Halide perovskite (HP) semiconductors exhibit unique strong coupling between the electronic and structural dynamics. The high-temperature cubic phase of HPs is known to be entropically stabilized, with imaginary frequencies in the calculated phonon dispersion relation. Similar calculations, based on the static average crystal structure, predict a stable tetragonal phase with no imaginary modes. This work shows that in contrast to standard theory predictions, the room-temperature tetragonal phase of CH$_{3} $NH$_{3} $PbI$_{3}$ is strongly anharmonic. We use Raman polarization-orientation (PO) measurements and \textit{ab initio} molecular dynamics (AIMD) to investigate the origin and temperature evolution of the strong structural anharmonicity throughout the tetragonal phase. Raman PO measurements reveal a new spectral feature that resembles a soft mode. This mode shows an unusual continuous increase in damping with temperature which is indicative of an anharmonic potential surface. The analysis of AIMD trajectories identifies two major sources of anharmonicity: the orientational unlocking of the [CH$_{3} $NH$_{3}$]$^+$ ions and large amplitude octahedral tilting that continuously increases with temperature. Our work suggests that the standard phonon picture cannot describe the structural dynamics of tetragonal CH$_{3} $NH$_{3} $PbI$_{3}$.
Lattice vibrations in CH$_3$NH$_3$PbI$_3$ are strongly interacting, with double well instabilities present at the Brillouin zone boundary. Analysis within a first-principles lattice dynamics framework reveals anharmonic potentials with short phonon quasi-particle lifetimes and mean-free paths. The phonon behaviour is distinct from the inorganic semiconductors GaAs and CdTe where three-phonon interaction strengths are three orders of magnitude smaller. The implications for the applications of hybrid halide perovskites arising from thermal conductivity, band-gap deformation, and charge-carrier s…
The assignment of an exact space group to the tetragonal CH$_3$NH$_3$PbI$_3$ perovskite structure is experimentally challenging and controversial in the literature. Average orientation of the methylammonium ion that gives symmetry to the experimental measurement is not captured in a static density functional theory calculation, although the quasi-I4cm and quasi-I4/mcm structures are commonly used in calculations. In this work we have developed a methodology to quantify the hidden symmetry of these structures using group theory, to enable use of symmetries in understanding spectroscopy and othe…
The hybrid halide perovskite CH3NH3PbI3 exhibits a complex structural behaviour, with successive transitions between orthorhombic, tetragonal and cubic polymorphs at ca. 165 K and 327 K. Herein we report first-principles lattice dynamics (phonon spectrum) for each phase of CH3NH3PbI3. The equilibrium structures compare well to solutions of temperature-dependent powder neutron diffraction. By following the normal modes we calculate infrared and Raman intensities of the vibrations, and compare them to the measurement of a single crystal where the Raman laser is controlled to avoid degradation of…
Recent advances of highly efficient solar cells based on organic-inorganic halide perovskites have triggered intense research efforts to establish the fundamental properties of these materials. In this work, we utilized diamond anvil cell to investigate the pressure-induced structural and electronic transformations in methylammonium lead iodide (CH$_3$NH$_3$PbI$_3$) up to 7 GPa at room temperature. The synchrotron X-ray diffraction experiment show that the sample transformed from tetragonal to orthorhombic phase at 0.3 GPa and amorphized above 4 GPa. Further high pressure IR spectroscopy exper…
This article reports on studies of chlorine-substituted MAPbI3 using combined temperature-dependent XRD synchrotron and Pb-L3 edge EXAFS to analyze the anharmonicity of the lead halide bond. The EXAFS parameters were described in the orthorhombic phase by an Einstein or T2 type behavior, which was then compared with the experimental EXAFS parameters of the tetragonal/cubic phase. In the orthorhombic phase, it was observed that the asymmetry of the pair distribution function (cumulant C3) in MAPbCl3 is much lower than in MAPbI3. Compared with the behavior in the orthorhombic phase, the anharmon…
High-throughput computational framework for lattice dynamics and thermal transport including high-order anharmonicity: an application to cubic and tetragonal inorganic compounds
Northwestern University（西北大学）；Portland State University（波特兰州立大学）
We investigate the hypothesis of dynamic tetragonal domains occuring in cubic CH$_3$NH$_3$PbI$_3$ using high-resolution neutron spectroscopy to study a fully deuterated single crystal. The $\textit{R}$-point scattering above the 327.5 K tetragonal-cubic phase transition is always resolution-limited in energy and therefore inconsistent with dynamic domain predictions. This behavior is instead consistent with the central peak phenomenon observed in other perovskites. The scattering may originate from small, static, tetragonal-phase domains nucleating about crystal defects, and the temperature de…
The extended carrier lifetime in hybrid halide perovskites was attributed to a quasi-indirect band gap that arises due to Rashba splitting in both conduction and valence band edges. In this paper, we present results for an effective relativistic band structure of (CH3NH3)PbI3 with the focus on the dispersion of electronic states near the band edges of (CH3NH3)PbI3 affected by thermal structural fluctuations. We establish a relation between the magnitude of Rashba splitting and a deviation of Pb-atom from its centrosymmetric site position in the PbI6 octahedron. For the splitting energy to reac…
In spite of the key role of hydrogen bonding in the structural stabilization of the prototypic hybrid halide perovskite, CH3NH3PbI3 (MAPbI3), little progress has been made in our in-depth understanding of the hydrogen-bonding interaction between the MA+-ion and the iodide ions in the PbI6-octahedron network. Herein, we show that there exist two distinct types of the hydrogen-bonding interaction, naming a- and b-modes, in the tetragonal MAPbI3 on the basis of symmetry argument and density-functional theory calculations. The computed Kohn-Sham (K-S) energy difference between these two interactio…
The family of organic-inorganic tri-halide perovskites including MA (MethylAmmonium)PbI$_{3}$, MAPbI$_{3-x}$Cl$_{x}$, FA (FormAmidinium)PbI$_{3}$ and FAPbBr$_{3}$ are having a tremendous impact on the field of photovoltaic cells due to their ease of deposition and efficiencies, but device performance can be significanly affected by inhomogeneities. Here we report a study of temperature dependent micro-photoluminescence which shows a strong spatial inhomogeneity related to the presence of microcrystalline grains, which can be both light and dark. In all of the tri-iodide based materials there i…
Defect engineering is applied to hybrid (CH$_3$NH$_3$)PbI$_3$ organic-inorganic perovskites. These materials have become one of the most promising low-cost alternatives to traditional semiconductors in the field of photovoltaics and light emitting devices. We use here Helium ion irradiation at low energy as a tool for the controlled introduction of point defects in both single crystals and polycrystalline thin films. The irradiation defects modify the opto-electronic properties as probed using photoluminescence spectroscopy from 10K to room-temperature. 2 Contrary to usual semiconductors, we o…
Ultrafast vibrational dynamics of inorganic-organic hybrid lead halide perovskite CH3NH3PbI$ in the room-temperature tetragonal phase is investigated under moderate photoexcitation slightly below the band gap. Time-resolved optical Kerr effect signal exhibits periodic modulations due to the libration and twisting of the methylammonium molecule at 4 and 8 THz, in addition to the inorganic sublattice deformation at 1.2 THz. These oscillations are heavily damped, and their frequencies exhibit blueshifts with increasing pump density, contrary to the expectation from conventional laser heating. Our…
SrTiO$_3$ has been extensively investigated owing to its abundant degrees of freedom for modulation. However, the microscopic mechanism of thermal transport especially the relationship between phonon scattering and lattice distortion during the phase transition are missing and unclear. Based on deep-potential molecular dynamics and self-consistent \textit{ab initio} lattice dynamics, we explore the lattice anharmonicity-induced tetragonal-to-cubic phase transition and explain this anomalous behavior during the phase transition. Our results indicate the significant role of the renormalization o…
Frustration of harmonic and solitonic helimagnetism on the body-centered tetragonal lattice of GdAlSi
The University of Tokyo（东京大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所 新兴物质科学中心）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；High Energy Accelerator Research Organization（高能加速器研究机构）；Nagoya University Synchrotron Radiation Research Center (NUSR), Nagoya University（名古屋大学同步辐射研究中心）
Understanding and predicting lattice dynamics in strongly anharmonic crystals is one of the long-standing challenges in condensed matter physics. Here we propose a first-principles method that gives accurate quasiparticle (QP) peaks of the phonon spectrum with strong anharmonic broadening. On top of the conventional first-order self-consistent phonon (SC1) dynamical matrix, the proposed method incorporates frequency renormalization effects by the bubble self-energy within the QP approximation. We apply the developed methodology to the strongly anharmonic $α$-CsPbBr$_3$ that displays phonon ins…
The high-temperature cubic-tetragonal phase transition of pure stoichiometric zirconia is studied by molecular dynamics (MD) simulations and within the framework of the Landau theory of phase transformations. The interatomic forces are calculated using an empirical, self-consistent, orthogonal tight-binding (SC-TB) model, which includes atomic polarizabilities up to the quadrupolar level. A first set of standard MD calculations shows that, on increasing temperature, one particular vibrational frequency softens. The temperature evolution of the free energy surfaces around the phase transition i…
We demonstrate an approach for calculating temperature-dependent quantum and anharmonic effects with beyond density-functional theory accuracy. By combining machine-learned potentials and the stochastic self-consistent harmonic approximation, we investigate the cubic to tetragonal transition in strontium titanate and show that the paraelectric phase is stabilized by anharmonic quantum fluctuations. We find that a quantitative understanding of the quantum paraelectric behavior requires a higher-level treatment of electronic correlation effects via the random phase approximation. This approach e…
We present an \textit{ab initio} framework to calculate anharmonic phonon frequency and phonon lifetime that is applicable to severely anharmonic systems. We employ self-consistent phonon (SCPH) theory with microscopic anharmonic force constants, which are extracted from density-functional calculations using the least absolute shrinkage and selection operator technique. We apply the method to the high-temperature phase of SrTiO$_{3}$ and obtain well-defined phonon quasiparticles that are free from imaginary frequencies. Here we show that the anharmonic phonon frequency of the antiferrodistorti…
We employ THz-range temperature-dependent Raman spectroscopy and first-principles lattice-dynamical calculations to show that the undoped sodium ion conductors Na$_3$PS$_4$ and isostructural Na$_3$PSe$_4$ both exhibit anharmonic lattice dynamics. The anharmonic effects in the compounds involve coupled host lattice -- Na$^+$ ion dynamics that drive the tetragonal-to-cubic phase transition in both cases, but with a qualitative difference in the anharmonic character of the transition. Na$_3$PSe$_4$ shows almost purely displacive character with the soft modes disappearing in the cubic phase as the…
We carry out first-principles density-functional calculations of the antiferrodistortive (AFD) and ferroelectric (FE) soft-mode instabilities in tetragonal SrTiO3, with the structural degrees of freedom treated in a classical, zero-temperature framework. In particular, we use frozen-phonon calculations to make a careful study of the anisotropy of the AFD and FE mode frequencies in the tetragonal ground state, in which an R-point AFD soft phonon has condensed. Because of the anharmonic couplings, the presence of this AFD distortion substantially affects both the AFD and FE mode frequencies. The…
Great success has been achieved in improving the photovoltaic energy conversion efficiency of the organic-inorganic perovskite-based solar cells, but with very limited knowledge on the thermal transport in hybrid perovskites, which would affect the device lifetime and stability. Based on the potential developed from the density functional theory calculations, we studied the lattice thermal conductivity of the hybrid halide perovskite CH3NH3PbI3 using equilibrium molecular dynamics simulations. Temperature-dependent thermal conductivity is reported from 160 K to 400 K, which covers the tetragon…
High-energy x-ray diffraction experiments peformed on rhombohedral (1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3(PZN-xPT) crystals with x= 4.5 and 8% show that an electric field applied along the [001] direction induces the tetragonal phase, as proposed by Park and Shrout. Our experiments reveal that in 4.5PT such phase change occurs via a third phase with monoclinic symmetry, MA, which is observed at intermediate field values. This is in agreement with first-principles calculations by Fu and Cohen predicting the rotation of the polarization between the rhombohedral and tetragonal phases in this material. A d…
We report inelastic neutron scattering measurements of phonon spectra in the parent superconductor iron-tuned chalcogenide Fe$_{1+x}$Te, for two different x contents (x $\leq$ 0.11), using neutron time-of-flight technique. Thermal neutron spectroscopy allowed to collect the low-temperature Stokes spectra over an extended Q-range, at 2, 40 and 120K - hence covering both the magnetic monoclinic and the paramagnetic tetragonal phases. Whereas cold-neutrons allowed to measure high-resolution anti-Stokes spectra at 140, 220 and 300K, thus covering the tetragonal phase. Our results evidence a spin-p…
We present first-principles calculations of metallic atomic hydrogen in the 400-600 GPa pressure range in a tetragonal structure with space group $I4_1/amd$, which is predicted to be its first atomic phase. Our calculations show a band structure close to the free-electron-like limit due to the high electronic kinetic energy induced by pressure. Bands are properly described even in the independent electron approximation fully neglecting the electron-electron interaction. Linear-response harmonic calculations show a dynamically stable phonon spectrum with marked Kohn anomalies. Even if the elect…
The mechanisms behind the exceptional photovoltaic properties of the metallorganic perovskites are still debated, and include a ferroelectric (FE) state from the ordering of the electric dipoles of the organic molecules. We present the first anelastic (complex Young's modulus) and new dielectric measurements on CH$_{3}$NH$_{3}$PbI$_3$, which provide new insight on the reorientation dynamics of the organic molecules, and the reason why they do not form a FE state. The permittivity is fitted within the tetragonal phase with an expression that includes the coupling between FE and octahedral tilt …
Halide perovskites make efficient solar cells due to their exceptional optoelectronic properties, but suffer from several stability issues. The characterization of the degradation processes is challenging because of the limitations in the spatio-temporal resolution in experiments and the absence of efficient computational methods to study the reactive processes. Here, we present the first effort in developing reactive force fields for large scale molecular dynamics simulations of the phase instability and the defect-induced degradation reactions in inorganic CsPbI$_{3}$. We find that the phase…
Multiferroics possess two or more switchable states such as polarization, magnetization, etc. Phonon excitations in multiferroic phase are strongly modified by magnetoelectric coupling, spin-phonon coupling, and anharmonic phonon-phonon interactions. Here, we have investigated the correlation between phonons and multiferroic order parameters in hexagonal BaMO3: M = Ti1-x(Mn/Fe)x systems using powder x-ray diffraction (PXRD), Raman spectroscopic, and magnetic measurements. The structural transformation from a polar tetragonal to a non-polar 6H-type hexagonal phase is observed as a function of d…
The organic-inorganic hybrid perovskite CH3NH3PbI3 has attracted significant interest for its high performance in converting solar light into electrical power with an efficiency exceeding 20%. Unfortunately, chemical stability is one major challenge in the development of the CH3NH3PbI3 solar cells. It was commonly assumed that moisture or oxygen in the environment causes the poor stability of hybrid halide perovskites, however, here we show from the first-principles calculations that the room-temperature tetragonal phase of CH3NH3PbI3 is thermodynamically unstable with respect to the phase sep…
We report the dynamics of soft phonon modes and their role towards the various structural transformations in Aurivillius materials by employing terahertz frequency-domain spectroscopy, atomic pair distribution function analysis, and first-principles calculations. We have chosen Bi4Ti3O12 as a model system and identified soft phonon modes associated with the paraelectric tetragonal to the ferroelectric monoclinic transition. Three soft phonon modes have been discovered which exhibit a strong temperature dependence. We have determined that the anharmonicity in Bi-O bonds plays a significant role…
Lead halide perovskites such as methylammonium lead triiodide (MAPI) have outstanding optical and electronic properties for photovoltaic applications, yet a full understanding of how this solution processable material works so well is currently missing. Previous research has revealed that MAPI possesses multiple forms of static disorder regardless of preparation method, which is surprising in light of its excellent performance. Using high energy resolution inelastic X-ray (HERIX) scattering, we measure phonon dispersions in MAPI and find direct evidence for another form of disorder in single c…
EuTiO_{3} undergoes a structural phase transition from cubic to tetragonal at T_S = 282 K which is not accompanied by any long range magnetic order. However, it is related to the oxygen ocathedra rotation driven by a zone boundary acoustic mode softening. Here we show that this displacive second order structural phase transition can be shifted to higher temperatures by the application of an external magnetic field (increased by 4 K for mu_{0}H = 9 T). This observed field dependence is in agreement with theoretical predictions based on a coupled spin-anharmonic-phonon interaction model.
Origin of the Temperature-Induced Gap Bowing of Formamidinium-Methylammonium Lead Iodide Perovskites: Role of Cationic Rattlers
Institut de Ciència de Materials de Barcelona, ICMAB-CSIC（巴塞罗那材料科学研究所）；University of Bath（巴斯大学）；University of Bristol（布里斯托大学）；Cardiff University（卡迪夫大学）；ICREA（加泰罗尼亚高级研究院）
We have used an effective model of ferroelectric PbTiO$_{3}$, which displays a representative soft mode-driven phase transition, to investigate how different features of the potential-energy surface affect the transition temperature $T_{\rm C}$. We find that the energy difference between PbTiO$_{3}$'s high-symmetry (cubic) and low-symmetry (tetragonal) phases (which we call ground state energy $E_{gs}$) is the parameter that most directly and strongly determines $T_{\rm C}$. We have also found that other simple features of the energy landscape, such as the amplitude of the distortion connectin…
The thermodynamics of CaSiO3 in Earth's lower mantle
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；National Centre for Computational Design and Discovery of Novel Materials (MARVEL)（新材料计算设计与发现国家中心）；Paul Scherrer Institut（保罗谢尔研究所）；Università di Roma Sapienza（罗马第一大学）
We investigated the influence of oxygen over-stoichiometry on apical oxygen disorder and magnetic correlations in Nd2NiO4+d (d~0.11) in the temperature range of 2-300 K by means of synchrotron x-ray powder diffraction, neutron single crystal and powder diffraction studies, combined with macroscopic magnetic measurements. In the investigated temperature range, the compound crystalizes in a tetragonal commensurate structure with the P42/ncm space group with excess oxygen atoms occupy the 4b (3/4 1/4 1/4) interstitial sites, coordinated by four apical oxygen atoms. Large and anisotropic thermal d…
The coherence of collective modes, such as phonons, and their modulation of the electronic states are long sought in complex systems, which is a cross-cutting issue in photovoltaics and quantum electronics. In photovoltaic cells and lasers based on metal halide perovskites, the presence of polaronic coupling, i.e., photocarriers dressed by the macroscopic motion of charged lattice, assisted by terahertz (THz) longitudinal optical (LO) phonons, has been intensely studied yet still debated. This may be key for explaining the remarkable properties of the perovskite materials, e.g., defect toleran…
