Kikuchi et al. Reply: In the preceding Comment [1], Gu and Su (GS) reported the finite temperature transfer matrix renormalization group (TMRG) method results for the distorted diamond chain (DDC) model. They pointed out that the double-peak behavior of T found in experiment cannot be reproduced by our parameter set J 1 :J 2 :J 3 1:1:25:0:45 [2], but well fitted by J 1 :J 2 :J 3z 1:1:9: ÿ 0:3 with J 3x =J 3z J 3y =J 3z 1:7.In response to GS's Comment, we have performed the additional density matrix renormalization group (DMRG) and the exact diagonalization calculations for the magnetization curve MH at T 0 of the DDC model with GS's parameter set. As can be seen from Fig. 1, the DMRG MH curve with GS's parameter set does not well explain the experimental results.The positional relations between Cu 2 ions corresponding to J 1 and J 3 are very similar to each other as can be seen in the schematic view of the crystal structure of Cu 3 CO 3 2 OH 2 in Fig. (1b) of our previous Letter [2]. The distance of two Cu 2 ions corresponding to J 1 is 327.5 pm with bond angle 113.7 and that to J 3 is 329.0 pm with bond angle 113.5 . Thus it is unlikely that J 1 is antiferromagnetic without the XXZ anisotropy while J 3 is ferromagnetic with strong XXZ anisotropy. Further, as far as we know, such a strong XXZ anisotropy has not been observed at all in the S 1=2 spin systems of Cu 2 ions.The double-peak behaviors of T and CT are not necessarily attributed to the frustration effect. The mechanism for the double-peak behaviors will be as follows. In the case of J 2 J 1 , jJ 3 j as lowering the temperature, spins coupled by J 2 are going to form singlet dimers at first. The remaining spins are nearly free because they are separated PRL 97,

An S = 9 Heisenberg antiferromagnet on a triangular lattice CuCr02, in which stacking of the triangular lattice of magnetic Cr atoms forms a layered rhombohedral antiferromagnet, is studied by neutron powder diffraction. In the paramagnetic phase the powder diffraction pattern shows asymmetry, which proves a two-dimensional character. In the ordered phase, magnetic Bragg scattering has large width, indicating that the scattering is distributed on a line ($4 b) with peaks where 5 takes integer values. Although the magnetic long-range order is established in the c plane, correlation in the c direction is finite or the modulation vector is distributed on the line. Intensity of magnetic reflections is consistent with the 120" structure in the a-c plane with moment (3.1 2 0 . 2 ) ~~.

Azurite (Cu3(CO3)2(OH)2) is a model substance of a diamond spin chain, one of frustrated antiferromagnetic quantum spin chains. The high field magnetization up to 60 T, magnetic susceptibility, magnetic entropy, muon spin relaxation and 1 H-NMR of azurite have been measured using single crystals. A distinct 1/3 magnetization plateau is confirmed to be present in the magnetization curve. Two resonance peaks of 1 H-NMR were observed. By analyzing temperature dependencies of their hyperfine shift, we found two different local susceptibilities which correspond to susceptibility of dimer and monomer spins, respectively. New field induced phase transition was found to occur at a critical field where the magnetic plateau onsets. A short range magnetic ordering developed in a peculiar two-stage process, which was revealed by temperature dependence of the magnetic specific heat and susceptibility.

High-field magnetization measurements were performed for the quasi-one-dimensional S = 1 antiferromagnet Ni(C2HgN2)2N02(C104) up to 39 T. Applied magnetic fields parallel and perpendicular to the chain axis induce a transition from the nonmagnetic to the magnetic state at a critical field, He =9.8 T and i/ c x -• 13.1 T, indicating clear evidence for the existence of the Haldane gap. The observed gaps are markedly different from those in neutron-scattering experiments.PACS numbers: 75.10Jm, 75.40.Cx, 75.50.Ee Haldane has predicted the existence of a quantum energy gap between the singlet ground state and the lowest excited state in a one-dimensional Heisenberg antiferromagnet (ID HAF) with integer spin. After some controversy this prediction has been verified by numerical simulations 2,3 and by rigorous proof for a solvable model. 4 The first experimental evidence for the Haldane gap was given by Buyers et al. 5 and subsequently by Steiner et al. 6 from inelastic neutron-scattering experiments of CsNiCb. Renard et al., 1 however, pointed out that CsNiCb is far from the best candidate for a model substance to test the Haldane gap since the relatively large interchain interaction (J'/J = 10~2) induces a longm 0.5h oL 0.5r 0 10 20 30 40 Magnetic Field (T) FIG. 1. Magnetization M and the field-derivative dM/dH curves in the magnetic field applied parallel to the chain axis. The critical field He is indicated by an arrow in the top figure.range order at 7^=4.85 K. They suggested that an organic crystal Ni^HglNb^NC^ClO^ abbreviated to NENP by them, is a much better system of a nearly ideal S = l ID HAF having a large intrachain interaction (J/k -50 K), a small anisotropy {D/k -\ K), and a small interchain interaction. In fact, no 3D long-range order has been observed down to 1. K. They concluded 8 that the observed gaps for the longitudinal and transverse excitations, EG -30 K and EG -14 K, result from the splitting of the Haldane gap of the pure Heisenberg chain given by E G Q = (EG+EG )/-2K, in the presence of the large planar anisotropy D -10 K.The aim of the present study is to observe a gap in NENP by the high-field magnetization measurement. The appearance of a gap between the singlet ground state and the lowest excited triplet state results in zero susceptibility at low temperatures. The application of a strong magnetic field is expected to induce a finite susceptibility at some critical field corresponding to the gap energy as a result of level crossing between the ground state and the excited state. A preliminary report for a powder sample has shown an interesting behavior. 8 High-field magnetization curves of the single-crystal NENP were measured at constant temperatures 4.2 and 1.7 K in high magnetic fields up to 39 T applied parallel and perpendicular to the chain axis. The measurement was made using an induction method with a multilayer pulse magnet at the Ultra-High Magnetic Field Laboratory, Institute for Solid State Physics, Tokyo. The sample was prepared using a known procedure. 9 The single crystal...