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Next: 4.3.2 The 2-leg ladder Up: 4.3 SR measurements Previous: Longitudinal-field measurements

5.2.3 Discussion

We compare in Table 3 the ordering temperatures of the Sr(Ca)-Cu-O series of compounds, which is a one-dimensional chain system for Sr2CuO3 [55], and a two-dimensional layer system for Ca0.86Sr0.14CuO2 (n$\rightarrow$$\infty$ structure of the spin-ladder series) [56]. The ordering temperature of the 3-leg ladder system is between those of the chain system (Sr2CuO3) and the layer system (Ca0.86Sr0.14CuO2). Suppression of $T_{\rm N}$ in the chain system has been explained as an effect of the low-dimensionality [55]; the intermediate ordering temperature for the 3-leg system is consistent with this idea, because the 3-leg ladder structure is the smallest extension of the one-dimensional chain toward two-dimensionality.
 
Table 3: Structure and magnetic behavior of Sr(Ca)-Cu-O compounds
compound structure magnetic order
Sr2CuO3 CuO chain (1D) $T_{\rm N}$$\sim$5 K$^{\rm a}$
Sr4Cu6O10 3-leg ladder T$\sim$52$\pm$5 K$^{\rm b}$
Ca0.86Sr0.14CuO2 CuO2 plain (2D) $T_{\rm N}$$\sim$540 K$^{\rm c}$
$^{\rm a}$Obtained by $\mu$SR [55].
$^{\rm b}$Obtained by $\mu$SR: this work [1].
$^{\rm c}$Obtained by neutron scattering [57] and $\mu$SR [55].

Another feature of the magnetic order in the 3-leg ladder system is the absence of critical slowing down of the Cu moments in the $\mu$SR time window ($\sim 10\mu$s). In Fig.31, we show $\mu$SR spectra at long times. No enhancement of the relaxation rate was observed around the transition temperatures. This `abrupt' onset of magnetic order has been observed in other one-dimensional systems, such as antiferromagnets Sr2CuO3 [55], Ca2CuO3 [58] and a spin-density-wave system (TMTSF)2-PF6 [59]. In these systems, the absence of critical slowing down have been explained as follows; in one-dimensional systems, the ordering temperature is determined by the small inter-chain interactions, and therefore, there may be preformed short-range ordered regions before the three-dimensional order takes place [60]. Then the ordering process is a phase-lockings of these short-range ordered regions, which do not involve a slowing down of the moments. The absence of the critical slowing down in the 3-leg ladder system may also reflect its low-dimensionality, if the `phase-locking' picture of the magnetic order is relevant.

  
Figure 31: LF=100 G $\mu$SR spectra around the transition temperatures.
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next up previous contents
Next: 4.3.2 The 2-leg ladder Up: 4.3 SR measurements Previous: Longitudinal-field measurements