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Anomalous Magnetization Process of Two-Dimensional Frustrated Quantum Antiferromagnets

Tôru Sakai

Published Jul 26, 2016• 0 citations
OpenAlex

Abstract

The magnetization process of the frustrated magnet is theoretically investigated using the numerical diagonalization and the finite-size scaling analysis. It is found that a new spin flop phenomena possibly occurs.

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Using the numerical exact diagonalization of finite-size clusters up to 39 spins, we investigate the magnetization process of the Kagome lattice antiferromagnet, as well as the triangular lattice antiferromagnet. A finite-size scaling analysis at 1/3 of the saturation magnetization indicates that an unconventional quantum phase transition, so called a magnetization ramp, occurs for the Kagome lattice antiferromagnet. In contrast, the triangular lattice antiferromagnet is revealed to exhibit a conventional 1/3 magnetization plateau. These conclusions are based on the estimated critical exponet δ defined as | m – m c | ∼ | H – H c | 1/ δ . The exponents at the lower and higher field sides of m = 1/3 δ − and δ + are estimated as δ − = 1.9 ± 1.0 and δ + = 0.5 ± 0.2 for the Kagome kattice, while δ − = 1.0 ± 0.2 and δ + = 0.8 ± 0.2 for the triangular lattice.
The magnetization process of the S=1/2 Kagome-lattice quantum antiferromagnet is investigated using the numerical exact diagonalization up to 39-site clusters, comparing with the triangular-lattice antiferromagnet. Our previous finite-size scaling analysis with the rhombic clusters indicated the “magnetization ramp” as a novel field-induced quantum phase transition at 1/3 of the saturation magnetization. As another possible exotic behavior, we focus on the feature of the magnetization curve at the 2/3 of the saturation. The same critical exponent analysis indicates that a different singular behavior occurs at the 2/3 magnetization of the Kagome-lattice antiferromagnet, while no anomaly in the triangular-lattice one.
The magnetization process of the S = 1/2 kagome-lattice quantum antiferromagnet is investigated using the numerical exact diagonalization up to 36-site clusters. Our previous finite-size scaling analysis with rhombic clusters indicated the “magnetization ramp” as a novel field-induced quantum phase transition at 1/3 the saturation magnetization. As another possible exotic behavior, we focus on the feature of the magnetization curve at 2/3 the saturation. The critical exponent analysis indicates that a different singular behavior occurs at the 2/3 magnetization.
The magnetization processes of the S = 3/2 and S = 2 antiferromagnetic chains with the biquadratic interaction are investigated using the numerical diagonalization of the finite-size cluster. It is found that the system does not exhibit the spin nematic phase, which was predicted to occur for the S = 1 antiferromagnetic chain. Instead, the present analysis reveals that the quantum spin triatic and quatic liquid phases appear below the saturation magnetization for sufficiently large negative biquadratic interaction, for S = 3/2 and S = 2 chains, respectively. In addition it is also found that the magnetization jump up to the saturation magnetization appears for the small negative biquadratic interaction. The phase diagrams with respect to the negative biquadratic interaction and the magnetization are presented for the S = 3/2 and S = 2 antiferromagnetic chains.
The magnetization process of the one-dimensional antiferromagnetic Heisenberg model with the Ising-like anisotropic exchange interaction is studied by the exact diagonalization technique. It results in the evidence of the first-order spin-flop transition with a finite magnetization jump in the N\'eel ordered phase for S> 1.S>~1.S> 1. It implies that the S=12S=\frac{1}{2}S=21​ chain is an exceptional case where the metamagnetic transition becomes second order due to large quantum fluctuations.