Semiclassical description of angle-dependent magnetoresistance oscillations in quasi-one-dimensional metals

We use a semiclassical model to calculate the angle-dependent magnetoresistance oscillations (AMROs) in quasi-one-dimensional (q1D) organic conductors. A number of contrasting models have been proposed to explain this effect, mainly in the context of the (TMTSF${)}_2$X (where TMTSF is tetramethyltetraselenafulvalene and X=${\mathrm{ClO}}_4$ or ${\mathrm{PF}}_6$) family; some of the models concentrate on the role of electron-electron interactions while others postulate Fermi-surface hotspots or even field-dependent hopping renormalization. Instead, we have used a more intuitive semiclassical approach to calculate the angle-dependent magnetoresistance oscillations for a completely general class of q1D Fermi surfaces. The model demonstrates how the details of the Fermi surface corrugation give particular features in the experimental data and illustrates the important roles played by both open and closed orbits. The AMRO observed in (TMTSF${)}_2$${\mathrm{ClO}}_4$ when the magnetic field is rotated close to the a axis are discussed in this context. The results are particularly applied to the organic charge transfer salt (ET${)}_2$KHg(SCN${)}_4$ [where ET is bis(ethylenedithio)tetrathiafulvalene]; this material is interesting because the Fermi surface undergoes a transition from predominantly q1D to quasi-two-dimensional (q2D) character at ∼22 T, a result which has been primarily established on the basis of AMRO experiments.

Higher order Fourier components in the corrugation of the Fermi sheet are shown to be essential to explain the observed AMROs and the size of the magnetoresistance in this material. The absence of q1D AMROs in most organic metals with q1D Fermi surfaces is explained, illustrating in particular why q1D AMROs are absent above 22 T in (ET${)}_2$KHg(SCN${)}_4$ even though the Fermi surface contains q1D sections. We discuss the failure of previous models to explain the AMRO effect in this salt and demonstrate the advantages of adopting a semiclassical approach. © 1996 The American Physical Society.