Autopresentation. Małgorzata Sternik

Transcription

1 Załącznik 3 Autoreferat w języku angielskim Autopresentation Małgorzata Sternik includes: personal data scientific work history list of selected monothematic publications introduction overview of selected papers summary page Kraków, 2012

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3 PERSONAL DATA Names: Surname: Małgorzata Ewa Sternik Date of Birth: Place of birth: Ostrowiec Świętokrzyski Place of Employment: Department of Materials Research by Computers, Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, Kraków Diploma and scientific degrees: Studies of physics at the Faculty of Mathematics and Physics of the Jagiellonian University, Kraków 1987 MSc degree in physics at the Faculty of Mathematics and Physics of the Jagiellonian University MSc thesis in polish: Badanie funkcji wzbudzenia w reakcjach 165Ho(16O,4nγ)177Re i 148Nd(19F,4nγ)163Tm prepared in Department of Nuclear Physics of the Institute of Physics JU PhD studies in the Institute of Physics of the Jagiellonian University 1992 Doctoral degree in Physics at Faculty of Mathematics and Physics of the Jagiellonian University PhD thesis in polish: Oddziaływanie domieszka domieszka w rozcieńczonych roztworach stałych srebra, prepared in Department of Nuclear Physics of the Institute of Physics JU Professional career: assistant in Department of Nuclear Physics of Institute of Physics JU assistant in the Institute of Nuclear Physics sdjunct in the Institute of Nuclear Physics maternity leave 1

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5 3 The course of scientific work including the description of the most important scientific achievements My initial scientific interests were associated with nuclear physics. I graduated defending my MSc thesis on the spectroscopic studies of gamma rays produced in nuclear reactions of heavy ions. After graduation my interest shifted to the field of applications of the nuclear methods in the investigation of the condensed matter. The alloys based on silver as a host component in which two impurity elements were dissolved: 111In as a nuclear probe atom and Mn, Ni, Co, Cu, Zn, Ga, Ge, Al or Rh atoms as second impurities. Measurements were performed using the time dependent perturbed angular correlation of gamma rays, and the Mössbauer technique (in the case of Co impurities). The main aim of the investigations was determination of the interaction energies between probe and impurity atoms and comparison of the experimental data with results of theoretical calculations. The results were published in References [1 4]. (Numbering of references according to the Annex 1). In addition, it was shown that using the same method, one can determine the solubility limits of impurities and investigations of different precipitations in the case of impurities weakly soluble in Ag [6,9]. Results of these studies were included into my PhD thesis. In 1992, just after defending the PhD thesis, I was employed in the Institute of Nuclear Physics, where under the guidance of Prof. Krzysztof Parlinski I started to explore the issues related to the computer simulations in the condensed matter physics. My studies relied on the modeling of crystals, and the simulations of the phase transitions using the molecular dynamics technique. The domain structures formed in the system, being a consequence of the phase transition, was analyzed. The evolution of the microstructure was observed on the two dimensional maps that demonstrated the state of a system in time. To deal with a huge number of degrees of freedom in a real crystal, Prof. K. Parlinski introduced so called rational model, reducing the number of internal degrees of freedom to those which are necessary to construct the order parameter of the investigated crystal. This model allowed to introduce a coupling between two quantities responsible for a structural phase transition: the soft phonon mode and elastic constants. This method was e.g. applied to model the structural properties of the high temperature superconductor YBa2Cu3O7 δ. In Ref. [5], it was shown that the transition temperature from the tetragonal to the orthorhombic phase depends on oxygen concentration. In addition, the formation and evolution of the microstructure in such a system were presented in Refs [5,7,12]. In the next paper the model was enriched by adding one more orthorhombic phase observed experimentally [13]. The microstructure simulations in the crystal with two orthorhombic phases, OI and OII, led to the conclusion that in the crystal consisted simultaneously both of them as precipitates, heating of the microstructure takes place more slowly than in the crystal with a single orthorhombic phase. The model based on the same idea was also used to determine the phase diagram of one and two dimensional modulated phases in tetragonal crystals. It was shown that the formation of a stable phases with incommensurate modulations was very sensitive to the choice of the potential energy parameters, especially those associated with the phonon dispersion curve curvature along the modulation direction [8,10]. These phenomenological models led to the qualitative description of empirical observations only. They were confined to reproduce properties of the crystals in the specified conditions. In the next step, I participated in development of a new algorithm for evaluation of phonon dispersion relations from the molecular dynamics. The algorithm was successfully applied to model the dispersion relations in the argon crystal [11]. The input data for calculations were obtained using the commercial computer program HyperChem.

6 4 From 1995, the Prof. K. Parlinski group extended rapidly and in 1996 the Department of Materials Research by Computers was founded in the Institute of Nuclear Physics. The department's main fields of interest were investigations of structural and dynamical properties of crystals and the related phenomena, for example: thermodynamical properties, phase transitions and elastic properties. The calculations based on the quantum mechanical techniques implemented in CASTEP and VASP packages. These programs were used to determine the optimal atomic positions, lattice parameters and interatomic forces. The dynamical properties were calculated using the direct method formulated by Prof. K. Parlinski and implemented in PHONON software. The calculations were performed for the appropriately chosen supercell that is a multiplication of a primitive unit cell. At first, the studied materials were rather simple nonmetallic crystals with the supercell containing no more than eighty atoms. The single point in the reciprocal space was sufficient to accurately estimate the electronic density of states. The first two papers, I was involved, were published in They concerned calculations for the simple systems: TiC crystal with the NaCl structure [15] and GaAs crystal doped with Al impurities [14]. In the first case, a doubled in three directions unit cell containing 64 atoms was used as the supercell. In the second case, the supercell with dimensions 1x1x1 containing 8 atoms was used and the disordered alloy was approximated by the perfectly ordered structure with the fixed impurity concentration. In spite of all these simplifications, the calculated dispersion curves reproduced the experimental data satisfactorily. Moreover, the calculations allowed to determine the elastic constants for TiC and to analyze the influence of Al impurities on the dispersion curves and phonon density of states of (Ga,Al)As. However, the available at that time computing power was not sufficient to perform ab initio calculations for YBa2Cu3O7. From July 1998 to the end of 2002, I benefited from the maternity leave to take care of my two sons: Andrzej born in 1998 and Krzysztof born in In January 2003, I returned to the Institute of Nuclear Physics and continued my work in the Department of Materials Research by Computers. The substantial increase of computing power allowed to study the systems with more complicated crystallographic and electronic structures. My studies were mainly focused on problems related to the structural phase transitions and the stability of artificial structures which are not found in the nature. The results of these investigations were published in 16 articles. Seven papers form a monothematic set entitled Lattice dynamics and the stability of crystals and monolayers which I consider as essential in my post doctoral scientific research. They were chosen as a habilitation thesis. Three papers of this set were concern investigations of the structural phase transitions in ZrO 2 [16,17] and MgSiO3 [18] crystals. The next two papers, inspired by Prof. J. Korecki, regard investigations of the stability of Fe/Au multilayers [19,20]. In these papers, the results of the detailed analysis of the ab initio calculations are presented and compared with already existing experimental data. The last two papers which concern the metastable bcc phase in cobalt [24] and the L1 0 phase in FePt [28] were performed in the cooperation with the experimental group from the Catholic University of Leuven. The problems touched in these seven publications and the deduced results are presented in detail in the next section of the. The remaining papers are mainly related to the scientific projects in which I was involved. The articles published in frame of COST 19 project Multiscale modeling of materials concern investigations of miscellaneous properties of several materials: paramagnetic, intermetallic compound Mo3Sb7. This is a superconducting material with a critical temperature Tc=2.2 K. In spite of the suggestions coming from the experimental studies that the conventional electron phonon interaction might be responsible for the superconductivity in this material, some unusual properties indicated that spin fluctuations play a significant role. The ab initio approach which involves calculations of the electronic structure and the phonon spectra allowed to qualify Mo 3Sb7 as a medium

7 5 electron phonon coupling superconductor. The spin fluctuations might exist in that material, but the electron paramagnon interaction cannot be very strong [21]. Calculated phonon dispersion relations and phonon density of states were confirmed by experimental investigations using the inelastic neutron scattering [32]. the α and σ phases of disordered FeCr alloys [27]. The ab initio computations of lattice dynamics of alloys is non trivial due to the huge number of possible atomic configurations in the disordered alloy. Nevertheless, we have found that calculated for a few appropriately chosen configurations the partial Fe phonon density of states of the α and σ phase well correspond with densities measured using the NRIXS (nuclear resonant inelastic X ray scattering) method. magnetocaloric compound MnAs [25]. In this crystal the magnetic phase transition at 315 K is accompanied by the huge entropy change. The calculated phonon dispersion relations revealed the softening of the optical mode at high symmetry point M which induces the structural phase transition from the hexagonal to orthorhombic phase and leads to the disordering of magnetic moments and the disappearance of the total magnetization. It was proven that the huge entropy change is not generated by the lattice vibrations. In frame of the international geophysical project C2C ( Crust to core fate of the subducted material ) our group was responsible for calculations and analysis of the structural and electronic properties of some minerals: magnesium and iron orthosilicates, Mg 2 xfexsio4 important mineral occurring in the Earth's interior. Their dynamical, electronic and magnetic properties were calculated and presented in several publications [23,26,30,31]. Stability of different Mg 2SiO4 phases were studied at wide range of pressures and temperatures. brucite, Mg(OH)2 [29]. The calculations of structural and elastic properties were performed. Then using the molecular dynamics method the behavior of the hydrogen atoms at different temperatures was studied. The investigation revealed that the hydrogen atoms are weakly bounded with the rest of the lattice. kanemite, NaHSi2O5 3H2O [22], a mineral with complicated structure containing 72 atoms in the primitive unit cell. Its physical properties are strongly related to hydrogen bonds, therefore our investigations of the structure and lattice dynamics were mainly focused on that problem. It was shown that at low temperature the stability of the system requires introduction of the additional hydrogen bond which in turn lowers the crystal symmetry suggesting the possible phase transitions. Concluding, my interest in physics evolved from the nuclear physics, through the methods of nuclear physics applied to studies of materials, to condensed matter physics. From the experimental physics through the computer simulations based on the phenomenological models to the first principle calculations. Investigations covered miscellaneous properties of materials and very wide range of topics. They were often developed in cooperation with other groups. Their excellent knowledge of studied properties allowed to exchange experiences and to prepare good papers published in journals with high Impact Factors (Annex 4). Our results were also presented during international conferences (Annex 5), for example, during the series Workshop on ab initio phonon calculations that were organized by our group. My research, the purchase of computers and software, were mainly funded by several European and Polish research grants (Annex 5).

8 6 Present scientific activity My present scientific activity is focused on continuation of the investigations of the ordered FePt alloys and nanostructures. These studies are performed in frame of the international project COST (European Cooperation in Science and Technology Action) Nanoalloys as advanced materials: from structure to properties and applications (NANOALLOY) and the polish project of NCN The study of structural, dynamic and magnetic properties of nanoparticles, multilayers, thin films and surfaces containing transition metals and rare earths from first principles calculations. Moreover, I investigate the point defects in SiC crystals in frame of the project Development of technology for advanced semiconducting materials based on silicon carbide (SICMAT). This subject covers the calculations of formation energy of 6H SiC crystal with different impurities: V, N, Al, B placed in various crystallographic positions. The research are carried out within the project Development of technology for advanced semiconducting materials based on silicon carbide (SICMAT). The continuation of the work on the FeCr alloys is also planned, in particular investigations of the phonon density of states for alloys with various iron concentrations at different temperatures. These studies are inspired by the already existing experimental data.

9 7 monothematic publications selected for the purpose of habilitation procedure: Lattice dynamics and the stability of crystals and multilayered structures Selected papers: H1 Lattice vibrations in cubic, tetragonal and monoclinic phases of ZrO 2, M. Sternik (80 %) and K. Parlinski, J. Chem. Phys. 122, (2005). H2 Free energy calculations of the cubic ZrO2 crystal as an example of a system with a soft mode, M. Sternik (80 %) and K. Parlinski, J. Chem. Phys. 123, (2005). H3 Ab initio calculations of the stability and lattice dynamics of the MgSiO 3 post perovskite, M. Sternik (80 %) and K. Parlinski, J. Phys. Chem. Sol. 67, 796 (2006). H4 Fem/Aun multilayers from first principles, M. Sternik (80 %), K. Parlinski and J. Korecki, Phys. Rev. B 47, (2006). H5 First principles studies of the interlayer exchange coupling in fine layered Fe/Au multilayers, M. Sternik (80 %) and K. Parlinski, Phys. Rev. B 75, (2007). H6 Probing the dynamical properties of the metastable bcc FexCo1 x phase, B. Laenens, N. Planckaert, M. Sternik (45 %), P. T. Jochym, K. Parlinski, A.Vantomme and J. Meersschaut, Phys. Rev. B79, (2009) H7 Anisotropic lattice dynamics of FePt L10 thin films, S. Couet, M. Sternik (45 %), B. Laenens, A. Siegel, K. Parlinski, N. Planckaert, F. Gröstlinger, A.I. Chumakov, R. Rüffer, B. Sepioł, K. Temst, and A. Vantomme, Phys. Rev. B 82, (2010) My contribution to each publication (expressed in per cent) was given in the brackets behind my name.

10 8 Introduction The computational methods based on the density functional theory (DFT) are currently widely applied to study the structure as well as electronic, magnetic and dynamic properties of materials. In the papers mentioned above, these methods are used to determine the stability limits of crystallographic phases of materials occurring in nature and to confirm the stability of the artificial structures formed in a laboratory. All papers concern investigations of materials of significant scientific and technological importance: ZrO2 zirconium dioxide, the ceramic material that has useful mechanical properties, low reactivity in chemical reactions and high melting temperature leading to wide medical and engineering applications. MgSiO3 magnesium silicate, the mineral of the highest abundance in the lower Earth's mantle. Its crystal structure changes with the increased pressure and temperature influencing the speed of the seismic waves. Fe/Au multilayers they do not occur in this form in nature but they can be produced by a molecular beam epitaxy technique in the laboratory. This material is applied in spintronics in the form of spin valves among others for constructions of magnetic memories. the ordered FePt alloy naturally occurring in L10 phase is a special case of multilayered structure consisted of alternating Fe and Pt monoatomic layers. On account of the magnetic properties FePt alloy is used in the production of magnetic reading heads in the hard disk drives. bcc Co the phase of cobalt which does not exist in nature. It can be produced in a laboratory. The first step in the investigations of these materials was the optimization of the lattice constants and atomic positions in crystals and the interlayer distances and relaxation of atoms in multilayered structures. These data were calculated using the VASP package (Vienna Ab Initio Simulation Package) created at the University of Vienna. The DFT methods implemented in this code allows to find the energy of the ground state by minimization of the total energy of the crystal with respect to the electron distribution, lattice parameters and atomic positions. The application of the spin polarized method allows to study the magnetic materials such as the multilayered Fe/Au structure, the Co crystal or the ordered FePt alloys. The next step of calculations include estimation of forces generated on each atom when one of the atoms is displaced from its crystallographic position (so called Hellmann Feynman forces). These forces are used in already mentioned direct methods to calculate the force constants and to construct the dynamical matrix. The diagonalization of the dynamical matrix gives the eigenvalues of energy and eigenvectors (i.e. polarization vectors) of vibrational modes of the crystalline lattice. The program PHONON, written by Prof. K. Parlinski, was used to calculate the phonon dispersion curves, phonon density of states and the thermodynamical functions related to the lattice vibrations. All these quantities are calculated in the harmonic approximation. They are essential for studying the stability of crystal phases, because usually the phonons determine the thermodynamic properties of the materials. The temperature range of the phase stability at pressure p=0 could be obtained by comparing the free energies of the possible crystal phases: F(T)=U+Fvib(T), where U an internal energy of the ground state determined using the DFT method (the total energy of the ground state), and Fvib(T) a vibrational free energy calculated from the phonon spectrum. The phase with the lowest free energy F(T) at fixed temperature is the stable phase [H1,H2]. In the case of nonzero pressure the Gibbs free enthalpy should be used: G(p,T)=F(T)+pV, where p and V are the external pressure and the volume of the system corresponding to this pressure

11 9 [H3]. The DFT calculations are performed under assumption that the temperature of the system equals to zero kelvins, thus the phonon dispersion relations and phonon density of states calculated for the optimized structure refer to the volume and the atomic positions at T = 0 K. It is possible to include the temperature effects associated with the thermal expansion of crystals to the phonon spectra assuming that the phonon frequencies are volume dependent (so called quasiharmonic approximation). In this approach the free energy is written as: F(V,T)=U(V)+Fvib(V,T). This procedure has to be performed for a number of volumes which significantly increases calculations. Nevertheless currently it could be applied as a standard method due to the progress in computing power. The quasiharmonic approach was adopted to find a phase diagram of MgSiO 3 [H3]. The phonon spectra calculated in a harmonic approximation can exhibit imaginary frequencies (so called soft modes). It means that from the dynamical point of view the system is unstable. Considering the total energy of the structure, it is a case when the interatomic interactions place this system at saddle point on the potential energy surface rather than at minimum as for statically stable structures. At higher temperatures, when the contribution of vibrational entropy is sufficiently large, decrease of the free energy can stabilize a system as it happens for the cubic zirconium dioxide. Since up to now there is hardly any method based on ab initio calculations which allows to find the contribution from the anharmonic soft modes to the crystal free energy, the structural phase transition between cubic and tetragonal phases in ZrO2 was not described properly [H2]. It is also possible to stabilize the structure which exhibits the imaginary frequencies by removing symmetry imposed on a supercell and allowing relaxation of atoms according with the soft mode vibrations. The recalculation of optimal atomic positions and lattice parameters can lead to a stable structure with lower total energy but with lower symmetry. This method was applied to determine displacements of atoms necessary to stabilize two multilayered structures: Fe 1/Au1 and Fe1/Au3 [H4]. As a result of calculations it was found that the perfect multilayer structure of Fe1/Au1 type does not exist in contradistinction to the structure of Fe 1/Pt1 which exists in the ordered FePt alloy [H7]. The multilayer structures which contain alternating magnetic and nonmagnetic layers have various interesting properties. In the following I present the paper on the magnetic interactions in the stable Fem/Aun structures with different thicknesses of magnetic (m) and nonmagnetic (n) layers [H5]. The next method of system stabilization are deposition of atoms on appropriate substrate or a doping of unstable material with impurities, as it takes place for the unstable bcc Co phase stabilized by Fe atoms [H6]. The stabilization could be forced either mechanically by the variation of the atomic positions (the strain applied to the system) or by the changes in the interatomic interactions caused by the variations of the force constants. The brief overview of the selected papers (All figures and tables presented in this part of the text have been taken from the relevant papers [H1] [H7].) [H1] At ambient pressure, ZrO2 crystalizes in three phases. With increasing temperature the successive phase transitions occur: from monoclinic to tetragonal and from tetragonal to cubic phases. The mechanism of both phase transitions have been analyzed on the basis of the group theory. These studies lead to conclusion that the condensation of X mode in the cubic lattice is the 2 origin of the transformation from cubic to tetragonal phase. The next phase transition to the monoclinic phase is suggested to be a result of the subsequent condensation in the tetragonal structure of a phonon mode at the M point of the Brillouin zone. In 1997, the phonon dispersion relations of the cubic phase have been calculated by Prof. K. Parlinski. The existence of the soft mode

12 10 connected with the vibrations of the oxygen atoms was observed at the X point. The main purpose of this work was to determine the phonon dispersion relations for all three phases of ZrO2 and to analyze the phase transition from the monoclinic to the tetragonal phase. The calculations proved the existence of imaginary frequencies in the phonon spectra of the cubic phase (shown as a dispersion branch with negative frequencies) and showed that for the tetragonal and monoclinic phases all frequencies are real. Especially we did not observe expected softening of any mode at the M point in the tetragonal phase (Fig.1). In calculations of the phonon dispersion relations, the LO TO splitting at the Г point related to the influence of macroscopic electric field generated in polar crystals on the vibrations with infrared frequencies was added. In the monoclinic and tetragonal phases, it causes the appearance of dispersion relations discontinuity. In the cubic crystal this effect does not occur due to the symmetry. Figure 1. Phonon dispersion relations for three phases of ZrO2 (from left: for the cubic, tetragonal and monoclinic phases). All the phonon frequencies at the high symmetry points were analyzed in details. The frequencies at the Г point satisfactorily reproduced the measured values obtained using methods of the Raman and infrared spectroscopies. Since, in tetragonal and monoclinic phases all phonon frequencies are real the free energies of crystal in both phases were calculated from phonon spectra. From the crossing of the free energies curves, the tetragonal to monoclinic phase transition temperature was extracted to be 1560 K which reproduces quite well the measured value of about 1400 K. Figure 2. The free energy difference between the tetragonal and monoclinic phases of ZrO2. [H2] To determine the range of stability of tetragonal phase of ZrO2, it means to find the transition temperature from the tetragonal to the cubic phase it is necessary to calculate the free energy for a system with imaginary phonon frequencies (in the cubic phase). In this paper, the concept of treating the phonons with imaginary frequencies as noninteracting anharmonic modes oscillating in a double

13 11 minimum potential was verified. The double well potential may be described in two ways: in a parabola plus Gaussian form, and as a 2 4 polynomial. The first approach allows to include the anharmonic vibrations to the quantum mechanical calculations as it is done in the harmonic approximation. The second one enforced the use of classic thermodynamic formula. Firstly, the ground state energy as a function of soft mode amplitude was calculated (Fig. 3a). Amplitude of the soft mode X 2 could be also described as a distance of oxygen atoms from their equilibrium position, dz. The energy has a double well form with minima at dz=±0.042 and the barrier of 0.07 ev/zro2 at dz=0. As it was expected at the minima of the ground state energies the Hellmann Feynman (H F) forces are equal to zero (Fig. 3b) and the imaginary frequencies of the soft Figure 3. The dependence of the ground-state energy of the cubic ZrO2 crystal (a), the Hellmann-Feynman forces generated on an oxygen atom (b) and soft-mode frequencies (c) on the amplitude of the soft mode. modes become real (Fig. 3c). Calculated magnitude of dz parameter dz=0.042, which describe a position of the oxygen atom in the tetragonal cell is in agreement with the experimental data. The free energy was calculated separately for the harmonic and anharmonic modes. The total free energy equals to the sum of both contributions. Contribution of the harmonic modes to the free energy of the cubic phase (solid line in Fig.4) was compared wit the total free energy which includes contribution from the anharmonic modes calculated for the potential in the form of the gauss plus parabola function (dashed line in Fig. 4)) and the potential described as the polynomial function (dotted line in Fig. 4). The anharmonic vibrations reduce the free energy of the system, though in the latter case the shift of the free energy line to lower values is smaller. Figure 4. The difference of free energies calculated for the cubic and tetragonal phases with respect to the free energy of the monoclinic phase for ZrO2. For the cubic phase three lines are presented: solid line contribution from harmonic vibrations only, dotted line free energy including anharmonic contribution of the polynomial form, dashed line - free energy including anharmonic contribution of the gauss-plus-parabola form.

14 12 Nevertheless, both approaches do not reduce the free energy enough to describe the stabilization of the ZrO2 crystal in the cubic phase. It seems that in the complete description of the lattice dynamics in the system with the soft modes, the phonon phonon interaction should be included. All calculations presented in Refs. [H1,H2] are performed in the harmonic approximation, hence the thermal expansion of the crystal was neglected. [H3] This paper concerns investigations of the structural phase transition in MgSiO 3. Under the pressure and at temperature occurring in the Earth mantle the MgSiO 3 mineral crystallizes in the structure of a perovskite. In 2004, in two independent laboratories the MgSiO3 crystal with other structure, so called post perovskite, was produced at temperature 2500 K and under the pressure GPa. This structure have been also reproduced in ab initio calculations performed at zero kelvins. The pressure and temperature at which MgSiO3 with the post perovskite structure exists corresponds to the conditions which appear between the mantle and the core of the Earth. Changes of MgSiO3 structure in this region could account for some of the seismic irregularities as discontinuity of the speed of seismic waves. Figure 5: The p T coexistence lines of perovskite (Pmnb) and post-perovskite(cmcm) phases of MgSiO3. The squares indicate pressure and temperature conditions at which the postperovskite structure was observed experimentally. Ref.3 and Ref.8 are described in Ref. [H3] The discovery of a high pressure phase in MgSiO 3 have stimulated our ab initio calculations to determine regions of the stability regions of each phase as a function of pressure and temperature. The structural data, the phonon dispersion relations and phonon spectra were calculated for both phases under various pressures. Then, within the quasiharmonic approximation, the Gibbs free energies were estimated and the bulk modulus and the volume expansion coefficient were calculated. It was shown that the thermoelastic properties of both phases are comparable, therefore they can not be responsible for the discontinuities of the speed of seismic waves observed in the mentioned layer of the Earth. The source of them is probably the layered character of the post perovskite structure that causes the anisotropy of the compressibility along the different crystal axes. Finally, we have determined the p T coexistence line between the perovskite and the post perovskite phases (Fig. 5). At high temperature it is a straight line with the slope which agrees with the results of previous calculations performed using another method. [H4] The same techniques of calculations were applied to verify the stability of the multilayered Fem/Aun structures ( m,n a number of the monoatomic Fe and Au layers) for different combination of m and n. The formation energy calculated for this artificial systems is positive, proving that the formation of Fe/Au layered structures is energetically unfavorable. The largest formation energy is observed for Fe1/Au1 and Fe3/Au1. In terms of the lattice dynamics only structures containing

15 13 monoatomic layer of Fe or Au atoms are unstable. Their phonon dispersion relations exhibit existence of the soft modes (Fig. 6). The other multilayered structures Fem/Aun (m>1 and n>1) are stable. The calculations of the phonon dispersion relations shown in Fig. 6 are performed for the perfect structures where the Au and Fe atoms are placed in the high symmetry crystallographic sites with optimized values of the lattice constants. Figure 6. The phonon dispersion relations of the multilayers: : (a) Fe1/Au1, (b) Fe1/Au2, (c) Fe1 /Au3, (d) /Fe1/Au5, (e) Fe2/Au2, (f) Fe2/Au4, (g) Fe3/Au3, (h) Fe3/Au1. Figure 7. The phonon dispersion relations of the multilayers after atomic relaxations: (a) the Fe1/Au1, (b) Fe1/Au3. The stable configuration of the multilayer structure can be formed after the condensation of the soft phonon mode. Thus, using the displacement pattern of soft modes, the dynamically stable lower symmetry configurations for Fe1/Au1 and Fe1/Au3 multilayers were found (Fig. 7). In the case of Fe1/Au3 two subsequent optimizations procedures were necessary since the orthorhombic structure obtained after the first optimization was still unstable. The total energies of reconstructed systems decrease. In both relaxed structures, the Fe atoms are shifted from their initial positions in (x,y) plane only, and the Au atoms are also shifted along the z axis. Results of the calculations reproduce the experimental findings. The formation of good quality Fem/Aun multilayers with the atomic layer thickness larger than one monolayer is evidenced in many experiments whereas the obtained Fe1/Au1 structures always have limited degree of order. The ordering process in which monoatomic layers of Au and Fe are stacked alternately, forming the Fe1/Au1 structure, seems to be influenced by the complex growth of Fe monolayer on the Au surface. In the calculations, the ferromagnetic order of the iron magnetic moments was assumed. In comparison to the bulk Fe crystal the magnetic moments on iron atoms are enhanced. The largest values of the magnetic moments are observed for the structures with Fe monolayer. The Au layers are weakly magnetically polarized by the neighboring Fe layers. [H5] Artificial multilayered structures consisting of magnetic layers separated by nonmagnetic metal spacers have attracted much interest due to their unique physical properties and the

16 14 technological applicability. The subject of this paper is investigation of the magnetic interactions in the stable Fen/Aum multilayered structures. The calculations were performed for the configurations with parallel and antiparallel ordering of adjacent Fe layers ordered ferromagnetically. The magnitudes of the magnetic moments are independent weather the ferro or antiferomagnetic order of adjacent layers are considered (Fig. 8). The induced magnetic moments of Au atoms in the interfacial layer are parallel to the moments of the Fe atoms. Figure 8. Distribution of magnitudes of the magnetic moments in the cell of Fe2/Au10 and Fe4/Au8 for magnetic configurations with antiferromagnetic (upper panels) and ferromagnetic (lower panels) order of Fe layers separated by Au spacers. The induced Au moments are enlarger by a factor of 40. Analyzing the calculated distribution of magnitude of the magnetic moments in different Fe and Au monolayers four important conclusions can be formulated: the largest magnetic moments are observed on Fe atoms placed at the interfacial sites, and their magnitudes increase with the thickness of the Fe layer, the magnetic moments of the Fe and Au interface atoms do not depend on the Au spacer thickness, the magnitudes of the magnetic moments induced at Au atoms the interfacial layer are an order of magnitude smaller than those on the Fe atoms, the value of the magnetic moment of subsequent Au monolayers drops by an order of magnitude, and consequently it equals to zero for the middle Au monolayer, for the gold layers thicker than three monolayers. The main aim of the work was to determine which structure dominates for a particular set of the Fe and Au layers thicknesses (Table I). The ferromagnetic ordering is predicted in multilayers with small Au spacer thicknesses, up to 5 monolayers, independently on thickness of the iron layer. For Au spacer with 6 monolayers, different magnetic ordering is observed for structures with 2 or 4 Fe monolayers and with 6 Fe monolayers. The Fe 6/Au6 structure is still ferromagnetic, while Fe2/Au6 and Fe4/Au6 structures are antiferromagnetically ordered. For spacers with 8 Au monolayers, the antiferromagnetic arrangement is always the lowest energy configuration. The calculations should be very accurate since one has to confirm the total energies of the order of hundreds electronvolts per supercell and detect differences of the order of a few tens of milielectronvolts.

17 15 Table I. The difference of the total energies, ΔE = EAFM EFM between the antifferomagnetic and ferrro magnetic configurations of the magnetic moments of two iron layers separated by Au spacer of increasing size. In paranthesis, the number of atoms forming each supercell is presented. [H6] The paper presents the results of the experimental and theoretical studies on the metastable bcc phase of cobalt. The experimental group from the Catholic University of Leuven prepared the samples and performed measurements of the phonon density of states on the 57Fe probe atoms introduced to the stable fcc and metastable thin films of bcc cobalt, using the technique of nuclear resonant inelastic scattering of synchrotron radiation. The matastable bcc Co phase was produced as multilayered structure of a bcc Fe0.1Co0.9 layer placed between bcc Fe layers: [56Fe(2.4 nm)/57fe0.1co0.9(1.7 nm)]20. The results of experiments inspired us to perform the theoretical calculations. In the left panel of Fig. 10 the calculated phonon dispersion relations and phonon density of states spectra for the pure fcc Co and bcc Co crystals, and the bcc Fe4/Co4 superlattice are presented. As it is shown only the fcc structure is stable (all phonon frequencies are positive). Figure 10: The phonon dispersion relations and the phonon density of states calculated for the pure fcc Co and bcc Co crystals and bcc Fe4/Co4 superlattice (left panel) and for the same structures doped with Fe atoms (right panel).

18 16 In our calculations, the structures with a specific Fe dopant concentration were approximated by the supercells with one of the Co atoms replaced by an additional Fe atom. The resulted Fe content in doped structures, , was slightly lower than the iron concentration in the samples used in the experiment. The phonon dispersion relations calculated for Fe doped structures are shown in the right panel of Fig. 10. The amount of Fe atoms introduced into the bcc Co phase seems to be insufficient to stabilize the bcc Co crystal contrary to the bcc Fe4/Co4 layered structure that becomes stable. Concluding, it was proven that the metastable bcc Co layer placed between Fe layers can be stabilized by the addition of Fe atoms. The iron atoms included into the bcc Co cause the increase of the force constants and stabilizes its surroundings in the bcc structure which is forced by neighboring bcc Fe layers. Thus both the Fe layers and the Fe atoms diluted in the Co layer play very important role in the stabilization process of the bcc Co phase. Additionally, the shifts of the highest frequency peak observed experimentally in the phonon density of states measured for bcc Fe, bcc Fe0.1Co0.9 and fcc Fe crystals were reproduced in the calculations. [H7] The ordered FePt alloy with L1 0 structure is a multilayered structure which can be called the Fe1/Pt1 structure using the notation applied previously for Fe m/aun multilayers. Our calculations showed that contrary to the Fe 1/Au1, Fe1/Pt is dynamically stable since the all calculated phonon frequencies are real. The aim of the work was to investigate the phonon densities of states of the FePt alloy along different crystallographic axes of the tetragonal cell. The experimental group from the Catholic University of Leuven performed measurements of the phonon density of states for two thirty nanometers thick samples grown on MgO(100) and MgO(110) substrates which allowed to measure the phonon density of states along two directions corresponding to the (1,0,0) and (1,0,1) directions in the tetragonal FePt crystal. Then the phonon density of states along (0,0,1) direction, it means along the tetragonal c axes, was extracted. It was observed that the a axis projected vibrations were found in a wide range of phonon frequencies contrary to the c axis density of states which shows mainly one mode at about 29 mev. This strong anisotropy in the phonon density of states along the a and c axes was confirmed in the ab initio calculations (Fig. 11). Figure 11. The Fe partial phonon densities of states measured (black points) and calculated (red solid line) along the different crystalline axes of the FePt crystal. Taking into account that the experimental spectra reflect mainly the dynamic behavior of the monolayers closed to the surface of the sample, additional calculations were performed for a system composed of three FePt atomic bilayers which simulate the (100) oriented sample with two free

19 17 surfaces Fe and Pt. Comparison of the calculated phonon densities with the experimental data allows to conclude that the FePt(100) multilayer structure is Pt terminated. The Fe terminated surface should impose generation of the low energy modes which are not observed experimentally. Summary The first three of the presented papers concern the determination of the stability limits in the various phases of the bulk crystals. The calculations were performed for ZrO2 at ambient pressure within the harmonic approximation [H1,H2] and for MgSiO3 under high pressure using the quasiharmonic approximation [H3]. The main results are: calculations and analysis of the dispersion relations of all three phases of ZrO2 under ambient pressure, estimation of the free energies for tetragonal and monoclinic phases of ZrO2 that allows to describe the phase transition as a first order one and to determine the transition temperature, verification that approximation with the noninteracting anharmonic vibrations in the double well potential does not reduce the free energy sufficiently to describe properly the phase transition with the soft phonon mode, determination of the coexistence line between the perovskite and post perovskite phases of MgSiO3 in the p T phase diagram, finding that the thermoelastic properties of both MgSiO 3 phases occurring in the Earth's mantle are similar. Two subsequent papers [H4,H5] concern investigations of the stability and the magnetic properties of the artificially produced multilayered structures Fe m/aun. The limited stability of the low periodicity Fem/Aun multilayers explains the experimentally observed difficulties in the preparation of the materials with monoatomic layers of Fe or Au. It was demonstrated, how to get the stable Fe1/Au1 or Fe1/Au3 structures allowing the atomic relaxation corresponding to the displacements of the atoms in agreement with the soft mode. The stable Fe 1/Au1 or Fe1/Au3 multilayered structures after relaxation are presented. The calculations which included the spin polarization allowed to determine distribution of magnitudes of the magnetic moments in different monolayers. It was shown that for the Au spacer with more than five monolayers, magnetic order of Fe layers separated by this spacer changes from the ferromagnetic to the antiferromagnetic. For comparison, in Ref. [H7] calculations of the dynamical properties of ordered FePt alloy, being an example of the multilayered Fe1/Pt1 structure occurring naturally, are reported. The calculations have confirmed the existence of the strong anisotropy of the phonon density of states observed experimentally. It is expected that the main features of the anisotropic phonon density of states are not limited to Fe1/Pt1 but are representative for the other multilayered structures. In addition, it was shown that the Fe/Pt multilayer Fe/Pt is Pt terminated. The problem of the stabilization of the metastable bcc Co phase which does not occur in the nature is the subject of the paper [H6]. It was shown, that the bcc Co is dynamically unstable. However, both experimental and theoretical studies have proved that the bcc Co layer closed between two bcc Fe layers can be stabilized by the Fe dopant atoms. The publications [H1] [H5] present results of the ab initio calculations which were inspired to the large extend by the already existing experimental data. The papers [H6] and [H7], were done together with the experimental group from the Catholic University of Leuven. They contain both the experimental data and the results of the ab initio theoretical calculations.