Stability and magnetism of infinite atomic chains

Jaime Ferrer

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

ACKNOWLEDGMENTS

DISCUSSIONS SIESTA team

C. Untiedt AlicanteJ. J. Palacios Alicante

A. Vega ValladolidF. Flores Madrid

C. J. Lambert Lancaster S. Sanvito Dublin

P. Major BudapestJ. Cserti BudapestS. Sirichantaropass Lancaster

L. Fernández-Seivane - Oviedo

V. M. García-Suárez - Lancaster

Infinite Atomic Chains

Conductance oscillations in atomic chains - The experiments

R. H. Smit et al. PRL 87, 266102 (2001); 91, 076805 (2003)

MotivationInfinite Atomic Chains

The SMEAGOL method for spin- and molecular electronics

A. RochaS. Sanvito

S pin and

M olecular

E lectronics in

A tomically

G enerated

O rbital

L andscapes

S. BaileyC. Lambert

V. García-Suárez J. Ferrer

PRB 73, 085414 (06) http://www.smeagol.tcd.ie

Infinite Atomic Chains Motivation

Stability and conductance of infinite Pt chains

Zigzag vs linear chainsSame bond distance d = 2.38 ÅAngle with z-axis = 25º

Conductance of zigzag chains as function of dz

Energy of zigzag and linear chains as function of dz

dz

dz

Infinite Atomic Chains Motivation

García-Suárez et al. PRL 95, 256804 (2005)

For Gold chains, see Sánchez-Portal, PRL 83 (99)

Stability of finite length Pt chains attached to electrodes

Atomic configuration of the constriction1-, 2- and 4- atom chainsFull Molecular Dynamics relaxation for fixed dz

Cohesion energy of relaxed chains as function of dz2-, 3-, 4- and 5- atoms chains

Infinite Atomic Chains Motivation

García-Suárez et al. PRL 95, 256804 (2005)

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 dz

Infinite Atomic Chains MotivationMotivation

García-Suárez et al. PRL 95, 256804 (2005)

Zigzag versus linear chains: maybe Spin-Orbit interaction?

Infinite Atomic Chains MotivationMotivation

Spin-Orbit hamiltonian

TheoryExperiments

SLrV=H

S>L<rVE

Magnetic anisotropy

>S<LrVE

Chain stiffnessFrustration

Infinite Atomic Chains Simulations set-up

dz

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

HgAuPtIrOsReWTaHfLa

CdAgPdRhRuTeMoNbZrY

ZnCuNiCoFeMnCrVTiSc

Al, Pb

Infinite Atomic Chains The case of Ir & Pt

Ir Pt

Zigzag

Ladder

Zigzag

Ladder

Linear chains Delin & Tossati, PRB 68 (2003)

Infinite Atomic Chains Stability 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)

T =∂ E∂ d z

Zigzag minimum exists if T becomes negative

Infinite Atomic Chains Stability 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

Infinite Atomic Chains Stability of atomic chains

Importance of Spin polarization & Spin-Orbit interaction for the stability

Infinite Atomic Chains Stability 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 nanowireRHM Smit Thesis manuscript, Leiden (2003)

Infinite Atomic Chains Stability of atomic chains

Elements that make chains – experimental evidence

From quantum point contacts to monatomic chains: fabrication and characterization of the ultimate nanowireRHM 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

Infinite Atomic Chains Stability of atomic chains

Tension of chains of different TM elements

Only Ir, Pt & Au have energy minima

AuPtIr

AgPdRh

CuNiCo

Infinite Atomic Chains Stability 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

Infinite Atomic Chains Magnetic anisotropies

Magnetism & magnetic anisotropies

Magnetism (& Spin-Orbit effects) in gold are negligible

Infinite Atomic Chains Magnetic anisotropies

Magnetism of Os

W displays similar behavior

Infinite Atomic Chains Summary

Summary

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.