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According to band structure calculations, the Fermi surface of the quasi-twodimensional metal $\theta$-(ET) 4 ZnBr 4 (C 6 H 4 Cl 2) illustrates the linearchain of coupled orbits model. Accordingly, de Haas-van Alphen oscillationsspectra recorded in pulsed magnetic field of up to 55 T evidence many Fouriercomponents, the frequency of which are linear combinations of the frequenciesrelevant to the closed $\alpha$ and the magnetic breakdown $\beta$ orbits. Thefield and temperature dependence of these component's amplitude arequantitatively accounted for by analytic calculations including, beyond theLifshitz-Kosevich formula, second order terms in damping factors due to theoscillation of the chemical potential as the magnetic field varies. Whereasthese second order terms are negligible for the orbits $\alpha$, $\beta$ and2$\beta$ -- $\alpha$, they are solely responsible for the 'forbidden orbit'$\beta$ -- $\alpha$ and its harmonic and have a significant influence onFourier components such as 2$\alpha$ and $\beta$ + $\alpha$, yielding stronglynon-Lifshitz-Kosevich behaviour in the latter case.

Non-Lifshitz-Kosevich field-and temperature-dependent amplitude of  quantum oscillations in the quasi-two dimensional metal $\theta$-(ET) 4 ZnBr  4 (C 6 H 4 Cl 2 )