Observation of the Underscreened Kondo Effect in a Molecular Transistor

Abstract

We present first quantitative experimental evidence for the underscreened Kondo effect, an uncomplete compensation of a quantized magnetic moment by conduction electrons, as originally proposed by Nozières and Blandin. The device consists of an even charge spin S = 1 molecular quantum dot, obtained by electromigration of C60 molecules into gold nanogaps and operated in a dilution fridge. The persistence of logarithmic singularities in the low temperature conductance is demonstrated by a comparison to the fully screened configuration obtained in odd charge spin S = 1/2 Coulomb diamonds. We also discover an extreme sensitivity of the underscreened Kondo resonance to magnetic field, that we confirm on the basis of numerical renormalization group calculations. PACS numbers:When a magnetic impurity is inserted in a piece of metal, its magnetic moment can be completely screened by the conduction electrons, owing to their quantized spin 1/2. This general phenomenon, the Kondo effect, has been thoroughly studied in diluted magnetic alloys [1] and has attracted considerable attention in the more recent quantum dot systems [2]. Clearly, impurities carrying a spin S greater that 1/2 need to bind several electronic orbitals in order to fully quench their magnetism, and Nature seems to conspire in always providing enough screening channels for that situation to occur in general [3]. Therefore, the possibility that screening may happen to be incomplete, as initially proposed on theoretical grounds by Nozières and Blandin [4], has remained elusive for almost thirty years, despite the great experimental control that one can achieve with artificial quantum dot setups. The observation of the underscreened Kondo effect, in addition to its overscreened counterpart [5], is also especially appealing since it constitutes one of the simplest cases where standard Fermi Liquid Theory is violated [6,7].We demonstrate in this Letter that molecular quantum dots obtained through electromigration [8] are perfect candidates for achieving underscreened Kondo impurities. Indeed point contact tunneling (single mode) and important left/right asymmetry of the transport electrodes ensure a large window of energies where a single screening channel is active. In addition, the Kondo phenomenon in molecules can set in already at several kelvins [9,10,11,12] thanks to relatively important charging energies, allowing a complete study of Kondo crossovers on a sufficient range of temperatures. Both conditions of single channel and large Kondo temperature are difficult to meet altogether in other quantum dot devices, where Kondo effects associated with higher spin states have been previously found, but yet not investigated in detail [13,14,15,16,17]. We report here on the first observation of the anomalous logarithmic behavior in the temperature and bias voltage dependent conductance in a spin S = 1 quantum dot below the Kondo scale, as previously predicted for underscreened impurities [4,6,7,18], and successfully confront our results with quantitative nume...

Universal transport signatures in two-electron molecular quantum dots: gate-tunable Hund’s rule, underscreened Kondo effect and quantum phase transitions

“…However, the doublet phase corresponding to D z < 0 was not accessible in this experiment, so that the QPT was not fully examined. As was noted previously [43,45], the magnetic anisotropy term is less relevant than the Zeeman splitting discussed in the previous paragraph and in our work [18], leading to a threshold behavior at D z T S=1 K for the splitting of the non-linear conductance (very similar to the Zeeman effect in S = 1/2 quantum dots). This effect is quite clearly observed in the data of Parks et al [19].…”

“…Because of the near-equilibrium approximation for the T-matrix, we cannot pretend to a full quantitative agreement with the experimental data, as was however achieved for the Kondo related features at zero bias [18]. However, the precise determination of the many parameters in the two-orbital Anderson model (2) remains a very challenging task, so that we can only hope to capture the qualitative details of the experiment.…”

“…Kondo physics has been widely reported in a variety of quantum dot systems, based on semiconducting heterostructures [9,10], carbon nanotubes [11] and molecular devices [12,13,34,18,14], showing the great universality of this phenomenon. Usually the Kondo effect is best observed for odd charge quantum dots, because the formation of a net spin S = 1/2 is always guaranteed in that case (for even charge dots, the ground state turns out often to be a non-magnetic singlet).…”

“…Interestingly, this situation gives rise to both underscreening physics [17,18] and an unscreening singlettriplet quantum phase transition (QPT). In that case, a zero-temperature phase transition can take place between a non-magnetic singlet state and a partially compensated spin S = 1 (giving an remanent spin S = 1/2 in the ground state).…”

Application of theS=1underscreened Anderson lattice model to Kondo uranium and neptunium compounds

“…27 Very recently, the underscreened impurity problem has been widely discussed in relation with experiments performed on quantum dots coupled to ferromagnetic leads, 28 and in molecular quantum dots (so called molecular transistors). 29 In a concentrated Kondo system, these reduced effective spins S eff = S − n/2 interact ferro-or antiferromagnetically through RKKY exchange interaction, leading to magnetic ordering of the reduced moments. Thus coexistence of magnetic ordering and Kondo effect is expected to occur more easily in the underscreened case than in the standard S = 1/2 Kondo lattice.…”