Nonanalytical magnetoresistance, the third angular effect, and a methodto investigate Fermi surfaces in quasi-two-dimensional conductors

Abstract

We demonstrate that transverse magnetoresistance is a nonanalytical function of the magnetic field, ${\mathrm{\ensuremath{\rho}}}_{\mathrm{\ensuremath{\perp}}}$(H)\ensuremath{\sim}|H${\mathrm{|}}^{1\mathrm{/}2}$, if a magnetic field is parallel to the plane of anisotropy and normal to the Fermi surface at an inflection point in a quasi-two-dimensional (Q2D) conductor. The so-called ``third angular effect,'' recently discovered in organic conductors (TMTSF${)}_{2}$X (X=${\mathrm{ClO}}_{4}$,${\mathrm{PF}}_{6}$) and (DMET${)}_{2}$${\mathrm{I}}_{3}$, is interpreted in terms of the existence of an inflection point on their Fermi surfaces. Nonanalytical magnetoresistance is predicted to appear when the magnetic field is applied at the ``third magic angles,'' \ensuremath{\Theta}=\ifmmode\pm\else\textpm\fi{}${\mathrm{\ensuremath{\Theta}}}_{\mathrm{c}}$. It is also shown that at arbitrary directions of the in-plane magnetic field the magnetoresistance does not depend on relaxation time and obeys the law ${\mathrm{\ensuremath{\rho}}}_{\mathrm{\ensuremath{\perp}}}$(H)\ensuremath{\sim}A|H| with factor A being a function of local characteristics of a Q2D Fermi surface. The above-mentioned phenomena provide useful methods to investigate Fermi surfaces in strongly anisotropic Q2D conductors including organic and high-${\mathrm{T}}_{\mathrm{c}}$ superconductors.