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Theoretical Description of the Electron-Lattice Interaction in Molecular and Magnetic Crystals
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, Faculty of Science & Engineering.
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Electron-lattice interactions are often considered not to play a major role in material's properties as they are assumed to be small, the second-order effects. However, this study shows the importance of taking these effects into account in the simulations. My results demonstrate the impact of the electron-lattice interaction on the physics of the material and our understanding from it. One way to study these effects is to add them as perturbations to the unperturbed Hamiltonians in numerical simulations. The main objective of this thesis is to study electron-lattice interactions in molecular and magnetic crystals. It is devoted to developing numerical techniques considering model Hamiltonians and first-principles calculations to include the effect of lattice vibrations in the simulations of the above mentioned classes of materials.

In particular, I study the effect of adding the non-local electron-phonon coupling on top of the Holstein Hamiltonian to study the polaron stability and polaron dynamics in molecular crystals. The numerical calculations are based on the semi-empirical Holstein-Peierls model in which both intra (Holstein) and inter (Peierls) molecular electron-phonon interactions are taken into account. I study the effect of different parameters including intra and intermolecular electron-phonon coupling strengths and their vibrational frequencies, the transfer integral and the electric field on polaron stability. I found that in an ordered two dimensional molecular lattice the polaron is stable for only a limited range of parameter sets with the polaron formation energies lying in the range between 50 to 100 meV. Using the stable polaron solutions, I applied an electric field to the system and I observed that the polaron is dynamically stable and mobile for only a limited set of parameters. Adding disorder to the system will result in even more restricted parameter set space for which the polaron is stable and moves adiabatically with a constant velocity. In order to study the effect of temperature on polaron dynamics, I include a random force in Newtonian equations of motion in a one dimensional molecular lattice. I found that there is a critical temperature above which the polaron destabilizes and becomes delocalized.

Moreover, I study the role of lattice vibrations coupled to magnetic degrees of freedom in finite temperature paramagnetic state of magnetic materials. Calculating the properties of paramagnetic materials at elevated temperatures is a cumbersome task. In this thesis, I present a new method which allows us to couple lattice vibrations and magnetic disorder above the magnetic transition temperature and treat them on the same footing. The method is based on the combination of disordered local moments model and ab initio molecular dynamics (DLM-MD). I employ the method to study different physical properties of some model systems such as CrN and NiO in which the interaction between the magnetic and lattice degrees of freedom is very strong making them very good candidates for such a study.

I calculate the formation energies and study the effect of nitrogen defects on the electronic structure of paramagnetic CrN at high temperatures. Using this method I also study the temperature dependent elastic properties of paramagnetic CrN. The results highlight the importance of taking into account the magnetic excitations and lattice vibrations in the studies of magnetic materials at finite temperatures. A combination of DLM-MD with another numerical technique namely temperature dependent effective potential (TDEP) method is used to study the vibrational free energy and phase stability of CrN. We found that the combination of magnetic and vibrational contributions to the free energy shifts down the phase boundary between the cubic paramagnetic and orthorhombic antiferromagnetic phases of CrN towards the experimental value.

I used the stress-strain relation to study the temperature-dependent elastic properties of paramagnetic materials within DLM-MD with CrN as my model system. The results from a combinimation of DLM-MD with another newly developed method, symmetry imposed force constants (SIFC) in conjunction with TDEP is also presented as comparison to DLM-MD results.I also apply DLM-MD method to study the electronic structure of NiO in its paramagnetic state at finite temperatures. I found that lattice vibrations have a prominent impact on the electronic structure of paramagnetic NiO at high temperatures and should be included for the proper description of the density of states.

In summary, I believe that the proposed techniques give reliable results and allow us to include the effects from electron-lattice interaction in simulations of materials.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. , 85 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1766
Keyword [en]
Molecular crystals, Charge transport, Polaron, Magnetic materials, Paramagnetic state, Molecular dynamics
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:liu:diva-130517DOI: 10.3384/diss.diva-130517ISBN: 9789176857625 (Print)OAI: oai:DiVA.org:liu-130517DiVA: diva2:952139
Public defence
2016-09-16, Plank, Fysikhuset, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2016-08-23 Created: 2016-08-11 Last updated: 2016-08-23Bibliographically approved
List of papers
1. Polaron stability in molecular crystals
Open this publication in new window or tab >>Polaron stability in molecular crystals
2012 (English)In: Physics Letters A, ISSN 0375-9601, Vol. 376, no 22, 1807-1811 p.Article in journal (Refereed) Published
Abstract [en]

A semi-empirical Peierls-Holstein model is applied to studies of the stability of polarons in two-dimensional molecular crystal systems. Calculations for a broad range of intra- and inter-molecular parameters within this model were performed in order to obtain detailed knowledge concerning the stability of the polaron solution with respect to a rigid lattice band solution. For realistic values of the parameters the polaron solution is stable with a polaron energy in the range 50-100 meV. A metastable polaron solution is also identified. The polarons that result from our model are highly localized and it is questionable if adiabatic polaron transport can occur in the system.

Place, publisher, year, edition, pages
Elsevier, 2012
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-78584 (URN)10.1016/j.physleta.2012.04.007 (DOI)000304338100010 ()
Note
Funding Agencies|Swedish Research Council (VR)||Available from: 2012-06-15 Created: 2012-06-15 Last updated: 2016-08-23
2. Polaron dynamics in a two-dimensional Holstein-Peierls system
Open this publication in new window or tab >>Polaron dynamics in a two-dimensional Holstein-Peierls system
2013 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 138, no 18, 184104- p.Article in journal (Refereed) Published
Abstract [en]

A semiclassical model for studying charge transport in a two-dimensional molecular lattice is presented and applied to both a well ordered system and a system with disorder. The model includes both intra- and inter-molecular electron-lattice interactions and the focus of the studies is to describe the dynamics of a charge carrier in the system. In particular, we study the dynamics of the system in which the polaron solution is dynamically stable. It is found that the parameter space for which the polaron is moving through the system is quite restricted and that the polaron is immobile for large electron-phonon coupling and weak intermolecular electron interactions and dynamically unstable and disassociates into a delocalized electronic state decoupled from the lattice for small electron-phonon coupling and strong intermolecular electron interactions. Disorder further limits the parameter space in which the polaron is mobile.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-88110 (URN)10.1063/1.4803691 (DOI)000319290800009 ()23676026 (PubMedID)
Note

Funding Agencies|Swedish Research Council (VR)||

Available from: 2013-01-30 Created: 2013-01-30 Last updated: 2016-08-23Bibliographically approved
3. Role of N defects in paramagnetic CrN at finite temperatures from first principles
Open this publication in new window or tab >>Role of N defects in paramagnetic CrN at finite temperatures from first principles
2015 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 91, no 9, 094101- p.Article in journal (Refereed) Published
Abstract [en]

Simulations of defects in paramagnetic materials at high temperature constitute a formidable challenge to solid-state theory due to the interaction of magnetic disorder, vibrations, and structural relaxations. CrN is a material where these effects are particularly large due to a strong magnetolattice coupling and a tendency for deviations from the nominal 1: 1 stoichiometry. In this work, we present a first-principles study of nitrogen vacancies and nitrogen interstitials in CrN at elevated temperature. We report on formation energetics, the geometry of interstitial nitrogen dimers, and the impact on the electronic structure caused by the defects. We find a vacancy formation energy of 2.28 eV with a small effect of temperature, i.e., a formation energy for N interstitial in the form of a less than 111 greater than -oriented split bond of 3.77 eV with an increase to 3.97 at 1000 K. Vacancies are found to add three electrons, while split-bond interstitial adds one electron to the conduction band. The band gap of defect-free CrN is smeared out due to vibrations, although it is difficult to draw a conclusion about the exact temperature at which the band gap closes from our calculations. However, it is clear that at 900 K there is a nonzero density of electronic states at the Fermi level. At 300 K, our results indicate a border case where the band gap is about to close.

Place, publisher, year, edition, pages
American Physical Society, 2015
National Category
Physical Sciences Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:liu:diva-116954 (URN)10.1103/PhysRevB.91.094101 (DOI)000350994400001 ()
Note

Funding Agencies|Swedish Research Council (VR) [621-2011-4426]; Ministry of Education and Science of the Russian Federation [14.Y26.31.0005]; Tomsk State University Academic D. I. Mendeleev Fund Program; VR [621-2011-4417]

Available from: 2015-04-13 Created: 2015-04-10 Last updated: 2016-08-23
4. Finite-temperature elastic constants of paramagnetic materials within the disordered local moment picture from ab initio molecular dynamics calculations
Open this publication in new window or tab >>Finite-temperature elastic constants of paramagnetic materials within the disordered local moment picture from ab initio molecular dynamics calculations
Show others...
2016 (English)In: Physical Review B, ISSN 2469-9950 (print); 2469-9969 (online), Vol. 94, no 5, 054111Article in journal (Refereed) Published
Abstract [en]

We present a theoretical scheme to calculate the elastic constants of magnetic materials in the high-temperature paramagnetic state. Our approach is based on a combination of disordered local moments picture and ab initio molecular dynamics (DLM-MD). Moreover, we investigate a possibility to enhance the efficiency of the simulations of elastic properties using the recently introduced method: symmetry imposed force constant temperature-dependent effective potential (SIFC-TDEP). We have chosen cubic paramagnetic CrN as a model system. This is done due to its technological importance and its demonstrated strong coupling between magnetic and lattice degrees of freedom. We have studied the temperature-dependent single-crystal and polycrystalline elastic constants of paramagentic CrN up to 1200 K. The obtained results at T = 300 K agree well with the experimental values of polycrystalline elastic constants as well as the Poisson ratio at room temperature. We observe that the Young’s modulus is strongly dependent on temperature, decreasing by 14% from T = 300 K to 1200 K. In addition we have studied the elastic anisotropy of CrN as a function of temperature and we observe that CrN becomes substantially more isotropic as the temperature increases. We demonstrate that the use of Birch law may lead to substantial errors for calculations of temperature induced changes of elastic moduli. The proposed methodology can be used for accurate predictions of mechanical properties of magnetic materials at temperatures above their magnetic order-disorder phase transition.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2016
National Category
Physical Sciences Condensed Matter Physics
Identifiers
urn:nbn:se:liu:diva-130779 (URN)10.1103/PhysRevB.94.054111 (DOI)000381475300002 ()
Note

Funding agencies. Swedish Research Council (VR) [621-2011-4426, 621-2011-4417, 330-2014-6336]; Swedish Foundation for Strategic Research (SSF) program SRL [10-0026]; Ministry of Education and Science of the Russian Federation [K2-2016-013, 14.Y26.31.0005]; Marie Sklodowska

Available from: 2016-08-23 Created: 2016-08-23 Last updated: 2016-09-26Bibliographically approved
5. Vibrational free energy and phase stability of paramagnetic and antiferromagnetic CrN from ab initio molecular dynamics
Open this publication in new window or tab >>Vibrational free energy and phase stability of paramagnetic and antiferromagnetic CrN from ab initio molecular dynamics
Show others...
2014 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 89, no 17, 174108- p.Article in journal (Refereed) Published
Abstract [en]

We present a theoretical first-principles method to calculate the free energy of a magnetic system in its high-temperature paramagnetic phase, including vibrational, electronic, and magnetic contributions. The method for calculating free energies is based on ab initio molecular dynamics and combines a treatment of disordered magnetism using disordered local moments molecular dynamics with the temperature-dependent effective potential method to obtain the vibrational contribution to the free energy. We illustrate the applicability of the method by obtaining the anharmonic free energy for the paramagnetic cubic and the antiferromagnetic orthorhombic phases of chromium nitride. The influence of lattice dynamics on the transition between the two phases is demonstrated by constructing the temperature-pressure phase diagram.

Place, publisher, year, edition, pages
American Physical Society, 2014
National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-110985 (URN)10.1103/PhysRevB.89.174108 (DOI)000341308600001 ()
Note

Funding Agencies|Erasmus Mundus Joint European Doctoral Programme DocMASE; SECO Tools AB; Swedish Research Council [621-2011-4426, 621-2011-4417]; Swedish Foundation for Strategic Research (SSF) programs SRL [10-0026]; project Designed Multicomponent Coatings (MultiFilms); Knut and Alice Wallenberg Foundation (KAW)

Available from: 2014-10-01 Created: 2014-10-01 Last updated: 2016-08-23Bibliographically approved

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