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

We demonstrate that transverse magnetoresistance is a nonanalytical function of the magnetic field, rho(perpendicular to)(H) similar to \H\(1/2), 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 = ClO4,PF6) and (DMET)(2)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,'' Theta = +/-Theta(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 rho(perpendicular to)(H) similar to 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-T-c superconductors.