# Schools

## KKR Green functions for calculations of spectroscopic, transport and magnetic properties

### Organisers

- Martin Lueders
*(Daresbury Laboratory, United Kingdom)* - Julie Staunton
*(University of Warwick, United Kingdom)* - Jan Minar
*(Dept. Chemie, Phys. Chemie, Ludwig Maximilians University, Munich, Germany)*

### Supports

### Description

Over the past couple of decades First-Principles-Calculations have become one of the key research methodologies in condensed matter physics and materials science. Density-functional theory computational codes enable calculations of many properties, which can be either compared to experiment or guide the development of simpler phenomenological models. In this context codes built around the computation of the Kohn-Sham Green Function, in particular those based on the KKR method, give immediate access to spectroscopic properties and careful scrutiny of Fermi surfaces, provide the ideal components for evaluation of transport and response functions and so on.

Green function-KKR codes are especially useful for the study of electron systems with narrow electron bands of d- or f-like character, arising from a sharp scattering resonance of a transition metal or rare earth atom. A host of important new physical phenomena occur when such narrow bands lie near to the Fermi level, including itinerant magnetism, local moment formation, intermediate valence, Mott-Hubbard metal insulator phase transitions and Kondo-like physics and related effects. Treatments of strong electron correlations beyond standard DFT are crucial and new models are being developed. Due to its all-electron nature and often fully relativistic implementation, the KKR method is particularly well suited to study such narrow d- or f-band materials. The experimental study of these materials is one of the largest and most important areas of condensed matter physics, in which major investments have been made in experimental facilities world-wide such as the ESRF and SNS at Grenoble, ISIS and Diamond facilities at RAL, High Field Magnet facilities in Toulouse, and in crystal growth and low temperature experimental facilities at many major European universities. With such a large investment in experimental research in the field, it is crucial to provide training for both experimentalists and theoreticians in the use of computational codes, which are powerful enough to access the unique and varied physical properties of narrow d- or f-band electron materials. Green function-KKR codes are very well suited for this purpose owing to the following specific features:

• The KKR multiple scattering (MS) approach which deals with narrow bands most effectively by associating them with sharp scattering resonances, simplifying the treatment of narrow bands.

• By treating separately (i) the scattering at each atomic site, and (ii) the sum of scattering sites over the entire material, the KKR method, unlike other methodologies, can treat disorder such as that occurring in alloys.

• This same methodology implies that KKR theories can be adapted to describe finite temperature fluctuations and hence provides a route to first-principles treatments of phase transitions described by Landau Theories of symmetry breaking.

• With the use of the Dyson equation for the Green function, the KKR can treat aperiodic perturbations in solids which circumvents computationally costly and approximate supercell approaches (e.g. impurities, disordered alloys, clusters on surfaces, interfaces and truly semi infinite systems).

• Unlike other electronic structure methods which focus on electron wave functions and total energies, MS-based methods yield directly the electron Green’s function and are therefore ideal for calculating spectroscopies, response functions and transport phenomena, such as electrical and spin conductivities.

• In its constant energy (E) mode the KKR is the most efficient band structure method to describe Fermi surfaces. Therefore it directly provides one of the most useful quantities, which experimentalists want to study.

• The KKR method in its fully relativistic implementation has no problems dealing with even the heaviest elements and their compounds, since it is formulated using the Dirac equation for the electrons, in which all spin-orbit effects are fully incorporated.

• It is an all-electron method, so that both core and valence electrons are treated fully, eliminating the need to develop ‘good’ pseudopotentials.

• Electron-electron interaction effects beyond the usual Local Spin Density Approximation (LSDA) can be treated with a variety of methods and new approximations developed.

We propose therefore to organise an intensive 4-day tutorial on Green Function-KKR methods open to both condensed matter theorists and experimentalists to provide training on how to carry out calculations useful for disparate research needs.

A few recent pertinent applications of the Green function-KKR method have been reviewed recently [1] and are also illustrated by the following additional novel publications including calculations of (i) electronic structure of topological insulators [2], (ii) magnetic interactions to determine the magnetic structure of ultrathin magnets [3], magnetic excitations [4] and Gilbert damping in ferromagnets [5], (iii) transport calculations and Berry phase [6] and (iv) angle-resolved photoemission spectra [7]. Moreover recently the dynamical mean-field theory (DMFT) for strong electron correlations has been successfully implemented into the KKR [8]. Furthermore, its formal framework makes the KKR the method of choice to describe nanoclusters, surfaces and interfaces, defects and impurities [9].

Program

Monday,

16:00 - 18:00 Registration

Tuesday,

08:00 - 09:00 Registration

09:00 - 09:30 J. Minar Welcome + Introduction

09:30 - 10.30 M. Lueders DFT

10:30 - 12:00 H. Ebert SPR-KKR package and xband

12:00 - 13:30 Lunch break

13:30 - 15:30 Computer session

15:30 - 16:00 Coffee break

16:00 - 16:30 Poster flash presentations

16:30 - 19:00 Poster session

Wednesday,

09:00 - 10:00 P. Dederichs The KKR as a Green's function method

10:00 - 11.00 D. Koedderitzsch Transport

11:00 - 12:00 J. Staunton Magnetic Interactions

12:00 - 13:30 Lunch break

13:30 - 15:30 Computer session

15:30 - 16:00 Coffee break

16:00 - 18:00 Computer session

19:00 - Conference Dinner

Thursday,

09:00 - 10:00 R Zeller KKR and massively parallel computing

10:00 - 11:00 S. Lounis Novel Applications 1 – Magnetic nanostructures

11:00 - 12.00 J. Minar KKR+DMFT/Spectroscopy

12:00 - 13:30 Lunch break

13:30 - 15:30 Computer session

15:30 - 16:00 Coffee break

16:00 - 18:00 Computer session

Friday,

09:00 - 10:00 A. Ernst Novel Applications 2 - Topological Insulators

10:00 - 10:30 Coffee Break

10:30 - 12:00 Computer Session

12:00 - 13:30 Lunch break

13:30 - 15:00 Computer session

15:00 - 15:30 Coffee break

15:30 - 16:30 Roundup and Discussions

16:30 Julie Staunton Closing Remarks

### References

[1] H Ebert and D Koedderitzsch and J Minar: Calculating condensed matter properties using the KKR-Green's function method-recent developments and applications, Rep. Prog. Phys. 74, 096501 (2011)

[2] Eremeev, S. V., Landolt, G., Menshchikova, T. V., Slomski, B., Koroteev, Y. M., Aliev, Z. S., Babanly, M. B., Henk, J., Ernst, A., Patthey, L., Eich, A., Khajetoorians, A. A., Hagemeister, J., Pietzsch, O., Wiebe, J., Wiesendanger, R., Echenique, P. M., Tsirkin, S. S., Amiraslanov, I. R., Dil, J. H., Chulkov, E. V.: Atom-specific spin mapping and buried topological states in a homologous series of topological insulators, Nature Communications 3, (6), pp 635/1-7 (2012);

A. Nuber, J. Braun, F. Forster, J. Minár, F. Reinert, and H. Ebert: Surface versus bulk contributions to the Rashba splitting in surface systems, Phys. Rev. B 83, 165401 (2011).

[3] I. D. Hughes, M. Däne, A. Ernst, W. Hergert, M. Lüders, J. Poulter, J. B. Staunton, A. Svane, Z. Szotek and W. M. Temmerman, Lanthanie contraction and magnetism in the heavy rare earth elements, Nature, 446, 650-653 (5 April 2007);

M. dos Santos Dias, J. B. Staunton, A. Deak and L.Szunyogh, Anisotropic spin-spin correlations in Mn(1)/X(111) (X = Pd, Pt, Ag, and Au), Physical Review B 83, 054435, (2011).

[4] Sandratskii, L. M., Buczek, P.: Lifetimes and chirality of spin waves in antiferromagnetic and ferromagnetic FeRh from the perspective of time-dependent density functional theory, Physical Review B 85, (2), pp 020406(R)/1-4 (2012);

Buczek, P., Ernst, A., Sandratskii, L. M.: Interface electronic complexes and Landau damping of magnons in ultrathin magnets

Physical Review Letters 106, (15), pp 157204/1-4 (2011);

N. H. Long, M. Ogura, H. Akai, Phys. Rev. B 85, 224437 (2012)

[5] H. Ebert, S. Mankovsky, D. Ködderitzsch, and P. J. Kelly: Ab-initio calculation of the Gilbert Damping Parameter via the Linear Response Formalism, Phys. Rev. Lett. 107, 066603 (2011).

[6] Lowitzer, S., Koedderitzsch, D., Ebert, H.:Coherent Description of the Intrinsic and Extrinsic Anomalous Hall Effect in Disordered Alloys on an Ab Initio Level, Phys. Rev. Lett. 105, 266604 (2010);

Lowitzer, S., Gradhand, M., Koedderitzsch, D., Fedorov, D. V., Mertig, I., Ebert, H.:Extrinsic and intrinsic contributions to the spin Hall effect of alloys, Physical Review Letters 106, (5), pp 056601/1-4 (2011);

Gradhand, M., Fedorov, D. V., Pientka, F., Zahn, P., Mertig, I., Gyorffy, B. L.: Calculating the Berry curvature of Bloch electrons using the KKR method Physical Review B 84, (7), pp 075113/1-12 (2011)

[7] Gray, A. X. and Papp, C. and Ueda, S. and Balke, B. and Yamashita, Y. and Plucinski, L. and Minar, J. and Braun, J. and

Ylvisaker, E. R. and Schneider, C. M. and Pickett, W. E. and Ebert, H. and Kobayashi, K. and Fadley, C. S., Probing Bulk Electronic Structure with Hard-X-Ray Angle-Resolved Photoemission: W and GaAs, Nature Materials, 10, 759 (2011)

J. Sanchez-Barriga, J. Braun, J. Minar, I. Di Marco, A. Varykhalov, O. Rader, V. Boni, V. Bellini, F. Manghi, H. Ebert, M. I. Katsnelson, A. I. Lichtenstein, O. Eriksson, W. Eberhardt, H. A. Dürr, and J. Fink: Effects of spin-dependent quasiparticle renormalization in Fe, Co, and Ni photoemission spectra:An experimental and theoretical study, Phys. Rev. B 85, 205109 (2012).

[8] Jan Minar: Correlation effects in transition metals and their alloys studied using the fully self-consistent KKR-based LSDA + DMFT scheme, J. Phys. Cond. Matt.: Topical Review 23, 253201 (2011).

[9] V. Sessi, K. Kuhnke, J. Zhang, J. Honolka, K. Kern, A. Enders, P. Bencok, S. Bornemann, J. Minár, and H. Ebert,

Cobalt nanoclusters on metal-supported Xe monolayers: Influence of the substrate on cluster formation kinetics and magnetism,

Phys. Rev. B 81, 195403 (2010);

A. Khajetoorians, J. Wiebe, B. Chilian, S. Lounis, S. Blügel, R. Wiesendanger: Atom-by-atom engineering and magnetometry of tailored nanomagnets, Nature Physics 8, 497503 (2012)