Mechanical control of spin states and the underscreened Kondo effect in spin-1 molecules J. J. Parks, A. R. Champagne, T. A. Costi, W. W. Shum, A. N. Pasupathy, E. Neuscamman, S. Flores-Torres, P. S. Cornaglia, A. A. Aligia, C. A. Balseiro, G. K.-L. Chan, H. D. Abruña, and D. C. Ralph

� We controllably stretch individual S = 1 molecules and simultaneously measure current flow through the molecule.

� We can mechanically control the spin states of the molecule, by modification of the molecular symmetry.

� G (T ) for the unstretched molecule exhibits S = 1 underscreened Kondo scaling.

� Magnetic-field measurements demonstrate the presence of spin anisotropy.

Influence of symmetry on electronic states

� Distortion from octahedral symmetry and spin-orbit coupling leads to a zero-field splitting D.

� Co(tpy-SH)21+ complex: octahedrally coordinated.� Attachment to ligands splits the d-orbitals of the free ion.� Ground-state spin for Co1+ : S = 1.

Kondo effect in similar transition-metal complexes:Park group (Harvard), Natelson group (Rice), Hou group (USTC)

Sixty 15 mm x 6 mm chips are fabricated on a thin (200 µm) Si wafer.

Bonding pads are defined by photolithography.

Critical features are defined by e-beam lithography.

Device Fabrication

electromigration

A timed etch is used to suspend the junctions.

Mechanically controllable break junction

� We stretch individual molecules and simultaneously measure their conductance using mechanically controllable break junction devices.

Electrode motion calibration:

Junction stability:

~1 pm variation

The Kondo peak splits with molecular distortion

� A single zero-bias peak evolves into two finite-bias peaks with stretching.

� Implies that the degeneracy required for the Kondo effect is lifted.

Conductance peaks at V = ±D/e due to inelastic tunneling.

Kondo in half-integer spins with anisotropy:Sander Otte, Andreas Heinrich (IBM)

Kondo in molecular magnets (theory):Romeike, Wegewijs, Hofstetter, Schoeller

Predicted G(T ) for a spin coupled to one screening channel

NRG calculations by Theo CostiAlso see: F. Mallet et al., Phys. Rev. Lett. 97, 226804 (2006)Fitting function based on Goldhaber-Gordon form, Phys. Rev. Lett. 81, 5225 (1998)

� Nozières and Blandin (1980): an impurity of spin Srequires coupling to 2S screening channels.

� For < 2S screening channels: underscreenedKondo regime.

� G (T ) for an underscreened system shows a very slow approach to saturation for T < TK.

� Empirical fitting function:

Underscreened S = 1 Kondo scaling for Co(TpySH)21+

� Fits show large deviations from a fully screened Kondo effect, and instead agree with an S = 1 underscreened Kondo effect.

� Seven of ten devices exhibit this behavior.

Scaled data from 7 different devices

Also see: N. Roch et al., Phys. Rev. Lett. 103,197202 (2009)

� Good agreement of scaled data from 7 devices to S = 1 underscreened Kondo scaling.

Magnetic-field dependence of S =1 states for D > 0

� In the presence of anisotropy, the spin states show a strong dependence on the magnetic-field angle and the magnetic-field strength relative to the zero-field splitting D.

� Consider 4 limiting cases:� Perpendicular field, D ~ gμBB : peaks split with curvature.� Perpendicular field, D >> gμBB : weak dependence, negative slope.� D ~ 0 : Linear splitting.� Parallel field, D ~ gμBB : peaks move together linearly.

Evolution of peaks in a perpendicular magnetic field

� For D ~ gμBB , we observe a splitting of the Kondo peaks with measurable curvature.

� For D << gμBB , the Kondo peak positions show small changes, and the negative slope suggests a small misalignment angle and that D > 0.

Evolution of peaks in a parallel magnetic field

� For D ~ 0, we observe a linear splitting of the Kondo peak.� For D ~ gμBB , the peaks shift strongly to smaller |V |,

pass through zero, and split.

Conclusions

� We have demonstrated mechanical control of spin states in a S = 1 transition-metal complex, by modification of the molecular symmetry.

� For the unstretched molecule, the temperature dependence of the conductance exhibits underscreened S = 1 Kondo scaling.

� The magnetic-field evolution of the Kondo peaks reflect the presence of spin anisotropy in the stretched state.