1) Researchers controllably stretched individual spin-1 molecules and measured current flow, demonstrating mechanical control over the molecule's spin states by modifying symmetry. 2) Conductance measurements on unstretched molecules exhibited scaling consistent with an underscreened Kondo effect characteristic of spin-1 systems. 3) Magnetic field measurements on stretched molecules showed the presence of spin anisotropy, with the evolution of Kondo peaks under perpendicular and parallel fields reflecting the spin states' dependence on field angle and strength relative to the zero-field splitting.

1. 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.

2. Influence of symmetry on electronic states
Distortion from octahedral symmetry and spin-
orbit coupling leads to a zero-field splitting D.
Co(tpy-SH)2
1+ 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)

3. 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.

4. 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

5. 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

6. Predicted G(T ) for a spin coupled to one screening channel
NRG calculations by Theo Costi
Also 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 S
requires coupling to 2S screening channels.
For < 2S screening channels: underscreened
Kondo regime.
G (T ) for an underscreened system shows a
very slow approach to saturation for T < TK.
Empirical fitting function:

7. Underscreened S = 1 Kondo scaling for Co(TpySH)2
1+
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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.