Exotic Kondo effect from magnetic trimers

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

We review here some universal aspects of the physics of two-electron molecular transistors in the absence of strong spin-orbit effects. Several recent quantum dot experiments have shown that an electrostatic backgate could be used to control the energy dispersion of magnetic levels. We discuss how the generally asymmetric coupling of the metallic contacts to two different molecular orbitals can indeed lead to a gate-tunable Hund's rule in the presence of singlet and triplet states in the quantum dot. For gate voltages such that the singlet constitutes the (non-magnetic) ground state, one generally observes a suppression of low voltage transport, which can yet be restored in the form of enhanced cotunneling features at finite bias. More interestingly, when the gate voltage is controlled to obtain the triplet configuration, spin S = 1 Kondo anomalies appear at zero bias, with non-Fermi liquid features related to the underscreening of a spin larger than 1/2. Finally, the small bare singlet-triplet splitting in our device allows fine-tuning with the gate between these two magnetic configurations, leading to an unscreening quantum phase transition. This transition occurs between the non-magnetic singlet phase, where a two-stage Kondo effect occurs, and the triplet phase, where the partially compensated (underscreened) moment is akin to a magnetically 'ordered' state. These observations are put theoretically into a consistent global picture by using new numerical renormalization group simulations, tailored to capture sharp finite-voltage cotunneling features within the Coulomb diamonds, together with complementary out-of-equilibrium diagrammatic calculations on the two-orbital Anderson model. This work should shed further light on the complicated puzzle still raised by multi-orbital extensions of the classic Kondo problem.

Transition-metal dimers and physical limits on magnetic anisotropy

Recent advances in nanoscience have raised interest in the minimum bit size required for classical information storage. This bit size is determined by the necessity for bistability with suppressed quantum tunnelling and energy barriers that exceed ambient temperatures. In the case of magnetic information storage, much attention has centred on molecular magnets with bits consisting of about 100 atoms, magnetic uniaxial anisotropy energy barriers of about 50 K and very slow relaxation at low temperatures. Here, we draw attention to the remarkable magnetic properties of some transition-metal dimers, which have energy barriers approaching 500 K with only two atoms. The spin dynamics of these ultrasmall nanomagnets is strongly affected by a Berry phase, which arises from quasi-degeneracies at the electronic highest occupied molecular orbital energy. In a giant-spin approximation, this Berry phase makes the effective reversal barrier thicker.

Exchange interaction between single magnetic adatoms

The magnetic coupling between single Co atoms adsorbed on a copper surface is determined by probing the Kondo resonance using low-temperature scanning tunneling spectroscopy. The Kondo resonance, which is due to magnetic correlation effects between the spin of a magnetic adatom and the conduction electrons of the substrate, is modified in a characteristic way by the coupling of the neighboring adatom spins. Increasing the interatomic distance of a Cobalt dimer from 2.56 to 8.1 A we follow the oscillatory transition from ferromagnetic to antiferromagnetic coupling. Adding a third atom to the antiferromagnetically coupled dimer results in the formation of a collective correlated state.

Effective Kondo model for a trimer on a metallic surface

I consider a Hubbard-Anderson model which describes localized orbitals in three different atoms hybridized both among themselves and with a continuum of extended states. Using a generalized Schrieffer-Wolf transformation, I derive an effective Kondo model for the interaction between the doublet ground state of the isolated trimer and the extended states. For an isoceles trimer with distances a, l, l between the atoms, the Kondo temperature is very small for l<a and has a maximum for finite l>a when a is small. The results agree with experiments for a Cr trimer on Au(111).

Magnetically tunable Kondo-Aharonov-Bohm effect in a triangular quantum dot

The role of discrete orbital symmetry in mesoscopic physics is manifested in a system consisting of three identical quantum dots forming an equilateral triangle. Under a perpendicular magnetic field, this system demonstrates a unique combination of Kondo and Aharonov-Bohm features due to an interplay between continuous [spin-rotation SU(2)] and discrete (permutation C3v) symmetries, as well as U(1) gauge invariance. The conductance as a function of magnetic flux displays sharp enhancement or complete suppression depending on contact setups.

Kondo screening in a magnetically frustrated nanostructure: exact results on a stable non-fermi-liquid phase

Triangular symmetry stabilizes a novel non-Fermi-liquid phase in the three-impurity Kondo model with frustrating antiferromagnetic interactions between half-integer impurity spins. The phase arises without fine-tuning of couplings, and is stable against magnetic fields and particle-hole symmetry breaking. We find a conformal field theory describing this phase, verify it using the numerical renormalization group, and extract various exact, universal low-energy properties. Signatures predicted in electrical transport may be testable in scanning tunneling microscopy or quantum-dot experiments.