De Haas-van Alphen oscillations are studied for Fermi surfaces illustrating the Pippards model, commonly observed in multiband organic metals. Field- and temperature-dependent amplitude of the various Fourier components, linked to frequency combinations arising from magnetic breakdown between different bands, are considered. Emphasis is put on the Onsager phase factor of these components. It is demonstrated that, in addition to the usual Maslov index, field-dependent phase factors must be considered to precisely account for the data at high magnetic field. We present compelling evidence of the existence of such contributions for the organic metal theta-(BEDT-TTF)4CoBr4(C6H4Cl2).
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