar phases. We find a substantial difference in the temperature scales of the order by disorder effect related to different degeneracy of the low- and the high-field classical ground states in the kagom…
Recently, it has become possible to tune optical lattices continuously between square and triangular geometries. We compute thermodynamics and spin correlations in the corresponding Hubbard model using determinant quantum Monte Carlo and show that the frustration effects induced by the variable hopping terms can be clearly separated from concomitant bandwidth changes by a proper rescaling of the interaction. An enhancement of the double occupancy by geometric frustration signals the destruction of nontrivial antiferromagnetic correlations at weak coupling and entropy $s\lesssim \ln(2)$ (and re…
We study the ground-state phase diagram of a Heisenberg model with spin $S=\frac{1}{2}$ on a diamond-like decorated square lattice. A diamond unit has two types of antiferromagnetic exchange interactions, and the ratio $λ$ between the length of the diagonal bond and that of the other four edges determines the strength of frustration. It has been pointed out [J. Phys. Soc. Jpn {\bf85}, 033705 (2016)] that the so-called tetramer-dimer states, which are expected to be stabilized in an intermediate region of $λ_{\rm c}<λ<2$, are identical to the square-lattice dimer covering states, which ignited …
The excitation spectrum of a S=1/2 2D triangular quantum antiferromagnet is studied using 1/S expansion. Due to the non-collinearity of the classical ground state significant and non-trivial corrections to the spin wave spectrum appear already in the first order in 1/S in contrast to the square lattice antiferromagnet. The resulting magnon dispersion is almost flat in a substantial portion of the Brillouin zone. Our results are in quantitative agreement with recent series expansion studies by Zheng, Fjaerestad, Singh, McKenzie, and Coldea [PRL 96, 057201 (2006) and cond-mat/0608008].
We report a spin S = 3/2 triangular antiferromagnet with nearest-neighbor coupling J = 0.29 meV in La2Ca2MnO7. A genuinely two-dimensional, three-sublattice order develops below 2.80 K << the Weiss constant (25 K). The spin excitations deviate substantially from linear spin-wave theory, suggesting that magnon breakdown occurs in the material. Such a breakdown has been anticipated in recent theoretical studies, although the excitation spectrum remains to be accounted for.
The $120^0$ ordered antiferromagnetic state of the Hubbard model on a triangular lattice presents an interesting case of $U$-controlled competing interactions and frustration. The spin stiffness is found to vanish at $U^* _{\rm stiff} \approx 6$ and the spin-wave energy $ω_M$ at ${\bf q}_M=(2π/3,0)$ etc. is found to vanish at $U_M ^* \approx 6.8$ due to competing spin couplings generated at finite $U$. The loss of magnetic order due to the magnetic instability at ${\bf q}_M$ yields a first-order quantum phase transition in the insulating state at $U=U_{\rm M}^*$. Implications of the quantum sp…
We study ferrimagnetism in the ground state of the antiferromagnetic Heisenberg model on the spatially anisotropic kagome lattice, in which ferrimagnetism of the conventional Lieb-Mattis type appears in the region of weak frustration whereas the ground state is nonmagnetic in the isotropic case. Numerical diagonalizations of small finite-size clusters are carried out to examine the spontaneous magnetization. We find that the spontaneous magnetization changes continuously in the intermediate region between conventional ferrimagnetism and the nonmagnetic phase. Local magnetization of the interme…
Neutron scattering experiment on NiS2 single crystal revealed a honeycomb pattern of the intensity distribution in reciprocal lattice space (continuous-line structure along the fcc zone boundary) providing the first direct evidence for nearly frustrated antiferromagnetism (AF) on the face centered cubic (fcc) lattice. A small but finite lattice distortion below 30.9 K lifts the degeneracy of the magnetic ground state due to the frustration and eventually result in the coexistence of the type I and the type II AF long range orderings, which are mutually incompatible in the fcc symmetry at highe…
Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond nearest neighbour. We show that the first-order transition from the stripe state to the paramagnet can be split, giving rise to an intermediate nematic phase in which algebraic correlations coexist with a broken symmetry. Furthermore, we demonstrate the emergence of several properties of a more topological nature such as fractional edge excitations in the stripe state, the proliferation of double domain walls in the nematic phase, and the Kastel…
We study the magnetic properties of the two-dimensional anisotropic antiferromagnetic spin-1/2 Heisenberg model with Dzyaloshinskii-Moriya interaction and in-plane frustration included. The method of spin Green functions within the framework of Tyablikov's random-phase-approximation decoupling scheme is used in order to derive expressions for the spin-wave spectrum, sublattice magnetization and transition temperature. Based on these expressions we perform a detailed analysis of the influence of varying values of model parameters on its magnetic properties. The model is also applied to the high…
We report on the emergence of antiferromagnetic spin chains from two-dimensionally aligned spins on the anisotropic triangular lattice (ATL) in the insulating calcium rhenium oxychloride Ca3ReO5Cl2. The compound contains Re6+ ions each with one unpaired electron in the dxy orbital, which are arranged to form a spin-1/2 ATL with J'/J ~ 0.32 and J = 41 K, where J and J' are magnetic interactions in and between the chains, respectively. In spite of the apparent two dimensionality, we observe clear evidence of a gapless spin liquid that is characteristic of the spin-1/2 Heisenberg chain. This one-…
We present a detailed investigation of the magnetic properties of the spin-$\frac{3}{2}$ system Li$_2$Co(WO$_4$)$_2$ by means of magnetic susceptibility and specific heat. Our experimental results show that in Li$_2$Co(WO$_4$)$_2$ a short-range antiferromagnetic (AFM) correlations appear near $χ$$_{max}$ $\sim$ 11 K and two successive long-range AFM phase transitions are observed at T$_{N1}$$\sim$ 9 K and T$_{N2}$$\sim$ 7 K. The frustration factor, $\mid$$Θ$$\mid$/T$_{N1}$$\sim$3, indicates that the system is moderately frustrated, which is identifiable by the broken triangular symmetry within…
Quantum simulators based on cold atomic gases can provide an ideal platform to study the microscopic mechanisms behind intriguing properties of solid materials and further explore novel exotic phenomena inaccessible by chemical synthesis. Here we propose and theoretically analyze a coherently coupled binary mixture of Fermi atoms in a triangular optical lattice as a promising realization of synthetic frustrated antiferromagnets. We perform a cluster mean-field plus scaling analysis to show that the ground state exhibits several nontrivial magnetic phases and a novel spin reorientation transiti…
We report the first detailed investigation of K$_2$MnS$_2$ and K$_2$MnSe$_2$ from the K$_2$MnS$_2$ structure type and their magnetic solid solution K$_2$MnS$_{2-x}$Se$_x$ and find that compounds of this structure type consist of strongly-coupled pseudo-one-dimensional antiferromagnetic chains that collectively represent a frustrated two-dimensional triangular antiferromagnet. Bulk samples of K$_2$MnS$_{2-x}$Se$_x$ with $0 \leq x \leq 2$ are characterized using X-ray diffraction, neutron diffraction, magnetization and heat capacity measurements. An incommensurate cycloid magnetic structure with…
The S = 1/2 Heisenberg antiferromagnet on the two-dimensional pyramid lattice is studied by the numerical-diagonalization method. This lattice is obtained by the combination of the Lieb lattice and the square lattice. It is known that when interaction on the square lattice is increased from the ferrimagnetic limit of strong interaction on the Lieb lattice, this system shows gradual decrease and disappearance of spontaneous magnetization in the ground state. The present study treats the region near the case of the square-lattice antiferromagnet accompanied by isolated spins by numerical-diagona…
Interleaved bond frustration in a triangular lattice antiferromagnet
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Technical University of Munich（慕尼黑工业大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Cornell High Energy Synchrotron Source, Cornell University（康奈尔大学高能同步辐射光源，康奈尔大学）；Advanced Photon Source, Argonne National Laboratory（阿贡国家实验室先进光子源）
We investigate the Hubbard model on the anisotropic triangular lattice by means of the cellular dynamical mean field theory. The phase diagram determined in the Hubbard interaction versus temperature plane shows novel reentrant behavior in the Mott transition due to the competition between Fermi-liquid formation and magnetic correlations under geometrical frustration. We demonstrate that the reentrant behavior is characteristic of the Mott transition with intermediate geometrical frustration and indeed consistent with recent experimental results of organic materials.
We explore the interplay between randomness and magnetic frustration in the series of $S = 1/2$ Heisenberg square-lattice compounds Sr$_2$CuTe$_{1-x}$W$_x$O$_6$. Substituting W for Te alters the magnetic interactions dramatically, from strongly nearest-neighbor to next-nearest-neighbor antiferromagnetic coupling. We perform neutron scattering measurements to probe the magnetic ground state and excitations over a range of $x$. We propose a bond-disorder model that reproduces ground states with only short-ranged spin correlations in the mixed compounds. The calculated neutron diffraction pattern…
Phase inhomogeneity of otherwise chemically homogenous electronic systems is an essential ingredient leading to fascinating functional properties, such as high-$T_c$ superconductivity in cuprates, colossal magnetoresistance in manganites, and giant electrostriction in relaxors. In these materials distinct phases compete and can coexist due to intertwined ordered parameters. Charge degrees of freedom play a fundamental role, although phase-separated ground states have been envisioned theoretically also for pure spin systems with geometrical frustration that serves as a source of phase competiti…
Motivated by the absence of cooperative Jahn-Teller effect and of magnetic ordering in LiNiO$_2$, a layered oxide with triangular planes, we study a general spin-orbital model on the triangular lattice. A mean-field approach reveals the presence of several singlet phases between the SU(4) symmetric point and a ferromagnetic phase, a conclusion supported by exact diagonalizations of finite clusters. We argue that one of the phases, characterized by a large number of low-lying singlets associated to dimer coverings of the triangular lattice, could explain the properties of LiNiO$_2$, while a fer…
We investigate the $S=1/2$ quantum spin antiferromagnets on the triangular and Kagome lattices in magnetic field, using the numerical exact diagonalization. Particularly we focus on an anomalous magnetization behavior of each system at 1/3 of the saturation magnetization. The critical exponent analyses suggest that it is a conventional magnetization plateau on the triangular lattice, while an unconventional phenomenon, called the magnetization ramp, on the Kagome lattice.
A brief review is provided of earlier work on the low temperature phases of $S=1$ kagome and triangular lattice antiferromagnets in which there is sufficiently strongly single-ion anisotropy $D$ that dominates over the antiferromagnetic exchange $J$.
We map certain highly correlated electron systems on lattices with geometrical frustration in the motion of added particles or holes to the spatial defect-defect correlations of dimer models in different geometries. These models are studied analytically and numerically. We consider different coverings for four different lattices: square, honeycomb, triangular, and diamond. In the case of hard-core dimer covering, we verify the existed results for the square and triangular lattice and obtain new ones for the honeycomb and the diamond lattices while in the case of loop covering we obtain new num…
Using the self-consistent Born approximation we study the delocalization of interlayer excitons in the bilayer Heisenberg quantum antiferromagnet. Under realistic conditions we find that the coupling between the exciton motion and the spin system is strongly enhanced as compared to the case of a single carrier, to a degree that it mimics the confinement physics of carriers in Ising spin systems. We predict that the "ladder spectrum" associated with this confinement physics should be visible in the c-axis exciton spectra of insulating bilayer cuprates such as YBa2Cu3O6. Our discovery indicates …
We apply the coupled cluster method and exact diagonalzation to study the uniform susceptibility and the ground-state magnetization curve of the triangular-lattice spin-1 Heisenberg antiferromagnet. Comparing our theoretical data for the magnetization curve with recent measurements on the s=1 triangular lattice antiferromagnet Ba3NiSb2O9 we find a very good agreement.
We investigate the paramagnetic-metal-to-antiferromagnetic-metal and antiferromagnetic-metal-to- antiferromagnetic-insulator transitions using a slave-boson mean-field theory. To this effect, we discuss the ground state of the half-filled Hubbard model as a function of t'/t and correlation strength U, where t and t' are the hopping amplitudes between nearest and next-nearest neighbors, respectively. The metal-insulator transition at a critical U_{MIT} is of second order for small levels of magnetic frustration, t'/t<0.06, and of first order for large ones, t'/t>0.06. The insulator is always an…
The ground state of the spin-$1/2$ Heisenberg antiferromagnet on a distorted triangular lattice is studied using a numerical-diagonalization method. The network of interactions is the $\sqrt{3}\times\sqrt{3}$ type; the interactions are continuously controlled between the undistorted triangular lattice and the dice lattice. We find new states between the nonmagnetic 120-degree-structured state of the undistorted triangular case and the up-up-down state of the dice case. The intermediate states show spontaneous magnetizations that are smaller than one third of the saturated magntization correspo…
Geometric frustration adds a new competing energy scale to the antiferromagnetic (AFM) Kondo lattice model (KLM). In this work, we systematically study the doniach phase diagram on the square and triangular lattices in the same theoretical framework and reveal unexpected responses of it on the two lattices. The potential energy created by the geometric frustration is comparable to the Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling, which completely suppresses the long-range antiferromagnetic (AFM) order on the half-filled triangular lattice. While, on the square lattice, the long-range AFM orde…
Frustration-driven unconventional magnetism in the Mn$^{2+}$ ($S=\frac{5}{2}$) based two-dimensional triangular-lattice antiferromagnet Ba$_{3}$MnTa$_{2}$O$_{9}$
