Singlet Ground State and Spin Gap in S = 1/2 Kagomé Antiferromagnet Rb₂Cu₃SnF₁₂

Abstract

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....

Quantum phase transition between disordered and ordered states in the spin-12kagome lattice antiferromagnet(Rb1−xCsx<

“…1(a); thus, the kagome lattice in Rb 2 Cu 3 SnF 12 is not uniform. 28 There are four sorts of nearestneighbor exchange interactions as depicted in Fig. 1 (c).…”

Influence of Dzyaloshinskii-Moriya interactions on magnetic structure of a spin-12deformed kagome lattice antiferromagnet

“…Magnetic susceptibility and magnetization measurements show that it is a magnetically-disordered 2D spin-gapped system. 30 As a model to describe the system, a spin-1/2 antiferrmagnetic Heisenberg model was considered with four different exchange couplings due to its deformed structure, labeled by J 1 , J 2 , J 3 , and coupling constants are estimated by fitting the thermodynamic data: J 1 , J 2 , and J 3 are quite similar in magnitude (∼200 K), while J 4 is about half of the others (J 1 > J 2 > J 3 ≫ J 4 ). The size of the spin gap is estimated to be ∆/k B =21 K.…”

Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice

“…16,17 Our results are accurate in the thermodynamic limit and converge at almost all temperatures (including T = 0). They also compare very well with the experimental data for the uniform susceptibility, confirming the pinwheel valence bond nature of the ground state of this material.…”