Spin-Liquid State Study of Equilateral Triangle S=3/2 Spin Tubes Formed in CsCrF₄

Abstract

Topological effects on spin frustration in equilateral triangle S ¼ 3=2 spin tubes formed in CsCrF 4 were studied by magnetic susceptibility, heat capacity [CðTÞ], and electron spin resonance experiments. The experimental data show that there is no magnetic long-range order down to T ¼ 1:3 K, and that no spin gap due to a chiral spin structure appears. Furthermore, since the CðTÞ curve has a T-linear component, a gapless spin-liquid ground state in one-dimensional antiferromagnets, the so-called Tomonaga-Luttinger liquid, is realized. This is characteristic of equilateral triangle spin tubes with S = half-integer. Spin gap systems in one-dimensional Heisenberg antiferromagnets with S ¼ 1=2, such as two-leg ladders, 1,2) have been studied extensively. In even-leg ladders, a gapped ground state is realized, while in odd-leg ladders, a gapless ground state is realized. 3,4) If N-leg ladders (N ! 3) are connected to a periodic boundary along the rung direction, spin tubes are formed. Odd-leg tubes with an antiferromagnetic rung coupling have attracted considerable interest because they possess spin frustration along the rung.5-9) A chiral spin structure in equilateral triangle spin tubes with S ¼ 1=2 causes a finite spin gap because of frustrated three-leg coupling.9,10) When the strength of a magnetic field (H) and the ratio of rung coupling to leg coupling vary, a gapless spin-liquid state, the so-called Tomonaga-Luttinger liquid (TLL), 11) is expected to appear. 7,8) TLLs are described by gapless low-energy properties, e.g., a k-linear energy dispersion and a spin correlation having an algebraic decay. TLLs are common in onedimensional physics such as in strongly correlated electron systems (e.g., solids, 12) electron gases, 13) and quantum wires 14) ) and trapped one-dimensional cold atoms. 15) On the other hand, a system where S = integer and H ¼ 0 is predicted to conserve a gapped state. In this study, therefore, to experimentally confirm topological effects on spin frustration, we focused on odd-leg spin tubes with S = half-integer.Few experimental candidate compounds for odd-leg spin tubes with S ¼ 1=2 exist, including the vanadium oxide Na 2 V 3 O 7 , [16][17][18] C for more than 48 h under vacuum at P < 1 Â 10 À3 Pa to dehydrate crystal water. Then, they were kept at 700 C for more than 50 h under a flow of N 2 gas (50 cm 3 /min). The samples are dark green or gray. From the differential thermal analysis of CsCrF 4 , we found that a structural phase transition occurs at T ¼ 750 { 800 C and the melting temperature is above 1350 C. Therefore, the growth of single crystals by the Bridgman method was eliminated, and the maximum temperature was set well below 750 C. We examined the crystal structure and phase purity of the present compound by X-ray diffraction analysis, and confirmed its space group at room temperature to be hexagonal, P " 6 62m, which is consistent with that reported in, and ¼ 120). The starting materials CsF and CrF 3 . 3H 2 O are easily oxidized if dehydration occurs under low-vacuum pressu...

Determination of Tomonaga-Luttinger parameters for a two-component liquid

“…Fig. I shows an example with three legs, relevant for modelling quasi one-dimensional compounds such as [(CuCl 2 tachH) 3 Cl]Cl 2 [32] and CsCrF 4 [33], and to which recent theoretical works [29,[34][35][36] have been devoted.…”

Spin gap of the three-legS=32Heisenberg tube

“…7), which is an ideal three-leg straight spin tube system formed by Cr 3+ ions, has been reexamined experimentally from the point of view of spin frustration. 8 Since the magnetic moment comes from the e 2 g state of Cr 3+ ion, the magnitude of spin on each site is S = 3 2 . By performing magnetic susceptibility, heat capacity C(T ), and electron spin resonance measurements, it was reported that no magnetic long-range order is observed down to T = 1.3 K. In particular, a gapless spin-liquid state (or a TL liquid state) is indicated from the finite T -linear component of C(T ); this result raises a more absorbing question because a gapped ground state is expected in an odd-leg spin-half-integer straight spin tube system.…”

Exotic Quantum Phenomena of the Spin Nanotubes

“…One of interesting features is that the system has a spin gap [2], while the S = 1/2 three-leg spin ladder is gapless. Although no clear evidence of the spin gap was observed in any candidate materials of the three-leg spin tube so far [3,4], many theoretical works [5][6][7][8][9][10][11] have supported the existence of it.…”