V. Thanh Ngo, H. T. Diep
We show in this paper by using the Wang-Landau flat-histogram Monte Carlo method that the phase transition in the XY stacked triangular antiferromagnet is clearly of first-order, confirming results from latest Monte Carlo simulation and from a nonperturbative renormalization group, putting an end to a long-standing controversial issue.
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We study the spin stiffness of stacked triangular antiferromagnets using both heat bath and broad histogram Monte Carlo methods. Our results are consistent with a continuous transition belonging to the chiral universality class first proposed by Kawamura.
We study the reductions of spin values of the ground state on a stacked triangular antiferromagnet using the spin-wave approach. We find that the spin reductions have sublattice asymmetry due to the cancellation of the molecular field. The sublattice asymmetry qualitatively analyzes the NMR results of CsCoBr$_3$.
We study a stacked triangular lattice Ising model with both intra- and inter-plane antiferromagnetic interactions in a field, by Monte Carlo simulation. We find only one phase transition from a paramagnetic to a partially disordered phase, which is of second order and 3D XY universality class. At low temperatures we identify two highly degenerate phases: at smaller (larger) fields the system shows long-range ordering in the stacking direction (within planes) but not in the planes (stacking direction). Nevertheless, crossovers to these phases do not have a character of conventional phase transi…
By using the Wang-Landau flat-histogram Monte Carlo (MC) method for very large lattice sizes never simulated before, we show that the phase transition in the frustrated Heisenberg stacked triangular antiferromagnet is of first-order, contrary to results of earlier MC simulations using old-fashioned methods. Our result lends support to the conclusion of a nonperturbative renormalization group performed on an effective Hamiltonian. It puts an end to a 20-year long controversial issue.
An Ising antiferromagnet on a stacked triangular lattice in zero field is studied by Monte Carlo simulations, focusing on the character of the low-temperature phase and the effect of the relative strength of the exchange interaction in the stacking direction α. Our results support the presence of the 3D Wannier phase, with the sublattice magnetization structure (m, -m, 0) and power-law decaying m with the lattice size. The extent of this low-temperature phase shrinks with decreasing α, however, it appears even at very low values if it is accessed from higher temperatures by sufficiently slow c…
``Chirality'' is a multispin quantity representing the sense or the handedness of the noncollinear spin structures induced by spin frustration. Recent studies have revealed that the chirality often plays an important role in the ordering of certain frustrated magnets. Here I take up two such examples, stacked-triangular antiferromagnets and spin glasses, where the inherent chiral degree of freedom affects underlying physics and might lead to novel ordering phenomena. The first topic is the criticality of the magnetic phase transition of vector (i.e., XY or Heisenberg) antiferromagnets on the t…
We study low-temperature magnetization processes in a stacked triangular Ising antiferromagnet by Monte Carlo simulations. In increasing and decreasing magnetic fields we observe multiple steps and hysteresis corresponding to formation of different metastable states. Besides the equidistant threefold splitting of the 1/3 ferrimagnetic plateau, we additionally confirm a fourth plateau in the field-increasing branch and a sizable remanence when the field is decreased to zero. The newly observed plateau only appears at sufficiently low temperature and sufficiently large exchange interaction in th…
We study the possibility of long-range ordering (LRO) in a 3D system of vertically stacked layers of Ising antiferromagnet on a kagome lattice (SIAKL). Monte Carlo simulations are carried out for a varying interlayer coupling strength and a finite-size scaling analysis is performed for selected cases. Unlike in the related Ising system on a triangular lattice, in which even a finite number of the layers can stabilize LRO, or the Heisenberg system on the same kagome lattice, in which LRO emerged in 3D for a sufficient strength of the interlayer coupling, no LRO could be observed in the present …
We study the ordered phases and the phase transitions in the stacked triangular antiferromagnetic Ising (STAFI) model with strong interplane coupling modeling CsCoCl$_3$ and CsCoBr$_3$. We find that there exists an intermediate phase which consists of a single phase of so-called partial disordered (PD) type, and confirm the stability of this phase. The low temperature phase of this model is so-called two-sublattice ferri magnetic phase. The phase transition between the PD phase and two-sublattice ferri magnetic phase is of the first order. This sequence of the phases is homomorphic as that in …
With the help of the improved Monte Carlo renormalization-group scheme, we numerically investigate the renormalization group flow of the antiferromagnetic Heisenberg and XY spin model on the stacked triangular lattice (STA-model) and its effective Hamiltonian, 2N-component chiral $ϕ^4$ model which is used in the field-theoretical studies. We find that the XY-STA model with the lattice size $126\times 144 \times 126$ exhibits clear first-order behavior. We also find that the renormalization-group flow of STA model is well reproduced by the chiral $ϕ^4$ model, and that there are no chiral fixed …
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$_4$.
The quantum Heisenberg antiferromagnet on the stacked triangular lattice with the intralayer nearest-neighbor exchange interaction J and interlayer exchange J' is considered within the non-linear $σ$-model with the use of the renormalization group (RG) approach. For J' << J the asymptotic formula for the Neel temperature $T_{Neel}$ and sublattice magnetization are obtained. RG turns out to be insufficient to describe experimental data since it does not take into account the $\mathcal{Z}_2$-vortices. Therefore $T_{Neel}$ is estimated using the Monte-Carlo result for the 2D correlation length [1…
Effects of interlayer coupling and spatial anisotropy on spin-wave excitation spectra of a three-dimensional spatially anisotropic, frustrated spin-$\half$ Heisenberg antiferromagnet (HAFM) is investigated for the two ordered phases using second-order spin-wave expansion. We show that the second-order corrections to the spin-wave energies are significant and find that the energy spectra of the three-dimensional HAFM shares similar qualitative features with the energy spectra of the two-dimensional HAFM on a square lattice. We also discuss the features that can provide experimental measures for…
The antiferromagnetic Heisenberg model on a stacked triangular geometry with a finite number of layers is studied using Monte Carlo methods. A topological phase transition occurs at finite temperature for all film thicknesses. Our results indicate that topological excitations are important for a complete understanding of the critical properties of the model between two and three dimensions.
Recent theoretical and experimental studies on the critical properties of frustrated antiferromagnets with the noncollinear spin order, including stacked-triangular antiferromagnets and helimagnets, are reviewed. Particular emphasis is put on the novel critical and multicritical behaviors exhibited by these magnets, together with an important role played by the `chirality'.
We study Ising antiferromagnets that have nearest-neighbour interactions on multilayer triangular lattices with frustrated ($abc$ and $abab$) stacking, and make comparisons with the unfrustrated ($aaa$) stacking. If interlayer couplings are much weaker than in-plane ones, the paramagnetic phase of models with frustrated stackings has a classical spin-liquid regime at low temperature, in which correlations are strong both within and between planes, but there is no long-range order. We investigate this regime using Monte Carlo simulations and by mapping the spin models to coupled height models, …
Magnetic phase diagram of a spatially anisotropic, frustrated spin-1/2 Heisenberg antiferromagnet on a stacked square lattice is investigated using second-order spin-wave expansion. The effects of interlayer coupling and the spatial anisotropy on the magnetic ordering of two ordered ground states are explicitly studied. It is shown that with increase in next nearest neighbor frustration the second-order corrections play a significant role in stabilizing the magnetization. We obtain two ordered magnetic phases (Neel and stripe) separated by a paramagnetic disordered phase. Within second-order s…
We study, within the Schwinger-boson approach, the ground-state structure of two Heisenberg antiferromagnets on the triangular lattice: the J1-J2 model, which includes a next-nearest-neighbor coupling J2, and the spatially-anisotropic J1-J'1 model, in which the nearest-neighbor coupling takes a different value J'1 along one of the bond directions. The motivations for the study of these systems range from general theoretical questions concerning frustrated quantum spin models to the concrete description of the insulating phase of some layered molecular crystals. For both models, the inclusion o…
Histogram Monte Carlo simulation is used to investigate effects of biquadratic exchange $J_{2}$ on phase transitions of a 3D classical XY antiferromagnet with frustration induced by the antiferromagnetic exchange $J_{1}$ and the stacked triangular lattice geometry. The biquadratic exchange is considered negative (antiferroquadrupolar) within the triangular planes and positive (ferroquadrupolar) between the planes. The phase diagram obtained features a variety of interesting phenomena arising from the presence of both the biquadratic exchange and frustration. In a strong biquadratic exchange li…
Critical scaling and universality in the short-time dynamics for antiferromagnetic models on a three-dimensional stacked triangular lattice are investigated using Monte Carlo simulation. We have determined the critical point by searching for the best power law for the order parameter as a function of time and measured the critical exponents. Our results indicate that it is possible to distinguish weak first-order from second-order phase transitions and confirm that XY antiferromagnetic systems undergo a (weak) first order phase transition.
We present a Monte Carlo study of the magnetic properties of an Ising multilayer ferrimagnet. The system consists of two kinds of non-equivalent planes, one of which is site-diluted. All intralayer couplings are ferromagnetic. The different kinds of planes are stacked alternately and the interlayer couplings are antiferromagnetic. We perform the simulations using the Wolff algorithm and employ multiple histogram reweighting and finite-size scaling methods to analyze the data with special emphasis on the study of compensation phenomena. Compensation and critical temperatures of the system are o…
We study the phase transition behavior of a frustrated Heisenberg model on a stacked triangular lattice by Monte Carlo simulations. The model has three types of interactions: the ferromagnetic nearest-neighbor interaction $J_1$ and antiferromagnetic third nearest-neighbor interaction $J_3$ in each triangular layer and the ferromagnetic interlayer interaction $J_\perp$. Frustration comes from the intralayer interactions $J_1$ and $J_3$. We focus on the case that the order parameter space is SO(3)$\times C_3$. We find that the model exhibits a first-order phase transition with breaking of the SO…
The nature of the phase transition for the XY stacked triangular antiferromagnet (STA) is a controversial subject at present. The field theoretical renormalization group (RG) in three dimensions predicts a first order transition. This prediction disagrees with Monte Carlo (MC) simulations which favor a new universality class or a tricritical transition. We simulate by the Monte Carlo method two models derived from the STA by imposing the constraint of local rigidity which should have the same critical behavior as the original model. A strong first order transition is found. Following Zumbach w…
The critical behaviour of helimagnets and stacked triangular antiferromagnets is analyzed in (4 - ε) dimensions within three-loop approximation. Numerical estimates for marginal values of the order parameter dimensionality N obtained by resummation of corresponding ε-expansions rule out the possibility of continuous chiral transitions in magnets with Heisenberg or planar spins.
Monte Carlo methods are used to study a family of three dimensional XY frustrated models interpolating continuously between the stacked triangular antiferromagnets and a variant of this model for which a local rigidity constraint is imposed. Our study leads us to conclude that generically weak first order behavior occurs in this family of models in agreement with a recent nonperturbative renormalization group description of frustrated magnets.
Three-state Potts nematic order in stacked frustrated spin models with SO(3) symmetry
该研究提出堆叠受挫自旋模型，通过反铁磁三角与铁磁六重子格实现Z3 Potts向列序，并用蒙特卡洛揭示亚铁磁基态上的复合向列相，且双二次交换可由涨落自动诱导，便于实验实现。
Starting from the hypothesis of a second order transition we have studied modifications of the original Heisenberg antiferromagnet on a stacked triangular lattice (STA-model) by the Monte Carlo technique. The change is a local constraint restricting the spins at the corners of selected triangles to add up to zero without stopping them from moving freely (STAR-model). We have studied also the closely related dihedral and trihedral models which can be classified as Stiefel models. We have found indications of a first order transition for all three modified models instead of a universal critical …
The ground state of the quantum spin system kappa-(BEDT-TTF)2Cu2(CN)3 in which antiferromagnetically-interacting S=1/2 spins are located on a nearly equilateral triangular lattice attracts considerable interest both from experimental and theoretical aspects, because a simple antiferromagnetic order may be inhibited because of the geometrical frustration and hence an exotic ground state is expected. Furthermore, recent two reports on the ground state of this system have made it further intriguing by showing completely controversial results; one indicates the gapless state and the other gapped. …
Spontaneous Parity Breaking in Quantum Antiferromagnets on the Triangular Lattice
本研究揭示了量子三角晶格反铁磁体中自发宇称破缺的机制，通过张量网络计算展示了其在不同自旋和双层系统中的相变行为。
The teaching from entanglement: 2D SU(2) antiferromagnet to valence bond solid deconfined quantum critical points are not conformal
本研究从量子纠缠视角出发，通过增量算法计算费米子退禁闭量子临界点的纠缠熵，证明二维SU(2)反铁磁到价键固体的退禁闭量子临界点不具有共形性，解决了该领域长达数十年的争议。
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