Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J₁ and J₂, respectively. PTs in these models are analyzed for the ratio r = J₂/J₁ of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J₁ < 0 and J₂ < 0 exhibits a first-order PT in the range of 0 ? r < 0.2, whereas, in the interval 0.2 ? r ? 1.0, frustrations arise in the system. At the same time, for J₁ > 0 and J₂ < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ? |r| ? 1/3, the model exhibits a second-order PT.     

Magnetic interactions in the geometrically frustrated triangular lattice antiferromagnet CuFeO2

The spin-wave excitations of the geometrically frustrated triangular lattice antiferromagnet CuFeO2 have been measured using high resolution inelastic neutron scattering. Antiferromagnetic interactions up to third nearest neighbors in the ab plane (J1, J2, J3, with J{2}/J{1} approximately 0.44 and J{3}/J{1} approximately 0.57), as well as out-of-plane coupling (J{z}, with J{z}/J{1} approximately 0.29) are required to describe the spin-wave dispersion relations, indicating a three-dimensional character of the magnetic interactions. Two energy dips in the spin-wave dispersion occur at the incommensurate wave vectors associated with multiferroic phase and can be interpreted as dynamic precursors to the magnetoelectric behavior in this system.     

Phase transitions in the antiferromagnetic Heisenberg model on a layered triangular lattice with the next-nearest neighbor interactions

Phase transitions in the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice with the next-nearest neighbor interactions have been studied by the histogram Monte Carlo method. Phase transitions in this model have been studied in the range of the next-nearest neighbor interactions from 0.0 to 1.0. The first-order phase transition has been revealed in the considered interval in the studied model.     

Critical properties of a frustrated Heisenberg model on a stacked triangular lattice with allowance for second-nearest neighbor interaction

The critical properties of the three-dimensional antiferromagnetic Heisenberg model are investigated using the Monte Carlo method with allowance for second-nearest neighbor interaction. Pseudo-universal critical behavior of this model is observed for small lattices. A complete set of the main static magnetic and chiral indices is calculated with the use of finite-dimensional scaling theory.     

Quantum phase transition of the randomly diluted heisenberg antiferromagnet on a square lattice

Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.     

Phase transitions and critical properties of the frustrated Heisenberg model on a layer triangular lattice with next-to-nearest-neighbor interactions

The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J ₁) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J ₁/J| = 0?C0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.     

Bond operator theory for the frustrated anisotropic Heisenberg antiferromagnet on a square lattice

The quantum anisotropic antiferromagnetic Heisenberg model with single ion anisotropy, spin S=1 and up to the next-next-nearest neighbor coupling (the J₁–J₂–J₃ model) on a square lattice, is studied using the bond-operator formalism in a mean field approximation. The quantum phase transitions at zero temperature are obtained. The model features a complex T=0 phase diagram, whose ordering vector is subject to quantum corrections with respect to the classical limit. The phase diagram shows a quantum paramagnetic phase situated among Neél, spiral and collinear states.     

Phase diagram of a nearest neighbor triangular antiferromagnet in an external field

The order-disorder transition in a nearest neighbor antiferromagnetic triangular lattice in a magnetic field is examined using a Monte Carlo method. Comparisons are made with the Kikuchi approximation of Burely. The phase diagram takes the form conjectured by Domb.     

Structure and frustrated magnetism of the two-dimensional triangular lattice antiferromagnet Na2BaNi(PO4)2

A new frustrated triangular lattice antiferromagnet Na₂BaNi(PO₄)₂ was synthesized by high temperature flux method. The two-dimensional triangular lattice is formed by the Ni²⁺ ions with S =1. Its magnetism is highly anisotropic with the Weiss constants θ_CW =-6.615 K (H⊥c) and -43.979 K (H||c). However, no magnetic ordering is present down to 0.3 K, reflecting strong geometric spin frustration. Our heat capacity measurements show substantial residual magnetic entropy existing below 0.3 K at zero field, implying the presence of low energy spin excitations. These results indicate that Na₂BaNi(PO₄)₂ is a potential spin liquid candidate with spin-1.     

阻挫三角反铁磁AgCrO2螺旋自旋序的第一性原理研究

基于密度泛函理论的广义梯度近似(GGA)和投影缀加波(PAW)方法,分别从共线和非共线磁性结构出发,研究了自旋阻挫三角反铁磁AgCrO₂的基态、磁性以及电子结构,从理论计算的角度给出了基态磁性结构.计算结果表明:AgCrO₂具有120°螺旋自旋序反铁磁基态,其自旋螺旋面平行于(110)面或(11^-0)面;由于Cr离子间的自旋几何阻挫,导致沿晶体的a,b和a+b方向上均形成了螺旋自旋转动角为120°的 关键词： 第一性原理 交换相互作用 阻挫 反铁磁     

First order phase transition in the frustrated triangular antiferromagnet CsNiCl3

By means of high-resolution ultrasonic velocity measurements, as a function of temperature and magnetic field, the nature of the different low temperatures magnetic phase transitions observed for the quasi-one-dimensional compound CsNiCl3 is established. Special attention has been devoted to the field-induced 120 degrees phase transition above the multicritical point in the H-T phase diagram where the elastic constant C44 reveals a steplike variation and hysteresis effects. These results represent the first experimental evidence that the 120 degrees phase transition is weakly first order and contradict the popular notion of new universality classes for chiral systems.     

Phase diagram of a diluted triangular lattice Ising antiferromagnet in a field

Magnetization processes and phase transitions in a geometrically frustrated triangular lattice Ising antiferromagnet in the presence of an external magnetic field and a random site dilution are studied by the use of an effective-field theory with correlations. We find that the interplay between the applied field and the frustration-relieving dilution results in peculiar phase diagrams in the temperature-field-dilution parameter space.     

Muon spin relaxation in diluted triangular‐lattice antiferromagnet

Zero and longitudinal field μSR measurements on diluted triangular‐lattice antiferromagnet LuFeMgO₄ have revealed gradual and highly anisotropic slowing‐down of spin fluctuation. Relaxation rate \lambda in the condition with initial muon spins perpendicular to the hexagonal c‐plane shows divergent behavior while that in the parallel configuration remains finite. At certain temperature range the fluctuation of spins is suppressed by a small external magnetic field. Monte Carlo calculation suggests that the correlation time for z(c)‐component of spins diverges first on cooling. This revised version was published online in July 2006 with corrections to the Cover Date.     

The two dimensional classical anisotropic Heisenberg ferromagnetic model with nearest- and next-nearest neighbor interactions

We use the self-consistent harmonic approximation (SCHA) to study the two-dimensional classical Heisenberg anisotropic (easy-plane) ferromagnetic model including nearest- and next-nearest neighbor exchange interactions. For temperatures much lower than the Kosterlitz-Thouless phase transition temperature T _KT, spin waves must be the most relevant excitations in the system and the SCHA must account for its behavior. However, for temperatures near T _KT, we should expect vortex pairs to be quite important. The effect of these vortex excitations on the phase transition temperature is included in our theory as a renormalization of the exchange interactions. Then, combining the SCHA theory to the renormalization effect due to vortex pairs, we calculate the dependence of T _KT as a function of the easy-plane anisotropies and exchange interactions. Received 3 April 2001 and Received in final form 20 September 2001