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Specific heat, magnetization, resistivity, and structure of delafossite oxide CuCr 1−x A x O 2 ͑A =Mg 2+ ,Ca 2+ ,Al 3+ ͒ have been investigated. With the substitution of nonmagnetic Mg 2+ for Cr 3+ ͑S =3/ 2͒, the peak of specific heat upon antiferromagnetic ͑AF͒ transition becomes sharper and the transition temperature increases. The peak is much affected by a magnetic field of 9 T when Cr 3+ is substituted by Mg 2+ . Comparing the substitution effect of Mg 2+ to those of other nonmagnetic Ca 2+ and Al 3+ , magnetization around the AF transition does not seem to correlate with randomness and lattice parameter but with itinerancy of the doped holes. These results suggest that the residual magnetic frustration stemming from a modulated triangular 120°s pin structure is partially broken by spin fluctuations, which are enhanced through the interaction between the hole introduced by Mg doping and the localized spin at the Cr site.

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...

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