Possible non-coplanar spin structure and large Hall effect in Na$_{x}$CoO$_{2}$

We present magnetotransport studies of Na$_{x}$CoO$_{2}$ ($x=$0.46) and its relation to possible non-coplanar spin texture. This compound exhibits a unique insulating state below temperature ($T)$ of 53 K related to charge-order which is different from other composition with metallic behavior. It also has frustrated local spin texture owing to its hexagonal structure. Previous works report a very large Hall signal for composition $x=$0.5 (M. Foo \textit{et al.}, Phys. Rev. Lett. 92, 247001 (2004)) at low magnetic field ($B)$ and prior high-field studies (L. Balicas \textit{et al.}, Phys. Rev. Lett. 94, 236402 (2005)) have found the existence of a small Fermi surface in the system and a two-fold angular magnetoresistance. Using pulse and hybrid magnets at NHMFL, we mapped out a detailed $T$-$B$ phase diagram up to 65 T which is strong enough to suppress the charge-order. When $B$ is applied along the $c$-axis, the charge-ordered state is suppressed at $B$ $\sim$ 41 T with highly non-monotonic shape in $\rho_{xy}$. We found that this Hall signal reaches a maximum around $T \sim$ 30 K and $B \sim$ 27 T and on further cooling the absolute change of $\rho_{xy}$ decreases significantly. Interestingly, we found no significant changes in field-dependent magnetization which suggests that this behavior does not come from the ordinary anomalous Hall effect. We discuss the origin of this unique Hall signal by existence of a non-coplanar spin structure that may exist in this compound (I. Martin, C. D. Batista, Phys. Rev. Lett. 101, 156402 (2008)).