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 MavropoulosIFF, 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)

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)

Appetizer: Adatoms and small clusters transition from atomic to bulk behaviour

I. Cabria et al., PRB 65, 054414 (2002)

Spin and orbital moments: 3d & 4d on Ag(001)

Orbital moments of Co clusters on Pt

P. Gambardella et al., Science 300, 1130 (2003)

Ingredients for the study of clusters

Magnetic clusterson surfaces

Surface electronic structure

Real-space embedding method

Charge and spin density

Non-collinear magnetism

Transport properties (STM)

Static and dynamic correlations

Spin and Orbital moments

Lattice relaxations







Static correlations

Dynamic correlations



?competinginteractions







Static correlations




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.

KKR Green-function method

G(E)ΔV(E)G(E)GG(E) 00

Green function G connected to G0

of a reference system via Dyson eq.:

KKR Representation of Green function:

',

''

'

)()()(

)()(

LL

nL

nn'LL'

nL

Lnn

nL

nL

RER

RHE-i

E

rr

rr

rRr,R nn

G

);G(

Method suitable for:•Bulk calculations, Interfaces, Surfaces •Impurity clusters on surfaces•Magnetism in clusters (non-collinear)•Disordered systems (CPA)•Electronic transport: STM etc.

Accurate calculation of:•Charges & magn. moments•Total energies•Forces on atoms•Lattice relaxations

P.H. Dederichs and R. Zeller, Jülich 1979-2004

Adatoms: FM vs. AFAtoms on Fe(001) and on Fe/Cu(001)

Stepanyuk et al, PRB 61, 2356 (2000)

Alexander-Anderson model

Adatoms on ferromagnetic surfaces

Nonas et al., PRB 57, 84 (1998)Stepanyuk et al, PRB 61, 2356 (2000)

3d and 4d adatoms on Fe (001)

3d on Fe

antiferro

ferro

•Early transition elements align antiferromagnetically

•Late transition elements align ferromagnetically

Interpretation via Alexander-Anderson model

3d adatoms on Ni (001)

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 behaviorSimilar on Ni(111) and Cu

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

Comparison: Fe clusters vs. Co clusters


?

Driving mechanism: magnetic frustration

Example: Mn dimer on Ni(001)

Collinear result (frustrated):Mn-Ni: ferro, Mn-Mn: antiferro

Competing interactions

Non-collinear resultθ=72.5º

E.g.:•Trimer on (111) of paramagnetic metal•Dimer/trimer on ferromagnetic surface

Dimers on Ni(001)-collinear vs. noncollinearCr 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)

Noncollinear: (Cr)=94.2,

Collinear result:Frustrated state

Non-collinear dimers and trimers• Fit to Heisenberg model: how good is it?

J is fit by collinear total energy calculationsof ferro- and antiferro allignment

Example: Mn trimer on Ni(001)Side view Top view

Plan: bigger clusters, include relaxations, relate to XMCD.

Mn-Ni: ferro, Mn-Mn: antiferro

Mn 1,Mn 3 Mn 2 Ni 1,2,3,5 Ni 4 Ni 6,7 Ni 8

θ(degrees) 22 151 6 7 4 11

φ(degrees) 180 0 180 0 0 0

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

Antiferro

Ferro

Antiferroc2×2

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 tosatisfy Friedel sum rule


Outlook:•Extend the theory to LDA•Impurity Green function from KKR•Describe Kondo behaviour of impurities in bulk and on surfaces

The Logan approximation captures low and high-energy characteristics:•Kondo-peak•Scaling behaviour•Correction to Hubbard bands

LDA GF → new GF: G(Kondo) = G(LDA) + G(LDA) Σ G(Kondo)

Scaling with U Scaling with 1/N

Conclusion: Realistic, material-specific description


Surface electronic structure + lattice relaxations




Static correlations




OK

OK

OK

OK

OK

OK (LDA+U)

OK

On the way

Mavropoulos et al., PRB(2004)

(to be published)

Non-collinear Green function method

GG

GG

G

G

0

0

0

0 GIm1

GF for spin up & spin down becomes a matrix in spin space

Density for spin up & spin down becomes density matrix

STM results

Papanikolaou et al, PRB 62, 11118 (2000)

Caculations with Tersoff-Hamann model


Outlook:•Extend the theory to LDA•Impurity Green function from KKR•Describe Kondo behaviour of impurities in bulk and on surfaces

The Logan approximation captures low and high-energy characteristics:•Kondo-peak•Scaling behaviour•Correction to Hubbard bands

LDA GF → new GF: G(Kondo) = G(LDA) + G(LDA) Σ G(Kondo)

Documents

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