Kikuchiet al.Reply:

Abstract

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,

Frustrated diamond-chain quantum XXZ Heisenberg antiferromagnet in a magnetic field

“…In some detail we have analyzed the magnetization curves which may have some relevance to recent measurements on magnetic compounds related to the localizedmagnon scenario. [4,8,9] If the applied field is directed along the z-axis the localizedmagnon picture holds: The operator S z commutes with the Hamiltonian H and therefore the eigenstates of H can be classified according to the number of magnons n = N/2 − S z . In the subspaces with n = 1, .…”

“…From the experimental point of view, we know that the lowtemperature magnetization curves for azurite with the field applied along chain direction and perpendicularly to chain direction are different [4,8] that indicates an anisotropic exchange interaction. Even stronger anisotropy effects have been recently observed for the spin dimer magnet Ba 2 CoSi 2 O 6 Cl 2 -a recently synthesized compound which should also exhibit localized-magnon physics.…”

“…However, a certain magnetic compound may be quite close to it. A fascinating example is the natural mineral azurite Cu 3 (CO 3 ) 2 (OH) 2 , [4,5] which is known as a realization of the frustrated diamond spin chain close to the flat-band point. [5,6] In our recent study [7] we have considered three localized-magnon systems (the diamond and dimer-plaquette chains and the two-dimensional square-kagome lattice) which belong to the monomer universality class [3] with small deviations from the ideal flat-band geometry and have elaborated effective low-energy theories which provide good description of the initial frustrated quantum isotropic (i.e., XXX) Heisenberg antiferromagnets in the low-temperature strong-field regime.…”

Entanglement, magnetic and quadrupole moments properties of the mixed spin Ising–Heisenberg diamond chain

“…The interest to this type of system has been increased since experimental work of Kikuchi and co-workers [28,29], where natural mineral azurite (Cu 3 (CO 3 ) 2 (OH) 2 ) has been recognized as an appropriate candidate for diamond chain compound. There have been proposed different types of theoretical Heisenberg models to explain the experimental measurements of magnetization plateau and the double peak behavior in the natural mineral azurite (the density-matrix and transfer-matrix renormalizationgroup techniques, density functional theory, high-temperature expansion, variation mean-field-like treatment, based on the Gibbs-Bogoliubov inequality) [30,31,32,33].…”

Entangled state teleportation through a couple of quantum channels composed ofXXZdimers in an Ising-XXZdiamond chain

“…It is interesting to consider the quantum antiferromagnetic Heisenberg model on a generalized diamond chain, because this model describes real materials such as Cu 3 (CO 3 ) 2 (OH) 2 , known as natural azurite [8]. One can associate this compound with the model of the spin system composed of geometrically frustrated spin on a diamond chain.…”