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Complex magnetism of small clusters on surfaces An approach from first principles

Complex magnetism of small clusters on surfaces An approach from first principles. Phivos Mavropoulos IFF, Forschungszentrum J ü lich Collaboration: S. Lounis, H. H öhler, R. Zeller, S. Bl ü gel, P.H. Dederichs ( FZ J ülich ) J. Kroha ( Universität Bonn )

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Complex magnetism of small clusters on surfaces An approach from first principles

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  1. Complex magnetism of small clusters on surfacesAn approach from first principles Phivos Mavropoulos IFF, Forschungszentrum Jülich Collaboration: S. Lounis, H. Höhler, R. Zeller, S. Blügel, P.H. Dederichs (FZ Jülich) J. Kroha (Universität Bonn) V. Popescu, H. Ebert (LMU München) N. Papanikolaou (NCRS “Demokritos”, Athens)

  2. Appetizer: Adatoms and small clusters transition from atomic to bulk behaviour Spin moments: 4d & 5d on Ag(001), shape & size dependence Wildberger et al, PRL 75, 509 (1995)

  3. Appetizer: Adatoms and small clusters transition from atomic to bulk behaviour Orbital moments of Co clusters on Pt P. Gambardella et al., Science 300, 1130 (2003) Spin and orbital moments: 3d & 4d on Ag(001) I. Cabria et al., PRB 65, 054414 (2002)

  4. Ingredients for the study of clusters Surface electronic structure Real-space embedding method Charge and spin density Magnetic clusters on surfaces Spin and Orbital moments Non-collinear magnetism Lattice relaxations Transport properties (STM) Static and dynamic correlations

  5. Ingredients for the study of clusters Surface electronic structure ? competing interactions Real-space embedding method Charge and spin density Magnetic clusters on surfaces Spin and Orbital moments Non-collinear magnetism Transport properties (STM) Static correlations Dynamic correlations

  6. Ingredients for the study of clusters Surface electronic structure Real-space embedding method Charge and spin density Magnetic clusters on surfaces Spin and Orbital moments Non-collinear magnetism Transport properties (STM) Static correlations Dynamic correlations

  7. Calculations from first principles • Density-functional theory • Maps the many-electron problem to effective mean-field problem. • Accurate for ground-state electronic & magnetic properties in bulk, surfaces, interfaces, defects. • Successful for transition metals. • No adjustable parameters. • Designed for ground state, but gives reasonable excitation spectrum in many cases. • Green-function method of Korringa, Kohn and Rostoker (KKR) • Multiple-scattering approach. • Reciprocal and real-space method. • Suitable for impurities & clusters, no supercell needed.

  8. KKR Green-function method Green function G connected to G0 of a reference system via Dyson eq.: KKR Representation of Green function: • Method suitable for: • Bulk calculations, Interfaces,Surfaces • Impurity clusters on surfaces • Magnetism in clusters (non-collinear) • Disordered systems (CPA) • Electronic transport:STMetc. • Accurate calculation of: • Charges & magn. moments • Total energies • Forces on atoms • Lattice relaxations P.H. Dederichs and R. Zeller, Jülich 1979-2004

  9. Adatoms: FM vs. AF Atoms on Fe(001) and on Fe/Cu(001) Alexander-Anderson model Stepanyuk et al, PRB 61, 2356 (2000)

  10. Adatoms on ferromagnetic surfaces 3d adatoms on Ni (001) 3d and 4d adatoms on Fe (001) ferro 3d on Fe antiferro Nonas et al., PRB 57, 84 (1998) Stepanyuk et al, PRB 61, 2356 (2000) • Early transition elements • align antiferromagnetically • Late transition elements • align ferromagnetically Interpretation via Alexander-Anderson model

  11. Fe clusters on Ni(001) Motivation: recent experimental results (Lau et al, PRL 89, 057201 (2002)) • Trend: spin moment as function of: • Cluster size • Coordination of Fe Result: linear behavior Similar on Ni(111) and Cu

  12. Fe clusters on Ni(111), Cu(001), Cu(111)

  13. Comparison: Fe clusters vs. Co clusters

  14. Non-collinear magnetism Driving mechanism: magnetic frustration • E.g.: • Trimer on (111) of paramagnetic metal • Dimer/trimer on ferromagnetic surface ? Example: Mn dimer on Ni(001) Collinear result (frustrated): Mn-Ni: ferro, Mn-Mn: antiferro Competing interactions Non-collinear result θ=72.5º

  15. Dimers on Ni(001)-collinear vs. noncollinear • Cr or Mn first neighbours are AF coupled. → Candidates for frustration • Second & third neighbours are always FM coupled to each other (coupling with substrate prevails). Cr dimer on Ni(001) Collinear result: Frustrated state Noncollinear: (Cr)=94.2, (Ni)=0.3

  16. Non-collinear dimers and trimers J is fit by collinear total energy calculations of ferro- and antiferro allignment • Fit to Heisenberg model: how good is it?

  17. Example: Mn trimer on Ni(001) Top view Side view Mn-Ni: ferro, Mn-Mn: antiferro Plan: bigger clusters, include relaxations, relate to XMCD.

  18. Fe clusters on W(001): c2×2 Antiferromagnetic order (Collaboration with P. Ferriani and S. Heinze. Recent experiment: Kubetzka et al.) Antiferro Ferro Antiferro c2×2

  19. Dynamical correlations: Kondo behaviour Approach based on the theory of Logan [Logan et al., J. Phys: C.M. 10, 2673 (1998)] UHF spin-polarised solution of Anderson model Impurity spin fluctuations within the RPA Construct Self-energy New Green function: Kondo peak emerges at Fermi level Self-consistency to satisfy Friedel sum rule

  20. Dynamical correlations: Kondo behaviour Scaling with 1/N Scaling with U • The Logan approximation • captures low and high-energy • characteristics: • Kondo-peak • Scaling behaviour • Correction to Hubbard bands • Outlook: • Extend the theory to LDA • Impurity Green function from KKR • Describe Kondo behaviour of • impurities in bulk and on surfaces LDA GF → new GF: G(Kondo) = G(LDA) + G(LDA)ΣG(Kondo)

  21. Conclusion:Realistic, material-specific description OK Surface electronic structure + lattice relaxations OK Real-space embedding method OK Charge and spin density Magnetic clusters on surfaces OK Spin and Orbital moments OK Non-collinear magnetism (to be published) OK (LDA+U) Static correlations OK Transport properties (STM) Mavropoulos et al., PRB(2004) On the way Dynamic correlations

  22. Non-collinear Green function method GF for spin up & spin down becomes a matrix in spin space Density for spin up & spin down becomes density matrix

  23. STM results Caculations with Tersoff-Hamann model Papanikolaou et al, PRB 62, 11118 (2000)

  24. Dynamical correlations: Kondo behaviour • The Logan approximation • captures low and high-energy • characteristics: • Kondo-peak • Scaling behaviour • Correction to Hubbard bands • Outlook: • Extend the theory to LDA • Impurity Green function from KKR • Describe Kondo behaviour of • impurities in bulk and on surfaces LDA GF → new GF: G(Kondo) = G(LDA) + G(LDA)ΣG(Kondo)

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