Origin of rapid oscillations in low-dimensional (TMTSF)2PF6

We report studies of the magnetoresistance anisotropy in ${(\mathrm{TMTSF})}_{2}\mathrm{P}{\mathrm{F}}_{6}$, that shed light on the origin of the ``rapid oscillations'' (ROs). We have found that (i) ROs exist only in the spin-ordered state and are absent in the metallic state, (ii) decreasing temperature causes nonmonotonic variation of the RO magnitude, however, it does not affect the frequency of ROs, (iii) the spin-ordered state, which had previously been believed to be insulating, is not totally gapped (at least for finite temperatures), (iv) the RO frequency depends only on the magnetic field component that is normal to the $a\text{\ensuremath{-}}b$ crystal plane. In our view, these results show that in the spin-ordered states there remains a vestigial Fermi surface comprising closed orbits in the $a\text{\ensuremath{-}}b$ crystal plane. The orbits are quantized in magnetic field and give rise to the ROs. While decreasing temperature does not change the size or orientation of the orbits, it does cause a depopulation of the delocalized states (closed orbits) in favor of localized ones; this results in the disappearance of the ROs at low temperatures. Our data agree qualitatively with a theory that considers the coexistence of two spin-density waves with two respective nesting vectors. It is the coexistence of these two spin-density waves that gives rise to the closed orbits and, consequently, causes the rapid oscillations.