Spin gap and hole pairing of Sr_14-xA_xCu₂₄O₄₁(A = Ca and La) single crystals studied by the electrical resistivity and thermal conductivity

We have measured the electrical resistivity ρ and the thermal conductivity κ of Sr_14-xA_xCu₂₄O₄₁(A = Ca and La) single crystals. The Arrhenius plot of In ρ vs T^-1 gives two kinds of activation energy with a boundary temperature T_ρ. The activation energy at T < T_ρ is in approximate agreement with the spin gap in the ladder estimated from the NMR measurements, suggesting that holes in the ladder are paired and localized at T < T_ρ. The observed κ has been analyzed to be composed of κ_ph, κ_spin and κ_hole due to phonons, spins and holes, respectively. The κ_ph exhibits a small peak at ∼ 30 K in every direction of every single-crystal. The contribution of κ_spin is observed along the c-axis except for x(Ca) ≥ 6, and the spin gap, which corresponds to the spin excitation from spin-singlet to spin-triplet, has been estimated to be ∼ 420 K. For x(Ca) ≥ 6, the spin gap, which corresponds to the destruction of spin-singlet pairs i.e. the dissociation of hole pairs, has been estimated from κ along the c-axis at T > T_ρ to decrease with increasing x(Ca).