Magnetic and dielectric properties of one-dimensional array of S = 1/2 linear trimer system Na₂Cu₃Ge₄O₁₂

Magnetic susceptibility χ, specific heat C, capacitance C_p, and ²³Na-NMR measurements have been carried out on polycrystalline samples of quantum spin linear trimer system Na₂Cu₃Ge₄O₁₂, which has the one-dimensional array of Cu₃O₈ trimers formed of edge-sharing three CuO₄ square planes. The exchange interactions between the Cu²⁺ (S = 1/2) spins have been determined by analyzing χ-T and C-T curves. By employing the isolated S = 1/2 Heisenberg trimer model above 70 K, the nearest-neighbor exchange couplings J₁ and the second-neighbor one J₂ in trimer have been evaluated to J₁/k_B = 30 ± 20 K (antiferromagnetic) and J₂/k_B = 340 ± 20 K. At low temperature region, two spins of the edge in the Cu₃O₈ trimers form a nonmagnetic singlet by strong antiferromagnetic interaction J₂, and the spin left in the center of the Cu₃O₈ trimer forms one-dimensional chains by the exchange interaction J₃ between the trimers. By employing the S = 1/2 uniform Heisenberg chain model below 70 K, we have evaluated to J₃/k_B = 18 ± 1 K. The mechanism of multiferroic behavior at T_c = 2 K is discussed.