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Analytical formulae for de Haas-van Alphen (dHvA) oscillations in linearchain of coupled two-dimensional (2D) orbits (Pippard's model) are derivedsystematically taking into account the chemical potential oscillations inmagnetic field. Although corrective terms are observed, basic (alpha) andmagnetic breakdown-induced (beta and 2beta - alpha) orbits can be accounted forby the Lifshits-Kosevich (LK) and Falicov-Stachowiak semiclassical models inthe explored field and temperature ranges. In contrast, the 'forbidden orbit'beta - alpha amplitude is described by a non-LK equation involving a product oftwo classical orbit amplitudes. Furthermore, strongly non-monotonic field andtemperature dependence may be observed for the second harmonics of basicfrequencies such as 2alpha and the magnetic breakdown orbit beta + alpha,depending on the value of the spin damping factors. These features are inagreement with the dHvA oscillation spectra of the strongly 2D organic metaltheta- theta-(ET)(4)CoBr(4)(C(6)H(4)Cl(2)).

Quantum oscillations in the linear chain of coupled orbits: the organic metal with two cation layers theta-(ET)(4)CoBr(4)(C(6)H(4)Cl(2))