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We have measured the thermal conductivity along the [101] direction,kappa_[101]_, along the [10-1] direction, kappa_[10-1]_, and along the b-axis,kappa_b_, of the quasi one-dimensional S=1/2 spin system Sr_2_V_3_O_9_ inmagnetic fields up to 14 T, in order to find the thermal conductivity due tospinons and to clarify whether the spin-chains run along the [101] or [10-1]direction. It has been found that both kappa_[101]_, kappa_[10-1]_ and kappa_b_show one peak around 10 K in zero field and that the magnitude of kappa_[10-1]_is larger than those of kappa_[101]_ and kappa_b_. By the application ofmagnetic field along the heat current, the peak of kappa_[10-1]_ is markedlysuppressed, while the peaks of kappa_[101]_ and kappa_b_ little change. Theseresults indicate that there is a large contribution of spinons to kappa_[10-1]_and suggest that the spin-chains run along the [10-1] direction.

Thermal Conductivity of the Quasi One-Dimensional Spin System Sr_2_V_3_O_9_