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The 5th Workshop on ab initio phonon calculations will be organized in the Institute of Nuclear Physics on December 3-6, 2019. From the beginning, the workshop was focused on the first-principles studies with a special emphasis on lattice-dynamical properties of materials. During the previous workshops, the lectures and posters presented recent developments in the computational techniques and softwares as well as applications of these methods to current scientific problems.
Phonons play an important role in solids and determine the thermal properties of all kinds of materials. Lattice vibrations are responsible for such phenomena like superconductivity and structural phase transitions. Many relevant quantities such as heat capacity, thermal expansion, mean-square displacements, dielectric functions, electric and heat conductivity can be derived from phonon spectra.
The aim of this workshop is to provide the fundamentals of phonon calculations based on the ab initio methods and present the applications of such methods to numerous physical problems. The lectures on the computational programs are presented by the experts who create and develop computer packages (VASP, Wien2k, Phonon, Alamode, TDEP).
Recent achievements in experimental and sample preparation techniques enable to study new classes of materials ranging from complex oxide heterostructures to very small nano-objects (like monoatomic layers or nanoparticles). This challenges the computational methods and stimulates further progress in theoretical physics. On the other hand, the information obtained from the calculations is very supportive for experiments such as the inelastic neutron and X-ray scattering, nuclear inelastic scattering, infrared and Raman measurements.
The workshop is a good opportunity for the experts from different areas of condensed matter physics to meet and discuss, and often it becomes a starting point of new studies and new collaborations.
The workshop in 2019 will present the recent theoretical and experimental achievements in a broad range of research fields such as:
Steering Committee:
Organizing Committee:
Describing atomic vibrations from first-principles accurately is of paramount importance to understand the thermodynamic and transport properties of solids. Phonon dispersions are routinely calculated within the harmonic approximation, and transport properties can be studied by estimating the electron-phonon and phonon-phonon interactions within perturbation theory. Nevertheless, whenever the amplitude of the atomic displacements largely exceeds the range in which the harmonic potential is valid, the harmonic approximation completely fails without allowing a perturbative expansion.
The stochastic self-consistent harmonic approximation (SSCHA) that we have developed [1--4] offers an efficient method to calculate vibrational properties of solids even when the harmonic approximation completely collapses. The method is variational and takes into account quantum and thermal effects rigorously. With our recent developments on the SSCHA method [3], we show how phonon frequencies should be defined from the second derivative of the free energy, which allows calculating the transition temperature of structural second-order phase transitions. Moreover, the new developments [3] allow calculating third-order anharmonic force-constants, which determine thermal properties, beyond the perturbative limit. Also we are now capable of calculating the stress tensor including quantum/anharmonic effects and perform structural relaxations in this quantum/anharmonic energy landscape, in contrast to the classical calculations just focused on the classical Born-Oppenheimer energy surface.
In this lecture we will present the method and several applications of it in superconducting hydrides, charge-density-wave systems, and thermoelectric materials.
Refs
[1] I. Errea, M. Calandra and F. Mauri, Phys. Rev. Lett. {\bf 111}, 177002 (2013).
[2] I. Errea, M. Calandra and F. Mauri, Phys. Rev. B {\bf 89}, 064302 (2014).
[3] R. Bianco, I. Errea, L. Paulatto, M. Calandra and F. Mauri, Phys. Rev. B {\bf 96}, 014111 (2017).
[4] L. Monacelli, I. Errea, M. Calandra and F. Mauri, Phys. Rev. B {\bf 98}, 024106 (2018).
{\it Ab initio} phonon calculation plays an essential role in the modern computational materials science study, which aims to predict and elucidate thermodynamic and transport properties of materials at finite temperature. The harmonic approximation in phonon calculation is very useful and has been successful for many materials. However, it naturally fails to describe anharmonic properties and often breaks down in many energy- and light-harvesting materials. Therefore, developing a more accurate and versatile phonon calculation method that can handle strong anharmonicity is vital.
To overcome the limitation of the conventional phonon calculation method, we have been developing the \textsc{alamode} [1], an opensource software for anharmonicity and thermal transport. In this talk, I will present several features of \textsc{alamode}, including the self-consistent phonon calculation [2] and the efficient estimation of force constants [3,4], as well as its applications to thermoelectric materials [5] and ceramics [6].
Refs
[1] https://github.com/ttadano/alamode
[2] T. Tadano and S. Tsuneyuki, Phys. Rev. B {\bf 92}, 054301 (2015); J. Phys. Soc. Jpn. {\bf 87}, 041015 (2018).
[3] F. Zhou, W. Nielson, Y. Xia and V. Ozoliņš, Phys. Rev. Lett. {\bf 113}, 185501 (2014).
[4] https://alm.readthedocs.io/en/develop/
[5] T. Tadano, Y. Gohda and S. Tsuneyuki, Phys. Rev. Lett. {\bf 114}, 095501 (2015); T. Tadano and S. Tsuneyuki, Phys. Rev. Lett. {\bf 120}, 105901 (2018).
[6] Y. Oba, T. Tadano, R. Akashi and S. Tsuneyuki, Phys. Rev. Materials {\bf 3}, 033601 (2019).
Applying principles similar to those used in creation the harmonic PHONON software, a novel nonperturbative approach of the anharmonic lattice dynamics of crystals is proposed. The method treats a crystal as an ensemble of supercells, each with atoms displaced from equilibrium positions, such that the created POSCAR mimics the atomic configuration arising from all allowed excited phonons with amplitudes determined by the requested temperature. Next, using VASP and PhononA softwares the computed phonon dispersion curves are averages over created atom configurations to show the anharmonic phonon peaks and their finite widths and shifts. The method also allows to treat directly the soft modes. The thermal conductivity can be estimated after adopting the Green-Kubo formalism to the present non-perturbative method. Anharmonic results for fcc-Pb, bcc-W, cubic-Si, fcc-MgO, mineral-MgSiO$_3$, AlN, MgB$_2$ and soft mode in NiTi will be shown. The calculated anharmonic behaviour of MgB$_2$ superconductor is well reproduced with the proposed method, including the giant width of $E_{2g}$ phonon branch in agreement to its x-ray measurements.
For other crystals, when available, the results are compared to measured data.
The complete formulations of the harmonic and anharmonic theories is only shortly presented. The details can be found in the recent paper of the author, Phys.\ Rev.\ B {\bf 98}, 054305 (2018). The method is highly parallel and computationally very fast, since using VASP, in general it requires only single run of ionic loop for each atomic configuration POSCAR. Typically, a comprehensive anharmonic study of a material takes less than a~(few) day(s).
The importance of anharmonicity for describing fundamental materials properties, starting from finite heat conductivity due to phonon-phonon scattering, can hardly be overemphasized. For crystalline matter, the pertinent information is captured to a large part by considering $q$-dependent phonon lifetimes, leading to a broadening in energy of the phonon dispersions. The prevalent way of computing these broadenings theoretically is by employing perturbation theory, being of comparable effort as the computation of the dispersions in the harmonic approximation. Conversely, the experimental determination of phonon linewidths is much more involved, and only a small number of data sets covering large parts of reciprocal space at elevated temperatures, where anharmonic effects will be most pronounced, have been reported. Thus, theoretical computations today go largely unvalidated.
Here I will consider the case of elemental Al at temperatures up to the melting point. I will present experimental data obtained by inelastic neutron scattering with consideration to the necessary steps in data analysis for being able to extract the inherent linewidths. Further, I will present calculations of $q$-dependent line broadenings on the basis of density-functional theory, both in the standard approach of perturbation theory as well as via ab initio molecular dynamics, and discuss their discrepancies. Finally, I will analyse the short-range atomic interactions and show how numerically efficient phenomenological potentials can be constructed that allow to compute anharmonic properties beyond the limitations of perturbation theory at very small computational effort.
We present recent developments using the temperature dependent effective
potential technique (TDEP) to model strongly non-harmonic materials. The
method employs model Hamiltonians that explicitly depend on temperature.
I will present applications pertaining to thermal conductivity,
inelastic neutron spectra and phase stabilities. In addition, we
investigate non-linear electron-phonon coupling and its influence on
phonon spectra, and recent additions to that deal with nuclear quantum
effects and efficient stochastic sampling.
Recently developed methods [1--3] of computational investigation of anharmonic and temperature-dependent aspects of lattice dynamics are based on building of some form of model potential. Parameters of such a model are derived from the forces acting on atoms and requires replication of the conditions of thermal equilibrium -- to obtain proper sampling of the phase space region occupied by the system. This requirement is very challenging when performing quantum mechanical calculations. Typically, it involves large number of atoms and long simulation times needed to approximate thermodynamical limit conditions. It is usually achieved by running a long molecular-dynamics calculation on the system, to thermalize all degrees of freedom, and selecting well-separated (independent) configurations from the obtained trajectory. While this approach provides good sampling of the phase space of the system, it is computationally very expensive and exceptionally wasteful. To obtain independent samples the selected times in the trajectory must be separated by multiple time steps -- often tenths or hundreds. Thus, we are throwing away a large amount of computational time, often above 80%, to obtain good sampling of the probability distribution of the system. Furthermore, in the case of lattice-dynamical calculations, we are utilizing only the positions from the trajectory - since the velocity information is not used in the process. Together, this makes the described procedure limited to fairly small systems.
In this work we present an alternative scheme for creating a representation of the probability distribution in the configuration space, which aims to faithfully reproduce densities generated by the molecular dynamics, while being more effective in terms of computational time. This approach uses well-known techniques of probability distribution modelling, and apply knowledge of the behaviour of the system in thermodynamic equilibrium to obtain low sample rejection rate in the procedure. The proposed method, coupled with the effective-potential modelling provides a promising path to tackle problems of anharmonic and temperature-dependent lattice dynamics even in systems with large and complicated unit cells.
This work was partially supported by National Science Centre (NCN, Poland) under grant UMO-2014/13/B/ST3/04393.
Refs
[1] O. Hellman, I. A. Abrikosov and S. I. Simak, Phys. Rev. B {\bf 84}, 180301(R) (2011).
[2] I. Errea, M. Calandra and F. Mauri, Phys. Rev. Lett. {\bf 111}, 177002 (2013).
[3] T. Tadano, Y. Gohda and S. Tsuneyuki, J. Phys. Condens. Matter {\bf 26}, 225402 (2014).
The extraction of harmonic and anharmonic force constants from {\it ab-initio} calculations is often the bottleneck when calculating thermal properties.
The commonly used direct approach is robust but suffers from poor scaling with respect to system symmetry, size, and force constant expansion order.
During the last decade regularized regression based approaches have proved viable for efficient and accurate extraction of anharmonic force constants.
Even though computational effort is saved at the {\it ab-initio} level the regression itself can still be a formidable task.
To this point no consensus exists about what regularization method to use nor have different regression methods been comprehensively compared.
In order to use regression methods in {\it e.g.}, high throughput computations, robust methods for sampling and fitting must be developed.
Thus a flexible framework which can easily interface to other codes is needed in order to study and benchmark different methods.
Here, we present the \textsc{hiphive} package, which is entirely written in Python for easy accessibility and interfaces well with libraries such as scikit-learn, which provides a rich set of methods for linear regression and validation.
The core goal of \textsc{hiphive} is to focus on the extraction of force constants while leaving the analysis ({\it e.g.}, phonon dispersions or thermal conductivity) to other more specialized packages.
We show that ordinary least-squares, especially in connection with feature elimination, often yields the best performance in terms of convergence with respect to training set size and sparsity of the solution.
The automatic relevance determination regression (ARDR) method also shows promising performance.
Regression based on the least absolute shrinkage and selection operator (LASSO) on the other hand, while useful in some cases, tends to yield a larger number of features, with a~noise level that has a detrimental effect on the prediction of {\it e.g.}, the thermal conductivity.
Finally, we also consider methods for the prediction of the temperature dependence of vibrational spectra from high-order FC expansions via molecular dynamics simulations as well as self-consistent phonons.
Nuclear Resonant Inelastic X-ray Scattering (NRIXS) is a spectroscopy method to study atomic vibrations and dynamics, currently done with synchrotron radiation at a few high energy third generation facilities. It finds a wide range of applications in condensed matter physics, materials science, chemistry, biophysics, geosciences, and high-pressure researches. Many atomic dynamics and lattice thermodynamics information can be derived from NRIXS measurements. Phonon Density of States (DOS) characterizes lattice dynamics of a material and can be derived under the {\it quasi}-harmonic approximation. Combined with modelling and simulations, results from NRIXS can provide unique and clarifying insights into many fields of research.
The interpretation of NRIXS measurements has been done mostly in the context of {\it quasi}-harmonic approximation. Phonon density of states and dynamic properties like mean kinetic energy and mean force constant can be derived.
Going beyond the harmonic lattice model, we show that the anharmonic terms in the lattice potential can be measured. This opens up the NRIXS method to study anharmonicities in materials.
Given any {\it ab initio} model or specific model of lattice potentials, one can calculate the moments of a would-be measured NRIXS spectrum. Comparing them with NRIXS measurement results will help to restrict and adjust the models and calculations.
We will present a study of lattice anharmonicity in the sigma phase of Fe-Cr alloy, particularly the anomalous effect of magnetic structure on lattice dynamics.
Phonon lifetimes and heat conductivity of wurtzite aluminum nitride has been studied by two different computational methodologies. The first method uses a molecular dynamics equilibrium Green-Kubo formalism to compute the thermal conductivity. It requires large simulation cells and long simulation times, practically accessible using classical forcefield methods. The method can be extended to calculate wavevector and frequency resolved thermal conductivities and phonon lifetimes by projecting the heat flux onto the vibrational modes. The second approach used in the present study is to calculate these anharmonic processes by explicitly evaluating the anharmonic force constants. This is done using the PhononA package (Parlinski, Ab initio determination of anharmonic phonon peaks, 2018) and is based on forces extracted from supercell calculations.
The search for unconventional states in quantum matter is at the forefront of current research in solid state physics. In this respect, frustrated quantum magnets are topical candidates since they are widely known to be able to realize atypical ground states. In this class of systems frustrated J1--J2 quantum spin chains have attracted special attention since they have been demonstrated to realize {\it e.g.} helimagnetic order giving rise to spin-current induced type-II multiferroicity or they are currently discussed as candidates for spin-nematic phases. We have investigated the lattice properties of such system, like {\it e.g.} CuBr$_2$, CuCrO$_4$, LiCuVO$_4$ and observed magnetically induced negative thermal expansion, partially extending far into the short range correlated antiferromagnetically regime.
Transition metal (TM) cyanides are an exceptional class of framework materials exhibiting remarkable physico-chemical aspects in terms of: (i) photoluminescence, (ii) dimensionality, i.e. these systems can be of a 1-D, 2-D or 3-D nature, and (iii) disorder, they can be subject to different types of disorder; like a site disorder on the TM site and/or a disorder of the C$\equiv$N bond, as well as stacking disorder in the 2-D (layers) case or a slipping disorder in the 1-D (chains) case.
The main interest in these materials goes beyond the above mentioned properties to cover intriguing phenomena like negative linear compressibility and negative thermal expansion (NTE). In some typical cases of TM cyanides, NTE can be colossal and extending over a wide temperature range, making it quite interesting and attractive both on the fundamental level as well as on the practical side for relevant applications.
Thermal properties are intimately linked to phonons in crystalline materials. Therefore studying phonon dynamics helps to gain deeper insights into the dynamical mechanisms of TM cyanides exhibiting anomalous thermal properties. Inelastic neutron spectroscopy (INS) is an appropriate technique to study lattice dynamics of crystalline materials on the microscopic level, offering the perfect tool to cover dynamics on the targeted length and time scales.
The presentation will focus on highlighting the relationship between lattice dynamics and the observed anomalous thermal behaviour in some selected one- two- and three-dimensional TM cyanide structures, to explore the microscopic mechanisms at the origin of their intriguing thermal expansion properties, by using a combined approach of INS, underpinned by ab-initio phonon calculations. For the sake of complementarity, results using other techniques (PDF, NMR, {\it etc.}) will also be indicated as to highlight the synergistic aspect of structure and dynamics in these fascinating materials.
Despite successful application of the phase-change materials from the ternary Ge--Sb--Te system in a variety of optical data storage devices (CDs, DVDs and blue-ray disks) as well as in non-volatile random access memories (non-volatile RAM) [1--2], a comprehensive understanding of the mechanism underlying the phase transitions in the GST compounds is still lacking. A typical example is the temperature induced structural phase transition in GeTe, which is the parent compound of the GST phase-change materials. In particular, the nature of phase transition (displacive or order-disorder) and the driving force of the rhombohedral-to-cubic phase transformation at $T_c\approx 600$~K along with accompanying effects (volume contraction and disappearance/persistence of the Peierls distorted Ge--Te bonds above $T_c$) still remain a source of controversy in spite of numerous experimental and theoretical studies carried out over last 30 years [3--10].
This presentation addresses results of the inelastic neutron scattering (INS) experiments on powder GeTe samples and ab initio molecular dynamics (AIMD) simulations which have been undertaken to revisit lattice dynamics of GeTe as a function of temperature and examine behaviour of the local versus average structure of this compound across the structural phase transition. Generally, results of our experimental and theoretical research support observations provided by the so-called local probes (EXAFS and PDF analysis of the high-energy x-ray scattering).
Refs
[1] M. Wuttig and N. Yamada, Nat. Mater. {\bf 6}, 824 (2007).
[2] S. Raoux, F. Xiong, M. Wuttig and E. Pop, MRS Bull. {\bf 39}, 703 (2014).
[3] E. F. Steigmeier and G. Harbeke, Solid State Commun. {\bf 8}, 1275 (1970).
[4] T. Chattopadhyay, J. X. Boucherele and H. von Schnering, J. Phys. C {\bf 20}, 1431 (1987).
[5] P. Fons, A. V. Kolobov, M. Krbal, J. Tominaga, K. S. Andrikopoulos, S. N. Yannopoulos, G. A. Voyiatzis and T. Uruga, Phys. Rev. B {\bf 82}, 155209 (2010).
[6] T. Matsunaga, P. Fons, V. Kolobov, J. Tominaga and N. Yamada, Appl. Phys. Lett. {\bf 99}, 231907 (2011).
[7] U. D. Wdowik, K. Parlinski, S. Rols and T. Chatterji, Phys. Rev. B {\bf 89}, 224306 (2014).
[8] T. Chatterji, C. Kumar and U. D. Wdowik, Phys. Rev. B {\bf 91}, 054110 (2015).
[9] D. Yang, T. Chatterji, J. A. Schiemer and M. A. Carpenter, Phys. Rev. B {\bf 93}, 144109 (2016).
[10] D. Dangić, A. R. Murphy, E. D. Murray, S. Fahy and I. Savić, Phys. Rev. B {\bf 97}, 224106 (2018).
Recent widespread interest in topological materials intensified studies on various compounds containing heavy elements, like Pb or Bi. This is of course related to the strong spin-orbit coupling (SOC), which should be present in such materials, and should strongly influence their physical properties. Because some of these materials exhibit superconductivity, a natural question arises what is the spin-orbit coupling effect of the electron-phonon interaction and superconductivity of such materials, containing heavy elements?
Thanks to the ongoing development of computational techniques, calculations of the electron-phonon interaction function, taking into account the spin-orbit coupling, became available recently. In this work we present several case studies, where the spin-orbit interaction effects on the electronic structure, phonons, and the electron-phonon coupling (EPC) is investigated using density-functional calculations. As the prime example we will discuss the role of spin-orbit interaction in determining the electronic and phononic properties of the type-I superconductor CaBi$_2$ [1]. In this case SOC, mainly via the modifications of the Fermi surface topology, reduces the strength of EPC almost twice. As the next two cases we will present Pb-Bi alloy, with extremely strong electron-phonon coupling, and noncentrosymmetric ThCoC$_2$, where SOC splits the Fermi surface but surprisingly has a~little impact on the electron-phonon interaction.
This work was supported by the National Science Center (Poland), project no. 2017/ 26/E/ST3/00119.
Refs
[1] S. Gołąb and B. Wiendlocha, {\it Electron-phonon superconductivity in CaBi$_2$ and the role of spin-orbit interaction}, Phys. Rev. B {\bf 99}, 104520 (2019).
Using an {\it ab initio} approach, we report a phonon soft mode in the tetragonal structure described by the space group $I4_{1}22$ of the $1$ K $5d$ superconductor Cd$_2$Re$_2$O$_7$. It induces an orthorhombic distortion to a crystal structure described by the space group $F222$ which hosts the superconducting state. This new phase has a lower total energy than the other known crystal structures of Cd$_2$Re$_2$O$_7$. Comprehensive temperature dependent Raman scattering experiments on isotope enriched samples, $^{116}$Cd$_2$Re$_2{^{18}}$O$_7$, not only confirm the already known structural phase transitions but also allow us to identify a new characteristic temperature regime around $\approx 80$ K, below which the Raman spectra undergo remarkable changes with the development of several sharp modes and mode splitting. Together with the results of the {\it ab initio} phonon calculations we take these observations as strong evidence for another phase transition to a novel low-temperature crystal structure of Cd$_2$Re$_2$O$_7$.
Understanding the charge-ordering tendencies exhibited by the cuprates might give valuable insight into the origin of superconductivity in these complex oxides. The charge correlations may appear to manifest themselves as an anomalous dispersion (softening) of the longitudinal Cu--O bond-stretching phonon mode both in the hole-doped [1,2] and electron-doped cuprates [3]. In electron-doped Nd$_{2-x}$Ce$_x$CuO$_4$, the Charge Density Wave (CDW) order was found at the two-dimensional wave vector (H,K) $\approx$ (0.2,0), approximately the same wave vector at which an anomalous optical phonon dispersion was observed [3]. I will present our temperature and doping depended inelastic x-ray scattering (IXS) studies of the optical phonon anomaly. I will discuss it in the context of the CDW order in this compound. Our IXS studies will be furthermore compared with the DFT calculations performed for the parent compound Nd$_2$CuO$_4$.
Refs
[1] D. Reznik {\it et al.}, Nature {\bf 440}, 1170 (2006).
[2] D. Reznik, Physica C {\bf 481}, 75 (2012).
[3] M. d'Astuto {\it et al.}, Phys. Rev. Lett. {\bf 88}, 167002 (2002).
Recent development in the high-pressure physics provides us with a new class of the superconducting materials, namely with the hydrogen-rich materials, such as silane (SiH$_4$, transition temperature $T_c$=17~K at pressure $p$=96~GPa), hydrogen sulphide (H$_{2/3}$S, $T_c$=203~K @ 150~GPa) or hydrogen lanthanide (H$_{1-x}$La, $T_c$=274--286~K @ 210~GPa).
We investigate the versatility of the molecular-to-atomic transitions in one-, two-, and quasi-three-dimensional hydrogen systems, using our own original approach -- the Exact Diagonalization Ab-Initio (\textsc{edabi}) method. Starting from the extended Hubbard model, we examine an electron-correlation-driven conductivity connected with the creation of high-symmetry hydrogen molecular and atomic planes, as well as a series of both structural and electronic-in-nature quantum phase transitions.
We discuss the suppression of molecular nature in a reversed Peierls-like transition under high pressure, as well as the proper van-der-Waals-like effective interaction derived from the first principles of quantum mechanics.
Using effective electron-phonon Hamiltonian we estimate both the zero-point motion of the lattice ions, as well as the electron-lattice coupling. Next, by using the McMillan formula we estimate the superconducting transition temperature versus the effective pressure (external and/or chemical).
We acknowledge the support of National Science Centre (NCN) grant OPUS, No. UMO-2018/29/B/ST3/02646 and the European Regional Development Fund in the IT4Inno-va-tions national supercomputing center -- path to exascale project, project number CZ 02.1.01/-0.0-/0.0-/16-013/0001791 within the Operational Programme Research, Development and Education.
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Theoretical description of nonzero temperatures, including effects of spin fluctuations, has been problematic for a long time. In recent years, the alloy analogy model (AAM) became popular for a treatment of finite-temperature effects from the first principles [1]. Phonons, described as uncorrelated displacements of atoms, can be combined with spin fluctuations (magnons) and chemical disorder. The realistic inclusion of spin fluctuations is crucial especially for spintronic properties such as the spin polarization of the electrical current.
The AAM within the tight-binding linear-muffin-tin orbital method and the coherent potential approximation (CPA) successfully describes electrical transport at nonzero temperatures even in multisublattice half-Heusler alloys [2]. In the previous studies (i) the Debye theory was employed for a conversion between displacements and temperature, (ii) the total magnetization as a function of temperature was obtained from experiments, and (iii) a change of a volume with temperature was neglected. These simplification will be addressed in details. A route to overcome it by proper ab initio approaches is envisaged. Obtained corrections are a few percents (compared to the previous techniques) for some materials. However, this more precise approach is essential for systems where the Debye theory fails. Moreover, the description of finite temperatures is finally obtained completely from the first principles. It is done by synergizing precise supercell methods with the numerically efficient CPA. We will present the usage of novel techniques for pure transition metals, both nonmagnetic and magnetic, but it can be easily generalized for more complex systems, such as previously studied random and ordered [2] alloys.
This work was supported by the European Regional Development Fund in the IT4-Inno-va-tions national supercomputing center -- path to exascale project, project number CZ.02.1.01/0.0/0.0/16{\textunderscore}013/0001791 within the Operational Programme Research, Development and Education and grant No. 17-27790S of the Czech Science Foundation and SGS project No.SP2019/110.
Refs
[1] D. Wagenknecht {\it et al.}, IEEE Trans. on Mag. {\bf 53} 11, 1700205 (2017).
[2] D. Wagenknecht {\it et al.}, J. Magn. Magn. Mater {\bf 474}, 517--521 (2019).
The coupling of spin waves to phonons allows to probe the collective spin dynamics in quantum materials via phonon spectroscopy. This allows for novel experiments and the control of magnetic interactions via lattice degrees of freedom. In this presentation, I~will show, that the strong magnon-phonon coupling in the triangular lattice Heisenberg antiferromagnets LiCrO$_2$ and PdCrO$_2$ enables the measurement of magnetic correlations throughout the Brillouin zone via inelastic x-ray scattering. Our studies reveal intrinsic details of the magnetoelastic excitation spectrum. We find single particle excitations with momentum dependent lifetime and continuum scattering at low temperature [1]. In a~high-pressure experiment at cryogenic temperatures we furthermore show that tuning the lattice allows for efficient control of magnetic interactions. With help of {\it ab initio} phonon calculations combined with linear spin wave theory we are able to quantify the spin lattice coupling and address the coupling to the two-magnon continuum. I furthermore introduce a novel methodology that allows for high-precision measurements of the full elasticity tensor from thermal diffuse scattering [2].
Refs
[1] S. Tóth, B. Wehinger, K. Rolfs, T. Birol, U. Stuhr, H. Takatsu, K. Kimura, T. Kimura, H.~M. Rønnow and Ch. Rüegg, {\it Electromagnon dispersion probed by inelastic X-ray scattering in LiCrO$_2$}, Nat. Commun. {\bf 7}, 13547 (2016).
[2] B. Wehinger, A. Mirone, M. Krisch and A. Bosak, {\it Full Elasticity Tensor from Thermal Diffuse Scattering}, Phys. Rev. Lett. {\bf 118}, 035502 (2017).
An effect of magnetism on lattice dynamics is considered as negligible. Such belief is based on calculations according to which the spin susceptibility of metal is not affected by the electron-phonon interaction (EPI) ([1] and references therein). Indeed, the effect of the EPI was estimated as E$_{\rm D}$/E$_{\rm F}$=10$^{-2}$ ([1] and references therein) where E$_{\rm F}$ is the Fermi energy, and E$_{\rm D}$ is the Debye energy. However, Kim showed [1] that the influence of the EPI on spin susceptibility can be significantly, i.e. by a factor of 100, enhanced by exchange interactions between electrons. In other words, the effect of the EPI on magnetic properties of metallic systems, and vice versa, is much more significant than generally believed. The Mössbauer spectroscopy (MS) is a well-suited method for studying the lattice dynamics via two spectral parameters viz. (1) center shift, CS, and (2) recoil-free factor, f. The former gives information on an average squared velocity of vibrations, <v$^2$>, while the latter is related to average squared amplitude of vibrations, <x$^2$>. Presented and discussed will be relevant results obtained with the MS for sigma-phase Fe--Cr and Fe--V alloys [2,3], C14 Laves phase NbFe$_2$ [4], spin-density waves Cr doped with $^{57}$Fe [5], and last but not least, the effect of magnetism on sound velocity in the $\sigma$-FeCr alloy studied with the nuclear inelastic scattering of synchrotron radiation [6].
Refs
[1] D. J. Kim, Phys. Rep. {\bf 171}, 129 (1988).
[2] S. M. Dubiel {\it et al.}, EPL {\bf 101}, 16008 (2013).
[3] S. M. Dubiel and J. Żukrowski, J. Magn. Magn. Mater., {\bf 441}, 557 (2017).
[4] J. Żukrowski and S. M. Dubiel, J. Appl. Phys. {\bf 123}, 223902 (2018).
[5] S. M. Dubiel {\it et al.}, J. Phys.: Condens. Matter {\bf 22}, 435403 (2010).
[6] S. M. Dubiel and A. I. Chumakov, EPL {\bf 117}, 56001 (2017).
I will give a review on augmented plane wave (APW) methods for the calculation of the electronic structure in solids starting with the original concept developed by J. Slater [1] long time ago up to the APW+lo method introduced by Sjöstedt {\it et al.} [2]. This latter method combines the superior convergence behaviour of the original APW method with the convenience of LAPW [3]. I will then give an overview of the implementation of APW+lo into the WIEN2k code [4] and summarize the available features and discuss in particular the possibilities connected with calculations of phonons.
Selected results will be discussed in more detail. This will include phase transitions in RbCaF$_3$ [5] and PbTiO$_3$ [6] as well as a finite temperature (phonon) related explanation of a double peak occurring in the B-K XANES spectra of h-BN [7].
Refs
[1] J. Slater, Phys. Rev. {\bf 51}, 151 (1937).
[2] E. Sjöstedt, L. Nordström and D. Singh, Solid State Commun. {\bf 114}, 15 (2000).
[3] G. K. H. Madsen, P. Blaha, K. Schwarz, E. Sjöstedt and L. Nordström, Phys. Rev. B {\bf 64}, 195134 (2001).
[4] http://www.wien2k.at
[5] S. Ehsan, A. Tröster, F. Tran and P. Blaha, Phys Rev. Mat. {\bf 2}, 093610 (2018).
[6] A. Tröster, S. Ehsan, K. Belbase, P. Blaha, J. Kreisel and W. Schranz, Phys. Rev. B {\bf 95}, 064111 (2017).
[7] F. Karsai, M. Humer, E. Flage-Larsen, P. Blaha and G. Kresse, Phys. Rev. B {\bf 98}, 235205 (2018).
UMo alloys appear to be the most promising nuclear fuels for the conversion of highly enriched fuels that are currently used in research reactor cores, such as U$_3$Si$_2$, UAl alloys, or U$_3$O$_8$. These alloys have been selected because of their high uranium density, as well as their cubic crystal structure that guarantee isotropic swelling under irradiation. It is therefore crucial that we get some basic understanding of their thermal properties via the determination of phonon spectra and density of states. However, while a lot of work has been dedicated to the electronic structure of UMo with respect to the Mo content, there is little data related to the phonon dispersion curves.
In this work, we run ab initio molecular dynamics and we use TDEP method [1--3] and its SIFC extension [4] in order to calculate the phonon spectra of UMo alloys over the whole range of Mo concentrations. We compare the results with those of pure bcc uranium and molybdenum, as well with experimental results [5] in order to get a consistent and comprehensive picture of UMo thermodynamic properties. We show how the interplay between the addition of Mo and the temperature stabilizes the uranium bcc structure and we calculate a number of thermal properties derived from the phonon density of states, such as Gibbs free energies, phonon and electron thermal conductivities, Gruneisen parameters, expansion coefficients, {\it etc.}
Refs
[1] O. Hellman {\it et al.}, Phys. Rev. B {\bf 87}, 104111 (2013).
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[5] D. Chaney, R. Springell, G. H. Lander, private commucation.
Magnetic frustration is found in magnetic material when the individual spin moments cannot simultaneously minimize their magnetic interactions with their neighbored moments. As such, magnetically frustrated systems often support a highly degenerate ground state exhibiting a number of exotic physical phenomena such as spin ice [1] and spin liquid [2] states. Probing the spin and lattice dynamics in these systems provides an avenue to better understand the nature of these exotic states.
Rare-earth langasites are characterized by geometric magnetic frustration, exhibiting magneto-electric effects, high piezoelectric properties, and are seen as a possible candidate for a spin-liquid ground state [3]. Phonon and crystal electric field spectra provide important information to unravel the interplay between the structural and magnetic properties of the langasite family. The langasite structure crystallizes in the P321 space group with a general formula A$_3$BC$_3$D$_2$O$_{14}$, where magnetic rare-earth elements are situated at the A site of the structure.
Our study presents spectra of several rare-earth langasites RE$_3$Ga$_5$SiO$_{14}$ (RE = La, Nd, Ho) using Fourier-transform infrared (FTIR) reflection spectroscopy. Experiments have been performed with polarized radiation along the principal crystallographic axes and under different sample temperatures. Phonon excitations at unusually low frequencies are observed that brings the crystal structure of langasites close to a lattice instability. The results in the rare-earth langasite Nd$_3$Ga$_5$SiO$_{14}$ (NGS) and in a holmium-substituted langasite Ho$_{0.03}$La$_{2.97}$Ga$_5$SiO$_{14}$ (Ho-LGS) are compared with pure La$_3$Ga$_5$SiO$_{14}$ (LGS) langasite compound that does not show magnetic frustration.
Spectra with polarization parallel to the b$*$-axis of the crystal show a number of phonons between 100 and 400~cm$^{-1}$ with a weak temperature dependence indicating a stable crystalline structure. This behavior was found in all three investigated samples. Although they have the same crystalline structure, differences in the obtained dielectric function can be observed especially at low frequencies.
Phonon spectra in c-direction are dominated by a large excitation at unusually low frequencies (less than 50~cm$^{-1}$). In contrast to the other phonons modes, strong temperature effects are observed for the low frequency mode. For NGS the lowest phonon softens from 50~cm$^{-1}$ at room temperature to 20~cm$^{-1}$ at 10K that can be correlated with high static dielectric permittivity. This effect can be seen on the other crystals as well, but the effects are weaker. All phonons above a frequency of 100~cm$^{-1}$ behave like those of the b$*$-axis, no substantial shift of the frequency can be detected.
Because of the observed phonon softening, an instability in the structure of the langasites along the c-direction can be expected. The intriguing prospect of how this abnormal phonon may affect the magnetic dynamics in the frustrated compounds is explored.
This work was supported by the Austrian Science Fund FWF in the frame of Doctoral College “Solids4Fun”, Project No. W1243-N16.
\newpage
Refs
[1] M. J. Harris, S. T. Bramwell, D. F. McMorrow, T. Zeiske and K. W. Godfrey, {\it Geometrical frustration in the ferromagnetic pyrochlore Ho$_2$Ti$_2$O$_7$}, Phys. Rev. Lett. {\bf 79}, 2554 (1997).
[2] L. Savary and L. Balents, {\it Quantum spin liquids: A review}, Rep. Prog. Phys. {\bf 80}, 016502 (2017).
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Europium monoxide (EuO) is the first rare-earth semiconducting oxide known for its giant magneto-optic Kerr [1] and Faraday [2] effects, metal-to-insulator transition and anomalous Hall effect [4]. Presently, it is one of the favored candidates for applications as a spin filter in future spintronic devices due to the large exchange splitting of its conduction band [5]. Employing inelastic X-ray scattering, nuclear inelastic scattering and first-principles theory we determined the lattice dynamics of this material and discovered a giant and anisotropic spin-phonon coupling [6]. This discovery imposed an intriguing question about the manifestation of this phenomenon in thin and ultrathin films related to the proposed applications. Using $\textit{in situ}$ nuclear inelastic scattering on $^{151}$Eu we investigated the phonon density of states of EuO films with thickness between 8 nm and of 1 atomic layer. The experimental results unveiled drastic lattice dynamics modifications in the ultrathin EuO films that can be comprehensively understood by the help of first-principles theory [7].
S. S. acknowledges the financial support by the Helmholtz Association (VH-NG-625) and BMBF (05K16VK4). A.\ M.\ O.\ kindly acknowledges support by National Science Centre (NCN) under Project No.\ 2016/23/B/ST3/00839 and the Alexander von Humboldt Fellowship (Humboldt-Forschungspreis). P. P. acknowledges support by NCN under Project No. 2017/25/B/ST3/02586 and the access to ESRF financed by the Polish Ministry of Science and High Education – decision number: DIR/WK/2016/19.
Refs
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In this paper, we would like to show how phonon calculations can be used to improve the thermodynamic description of III-nitride surfaces in the context of growth by epitaxial methods. Theoretical atomistic analysis of the system representing the crystal surface in contact with the gas phase are often performed. In particular, density functional theory (DFT) calculations are leading method in this field. Unfortunately, this method describes the system at the temperature of absolute zero. In the standard approach of atomistic thermodynamics, the free energy of the vapour phase at a given temperature is considered, whereas the surface is described by the total energy determined on the basis of DFT calculations at 0~K. Phonon calculations can be successfully used to improve the accuracy of this theoretical model. Recently, we presented such an analysis that more accurately describes the hot GaN surface under growth conditions [1]. We included a contribution derived from thermal vibrations determined on the basis of phonon calculations for slabs representing the surface. In this way, several temperature-dependent properties of surface, such as vibrational energy and vibrational entropy can be determined. The thermal dependence of surface free energy was included in predicting the evolution of surface reconstruction under growth conditions, and thus the phase diagrams of the GaN(0001) surface were improved. The example of hydrogen adsorption on the GaN(0001) surface has shown that adding of accurate entropy contributions (vibrational and configurational) can significantly change the predicted equilibrium hydrogen pressure above the surface [2].
This work was partially supported by the National Science Centre of Poland grant number 2017/27/B/ST3/01899, the MEXT GaN R$\&$D Project and the Collaborative Research Program of the Research Institute for Applied Mechanics, Kyushu University.
Refs
[1] P. Kempisty, Y. Kangawa, Phys. Rev. B {\bf 100}, 085304 (2019).
[2] P. Kempisty, P. Strak, K. Sakowski, Y. Kangawa and S. Krukowski, Phys. Chem. Chem. Phys. {\bf 19}, 29676 (2017).
The lattice dynamics and structural properties of short-period (AlN)$_m$(GaN)$_n$ ($m$+$n$=4,8 or 12 monolayers) superlattices (SLs) grown by MOVPE and PA MBE on the (0001) Al$_2$O$_3$ substrate are studied both theoretically and experimentally. The genesis of the SL phonon modes from the modes of bulk AlN and GaN crystals is established by applying a comprehensive group-theoretical analysis. The lattice dynamics is studied by {\it ab initio} calculations within the framework of the density functional theory. The dynamical matrix for a set of SLs is calculated within density functional perturbation theory (DFPT) and phonon eigenvalues and eigenvectors at the $\Gamma$-point of the Brillouin zone (BZ) are obtained. The eigenvectors analysis is performed to establish the irreducible representation of each vibrational mode. The number and symmetry of vibrational modes in the calculated phonon spectra are in complete agreement with the results of the group-theoretical analysis.
The Raman tensor components are calculated within DFPT and the theoretical Raman spectra are simulated and compared with experimental ones. The results of the {\it ab initio} calculations are in a good agreement with the experimental Raman data. The microscopic nature of the SLs vibrational modes is established by complex analysis of the results obtained both theoretically and experimentally. It is revealed that the phonon spectrum of GaN/AlN SLs is composed by mainly two types of phonon modes (localized and delocalized). It is found that the $E$(TO) modes are localized in the constituent SL layers and can be used to obtain information about the individual characteristics of each layer forming the SL. It is shown that the localized nature of the mode of this symmetry is preserved even in the SL with the thinnest constituent layers, i.e. for $m$+$n$=4. In turn, the $A_1$(TO) mode has a delocalized nature. This allows one to use the parameters of this mode to estimate the averaged characteristics of the SL as a whole. The correlation dependencies between the SL structure and the frequencies of the confined and delocalized polar phonons are obtained. The results of the study form the basis for the quantitative estimation of both strain in individual layers forming the SL and the Al(Ga) content averaged over the SL period. They also open new possibilities for the analysis other important parameters of short-period GaN/AlN SLs.
The work is supported by Russian Science Foundation Project (Grant No. 19-72-30040).
Nanostructures of transition metal silicides have a wide range of possible applications and constitute fundamental building blocks of current micro- and nanoelectronics [1--3]. Among these compounds, FeSi$_2$ is particularly interesting since it is the only representative that exists in both metallic and semiconducting bulk-phase [4]. The high-temperature metallic $\alpha$-phase can be stabilized at room temperature by growth of metastable, surface-stabilized nanostructures on Si surfaces. While the electronic and magnetic properties of this material are studied extensively and reveal noteworthy results [5,6], only particular thermodynamic properties have been investigated and the lattice dynamics remains unknown until now.
In this work [7], we present an experimental and theoretical study of the lattice dynamics of surface-stabilized $\alpha$-phase FeSi$_2$ nanostructures epitaxially grown on the Si(111) surface, with average heights and widths ranging from 1.5 to 20 nm and 18 to 72 nm, respectively. The crystallographic orientation, surface morphology and local crystal structure of the nanostructures were investigated by reflection high-energy electron diffraction, atomic force microscopy and X-ray absorption spectroscopy. The Fe-partial phonon density of states (PDOS), obtained by nuclear inelastic scattering, exhibits a pronounced damping and broadening of the spectral features with decreasing average island height. First-principles calculations of the polarization-projected Si- and Fe-partial phonon dispersions and PDOS enable the disentanglement of the contribution of the $xy$- and $z$-polarized phonons to the experimental PDOS. Modelling of the experimental data with the {\it ab intio} results unveils an enhanced damping of the $z$-polarized phonons, while the $xy$-polarized phonons remain mostly unaffected. This phenomenon is attributed to the fact that the low-energy $z$-polarized phonons exhibit a stronger coupling to the low-energy surface/interface vibrational modes. The thermodynamic and elastic properties obtained from the experimental data show a pronounced size-dependent behaviour.
S.S. acknowledges the financial support by the Helmholtz Association (VH-NG-625) and BMBF (05K16VK4). P.P. acknowledges support by the Narodowe Centrum Nauki (NCN, National Science Centre) under Project No. 2017/25/B/ST3/02586 and the access to ESRF financed by the Polish Ministry of Science and High Education, decision number: DIR/WK/2016/19.
Refs
[1] S. P. Murarka, Intermetallics {\bf 3}, 173 (1995).
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[3] A. T. Burkov, Phys. Status Solidi (a) {\bf 215}, 654 (2018).
[4] S. Liang {\it et al.}, J. Cryst. Growth {\bf 295}, 166 (2006).
[5] J. K. Tripathi {\it et al.}, Nanotechnology {\bf 23}, 495603 (2012).
[6] G. Cao {\it et al.}, Phys. Rev. Lett. {\bf 114}, 147202 (2015).
[7] J. Kalt {\it et al.}, submitted (2019).
Research studies into the subject of radiation damage effects in graphite began in the early 1940’s as a part of the development of nuclear weapons and nuclear power research. Extensive measurements were performed to study changes to the thermal and mechanical properties of irradiated graphite. Many of these properties such as the thermal expansion coefficient, heat capacity, thermal conductivity, bulk modulus and elastic constants have some level of dependency on the vibrational spectrum. In this work, a series of measurements of the phonon densities of states of different samples of irradiated nuclear graphite were performed at room temperature using the state-of-art Wide Angular-Range Chopper Spectrometer (ARCS) at the neutron spallation source in Oak Ridge National Laboratory. The samples were exposed to different levels of neutron damage (up to $\approx30$ dpa) and irradiation temperatures (300--750$^\circ$C) [1]. The main differences in the phonon dispersion relations and phonon densities of states for samples with different irradiation conditions (damage and/or temperature) are identified. In addition, first-principles phonon density of states calculations of ideal and defected (di- and tetra-vacancy as well as single and di-interstitial) graphite are performed and compared with measured ones.
The irradiation of the specimens was performed at the Oak Ridge National Laboratory (ORNL) and sponsored by Tokai Carbon Co., Ltd. (NFE-09-02345) with the U.S. Department of Energy. A portion of this research at ORNL’s High Flux Isotope Reactor and the Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. Oak Ridge National Laboratory is managed by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 for the U.S. Department of Energy. Travel and time of I. I. Al-Qasir was supported by the University of Sharjah, UAE. This material is based upon work that was conducted by I. I. Al-Qasir while a Visiting Research Fellow at the Shull Wollan Center -- the University of Tennessee and Oak Ridge National Laboratory’s Joint Institute for Neutron Sciences. First-principles calculations were performed at the high-performance computing facility (SAQR) at the University of Sharjah.
Refs
[1] A. A. Campbell, Y. Katoh, M. A. Snead and K. Takizawa, {\it Property changes of G347A graphite due to neutron irradiation}, Carbon {\bf 109}, 860--873 (2016).
The elastic properties are fundamental and important for crystalline materials as they relate mechanical properties to thermodynamic ones, e.g., to the phonon dispersion and structural phase transformation. However, a complete set of experimentally determined elastic properties is only available for a small number of known materials. Therefore, an automatic scheme for the derivations of elastic properties that is adapted to high-throughput computation is much demanding. Here, we present the AELAS code, an automated program to calculate second-order elastic constants, moduli, anisotropy and phase stability criteria for both two-dimensional as well as three-dimensional crystal materials with any symmetry. The implementation of the code has been critically validated by a lot of evaluations and tests on a broad class of materials including two-dimensional and three-dimensional materials, providing its efficiency and capability for high-throughput screening of specific materials with targeted mechanical properties. As examples we demonstrate the AELAS capabilities for the three-dimensional structures, e.g., diamond and BN allotropes, and for the two-dimensional structures, e.g., the MXenes family.
Authors acknowledge the Czech Science Foundation with the grant No. 17-27790S, and the European Regional Development Fund in the IT4Innovations national supercomputing center -- path to exascale project, project number CZ 02.1.01/0.0/0.0/16-013/0001791 within the Operational Programme Research, Development and Education.
Refs
S. H. Zhang, R. F. Zhang, {\it AELAS: Automatic ELAStic property derivations via high-throughput first-principles computation}, Comput. Phys. Commun. {\bf 220}, 403--416 (2017).
For many technological applications, it is important to predict the physical properties at finite temperature. For example, magnetic materials suitable for permanent magnet applications must show large saturation magnetization and high magneto-crystalline anisotropy at elevated temperatures. Thus, predictions made by using DFT calculations at $T$=0~K should be validated for finite temperatures. An interesting example is the Fe--Sn binary system with some phases, like Fe$_3$Sn, which is a ferromagnet, experimentally stabilized at temperatures above 750$^\circ$C [1]. At finite temperatures one of the main contributions to the free energy is due to the atomic vibrations and it can be estimated, in many cases, within the quasi-harmonic approximation. In the case of Fe--Sn binary systems, however, the account of lattice dynamics is necessary for an accurate description of phase diagram even at $T$=0~K. At low temperatures, there exist three experimentally observed structures: Fe$_3$Sn$_2$, FeSn, and FeSn$_2$. The DFT calculations at $T$=0~K predict that enthalpy of formation of all these phases is positive. In this work, we show that these experimentally observed phases are energetically stabilized by phonons. We also calculate the finite temperature phase diagram at elevated temperatures.
This work was supported by the European Regional Development Fund in the IT4In-no-va-tions national supercomputing center -- path to exascale project, project number CZ.02.1. 01/0.0/0.0/16--013/0001791 within the Operational Programme Research, Development and Education, grant No. 17-27790S of the Czech Science Foundation and SGS project No. SP2019/110.
Refs
[1] C. Echevarria-Bonet {\it et al.}, {\it Structural and magnetic properties of hexagonal Fe$_3$Sn prepared by non-equilibrium techniques}, Journal of Alloys and Compounds {\bf 769}, 843 (2018).
Two polymorphic forms have been reported for solid AgF$_2$ at ambient pressure: a layered Ag$^{\rm II}$F$_2$ ($\alpha$) and a charge density wave Ag$^{\rm I}$Ag$^{\rm III}$F$_4$ one ($\beta$). The $\alpha$ phase is better known of the two. It has recently received attention due to numerous structural and electronic similarities with oxocuprate precursors of high-temperature superconductors [1]. The key common feature of AgF$_2$ and undoped oxocuprates is the presence of antiferromagnetic sheets of A$^{\rm II}$B$_2$ stoichiometry(AgF$_2$ resp. CuO$_2$). Correspondingly, structural, electronic and magnetic properties of $\alpha$ form at ambient and high pressures have been thoroughly examined in number of experimental and theoretical studies [1--4]. $\beta$ form has been observed before only once as a red-brown amorphous product of reaction of AgBF$_4$ with KAgF$_4$ in anhydrous HF [5]. It is known to undergo rapid exothermic conversion to the alpha form when temperature is raised from $-80^\circ$C to ca. 0$^\circ$C: Ag$^{\rm I}$Ag$^{\rm III}$F$_4$ $\rightarrow$ 2Ag$^{\rm II}$F$_2$ [5] and its has been confirmed in an early theoretical study, which assumed that $\beta$ form adopts that of KAgF$_4$ type structure. In the present work, we have thoroughly scrutinized the relative thermodynamic stability and lattice dynamics of the two phases, Ag$^{\rm II}$F$_2$ and Ag$^{\rm I}$ Ag$^{\rm III}$F$_4$, in a comparative theoretical and experimental study employing Raman spectroscopy and Density Functional Theory (DFT). We provide theoretical evidence for dynamical stability of both polymorphs, calculate thermodynamic potentials, perform normal mode analysis and discuss relative thermodynamic stability of the two phases.
The individual Ag$^{\rm II}$F$_2$ $\alpha$-phase layers are isoelectronic with [CuO$_2$] sheets in oxocuprates [1]. Both systems are AFM semiconductors with charge-transfer band gap. In Ag$^{\rm II}$F$_2$ ($\alpha$) we have identified Ag--F bond stretching modes of $B_{2g}$ symmetry with unusually strong response to on-site Coulombic correlation. The response of electronic structure to the $B_{2g}$ mode is characterized by modulation of intervalence charge transfer (ICT), which is accompanied by bandgap closure and subsequent reopening as the system progresses from antiferromagnetic Ag$^{\rm II}$Ag$^{\rm II}$F$_4$ to diamagnetic mixed-valence Ag$^{\rm I}$Ag$^{\rm III}$F$_4$ state. AgF$_2$ in this respect is analogous to oxocuprates family.
Refs
[1] J. Gawraczyński {\it et al.}, Proc. Natl. Acad. Sci. USA {\bf 116}, 1495 (2019).
[2] J. Gawraczyński {\it et al.}, Inorg. Chem. {\bf 56}, 14651 (2017).
[3] D. Kurzydłowski {\it et. al.}, Chem. Commun. {\bf 54}, 10252 (2018).
[4] T. Jaroń and W. Grochala, Phys Stat Sol (RRL) {\bf 2}, 71 (2008).
[5] B. Žemva {\it et al.}, Inorg. Chem. {\bf 38}, 4570 (1999).
LiBi is a very intriguing material, as it is built up from the heaviest and the lightest nonradioactive metals in the periodic table. Bismuth is a semimetal with interesting Dirac-like electronic states, while lithium contains only one valence electron and has nearly free-electron Fermi surface.
LiBi superconducts below $T_c=2.45$~K and its crystal structure is tetragonal and can be seen as bcc structure distorted along $z$-axis.
In this work, theoretical and experimental studies of LiBi are presented. The experimental part consists of magnetic susceptibility and heat capacity measurements.
{\it Ab initio} calculations of the electronic structure, phonons and the electron-phonon interaction function were done. On this basis two important features of superconductivity are calculated, the transition temperature and electron-phonon coupling constant.
The band structure of LiBi is affected by structural distortion and is an interesting interplay between dominating $p$-states of Bi and states of Li, while phonons reflect the huge mass difference of these two elements. Superconductivity of this material is driven by the electron-phonon coupling with moderate magnitude.
Finally, our results are confronted with properties of NaBi, superconductor with $T_c=2.15$~K, which is isostructural and isoelectronic with LiBi and whose bandstructure was reported to show a topological character [1].
Refs
[1] R. Li, {\it et al.}, Scientific Reports {\bf 5}, 8446 (2015).
Magnetite is the first discovered magnetic material. At $T$=125~K, the Verwey phase transition is observed, in which the electric conductivity decreases by two orders of magnitude [1]. At room temperature, magnetite crystallizes in an inverse spinel structure, in which tetrahedrally coordinated A-sites are occupied by Fe$^{3+}$ ions, while octahedrally coordinated B-sites are occupied by randomly distributed Fe$^{3+}$ and Fe$^{2+}$ ions. At the Verwey temperature, magnetite exhibits the structural phase transition from the cubic to monoclinic phase with the charge-orbital order [2].
Using the density functional theory, we studied the lattice dynamical properties of magnetite in the cubic symmetry [3]. We found a strong electron-phonon coupling, which plays the important role in the Verwey transition. The anomalous phonon broadening resulting from this interaction was observed by the inelastic X-ray scattering studies [4]. The discrepancy between the calculated and measured phonon density of states (DOS) indicates the existence of short-range order with local deformations in the cubic phase. In contrast, the phonon DOS obtained for the monoclinic structure shows a very good agreement with the nuclear inelastic scattering [5]. The interplay between the structural and dynamical properties of magnetite was demonstrated by the recent pump-probe experiments [6], which revealed new features of the collective modes.
This work was partially supported by National Science Centre (NCN, Poland) under grant UMO-2017/25/B/ST3/02586.
Refs
[1] E. J. W. Verwey, Nature {\bf 144}, 327 (1939).
[2] M. S. Senn, J. P. Wright and J. P. Attfield, Nature {\bf 481}, 173 (2012).
[3] P. Piekarz, K. Parlinski and A. M. Oleś, Phys. Rev. Lett. {\bf 97}, 156402 (2006).
[4] M. Hoesch, P. Piekarz, A. Bosak, M. Le Tacon, M. Krisch, A. Kozłowski, A. M. Oleś and K. Parlinski, Phys. Rev. Lett. {\bf 110}, 207204 (2013).
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[6] S. Borroni, E. Baldini, V. M. Katukuri, A. Mann, K. Parlinski, D. Legut, C. Arrell, F. van Mourik, J. Teyssier, A. Kozłowski, P. Piekarz, O. V. Yazyev, A. M. Oleś, J. Lorenzana and F. Carbone, Phys. Rev. B {\bf 96}, 104308 (2017).