Magnetic-field-induced Fermi surface reconstruction in Na$_{0.5}$CoO$_2$

We have performed electrical transport measurements at low temperatures and high magnetic fields in Na$_{0.5}$CoO$_2$ single crystals. Shubnikov de Haas oscillations were observed for two frequencies F_1 150 and F_2 40 T corresponding respectively to 1 and .25% of the area of the orthorhombic Brillouin zone. These small Fermi surface (FS) pockets indicate that most of the original FS vanishes at the charge ordering (CO) transition. Furthermore, in-plane magnetic fields strongly suppress the CO state. For fields rotating within the conducting planes we observe angular magnetoresistance oscillations (AMRO), whose periodicity changes from two- to six-fold at the transition, suggesting that a reconstructed hexagonal FS emerges at a field of about 40 T.