Abstract
We have made NMR and magnetization measurements on a single crystal to investigate local magnetic properties of an antiferromagnet metal NaV${}_{2}$O${}_{4}$ with a frustrated double-chain structure. In the paramagnetic phase, we find there is a double exchange ferromagnetic interaction, which competes with a superexchange antiferromagnetic interaction, yielding a magnetic frustration. In the magnetically ordered state, we propose an incommensurate helical structure with the $bc$ helical plane, which appears due to the competition between the magnetic interactions, as a spin structure. Thus we conclude that the magnetic frustration closely related to a multi-band effect plays an essential role for the magnetic properties of NaV${}_{2}$O${}_{4}$.
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