In this material, the neighboring ladders are displaced by half the lattice constant, leading to a small inter-ladder interaction. Since the 90 Cu-O-Cu bonds mediate the inter-ladder interaction, the interaction may be ferromagnetic (-J'; see Fig.26b). The magnitude of the inter-ladder interaction has been theoretically estimated as J'/ [19,21]. The inter-ladder interaction brings about a geometrical frustration of the spins at the edge of the ladders, because of the triangular structure constituent of two ferromagnetic interactions (-J') and one antiferromagnetic interaction (J) [19,21].
Previous investigations of Srn-1Cun+1O2n have measured magnetic susceptibility (Fig.27; ) and 63Cu-NMR (Fig.28; ). In the 2-leg ladder system (n=3), the temperature dependence of the susceptibility and the T1 relaxation rate are well described by thermal excitations over a gap, which may correspond to the spin gap between the non-magnetic ground state and magnetic excited states. The magnitude of the gap has been reported as 420 K (susceptibility: ) and 680 K (63Cu-NMR: ).
The 3-leg ladder system (n=5), in contrast, has a finite susceptibility in the T0 limit, demonstrating that the ground state of this system can respond to the external magnetic field. Therefore, the ground state may exhibit magnetic order. In the 3-leg ladder system, the T1 relaxation rate of 63Cu nuclear moments was so large that it was hardly measurable with the conventional NMR technique. This result implies the existence of strong magnetic correlations in the 3-leg system .
As introduced in Chapter 2, continuous-beam muon spin relaxation (SR) is
a NMR-like local magnetic probe, but with a higher timing
resolution (1 ns) than typical NMR methods (10 s).
Consequently, SR is an adequate probe to study the 3-leg
ladder system, in which the NMR relaxation rate was beyond its time
resolution. Another advantage of SR is its high sensitivity to
small and/or dilute static moments. Using SR one can best investigate
the expected absence of static order in the 2-leg ladder system.
For our SR measurements, polycrystalline specimens of the spin ladder cuprates (Srn-1Cun+1O2n; n=3, 5) were prepared at the Institute for Chemical Research, Kyoto University, using a cubic anvil-type high pressure apparatus . Powder X-ray analysis of our samples showed the stoichiometric ladder structure, except for small amounts (10 Cu at.% ) of a CuO impurity phase . Since CuO is an antiferromagnet (230 K ), the impurity phase should not affect the muons which did not land within an impurity cluster. Therefore, in our SR measurements 90% of the signal amplitude comes from the pure ladder structure.