Determining ground states of correlated electron systems is fundamental to understanding novel phenomena in condensed matter physics. A difficulty, however, arises in a geometrically frustrated system in which the incompatibility between the global topology of an underlying lattice and local spin interactions gives rise to macroscopically degenerate ground states 1 , potentially prompting the emergence of quantum spin states, such as resonating valence bond (RVB) and valence bond solid (VBS). Although theoretically proposed to exist in a kagome lattice -one of the most highly frustrated lattices in two dimensions (2D) being comprised of corner-sharing triangles -such quantum-fluctuation-induced states have not been observed experimentally. Here we report the first realization of the "pinwheel" VBS ground state in the S = 1 2 deformed kagome lattice antiferromagnet Rb 2 Cu 3 SnF 12 . In this system, a lattice distortion breaks the translational symmetry of the ideal kagome lattice and stabilizes the VBS state.
We investigated the crystal structure of Rb 2 Cu 3 SnF 12 and its magnetic properties using single crystals. This compound is composed of Kagomé layers of corner-sharing CuF 6 octahedra with a 2a  2a enlarged cell as compared with the proper Kagomé layer. Rb 2 Cu 3 SnF 12 is magnetically described as an S ¼ 1=2 modified Kagomé antiferromagnet with four kinds of neighboring exchange interaction. From magnetic susceptibility and high-field magnetization measurements, it was found that the ground state is a disordered singlet with the spin gap, as predicted from a recent theory. Exact diagonalization for a 12-site Kagomé cluster was performed to analyze the magnetic susceptibility, and individual exchange interactions were evaluated. Antiferromagnets on highly frustrated lattices produce a rich variety of physics.1,2) In particular, a two-dimensional Heisenberg Kagomé antiferromagnet (2D HKAF) is of great interest from the viewpoint of the interplay of the frustration and quantum effects. There are many theoretical studies on the 2D HKAF. The spin wave theory for a large spin value predicted an ordered ground state with the so-called ffiffi ffi 3 p  ffiffi ffi 3 p structure, which is selected by quantum fluctuation from infinite classical ground states, 3,4) whereas for a small spin value, a disordered ground state was observed by various approaches.5-9) Recent careful analyses and numerical calculations for an S ¼ 1=2 case demonstrated that the ground state is a spin liquid state composed of singlet dimers only, and that the ground state is gapped for triplet excitations, but gapless for singlet excitations.10-12) Consequently, magnetic susceptibility has a rounded maximum at T $ ð1=6ÞJ=k B and decreases exponentially toward zero with decreasing temperature, while specific heat exhibits a power law behavior at low temperatures. 8,13) Specific heat also shows an additional structure, peak or shoulder at low temperatures after exhibiting a broad maximum at T $ ð2=3ÞJ=k B .The experimental studies of the S ¼ 1=2 HKAF have been limited, and the above-mentioned intriguing predictions have not been verified experimentally. The cupric com- 27) Unfortunately, these systems undergo structural phase transitions at T t ¼ 220 and 170 K, respectively, and also magnetic phase transitions at T N ' 24 K. 27) However, the magnetic susceptibilities observed at T > T t can be perfectly described using theoretical results for an S ¼ 1=2 HKAF with large exchange interactions J=k B $ 250 K. 28)In the present work, we synthesized the new hexagonal compound Rb 2 Cu 3 SnF 12 with a similar crystal structure as Cs 2 Cu 3 ZrF 12 and performed magnetic susceptibility and high-field magnetization measurements using single crystals. As shown below, we found that the ground state is a disordered singlet with a finite gap for magnetic excitations.Rb 2 Cu 3 SnF 12 crystals were synthesized via the chemical reaction 2RbF þ 3CuF 2 þ SnF 4 ! Rb 2 Cu 3 SnF 12 . RbF, CuF 2 , and SnF 4 were dehydrated by heating in vacuum at 60 -100 C for three days....
We report the crystal structure and unconventional magnetic ordering of Cs 2 Cu 3 CeF 12 , which is composed of buckled kagome lattice of Cu 2+ ions. The exchange network in the buckled kagome lattice is fairly anisotropic, so that the present spin system can be divided into two subsystems: alternating Heisenberg chains with strong antiferromagnetic exchange interactions and dangling spins. Although the direct exchange interactions between neighboring spins were found to be all antiferromagnetic, ferromagnetic magnetic ordering of the dangling spins was observed. Magnetization exhibits a plateau at one-third of the saturation magnetization. These observations can be understood in terms of the indirect interaction between dangling spins mediated by the chain spin.
We synthesized single crystals of the new hexagonal compounds A2Cu3SnF12 with A = Cs and Rb, and investigated their magnetic properties. These compounds are composed of Kagomé layers of corner-sharing CuF6-octahedra. Cs2Cu3SnF12 has the proper Kagomé layer at room temperature, and undergoes structural phase transition at Tt ≃ 185 K. The temperature dependence of the magnetic susceptibility in Cs2Cu3SnF12 agrees well with the result of the numerical calculation for S = 1/2 two-dimensional Heisenberg Kagomé antiferromagnet down to Tt with the nearest exchange interaction J/kB ≃ 240 K. Although the magnetic susceptibility deviates from the calculated result below T < Tt, the rounded maxima were observed at approximately T ≃ (1/6)J/kB as predicted by the theory. Cs2Cu3SnF12 undergoes threedimensional magnetic ordering at TN = 20 K. Rb2Cu3SnF12 has the Kagomé layer, whose unit cell is enlarged by 2a × 2a as compared with the proper Kagomé layer even at room temperature. From the viewpoint of crystal structure, the exchange interactions between nearest neighbor Cu 2+ -ions are classified into four kinds. From the magnetic susceptibility and high-field magnetization measurements, it was found that the ground state is a disordered singlet with the spin gap, as predicted by recent theory. Exact diagonalization method with 12-site Kagomé cluster was performed to analyze the magnetic susceptibility. By comparing the calculated results with the experimental data, the individual exchange interactions were evaluated.
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