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Journal of the Korean Physical Society

Novel field-induced quantum phase transition of the kagome-lattice antiferromagnet

Tôru Sakai, Hiroki Nakano

Published Aug 1, 2013• 2 citations
Publisher

Abstract

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.

DOI
10.3938/jkps.63.601

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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 process of the S = 1/2 kagome-lattice quantum antiferromagnet is investigated using the numerical exact diagonalization up to 39-site clusters. The finite-size scaling analysis with the rohmbic clusters indicated the "magnetization ramp" as a novel field-induced quantum phase transition at 1/3 of the saturation magnetization. The magnetization ramp is characterized by the following properties; (i) the field derivative dm/dH is divergent at the lower-field side, (ii) dm/dH is vanishing at the higher-field side, and (iii) there is a single critical field H c (no plateau). Applying the critical exponent analysis for the non-rohmbic clusters, as well as the rohmbic ones, we confirmed the above properties of the magnetization at 1/3 of the saturation for the kagome lattice antiferromagnet.
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.
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 antiferromagnet is investigated using the numerical diagonalization up to 42-spin clusters. The critical exponent analysis confirms the unconventional magnetization behavior around the 1/3 magnetization plateau-like anomaly; the field derivative is infinite at the low-field side, while it is zero at the high-field side. We also confirm that a magnetization jump appears at 1/3 of the saturation magnetization in distorted kagome-lattice antiferromagnets.
We investigate S=1/2S=1/2S=1/2 quantum spin antiferromagnets on the triangular and Kagome lattices in a magnetic field, using the numerical exact diagonalization. We focus particularly on an anomalous magnetization behavior of each system at one-third the saturation magnetization. Critical exponent analyses suggest that it is a conventional magnetization plateau on the triangular lattice, while an unconventional phenomenon, called the magnetization ramp, occurs on the Kagome lattice.
We clarify the existence of several magnetization plateaus for the kagome S=12S=\frac{1}{2}S=21​ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site m=13m=\frac{1}{3}m=31​, 59\frac{5}{9}95​, and 79\frac{7}{9}97​ of the saturation value. These results are confirmed using large-scale exact diagonalization on lattices up to 63 sites.