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Theoretical methods for the electronic structure and magnetism of strongly correlated materials
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory. Radboud University. (Materials Theory)
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this work we study the interesting physics of the rare earths, and the microscopic state after ultrafast magnetization dynamics in iron. Moreover, this work covers the development, examination and application of several methods used in solid state physics. The first and the last part are related to strongly correlated electrons. The second part is related to the field of ultrafast magnetization dynamics.

In the first part we apply density functional theory plus dynamical mean field theory within the Hubbard I approximation to describe the interesting physics of the rare-earth metals. These elements are characterized by the localized nature of the 4f electrons and the itinerant character of the other valence electrons. We calculate a wide range of properties of the rare-earth metals and find a good correspondence with experimental data. We argue that this theory can be the basis of future investigations addressing rare-earth based materials in general.

In the second part of this thesis we develop a model, based on statistical arguments, to predict the microscopic state after ultrafast magnetization dynamics in iron. We predict that the microscopic state after ultrafast demagnetization is qualitatively different from the state after ultrafast increase of magnetization. This prediction is supported by previously published spectra obtained in magneto-optical experiments. Our model makes it possible to compare the measured data to results that are calculated from microscopic properties. We also investigate the relation between the magnetic asymmetry and the magnetization.

In the last part of this work we examine several methods of analytic continuation that are used in many-body physics to obtain physical quantities on real energies from either imaginary time or Matsubara frequency data. In particular, we improve the Padé approximant method of analytic continuation. We compare the reliability and performance of this and other methods for both one and two-particle Green's functions. We also investigate the advantages of implementing a method of analytic continuation based on stochastic sampling on a graphics processing unit (GPU).

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2017. , p. 109
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1461
Keywords [en]
dynamical mean field theory (DMFT), Hubbard I approximation, strongly correlated systems, rare earths, lanthanides, photoemission spectra, ultrafast magnetization dynamics, analytic continuation, Padé approximant method, two-particle Green's functions, linear muffin tin orbitals (LMTO), density functional theory (DFT), cerium, stacking fault energy.
National Category
Natural Sciences Physical Sciences
Research subject
Physics with spec. in Atomic, Molecular and Condensed Matter Physics
Identifiers
URN: urn:nbn:se:uu:diva-308699ISBN: 978-91-554-9770-5 (print)OAI: oai:DiVA.org:uu-308699DiVA, id: diva2:1050660
Public defence
2017-02-03, Ång/10132, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2017-01-12 Created: 2016-11-29 Last updated: 2017-01-17
List of papers
1. Standard model of the rare earths analyzed from the Hubbard I approximation
Open this publication in new window or tab >>Standard model of the rare earths analyzed from the Hubbard I approximation
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2016 (English)In: PHYSICAL REVIEW B, ISSN 2469-9950, Vol. 94, no 8, article id 085137Article in journal (Refereed) Published
Abstract [en]

In this work we examine critically the electronic structure of the rare-earth elements by use of the so-called Hubbard I approximation. From the theoretical side all measured features of both occupied and unoccupied states are reproduced, without significant deviations between observations and theory. We also examine cohesive properties like the equilibrium volume and bulk modulus, where we find, in general, a good agreement between theory andmeasurements. In addition, we have reproduced the spin and orbital moments of these elements as they are reflected from measurements of the saturation moment. We have also employed the Hubbard I approximation to extract the interatomic exchange parameters of an effective spin Hamiltonian for the heavy rare earths. We show that the Hubbard I approximation gives results which are consistent with calculations where 4f electrons are treated as core states for Gd. The latter approach was also used to address the series of the heavy/late rare earths. Via Monte Carlo simulations we obtained ordering temperatures which reproduce measurements within about 20%. We have further illustrated the accuracy of these exchange parameters by comparing measured and calculated magnetic configurations for the heavy rare earths and the magnon dispersion for Gd. The Hubbard I approximation is compared to other theories of the electronic structure, and we argue that it is superior. We discuss the relevance of our results in general and how this makes it possible to treat the electronic structure of materials containing rare-earth elements, such as permanent magnets, magnetostrictive compounds, photovoltaics, optical fibers, topological insulators, and molecular magnets.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-303271 (URN)10.1103/PhysRevB.94.085137 (DOI)000381889700004 ()
Funder
eSSENCE - An eScience CollaborationSwedish Research CouncilKnut and Alice Wallenberg Foundation, 2013.0020 2012.0031EU, European Research Council, 338957 FEMTO/NANOThe Royal Swedish Academy of SciencesCarl Tryggers foundation Swedish Energy AgencySwedish Foundation for Strategic Research
Available from: 2016-09-16 Created: 2016-09-15 Last updated: 2016-11-29Bibliographically approved
2. Stacking fault energetics of alpha- and gamma-cerium investigated with ab initio calculations
Open this publication in new window or tab >>Stacking fault energetics of alpha- and gamma-cerium investigated with ab initio calculations
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2016 (English)In: PHYSICAL REVIEW B, ISSN 2469-9950, Vol. 93, no 9, article id 094103Article in journal (Refereed) Published
Abstract [en]

At ambient pressure the element cerium shows a metastable (t(1/2) similar to 40 years) double-hexagonal close-packed beta phase that is positioned between two cubic phases, gamma and alpha. With modest pressure the beta phase can be suppressed, and a volume contraction (17%) occurs between the gamma and the alpha phases as the temperature is varied. This phenomenon has been linked to subtle alterations in the 4f band. In order to rationalize the presence of the metastable beta phase, and its position in the phase diagram, we have computed the stacking fault formation energies of the cubic phases of cerium using an axial interaction model. This model links the total energy differences between hexagonal closed-packed stacking sequences and stacking fault energetics. Total energies are calculated by density functional theory and by dynamical mean-field theory merged with density functional theory. It is found that there is a large difference in the stacking fault energies between the alpha and the gamma phase. The beta-phase energy is nearly degenerate with the gamma phase, consistent with previous third-law calorimetry results, and dislocation dynamics explain the pressure and temperature hysteretic effects.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-283302 (URN)10.1103/PhysRevB.93.094103 (DOI)000372400100001 ()
Funder
Swedish Research CouncilSwedish Foundation for Strategic Research Knut and Alice Wallenberg Foundation
Available from: 2016-04-12 Created: 2016-04-12 Last updated: 2016-11-29Bibliographically approved
3. Ultrafast magnetization dynamics: Microscopic electronic configurations and ultrafast spectroscopy
Open this publication in new window or tab >>Ultrafast magnetization dynamics: Microscopic electronic configurations and ultrafast spectroscopy
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2015 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 92, no 6, article id 064403Article in journal (Refereed) Published
Abstract [en]

We provide an approach for the identification of the electronic and magnetic configurations of ferromagnetic Fe after an ultrafast decrease or increase of the magnetization. The model is based on the well-grounded assumption that, after an ultrafast variation of the magnetization, the system achieves a partial thermal equilibrium. With statistical arguments we show that the magnetic configurations are qualitatively different in the case of reduced or increased magnetization. The predicted magnetic configurations are then used to compute the dielectric response at the 3p (M) absorption edge, which is directly related to the changes observed in the experimental T-MOKE data. The good qualitative agreement between theory and experiment offers a substantial support for the validity of the model, and to the very existence of an ultrafast increase of the magnetization.

National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-261243 (URN)10.1103/PhysRevB.92.064403 (DOI)000358929600006 ()
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationEU, FP7, Seventh Framework Programme
Available from: 2015-09-07 Created: 2015-08-31 Last updated: 2017-12-04Bibliographically approved
4. Magnetic asymmetry around the 3p absorption edge in Fe and Ni
Open this publication in new window or tab >>Magnetic asymmetry around the 3p absorption edge in Fe and Ni
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(English)Manuscript (preprint) (Other academic)
Abstract [en]

This work is a joint theoretical and experimental study of the relation between the magneto- optical response of a material in the sub-picosecond timescale and its instantaneous magnetisation. We perform pump-probe experiments in the transverse magneto-optical Kerr effect (T-MOKE) geometry. We measure the magnetic asymmetry of elemental Fe and Ni before and after the laser pulse. The observed differences between the magnetic asymmetry curves for various photon energies suggest that the relation between asymmetry and sample magnetization is more complex than a simple proportionality. Further insight is obtained by means of theoretical simulations based on density-functional theory. Our calculations show that non-linear effects in the asymmetry are most prominent at energies corresponding to the absorption edge and that the proportionality is recovered outside of this region. In conclusion, our experimental and theoretical results emphasize the need of including the complex relation between asymmetry and magnetization in the interpretation of ultrafast magnetization experiments in terms of microscopic properties. 

Keywords
T-MOKE, ultrafast magnetization dynamics, Fe, iron, Ni, nikkel
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:uu:diva-308697 (URN)
Available from: 2016-11-29 Created: 2016-11-29 Last updated: 2016-12-07
5. Analytic continuation by averaging Pade approximants
Open this publication in new window or tab >>Analytic continuation by averaging Pade approximants
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2016 (English)In: PHYSICAL REVIEW B, ISSN 2469-9950, Vol. 93, no 7, article id 075104Article in journal (Refereed) Published
Abstract [en]

The ill-posed analytic continuation problem for Green's functions and self-energies is investigated by revisiting the Pade approximants technique. We propose to remedy the well-known problems of the Pade approximants by performing an average of several continuations, obtained by varying the number of fitted input points and Pade coefficients independently. The suggested approach is then applied to several test cases, including Sm and Pr atomic self-energies, the Green's functions of the Hubbard model for a Bethe lattice and of the Haldane model for a nanoribbon, as well as two special test functions. The sensitivity to numerical noise and the dependence on the precision of the numerical libraries are analyzed in detail. The present approach is compared to a number of other techniques, i.e., the nonnegative least-squares method, the nonnegative Tikhonov method, and the maximum entropy method, and is shown to perform well for the chosen test cases. This conclusion holds even when the noise on the input data is increased to reach values typical for quantum Monte Carlo simulations. The ability of the algorithm to resolve fine structures is finally illustrated for two relevant test functions.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-279570 (URN)10.1103/PhysRevB.93.075104 (DOI)000369399500001 ()
Funder
Swedish Research CouncileSSENCE - An eScience CollaborationKnut and Alice Wallenberg Foundation, KAW-2013.0020
Available from: 2016-03-02 Created: 2016-03-02 Last updated: 2018-10-10
6. Comparison between methods of analytical continuation for bosonic functions
Open this publication in new window or tab >>Comparison between methods of analytical continuation for bosonic functions
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2016 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 94, article id 245140Article in journal (Refereed) Published
Abstract [en]

In this article we perform a critical assessment of different known methods for the analytical con- tinuation of bosonic functions, namely the maximum entropy method, the non-negative least-square method, the non-negative Tikhonov method, the Pad ́e approximant method, and a stochastic sam- pling method. Four functions of different shape are investigated, corresponding to four physically relevant scenarios. They include a simple two-pole model function, two flavours of the tight bind- ing model on a square lattice, i.e. a single-orbital metallic system and a two-orbitals insulating system, and the Hubbard dimer. The effect of numerical noise in the input data on the analytical continuation is discussed in detail. Overall, the stochastic method by Mishchenko et al. [Phys. Rev. B 62, 6317 (2000)] is shown to be the most reliable tool for input data whose numerical precision is not known. For high precision input data, this approach is slightly outperformed by the Pad ́e approximant method, which combines a good resolution power with a good numerical stability. Although none of the methods retrieves all features in the spectra in the presence of noise, our analysis provides a useful guideline for obtaining reliable information of the spectral function in cases of practical interest. 

Keywords
Green's functions, analytical continuation
National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-308693 (URN)10.1103/PhysRevB.94.245140 (DOI)000391012400012 ()
Funder
Swedish Research CouncileSSENCE - An eScience CollaborationKnut and Alice Wallenberg FoundationEU, European Research Council, 338957 FEMTO/NANOSwedish National Infrastructure for Computing (SNIC)
Available from: 2016-11-29 Created: 2016-11-29 Last updated: 2018-10-10Bibliographically approved
7. A GPU code for analytic continuation through a sampling method
Open this publication in new window or tab >>A GPU code for analytic continuation through a sampling method
2016 (English)In: SoftwareX, ISSN 2352-7110Article in journal (Refereed) In press
Abstract [en]

We here present a code for performing analytic continuation of fermionic Green’s functions and self-energies as well as bosonic susceptibilities on a graphics processing unit (GPU). The code is based on the sampling method introduced by Mishchenko et al. (2000), and is written for the widely used CUDA platform from NVidia. Detailed scaling tests are presented, for two different GPUs, in order to highlight the advantages of this code with respect to standard CPU computations. Finally, as an example of possible applications, we provide the analytic continuation of model Gaussian functions, as well as more realistic test cases from many-body physics.

Place, publisher, year, edition, pages
Elsevier, 2016
Keywords
GPU, Analytic continuation, Parallelization, Green’s function
National Category
Natural Sciences
Research subject
Physics
Identifiers
urn:nbn:se:uu:diva-308687 (URN)10.1016/j.softx.2016.08.003 (DOI)
Funder
eSSENCE - An eScience CollaborationKnut and Alice Wallenberg FoundationSwedish Research CouncilSwedish National Infrastructure for Computing (SNIC)
Available from: 2016-11-29 Created: 2016-11-29 Last updated: 2018-10-10

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