Home page > Scientific production > News > Forbidden frequency combinations relevant to the model Fermi surface by Pippard are elucidated

*De Haas-van Alphen oscillations of the organic superconductor κ-( BEDT-TTF) _{2}Cu(SCN)_{2} are quantitatively explained by chemical potential oscillations within the canonical ensemble.*

**Fig.1:**- (a) de Haas-van Alphen oscillations and (b) corresponding Fourier analysis and Fermi surface of the organic superconductor k-(BEDT-TTF)
_{2}Cu(SCN)_{2}

The two-dimensional charge transfer salt k-(BEDT-TTF)_{2}Cu(SCN)_{2}, synthesized for the first time in 1988, is still probably the most studied organic superconductor. Remarkably, its Fermi surface is the first experimental realization of the linear chain of coupled orbits which is the model fermi surface proposed by Pippard in the early sixties to compute magnetic breakdown amplitudes in multiband metals (see the insert of Fig. 1b). Accordingly, its de Haas-van alphen (dHvA) oscillations spectrum is composed of linear combinations of the frequencies linked to the α and magnetic breakdown-induced β orbits at high enough magnetic field (see Fig. 1).

dHvA oscillations of three-dimensional metals are satisfactorily accounted for by the Lifshitz-Kosevich (LK) model which is based on a first order development of the free energy, in which the chemical potential is fixed and equal to the Fermi energy. In contrast, for the considered compound, not only the field and temperature dependence of several Fourier components, e.g. 2α and 2β, is not in agreement with the behaviour predicted by the LK formula, but also ’forbidden frequencies’, such as β-α which cannot correspond to a classical orbit, are nevertheless observed. These features, already reported from the beginning of the 1990’s, remained unexplained so far.

**Fig.2:**- Field and temperature dependence of the amplitude of the ’forbidden’ Fourier component β-α. Solid lines are best fits to the data.

We have determined dHvA oscillations amplitudes through magnetic torque measurements in pulsed magnetic fields of up to 55 T at liquid helium temperatures. The field and temperature dependence of all the observed Fourier components, in particular the ‘forbidden frequency’ β-α (see Fig. 2) and the harmonics 2α and 2β, are quantitatively accounted for by a calculation of the free energy, within the canonical ensemble, up to the second order in damping factors, taking into account oscillations of the chemical potential arising from the two-dimensional character of the Fermi surface.

More information :

A. Audouard, J.-Y. Fortin, D. Vignolles, V. N. Laukhin, N. D. Kushch and E. B. Yagubskii, New insights on frequency combinations and ’forbidden frequencies’ in the de Haas–van Alphen spectrum of κ-(ET)_{2}Cu(SCN)_{2}, J. Phys. : Condens. Matter 28 275702 (2016)

A. Audouard, J.-Y. Fortin, D. Vignolles,R. B. Lyubovskii, L. Drigo, G. V. Shilov, F. Duc, E. I. Zhilyaeva, R. N. Lyubovskaya and E. Canadell, Non-Lifshitz–Kosevich field- and temperature-dependent amplitude of quantum oscillations in the quasi-two dimensional metal θ-(ET)_{4}ZnBr_{4}(C_{6}H_{4}Cl_{2}), J. Phys. : Condens. Matter 27 315601 (2015)

A. Audouard, J.-Y. Fortin, D. Vignolles,R. B. Lyubovskii, L. Drigo, F. Duc, G. V. Shilov, G. Ballon, E. I. Zhilyaeva, R. N. Lyubovskaya and E. Canadell, Quantum oscillations in the linear chain of coupled orbits : The organic metal with two cation layers θ-(ET)_{4}CoBr_{4}(C_{6}H_{4}Cl_{2}), Europhysics Letters 97 57003 (2012)