The role of two types of trellis layer for metal-insulator transition and antiferromagnetic order in the one-dimensional conductor V6O13

V6O13 with a metal-insulator transition at Tc ≅ 150 K and an antiferromagnetic order at TN ≅ 50 K has a ddyz-type single trellis layer and a dxy-type double trellis layer, where x and y correspond to the a- and b-axis, respectively. Magnetic properties above Tc are consistent with theoretical results for a one-dimensional Hubbard model with the uniform electron concentration and a bandwidth comparable to the effective on-site Coulomb energy. Below Tc, in the light of properties of δ-phase vanadium bronzes, the spin-singlet state is considered to appear in the double trellis layer and the one-dimensional Heisenberg chain-like state is formed in the single layer, accompanied with valence order; and at TN, the antiferromagnetic order takes place in the single layer. The temperature dependence of the electrical resistivity for the one-dimensional chain above Tc is mainly due to antiferromagnetic spin fluctuations, and those for the normal directions nearly follow 1/T which is likely due to the renormalization effect of the Fermi surface by the fluctuations. The Hall coefficient above Tc is found to be roughly linear in T