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arXiv:0806.0393 · Physical Review B

Quantum phase transition induced by Dzyaloshinskii-Moriya interactions in the kagome antiferromagnet

O. Cépas, Manson Cheuk‐Man Fong, P. W. Leung, C. Lhuillier

Published Oct 23, 2008• 223 citations
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Abstract

We argue that the $S=1/2$ kagome antiferromagnet undergoes a quantum phase transition when the Dzyaloshinskii-Moriya coupling is increased. For $D<{D}_{c}$ the system is in a moment-free phase, and for $D>{D}_{c}$ the system develops antiferromagnetic long-range order. The quantum critical point is found to be ${D}_{c}\ensuremath{\simeq}0.1J$ using exact diagonalizations and finite-size scaling. This suggests that the kagome compound ${\text{ZnCu}}_{3}{(\text{OH})}_{6}{\text{Cl}}_{3}$ may be in a quantum critical region controlled by this fixed point.

DOI
10.1103/physrevb.78.140405

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We argue that the S=1/2S=1/2S=1/2 kagome antiferromagnet undergoes a quantum phase transition when the Dzyaloshinskii-Moriya coupling is increased. For D<DcD<{D}_{c}D<Dc​ the system is in a moment-free phase, and for D>DcD>{D}_{c}D>Dc​ the system develops antiferromagnetic long-range order. The quantum critical point is found to be Dc\ensuremath≃0.1J{D}_{c}\ensuremath{\simeq}0.1JDc​\ensuremath≃0.1J using exact diagonalizations and finite-size scaling. This suggests that the kagome compound ZnCu3(OH)6Cl3{\text{ZnCu}}_{3}{(\text{OH})}_{6}{\text{Cl}}_{3}ZnCu3​(OH)6​Cl3​ may be in a quantum critical region controlled by this fixed point.
We investigate the zero-temperature phase diagram of the nearest-neighbor kagome antiferromagnet in the presence of Dzyaloshinksii-Moriya interaction. We develop a theory for the transition between Z2{Z}_{2}Z2​ spin liquids with bosonic spinons and a phase with antiferromagnetic long-range order. Connections to recent numerical studies and experiments are discussed.
We theoretically study the spatially anisotropic spin-1/2 kagome antiferromagnet with a Dzyaloshinskii-Moriya (DM) interaction using a renormalization-group analysis in the quasi-one-dimensional limit. We identify the various temperature and energy scales for ordering in the system. For a very weak DM interaction, we find a low-temperature spiral phase with the plane of the spiral selected by the DM interaction. This phase is similar to a previously identified phase in the absence of the DM interaction. However, above a critical DM interaction strength we find a transition to a phase with coexisting antiferromagnetic and dimer order, reminiscent of one-dimensional antiferromagnetic systems with a uniform DM interaction. Our results help shed light on the fate of two-dimensional systems with both strong interactions and significant spin-orbit coupling.
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.
We revisit an antiferromagnetic quantum phase transition with $\mathbit{Q}=2{\mathbit{k}}_{F}$, where $\mathbit{Q}$ is an ordering wave vector and ${\mathbit{k}}_{F}$ is a Fermi momentum. Reformulating the Hertz-Moriya-Millis theory within the strong-coupling approach to diagonalize the spin-fermion coupling term and performing the scaling analysis for an effective-field theory with quantum corrections in the Eliashberg approximation, we propose an interacting fixed point for this antiferromagnetic quantum phase transition, where antiferromagnetic spin fluctuations become locally critical to interact with renormalized electrons. The emergence of local quantum criticality suggests a mechanism of $\ensuremath{\omega}/T$ scaling for antiferromagnetic quantum criticality, generally forbidden in the context of the Hertz-Moriya-Millis theory.
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.
Motivated by the recent neutron-scattering experiment on Rb2{}_{2}2​Cu3{}_{3}3​SnF12{}_{12}12​ [Nature Phys. 6, 865 (2010)], we investigate the effect of Dzyaloshinskii-Moriya interactions in a theoretical model for the magnetic structure of this material. Considering the valence bond solid ground state, which has a 12-site unit cell, we develop the bond operator mean-field theory. It is shown that the Dzyaloshinskii-Moriya interactions significantly modify the triplon dispersions around the $\ensuremath{\Gamma}$ point and cause a shift of the spin-gap (the minimum triplon gap) position from the KKK to $\ensuremath{\Gamma}$ point in the first Brillouin zone. The spin gap is also evaluated in exact diagonalization studies on a 24-site cluster. We discuss a magnetic transition induced by the Dzyaloshinskii-Moriya interactions in the bond operator framework. Moreover, the magnetization process under external magnetic fields is studied within the exact diagonalization approach. We find that the results of both approaches are consistent with the experimental findings.