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Development and application of Muffin-Tin Orbital based Green’s function techniques to systems with magnetic and chemical disorder
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics . Linköping University, The Institute of Technology.
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Accurate electronic structure calculations are becoming more and more important because of the increasing need for information about systems which are hard to perform experiments on. Databases compiled from theoretical results are also being used more than ever for applications, and the reliability of the theoretical methods are of utmost importance. In this thesis, the present limits on theoretical alloy calculations are investigated and improvements on the methods are presented.

A short introduction to electronic structure theory is included as well as a chapter on Density Functional Theory, which is the underlying method behind all calculations presented in the accompanying papers. Multiple Scattering Theory is also discussed, both in more general terms as well as how it is used in the methods employed to solve the electronic structure problem. One of the methods, the Exact Muffin-Tin Orbital method, is described extensively, with special emphasis on the slope matrix, which energy dependence is investigated together with possible ways to parameterize this dependence.

Furthermore, a chapter which discusses different ways to perform calculations for disordered systems is presented, including a description of the Coherent Potential Approximation and the Screened Generalized Perturbation Method. A comparison between the Exact Muffin-Tin Orbital method and the Projector Augmented-Wave method in the case of systems exhibiting both compositional and magnetic disordered is included as well as a case study of the MoRu alloy, where the theoretical and experimental discrepancies are discussed.

The thesis is concluded with a short discussion on magnetism, with emphasis on its computational aspects. I further discuss a generalized Heisenberg model and its applications, especially to fcc Fe, and also present an investigation of the competing magnetic structures of FeNi alloys at different concentrations, where both collinear and non-collinear magnetic structures are included. For Invar-concentrations, a spin-flip transition is found and discussed. Lastly, I discuss so-called quantum corrals and possible ways of calculating properties, especially non-collinear magnetism, of such systems within perturbation theory using the force theorem and the Lloyd’s formula.

Place, publisher, year, edition, pages
Institutionen för fysik, kemi och biologi , 2006.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1063
Keyword [en]
Mathematical physics, Theoretical Physics, Muffin-Tin Orbital method, Calculations, Magnetism, Lloyd’s formula
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:liu:diva-8231ISBN: 91-85643-28-9 (print)OAI: oai:DiVA.org:liu-8231DiVA: diva2:23072
Public defence
2006-12-15, Planck, Fysikhuset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2009-03-04
List of papers
1. Energy dependence of the Exact Muffin-Tin Orbitals structure constants
Open this publication in new window or tab >>Energy dependence of the Exact Muffin-Tin Orbitals structure constants
2007 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 75, no 11, 115117- p.Article in journal (Refereed) Published
Abstract [en]

We investigate the energy dependence of the exact muffin-tin-orbital slope matrix in the complex energy plane. Analytic expressions for the asymptotic behavior of the slope matrix and its first energy derivative for large imaginary energies are given. We demonstrate that a two-center Taylor type expansion of the slope matrix accurately reproduces the exact values within a complex energy range covering the usual energy window used in electronic structure calculations. As an application, we study the composition dependence of the lattice parameters of the MgY binary system, a candidate material for hydrogen storage applications.

Place, publisher, year, edition, pages
American Physical Society, 2007
Keyword
Magnesium alloys, yttrium alloys, linear muffin-tin orbital method, band structure, lattice constants
National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-14270 (URN)10.1103/PhysRevB.75.115117 (DOI)
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2017-12-13Bibliographically approved
2. Total energy calculations for systems with magnetic and chemical disorder
Open this publication in new window or tab >>Total energy calculations for systems with magnetic and chemical disorder
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2006 (English)In: Computational materials science, ISSN 0927-0256, E-ISSN 1879-0801, Vol. 35, no 1, 1-5 p.Article in journal (Refereed) Published
Abstract [en]

The accuracy of the exact muffin-tin orbitals method combined with the coherent potential approximation (EMTO-CPA) for total energy calculations for systems with magnetic and chemical disorder, which is present simultaneously, is investigated. The mixing enthalpy of ordered, as well as disordered FeCo, FeNi, and FeCu equiatomic ferromagnetic alloys is calculated with the EMTO-CPA method and with the full-potential projector augmented wave (PAW) method. The results are compared and found to be in excellent agreement with each other. The EMTO-CPA method, in combination with disordered local moment model, is then applied to calculate the mixing enthalpy of the random paramagnetic face-centered cubic (fcc) FeCo alloy, as well as body-centered cubic (bcc) FeCr and FeV alloys over the whole concentration range. The results are compared with experimental data and a very good agreement is found again.

Keyword
Exact muffin-tin orbitals method; Coherent potential approximation; Mixing energies; Local moments disorder
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-14271 (URN)10.1016/j.commatsci.2005.04.001 (DOI)
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2017-12-13
3. A critical test of ab initio and CALPHAD methods: The structural energy difference between bcc and hcp molybdenum
Open this publication in new window or tab >>A critical test of ab initio and CALPHAD methods: The structural energy difference between bcc and hcp molybdenum
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2005 (English)In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 29, no 1, 17-23 p.Article in journal (Refereed) Published
Abstract [en]

Ab initio calculations of the enthalpy of formation of bcc, fcc, and hcp Ru–Mo alloys have been performed for random, ordered, and partially ordered structures. The lattice stability of the bcc and hcp forms of Mo is isolated in order to compare the hcp–bcc difference calculated by ab initio and CALPHAD methods with experimental measurements of the enthalpy of formation of Ru–Mo alloys. The significance of this comparison in calculating the Mo–Ru phase diagram is illustrated. The results of these considerations suggest a rational method for coupling ab initio and CALPHAD techniques might be utilization of the ab initio methods for calculation of the isostructural energies of formation for binary bcc, hcp, and fcc solutions while retaining the CALPHAD lattice stabilities in the calculation of phase diagrams.

National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-14272 (URN)10.1016/j.calphad.2005.04.002 (DOI)
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2017-12-13
4. Thermodynamics of ordered and disordered phases in the binary Mo-Ru system
Open this publication in new window or tab >>Thermodynamics of ordered and disordered phases in the binary Mo-Ru system
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2007 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 75, no 18, 184203- p.Article in journal (Refereed) Published
Abstract [en]

Wehave performed ab initio calculations of the mixing enthalpy forthe Mo-Ru alloy system. Both completely random alloys on thefcc, bcc, and hcp lattices as well as ordered andpartially ordered structures based on the hcp lattice and a phase have been examined. Further, we have performed aground-state search for the Ru-rich region using ab initio derivedeffective interactions, and find a series of structures below thetie line of the simple compounds. Using the structures fromthis ground-state search, we are able to make an estimationof the contribution to the total energy due to orderingeffects in this system. We find unusually large deviations betweencalculated and experimental values of the mixing enthalpy for Ru-richhcp alloys. Our calculations indicate, in agreement with experiment, thatthere are ordering trends in the system. However, even underassumption of maximal order theoretical results differ substantially from theexperiment. Possible reasons for the disagreement are discussed.

Keyword
molybdenum alloys, ruthenium alloys, ab initio calculations, enthalpy, ground states, total energy
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-14273 (URN)10.1103/PhysRevB.75.184203 (DOI)
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2017-12-13
5. Theoretical study of the Mo-Ru sigma-phase
Open this publication in new window or tab >>Theoretical study of the Mo-Ru sigma-phase
2008 (English)In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 32, no 1, 171-176 p.Article in journal (Refereed) Published
Abstract [en]

The thermodynamic properties of the Mo-Ru binary σ-phase are investigated using a combination of ab initio calculations and CALPHAD modeling. Total energy calculations have been performed for the complete set of 32 end-member compounds of a 5-sublattice compound energy model. The internal crystallographic parameters for each end-member compound have been determined by minimising the total energy. A simpler, 3-sublattice model of the Mo-Ru σ-phase is formulated on the basis of calculated total energies. The site occupancy is acquired by minimising the free energy given by the compound energy model. A strong preference of Mo and Ru towards high-coordination sites and icosahedral sites in the Mo-Ru σ-phase is found and analysed in terms of the electronic structure.

Place, publisher, year, edition, pages
Elsevier, 2008
Keyword
Ab initio calculations, Sigma phase, Mo–Ru, Thermodynamic properties, Site occupancy
National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-14274 (URN)10.1016/j.calphad.2007.06.001 (DOI)
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2017-12-13Bibliographically approved
6. An ab initio effective Hamiltonian for magnetism including longitudinal spin fluctuations
Open this publication in new window or tab >>An ab initio effective Hamiltonian for magnetism including longitudinal spin fluctuations
2005 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 72, no 10, 104437- p.Article in journal (Refereed) Published
Abstract [en]

We discuss the use of the magnetic force theorem using different reference states upon which the perturbative approach is based. Using a fixed spin disordered local moment state one finds good Curie (or Neél) temperatures, and good energetics for planar spin spirals in the 3d magnets Fe, fcc Co, Ni, Mn, and Cr, though worse agreement for small θ spin spirals. On the other hand, the ferromagnetic reference state provides excellent energetics for small θ spin spirals in Fe, fcc Co, and Ni, and by extension magnon energies under the assumption of adiabacity. However, planar spin spiral energetics and transition temperatures show worse agreement. The reasons for this, and for the case of fcc Co where both approaches work very well, are discussed. We further provide an extension of the mapping of the quantum problem to include longitudinal fluctuations within force theorem based approaches, and discuss the role they will play in magnetic phase transitions. This construction is tested using planar spin spirals where q is fixed but the moment is allowed to relax. It is demonstrated that results from this approach and directly calculated ab initio values agree very well.

National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-14275 (URN)10.1103/PhysRevB.72.104437 (DOI)
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2017-12-13Bibliographically approved
7. Noncollinear order in the γ-Fe system: Generalized Heisenberg approach
Open this publication in new window or tab >>Noncollinear order in the γ-Fe system: Generalized Heisenberg approach
2006 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 73, no 10, 104443- p.Article in journal (Refereed) Published
Abstract [en]

We investigate the complex magnetic ordering in face-centered cubic (fcc) Fe (γ-Fe) using a mapping of the electronic structure problem to an effective Heisenberg model via Green's function perturbation theory. We find that low-moment ([approximate]0.6µB) spin spirals (SSs) are accurately captured by this Hamiltonian, but not SSs of intermediate-moment ([approximate]2.0µB). We attribute this latter result to a hybridization gap at the Fermi level, resulting from the specific symmetry of the SS, which is difficult to capture within a perturbative approach. Using a generalization of the usual Heisenberg approach, in which we include the moment size as well as orientational degrees of freedom, we find that the strong volume dependence of this system enters through the intrasite exchange term only. We confirm this result with direct calculations of fixed moment and relaxed moment spin spirals. This highlights the importance of intrasite magnetism in this system, and points toward the moment and not the volume as being the crucial quantity to compare with experiments.

Place, publisher, year, edition, pages
American Physical Society, 2006
Keyword
Iron, ferromagnetic materials, Heisenberg model, Green's function methods, magnetic moments, Fermi level
National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-14276 (URN)10.1103/PhysRevB.73.104443 (DOI)
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2017-12-13Bibliographically approved
8. Competition between Magnetic Structures in the Fe-Rich FCC FeNi Alloys
Open this publication in new window or tab >>Competition between Magnetic Structures in the Fe-Rich FCC FeNi Alloys
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2007 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 76, no 1, 014434- p.Article in journal (Refereed) Published
Abstract [en]

We report on the results of a systematic ab initio study of the magnetic structure of Fe rich fcc FeNi binary alloys for Ni concentrations up to 50 at. %. Calculations are carried out within density-functional theory using two complementary techniques, one based on the exact muffin-tin orbital theory within the coherent potential approximation and another one based on the projector augmented-wave method. We observe that the evolution of the magnetic structure of the alloy with increasing Ni concentration is determined by a competition between a large number of magnetic states, collinear as well as noncollinear, all close in energy. We emphasize a series of transitions between these magnetic structures, in particular we have investigated a competition between disordered local moment configurations, spin spiral states, the double layer antiferromagnetic state, and the ferromagnetic phase, as well as the ferrimagnetic phase with a single spin flipped with respect to all others. We show that the latter should be particularly important for the understanding of the magnetic structure of the Invar alloys.

Place, publisher, year, edition, pages
American Physical Society, 2007
Keyword
Iron alloys, nickel alloys, ferromagnetic materials, magnetic structure, ab initio calculations, density functional theory, linear muffin-tin orbital method, local moments
National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-14277 (URN)10.1103/PhysRevB.76.014434 (DOI)
Note
Original Publication: Igor A. Abrikosov, Andreas E. Kissavos, Francois Liot, Björn Alling, Sergey Simak, O. Peil and A. V. Ruban, Competition between Magnetic Structures in the Fe-Rich FCC FeNi Alloys, 2007, Physical Review B Condensed Matter, (76), 1, 014434. http://dx.doi.org/10.1103/PhysRevB.76.014434 Copyright: American Physical Society http://www.aps.org/Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2017-12-13Bibliographically approved

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