Finnish project leader: Kalevi Kokko Department of Physics and Astronomy University of Turku

German project leader: Wolfram Hergert Department of Physics Martin-Luther University

Short-range order effects in late transition metal alloys 1. Background Short-range order (SRO) effects, although important in many systems, have been often overlooked since the proper treatment of them has been usually a too difficult task. The properties of the materials depend directly on the details of the chemical composition, structure, defects, i.e. issues related to short-range order of the system. In alloys the atomic-SRO is a kind of pre-state of ordering to which the disordered alloy is tending at elevated temperatures. First-principles calculations based upon KKR-CPA and mean-field thermodynamics have been successful in predicting SRO effects and indentifying the background electronic ordering mechanism. [O10] However, many effects related to SRO have been remained hidden due to the lack of proper theoretical treatments of SRO in realistic systems. Using computational simulations with thermodynamics techniques it was shown recently that the SRO effects are significant in Fe-Cr by doubling the solubility limit of Cr at room temperatures. [O11] Multicomponent metallic systems and their surfaces play an important role in modern technology (catalysts, stainless steel products, etc.) Many of them first crystallize into a solid solution and order or phase separate if temperature is lowered. The theoretical description of such processes on an ab initio basis, i.e. the description of statistical mechanics and many-electron problem of the system on equal footing is still under development. The nonlocal CPA plays an important role [G7, G8, O4-O8] in this context. Short-range order effects are also important in magnetic systems (formation of the moment in the disordered local moment (DLM) state of Ni). The proposed project fits well to the main research lines of both groups. The Finnish and German groups have been working for a long time with first principles and semiempirical computational methods and the previous collaboration includes several investigations on spectroscopic and thermodynamic properties of solids. [FG1-FG4] 2. Objectives The main objectives of the project are to clarify if the anomalies found in the Ag-Pd alloy system are sensitive to the SRO, to study the influence of SRO to segregation effects and to extend the research to magnetic alloys. 3. Research methods Ab initio electronic structure codes are the main methods to be used in the proposed project. The Finnish group will mainly use the exact muffin-tin orbital (EMTO) method linked with thermophysical and statistical physics models. The main tool in the German

side will be the KKR method. The KKR-CPA method was used in our investigations of the last years mainly to study strongly correlated systems. [G1-G5] But also metallic systems have been considered continously (cf. [G6]). The nonlocal coherent potential approximation (NLCPA) is included in the code and can be applied to the problems of the project. [G7,G8] 4. Implementation A combination of ab initio electronic structure methods and statistical mechanics will be used. The calculations of the Finnish group are based on the EMTO [O9] method, one of the world leading tools in alloy theory. The German group will use the KorringaKohn-Rostoker (KKR) [G1-G5] multiple scattering approach. The coherent potential approximation (CPA), a single-site mean field approach to treat disorder, is implemented in both methods. The KKR method contains also the nonlocal CPA (NLCPA) [G7, G8, O4-O8] method. NLCPA goes beyond the single-site mean field level. Nonlocal potential fluctuations due to the disorder of the environment of each site are systematically taken into account. In the spirit of CPA the NLCPA requires that the excess scattering of an impurity cluster of real potentials embedded in the effective medium will be zero in average. It becomes exact in the limit of large cluster sizes and recovers the KKR-CPA for a single-site cluster. The statistical analysis is based on the total energy calculations of both methods. Activities 1. The investigations will be based on a multi-code approach. Therefore it will be indispensable to start with a careful comparison of the results of EMTO-CPA and KKR-CPA on the same system. We will compare the basic results of electronic structure calculations for the Ag-Pd and Cu-Pd alloy systems first. 2. We have to clarify, if the anomalies found in the Ag-Pd alloy system by means of the EMTO-CPA method can be reproduced by the KKR-CPA approach. In a next step we will introduce models of SRO to study, if the anomalies are sensitive to the SRO. 3. The investigations will be extended to the surfaces of the alloys to study the influence of SRO to segregation effects. For such calculations the NLCPA approach has to be extended to surfaces and interfaces. Code development is necessary for this subject. 4. In a next step magnetic alloys will be considered. 5. The combination of EMTO with a version of nonlocal CPA will be one ambitious goal of the Finnish group. Comparison with results from NLCPA-KKR will be very important during this development.

Plan for the visits of the researchers Dates of the Name Title Purpose of the visit Days visit 01/09/09 Hergert, Wolfram Prof. Test calculations Ag-Pd 14 Dr. 01/09/09 Ernst, Arthur PD Dr. Code development, Cu-Pd and 8 Ag-Pd calc. 01/10/09 Fischer, Guntram Doktor Short-range order and effective 8 and pair interactions 01/04/10 N.N. Diplom Alloy calculations 20 and 01/09/10 Hergert, Wolfram Prof. Discussion, publication 14 Dr. 01/03/11 Ernst, Arthur PD Dr. Code development, publication 8

Dates of the Name visit 01/12/09 Kokko, Kalevi

Title Doc.

Purpose of the visit Calculations for Ag-Pd, Cu-Pd and analysis of the results

Days 7

01/12/09

Nurmi, Eero

M.Sc. Development of the EMTO code to include short range order effects

14

01/05/10

Kokko, Kalevi

Doc.

Improving the statistical model of the thermodynamics of binary alloys

14

01/05/10

N.N.

M.Sc. Calculation of elastic properties of late transition metal alloys

14

01/11/10

Eero Nurmi

M.Sc. Calculations of mechanical properties of transition metal binary alloys with non-local EMTO-CPA

14

01/01/11

N.N.

M.Sc. Investigation of short range order effects on electronic and magnetic properties of transition metal alloys

01/04/11

Eero Nurmi

M.Sc. Analysis of the elastic properties and phase diagrams of transition metal alloys

7

14

5. Researchers and research environment The Finnish group includes three members: Doc. K. Kokko, M.Sc. E. Nurmi and a graduate student joining in the group during the year 2009. The German group includes four members: Prof. W. Hergert, PD Dr A. Ernst, post graduate student G. Fischer and a student joining to the group during the projet. The senior members of the group have a long experience on the computational materials physics and they have been leading several research projects, also joint projects in collaboration, successfully. The junior members of the groups concentrate on the development of the method and on performing the actual calculations under the supervision of the senior members of the groups. The complementarity of the contributions of the partners results mainly from the different methods used in the investigations. While the group of Dr. Kokko will use the EMTO-CPA method, the calculations of the German group are based on the KKR method. The functionality of the KKR code allows investigations beyond the CPA level. The long record of publications of the Finnish group in nonmagnetic alloy problems, bulk systems as well as surface systems have been considered (cf. [F1-F5] as a selection), serves as a solid ground for the ab initio calculation of physical properties of alloys and their surfaces. The methods of the Finnish group are restricted to the CPA mean field approach. The NLCPA in the KKR method can be used to study short-range order effects on the physical properties of the alloys, already studied by the Finnish group. The German group has great experience in studying magnetic systems. The combined expertise of both groups serve as an excellent basis to study magnetic alloys. A multi-code approach will be used to study new alloy systems. 6. Researcher training and and research career The junior members of the research groups have a benefit of being under supervision of more experienced researchers from both Finnish and German groups. The proposed project is also a part of the Ph.D. theses work of the graduate students of the groups.

7. Expected research results The project is a basic research project in theoretical solid state physics. Therefore the results will not have a direct industrial impact. Nevertheless, we hope that our theoretical investigations will stimulate new experimental work, if new interesting effects have to be proofed experimentally.

List of relevant publications of the German group: [G1]I.D. Hughes, M. Däne, A. Ernst, W. Hergert, M. Lüders, J.B. Staunton, Z. Szotek, and W.M. Temmerman, Onset of magnetic order in strongly-correlated systems from ab initio electronic structure calculations: applications to transition metal oxides, New J. Phys. 10, 063010 (2008) [G2]I.D. Hughes, M. Däne, A. Ernst, W. Hergert, M. Lüders, J. Poulter, J.B. Staunton, A. Svane, Z. Szotek, and W.M. Temmerman, Lanthanide contraction and magnetism in the

heavy rare earth elements, Nature 446, 650 (2007) [G3]S. Ostanin, A. Ernst, L.M. Sandratskii, P. Bruno, M. Däne, I.D. Hughes, J.B. Staunton, W. Hergert, I. Mertig, J. Kudrnovsky, Mn-Stabilized Zirconia: From Imitation diamonds to a New Potential High-TC Ferromangnetic Spintronics Material, Phys. Rev. Lett. 98,06101 (2007) [G4]M. Lüders, A. Ernst, M. Däne, Z. Szotek, A. Svane, D. Ködderitzsch, W. Hergert, B.L. Györffy, and W.M. Temmerman, Self-interaction correction in multiple scattering theory, Phys. Rev. B 71, 205109 (2005) [G5]M. Däne, M. Lüders, A. Ernst, D. Ködderitzsch, W.M. Temmerman, Z. Szotek, W. Hergert, Self-interaction correction in multiple scattering theory: application to transition metal oxides, J. Phys.: Condens. Matter 21, 045604 (2009) [G6]C. L. Gao, A. Ernst, G. Fischer, W. Hergert, P. Bruno, W. Wulfhekel, and J. Kirschner, Spin Wave Dispersion on Nanometer Scale, Phys. Rev. Lett. 101, 167201 (2008) [G7]D. Ködderitzsch, H. Ebert, D.A. Rowlands, and A. Ernst, Relativistic formulation of the Korringa–Kohn–Rostoker nonlocal coherent-potential approximation, New J. Phys. 9, 81 (2007) [G8]D. A. Rowlands, A. Ernst, B. L. Györffy, and J. B. Staunton, Density functional theory for disordered alloys with short-range order: Systematic inclusion of charge correlation effects, Phys. Rev. B 73, 165122 (2006) Some recent relevant publications of the Finnish group: [F1]E.K. Delczeg-Czirjak, L. Delczeg, M. Ropo, K. Kokko, M.P.J. Punkkinen, B. Johansson, and L. Vitos, Ab initio study of the elastic anomalies in Pd-Ag alloys, submitted to Phys. Rev. B [F2]L. Vitos, M. Ropo, K. Kokko, M. P. J. Punkkinen, J. Kollár, and B. Johansson, Exeptional surface stability in late transition metal alloys driven by lattice strain, Phys. Rev. B 77, 121401 (2008) [F3]M. Ropo, K. Kokko, L. Vitos, and J. Kollár, Electronic structure calculations: Segregation at the PdAg(111) surface, Phys. Rev. B 71, 045411 (2005) [F4]K. Kokko, M. Ropo, M.P.J. Punkkinen, P. Laukkanen, M. Alatalo, L. Vitos, J. Kollár, Surface core-level shift of Pd at the AgcPd1-c (111) surface, Surf. Sci 601, 5419 (2007) [F5]M. Ropo, K. Kokko, L. Vitos, and J. Kollár, B. Johansson, The chemical potential in surface segregation calculations:AgPd alloys, Surf. Sci. 600, 904 (206)

Selected publications from previous Finnish-German collaboration [FG1]Chr. Heiliger, F. Heyroth, F. Syrowatka, H. S. Leipner, I. Maznichenko, K. Kokko, W. Hergert, and I. Mertig, Orientation-dependent electron-enery-loss spectroscopy of TiO2: A comparison of theory and experiment, Phys. Rev. B 73, 045129 (2006) [FG2]K. Kokko, V. Kulmala, J. A. Leiro, and W. Hergert, Resonant inelastic x-ray scattering spectra of magnesium diboride, Phys. Rev. B 68, 052503 (2003) [FG3]D. I. Bazhanov, W. Hergert, V. S. Stepanyuk, A. A. Katsnelson, P. Rennert, K. Kokko, and C. Demangeat, One-dimensional magnetism of Rh chains on the Ag(001) surface, Phys. Rev. B 62, 6415 (2000) [FG4]K. Kokko, R. Laihia, M. Alatalo, P. T. Salo, M. P. Punkkinen, I. J. Väyrynen, W. Hergert, and D. Ködderitzsch, From x-ray-absorption near-edge structures to the d-hole

population in Pd-Ag alloys, Phys. Rev. B 60, 4659 (1999) Other investigations to the subject: [O1]A.V. Ruban, S. I. Simak, P. A. Korzhavyi, and B. Johansson, Theoretical investigation of bulk ordering and surface segregation in Ag-Pd and other isoelectronic alloys, Phys. Rev. B 75, 054113 (2007) [O2]E. Bruno, B. Ginatempo, and E. S. Giuliano, Fermi surfaces and electronic topological transitions in metallic random alloys. I. The influence of equilibrium properties, Phys. Rev. B 52, 14544 (1995) [O3]E. Bruno, B. Ginatempo, and E. S. Giuliano, Fermi surfaces and electronic topological transitions in metallic random alloys. II AgcPd1-c , Phys. Rev. B 52, 14557 (1995) [O4]D. A. Rowlands, X.-G. Zhang, and A. Gonis, Reformulation of the nonlocal coherentpotential approximation as a unique reciprocal-space theory of disorder, Phys. Rev. B 78, 115119 (2008) [O5]P. R. Tulip, J. B. Staunton, D. A. Rowlands, B. L. Györffy, E. Bruno, and B. Ginatempo, Nonsite diagonal properties from the Korringa-Kohn-Rostoker nonlocal coherentpotential approximation, Phys. Rev. B 73, 205109 (2006) [O6]D. A. Rowlands, A. Ernst, B. L. Györffy, and J. B. Staunton, Density functional theory for disordered alloys with short-range order: systematic inclusion of charge-correlation effects, Phys. Rev. B 73, 165122 (2006) [O7] D. A. Rowlands, J. B. Staunton, and B. L. Györffy, Korringa-Kohn-Rostoker nonlocal coherent-potential approximation, Phys. Rev. B 67, 115109 (2003) [O8]D. A. Rowlands, J. B. Staunton, B. L. Györffy, E. Bruno, and B. Ginatempo, Effects of short-range order on the electronic structure of disordered metallic systems, Phys. Rev. B 72, 045101 (2005) [O9]L. Vitos, Total-energy method based on the exact muffin-tin orbitals theory, Phys. Rev. B 64, 014107 (2001) [O10]J.B. Staunton, D.D. Johnson, F.J. Pinski, Theory of compositional and magnetic correlations in alloys: Interpretation of a diffuse neutron-scattering experiment on an iron-vanadium single crystal, Phys. Rev. Lett. 65, 1259 (1990) [O11]G. Bonny, P. Erhardt, A. Caro, R.C. Pasianot, L. Malerba, and M. Caro, The influence of short range order on the thermodynamics of Fe-Cr alloys, Modelling Simul. Mater. Sci. Eng. 17, 025006 (2009)