Long-Range Order of the Three-Sublattice Structure in the S=1 Heisenberg Antiferromagnet on a Spatially Anisotropic Triangular Lattice

Abstract

We study the S ¼ 1 Heisenberg antiferromagnet on a spatially anisotropic triangular lattice by the numerical diagonalization method. We examine the stability of the long-range order of a three-sublattice structure observed in the isotropic system between the isotropic case and the case of isolated one-dimensional chains. It is found that the longrange-ordered ground state with this structure exists in the range of 0:7 . J 2 =J 1 1, where J 1 is the interaction amplitude along the chains and J 2 is the amplitude of other interactions.KEYWORDS: Antiferromagnetic Heisenberg spin model, triangular lattice, frustration, spatial anisotropy, numerical diagonalization method, Lanczos methodFrustrated magnets have attracted much attention from the viewpoint of realizing exotic quantum states and phase transitions that occur between such states. One such magnet is the triangular-lattice Heisenberg antiferromagnet. Much effort has been devoted to studies of the S ¼ 1=2 model, particularly since Anderson 1) pointed out that this model is a possible candidate for the realization of the spin liquid ground state due to magnetic frustrations. Now, it is widely believed that the ground state of the S ¼ 1=2 model has a long-range order (LRO) with a small three-sublattice magnetization.2-6) This spin structure is also called the 120 deg structure from the directions of neighboring spins. However, estimating the magnetic order of a three-sublattice structure (3SS) quantitatively by direct methods that are unbiased beyond any approximation or variational method is still difficult even now. Numerical diagonalization data of small finite-size (FS) clusters of up to 36 sites of the S ¼ 1=2 model 5-7) were examined. 8) However, Leung and Runge 7) and Bernu et al. 6) reported the subtlety in quantitative extrapolation from their diagonalization data of spin correlation functions for observing the order directly.Since the LRO occurs as a consequence of the delicate balance of the frustrated situation, the instability of this order is an attractive issue in the case when the model includes factors additional to the triangular-lattice Heisenberg antiferromagnet. One such factor is the spatial anisotropy of interactions in the system. Let us consider that the interaction along a specific direction (J 1 ) is different from the interaction along the other two directions (J 2 ) among three equivalent directions in the isotropic case (see Fig. 1); here, we focus our attention on the range of 0 J 2 =J 1 1. In the case of J 2 ¼ 0, the system is reduced to isolated spin chains with an antiferromagnetic interaction, in which the LRO does not occur owing to the onedimensionality. Therefore, the order must disappear at a point in this range of 0 J 2 =J 1 1.In the classical case of S ¼ 1, the spiral ground state is realized in the range of 0 J 2 =J 1 1; the behavior is characterized by the canting angle between neighboring spins. In the quantum case, however, not only the canting angle but also sublattice magnetization in the spiral state can be chan...

Ground-state properties of the triangular-lattice Heisenberg antiferromagnet with arbitrary spin quantum number s

“…[55][56][57][58][59][60][61][62]. Although lattices of size N = 36 are common for ED calculations for spin s = 1/2, the system size N accessible for ED shrinks significantly, see, e.g., Refs.…”

“…Although lattices of size N = 36 are common for ED calculations for spin s = 1/2, the system size N accessible for ED shrinks significantly, see, e.g., Refs. [48,57,60,[63][64][65]. Hence, we use the ED here in order to complement the results of the CCM (that yields results in the limit N → ∞).…”

One dimensionalization in the spin-1 Heisenberg model on the anisotropic triangular lattice

“…On one side, numerical exact diagonalization studies 15 do not allow estimating a reliable critical value due to the small system sizes investigated; on the other hand, using series expansion, 16 Pardini and Singh estimated that the critical value between spiral magnetic and disordered phases is within the range 0.33 < J /J < 0.6. However, the lack of an unbiased study of the short range correlations did not allow discerning whether the effective reduction of the dimension actually occurs.…”

Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet

“…45 The usefulness of our program was previously confirmed in large-scale parallelized calculations. 19,27,46 The magnetization process for a finite-size system is obtained by considering the magnetization increase from M to M + 1 in the fieldunder the condition that the lowest-energy state with magnetization M and that with magnetization M + 1 become the ground state in specific magnetic fields. First, let us present our results of the magnetization processes for S = 1, 3/2, 2, and 5/2; results are shown in Fig.…”

“…45 The usefulness of our program was previously confirmed in large-scale parallelized calculations. 19,27,46 The magnetization process for a finite-size system is obtained by considering the magnetization increase from M to M + 1 in the field…”