New insights on frequency combinations and 'forbidden frequencies' in de Haas-van Alphen spectrum of k{appa}-(ET) 2 Cu(SCN) 2

De Haas-van Alphen oscillations of the organic metal \k{appa}-(ET) 2 Cu(SCN) 2 have been measured up to 55 T at liquid helium temperatures. The Fermi surface of this charge transfer salt is a textbook example of linear chain of orbits coupled by magnetic breakdown. Accordingly, the oscillation spectrum is composed of linear combinations of the frequencies linked to the $\alpha$ and magnetic breakdown-induced $\beta$ orbits. The field and temperature dependence of all the observed Fourier components, in particular the "forbidden frequency" $\beta$ -- $\alpha$ which cannot correspond to a classical orbit, are quantitatively accounted for by analytical calculations based on a second order development of the free energy, i.e. beyond the first order Lifshitz-Kosevich formula.