Analytical formulae for de Haas-van Alphen (dHvA) oscillations in linear chain of coupled two-dimensional (2D) orbits (Pippard's model) are derived systematically taking into account the chemical potential oscillations in magnetic field. Although corrective terms are observed, basic (α) and magnetic-breakdown-induced (β and 2β − α) orbits can be accounted for by the Lifshits-Kosevich (LK) and Falicov-Stachowiak semiclassical models in the explored field and temperature ranges. In contrast, the "forbidden orbit" β − α amplitude is described by a non-LK equation involving a product of two classical orbit amplitudes. Furthermore, strongly non-monotonic field and temperature dependence may be observed for the second harmonics of basic frequencies such as 2α and the magnetic breakdown orbit β + α, depending on the value of the spin damping factors. These features are in agreement with the dHvA oscillation spectra of the strongly 2D organic metal θ-(ET)4CoBr4(C6H4Cl2).

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Interlayer magnetoresistance and magnetisation of the quasi-two dimensional organic metal (BEDT-TTF)8Hg4Cl12(C6H5Br)2 have been investigated in pulsed magnetic fields extending up to 60 T and 33 T, respectively. About fifteen fundamental frequencies, composed of linear combinations of only three basic frequencies, are observed in the oscillatory spectra of the magnetoresistance. The dependencies of the oscillation amplitude on the temperature and on the magnitude and orientation of the magnetic field are analyzed in the framework of the conventional two-dimensional Lifshitz-Kosevitch (LK) model. This model is implemented by damping factors which accounts for the magnetic breakthrough occurring between electron and hole orbits yielding conventional Shubnikov-de Haas closed orbits (model of Falicov and Stachowiak) and quantum interferometers. In particular, a quantum interferometer enclosing an area equal to the first Brillouin zone area is evidenced. The LK model consistently accounts for the temperature and magnetic field dependence of the oscillation amplitude of this interferometer. On the contrary, although this model formally accounts for almost all of the observed oscillatory components, it fails to give consistent quantitative data in most other cases.

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