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Next: 4.3 SR measurements Up: 4 Spin-ladder system Previous: 4.1 Introduction

4.2 Spin-ladder material Srn-1Cun+1O2n

The spin-ladder material Srn-1Cun+1O2n, which is synthesized under high pressure and high temperature [49,50], takes the structure shown in Fig.26a. The lattice structure is composed of (n+1)/2-leg spin-ladders, namely, strips of CuO2 square lattice which have (n+1)/2- Cu2+ ions across their width. Each Cu2+ ion has spin S=1/2 with antiferromagnetic couplings within a ladder (strength: J), both in the `rung' and the `leg' directions. In the two directions, the difference of the coupling strengths are presumably small, because the 180$^{\circ}$ Cu-O-Cu bond lengths are almost equal for both directions [49].
  
Figure 26: (a) The `spin ladder' structure of Srn-1Cun+1O2n. Oxygen ions locate at each corner of the squares. The figure shows the 3-leg ladder structure (n=5). (b) A magnified ladder-edge. The dotted lines represent the 90$^{\circ}$ Cu-O-Cu bonds which mediate the ferromagnetic inter-ladder interaction (-J').
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In this material, the neighboring ladders are displaced by half the lattice constant, leading to a small inter-ladder interaction. Since the 90$^{\circ}$ 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'/$J\approx 0.1-0.2$ [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; [51]) and 63Cu-NMR (Fig.28; [52]). 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: [51]) and 680 K (63Cu-NMR: [52]).

The 3-leg ladder system (n=5), in contrast, has a finite susceptibility in the T$\rightarrow$0 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 [52].

As introduced in Chapter 2, continuous-beam muon spin relaxation ($\mu$SR) is a NMR-like local magnetic probe, but with a higher timing resolution ($\stackrel{<}{\sim}$1 ns) than typical NMR methods ($\sim$10 $\mu$s). Consequently, $\mu$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 $\mu$SR is its high sensitivity to small and/or dilute static moments. Using $\mu$SR one can best investigate the expected absence of static order in the 2-leg ladder system.

  
Figure: Susceptibility of the spin ladder materials Srn-1Cun+1O2n. Cite from Ref. [51].
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Figure: Temperature dependence of the 63Cu-NMR T1 relaxation rate (cite from [52]). The right axis is an estimated muon spin relaxation rate for the same relaxation mechanism. (See the discussion later.)
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For our $\mu$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 [53]. Powder X-ray analysis of our samples showed the stoichiometric ladder structure, except for small amounts ($\sim$10 Cu at.% ) of a CuO impurity phase [51]. Since CuO is an antiferromagnet ($T_{\rm N}$$\sim$230 K [54]), the impurity phase should not affect the muons which did not land within an impurity cluster. Therefore, in our $\mu$SR measurements $\sim$90% of the signal amplitude comes from the pure ladder structure.


next up previous contents
Next: 4.3 SR measurements Up: 4 Spin-ladder system Previous: 4.1 Introduction