1. Stability and magnetism of infinite atomic chains Jaime Ferrer

2. Three questions that will be addressed: –Which elements may produce atomic chains in MCBJ? –Which chains display magnetic behavior? –What is the anisotropy of magnetic atomic chains? OUTLINE Infinite Atomic Chains –Motivation: zigzag versus linear chains – Set-up of the simulations –The case of Ir and Pt –Stability of Transition Metal atomic chains –Magnetism and magnetic anisotropy of atomic chains

3. ACKNOWLEDGMENTS DISCUSSIONS SIESTA team C. UntiedtAlicante J. J. Palacios Alicante A. VegaValladolid F. Flores Madrid C. J. LambertLancaster S. Sanvito Dublin P. MajorBudapest J. Cserti Budapest S. Sirichantaropass Lancaster L. Fernández-Seivane - Oviedo V. M. García-Suárez - Lancaster Infinite Atomic Chains

4. Conductance oscillations in atomic chains - The experiments R. H. Smit et al. PRL 87, 266102 (2001); 91, 076805 (2003) MotivationInfinite Atomic Chains

5. The SMEAGOL method for spin- and molecular electronics A. Rocha S. Sanvito S pin and M olecular E lectronics in A tomically G enerated O rbital L andscapes S. Bailey C. Lambert V. García-Suárez J. Ferrer PRB 73, 085414 (06) http://www.smeagol.tcd.ie Infinite Atomic ChainsMotivation

6. Stability and conductance of infinite Pt chains Zigzag vs linear chains Same bond distance d = 2.38 Å Angle with z-axis = 25º Conductance of zigzag chains as function of d z Energy of zigzag and linear chains as function of d z dz Infinite Atomic ChainsMotivation García-Suárez et al. PRL 95, 256804 (2005) For Gold chains, see Sánchez-Portal, PRL 83 (99)

7. Stability of finite length Pt chains attached to electrodes Atomic configuration of the constriction 1-, 2- and 4- atom chains Full Molecular Dynamics relaxation for fixed d z Cohesion energy of relaxed chains as function of d z 2-, 3-, 4- and 5- atoms chains Infinite Atomic ChainsMotivation García-Suárez et al. PRL 95, 256804 (2005)

8. Conductance oscillations in zigzag Pt chains Smit et al, PRL (2003) Conductance averaged over distances ~ 1 A about equilibrium distance Conductance of 2, 3, 4 and 5 atoms chains as function of d z Infinite Atomic ChainsMotivation García-Suárez et al. PRL 95, 256804 (2005)

9. Zigzag versus linear chains: maybe Spin-Orbit interaction? Infinite Atomic ChainsMotivation Spin-Orbit hamiltonian TheoryExperiments Magnetic anisotropy Chain stiffness Frustration

10. Infinite Atomic ChainsSimulations set-up dz Simulations performed with SIESTA + Spin-Orbit Soler et al. JPCM (2002) Fernández-Seivane et al. JPCM (2006) Unit cells with 2 atoms to allow for zigzags (tests with 4, 6 atoms for Ir) Full relaxation of forces Hg AuPt Ir Os Re W TaHfLa CdAgPd Rh RuTeMoNbZrY ZnCuNiCoFeMnCrVTiSc Al, Pb

11. Infinite Atomic ChainsThe case of Ir & Pt IrPt Zigzag Ladder Zigzag Ladder Linear chains Delin & Tossati, PRB 68 (2003)

12. Infinite Atomic ChainsStability of atomic chains All chains have the absolute minimum that corresponds to ladders Few chains have the zigzag local minimum ( & its accompanying maximum) Look at the chain tension (slope) Tosatti et al., Science 291 (2001) Zigzag minimum exists if T becomes negative

13. Infinite Atomic ChainsStability of atomic chains Importance of Spin polarization & Spin-Orbit interaction for the stability Paramagnetic simulations tend to overestimate stability Spin-Orbit interaction does not affect much the stability of chains Ir Pt

14. Infinite Atomic ChainsStability of atomic chains Importance of Spin polarization & Spin-Orbit interaction for the stability

15. Infinite Atomic ChainsStability of atomic chains Elements that make chains – experimental evidence Length histograms of chains of different TM elements From quantum point contacts to monatomic chains: fabrication and characterization of the ultimate nanowire RHM Smit Thesis manuscript, Leiden (2003)

16. Infinite Atomic ChainsStability of atomic chains Elements that make chains – experimental evidence From quantum point contacts to monatomic chains: fabrication and characterization of the ultimate nanowire RHM Smit Thesis manuscript, Leiden (2003) Plots of average return lengths Stretch until breaking point (BP) and bring electrodes back to contact (C) Return length = length from BP to C

17. Infinite Atomic ChainsStability of atomic chains Tension of chains of different TM elements Only Ir, Pt & Au have energy minima AuPtIr AgPdRh CuNiCo

18. Infinite Atomic ChainsStability of atomic chains Tension of chains of different TM elements W & Os (and possibly Re) should form atomic chains Hg may make long atomic chains Pb (and Al) should not form chains

19. Infinite Atomic ChainsMagnetic anisotropies Magnetism & magnetic anisotropies Magnetism (& Spin-Orbit effects) in gold are negligible

20. Infinite Atomic ChainsMagnetic anisotropies Magnetism of Os W displays similar behavior

21. Infinite Atomic ChainsSummary Ab-initio simulations of infinite zigzag chains of TM elements Co, Ni, Cu, Rh, Pd, Ag, Al & Pb do not form stable zigzag chains Ir, Pt & Au form stable chains W, Os (and possibly Re) are predicted to form stable chains Hg may form long chains Ir & Pt chains are magnetic and show sizable MAEs W, Os, Au & Hg chains show no magnetic behavior.