Magnetic and dielectric properties of one-dimensional array of S = 1/2 linear trimer system Na{sub 2}Cu{sub 3}Ge{sub 4}O{sub 12}

Magnetic susceptibility χ, specific heat C, capacitance C{sub p}, and {sup 23}Na-NMR measurements have been carried out on polycrystalline samples of quantum spin linear trimer system Na{sub 2}Cu{sub 3}Ge{sub 4}O{sub 12}, which has the one-dimensional array of Cu{sub 3}O{sub 8} trimers formed of edge-sharing three CuO{sub 4} square planes. The exchange interactions between the Cu{sup 2+} (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 J{sub 1} and the second-neighbor one J{sub 2} in trimer have been evaluated to J{sub 1}/k{sub B} = 30 ± 20 K (antiferromagnetic) and J{sub 2}/k{sub B} = 340 ± 20 K. At low temperature region, two spins of the edge in the Cu{sub 3}O{sub 8} trimers form a nonmagnetic singlet by strong antiferromagnetic interaction J{sub 2}, and the spin left in the center of the Cu{sub 3}O{sub 8} trimer forms one-dimensional chains by the exchange interaction J{sub 3} between the trimers. By employing the S = 1/2 uniform Heisenberg chain model below 70 K, we have evaluated to J{sub 3}/k{sub B} = 18 ± 1 K. The mechanism of multiferroic behavior at T{sub c} = 2 K is discussed.