Mise en page 1 - Laboratoire National des Champs Magnétiques ...

METALS, SUPERCONDUCTORS... 2009Magnetic oscillations in a linear chain of compensated orbitsDue to their rather simple Fermi surface, organicmetals provide a rich playground for the investigationof quantum oscillations in physics. In that respect,the most well known example is provided by κ-(BEDT-TTF) 2 Cu(NCS) 2 (where BEDT-TTF stands for bisethylenedithio-tetrathiafulvalene)which can be regarded asthe experimental realization of the Fermi surface consideredby Pippard in the early sixties for his model. In theextended zone scheme, such a Fermi surface is composedof closed hole orbits and quasi-one dimensional sheets coupledby magnetic breakdown. This kind of Fermi surfaceyields quantum oscillations spectra with numerous frequencycombinations that cannot be accounted for by thesemi-classical model of Falicov and Stachowiak. This phenomenonwhich has generated great interest is generally attributedto either the formation of Landau bands and/or oscillationsof the chemical potential in a magnetic field.In the case where the effective masses linked to electronandhole-type orbits are the same (m ∗ e = m ∗ h), calculationsdemonstrate that chemical potential oscillations vanish forsuch a Fermi surface. More generally, in the case wherem ∗ e and m ∗ hare different, these oscillations are significantlydamped, all the more if the magnetic breakdown field issmall, as evidenced in figure 93.Figure 92: Calculated Fermi surface of the Bechgaard salt(TMTSF) 2 NO 3 in the temperature range below the anion orderingand above the spin density wave condensation, according toKang et al. [EPL 29 635 (1995)]. Solid blue and red lines arecompensated hole and electron orbits, respectively. This Fermisurface achieves linear chains of compensated orbits.Contrary to the above mentioned example, the Fermi surfaceof numerous organic metals is composed of compensatedelectron- and hole-type closed orbits, yieldingmany frequency combinations as well, as far as ShubnikovdeHaas oscillations are concerned. We have computedthe field and temperature dependence of the de Haas-vanAlphen oscillations spectra of an ideal two-dimensionalmetal whose Fermi surface achieves a linear chain ofsuccessive electron- and hole-type compensated orbits.Such a topology is realized e.g. in the Bechgaard salt(TMTSF) 2 NO 3 (where TMTSF stands for tetra-methyltetra-seleno-fulvalene)in the temperature range in-betweenthe anion ordering temperature and the spin density wavecondensation (see figure 92).Figure 93: Field dependence of the chemical potential for Fermisurface such as in figure 92 for m ∗ e = m 0 and m ∗ h = 2.5m 0 (m ∗ e andm ∗ h are the electron and hole orbit effective mass, respectively; m 0is the free electron mass) at a reduced temperature t = 10 −4 (t = T× k B m 0 A 0 /2π 2 , where A 0 is the unit cell area). b is the reducedmagnetic field (b = B × eA 0 /2π), b 0 is the reduced magneticbreakdown field. The inset compares the chemical potential oscillationsfor two electron orbits and two compensated orbits with,respectively, the same effective masses as in the main panel, in theabsence of magnetic breakdown (b 0 →∞).It appears from the analysis of the numerical resolutionof Landau levels, including the electron-hole band interaction,that the Lifshits-Kosevich semiclassical formalismcan be applied for the first harmonic, provided magneticbreakdown orbits, although with higher effective masses,are taken into account. The resulting high order terms canlead to apparent temperature-dependent effective mass forclean crystals in the high B/T limit in the case where onlyone effective mass is considered for the data analysis, as itis usually done. For example, in the absence of magneticbreakdown, m ∗ = min(m ∗ e, m ∗ h) in the low field range whilem ∗ = √ m ∗ em ∗ hat high field.On the contrary, strong deviation from the Lifshits-Kosevich behavior is observed for the second harmonic.The main feature of this latter component being the zeroamplitude occurring at a B/T value depending on the ratioof the two effective masses (m ∗ h /m∗ e), only, independent ofthe magnetic breakdown field value.A. AudouardJ.-Y. Fortin (Institut Jean Lamour, Nancy)68