The Cu-NMR nuclear relaxation rate, $^{63}$(1/${\mathit{T}}_{1}$) and Gaussian spin-echo decay rate, $^{63}$(1/${\mathit{T}}_{2\mathit{G}}$) have been measured in order to investigate the low-energy spin dynamics in the quasi-one-dimensional (1D) spin-1/2 antiferromagnetic (AF) cuprates such as ${\mathrm{Ca}}_{2}$${\mathrm{CuO}}_{3}$ with single chain, ${\mathrm{SrCuO}}_{2}$ at ambient pressure (AP) with zigzag chain coupled by weak ferromagnetic exchange interaction, ${\mathrm{SrCu}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{Sr}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{5}$ comprising of two- and three-leg ladder, respectively with isotropic AF exchange interaction along and between chains. In ${\mathrm{Ca}}_{2}$${\mathrm{CuO}}_{3}$, 1/${\mathit{T}}_{1}$ stays constantly close to the 3D magnetic ordering temperature, ${\mathit{T}}_{\mathit{N}}$\ensuremath{\sim}10 K, dominated by dissipation of overdamped spinons gas as shown theoretically by Sachdev. By contrast, in AP-${\mathrm{SrCuO}}_{2}$, 1/${\mathit{T}}_{1}$ below around 100 K decreases markedly down to the 3D magnetic ordering temperature, ${\mathit{T}}_{\mathit{N}}$\ensuremath{\sim}3 K, providing a signature that the frustrated ferromagnetic interaction between CuO zigzag chains makes the spin gap open. In the spin-1/2 ladder compounds of ${\mathrm{SrCu}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{Sr}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{5}$ consisting of two- and three-leg, respectively, the former was demonstrated in the literatures to have the spin gap amounting to a half of AF exchange constant, J/2 where J=1300 K. For the latter, on the other hand, the magnetic coherence length, \ensuremath{\xi}(T) grows up according to \ensuremath{\xi}(T)\ensuremath{\sim}1/(T-\ensuremath{\theta}) and as a result, the magnetic ordering emerges around 50--60 K accompanying the divergence of 1/${\mathit{T}}_{1}$.In the compounds composed of single and triple chains, it is shown that there is no analog of renormalized classical region identified in the 2D spin-1/2 cuprate such as ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$, but the spin dynamics is in the quantum critical regime over wide T range due to the finite size of chains, even though the 3D magnetic ordering takes place at very low temperature. This is considered because the spin correlators have a power-law decay only along the chain, but between chains is limited to the number of chains in contrast to the 2D square lattice. For the compounds with two chains, the exchange coupling between chains leads to the formation of spin gap phase regardless of whether its sign is antiferromagnetic or ferromagnetic. A result on doping into the two-leg ladder, ${\mathrm{SrCu}}_{2}$${\mathrm{O}}_{3}$ is argued in terms of the localization effect of carriers. \textcopyright{} 1996 The American Physical Society.
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Aug 30, 2002
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