Magnetism of Cu_6 Ge_6 O_{18}-x H_2 O (x = 0 ~ 6), a compound of the one-dimensional Heisenberg $S=1/2$ model with competing antiferromagnetic interactions

Abstract

We measured the magnetic susceptibilities of Cu${}_6$Ge${}_6$O${}_{18}$-xH${}_2$O ($x=0\sim 6$). Susceptibility above the antiferromagnetic (AF) transition temperature ($T_{\mathrm{N}}$) agrees with susceptibility of the one-dimensional Heisenberg $S=1/2$ model with competing AF interactions. From the estimated ratio between nearest-neighbor and next-nearest-neighbor AF exchange interactions, the spin system is probably located near a boundary between spin systems with gapless and gapped magnetic excitation. The value of $T_{\mathrm{N}}/T_{\max }$, where $T_{\max }$ is temperature at which the susceptibility is maximum, shows a unique dependence on $x$. The $x$ dependence can be explained qualitatively by taking phase transition as a function of $x$ and the effect of disorder into account.

4 pages, 4 figures, 1 table. submitted to Phys. Rev. Lett