Existence of two-dimensional closed orbits and delocalized carriers in the spin-ordered state of quasi one-dimensional (TMTSF)$_2$PF$_6$

We report studies of the magnetoresistance in the spin-ordered state of the quasi one-dimensional (TMTSF)$_2$PF$_6$. We have found that both frequency and anisotropy of the magnetoresistance oscillations are independent of temperature; this proves temperature independence of the geometry of two-dimensional closed contours at the Fermi level. On the other hand, the oscillation amplitude decay as temperature decreases, the latter result indicates depopulation of the closed contours in the $T=0$ limit. We propose an explanation for the above seemingly controversial results.