Zone-center Modes Research Articles

Adiabatic Dynamics of Coupled Spins and Phonons in Magnetic Insulators

In conventional methodologies, phonons are calculated by solving equations of motion involving static interatomic force constants and atomic masses. The Born-Oppenheimer approximation, where all electronic degrees of freedom are assumed to adiabatically follow the nuclear dynamics, is also adopted. This approach does not fully account for the effects of broken time-reversal symmetry in systems with magnetic order. Recent attempts to rectify this involve the inclusion of the velocity dependence of the interatomic forces in the equations of motion, which accounts for time-reversal symmetry breaking, and can result in chiral phonon modes with nonzero angular momentum even at the zone center. However, since the energy ranges of phonons and magnons typically overlap, the spins cannot be treated as adiabatically following the lattice degrees of freedom. Instead, phonon and spins must be treated on a similar footing. Focusing on zone-center modes, we propose a method involving Hessian matrices and Berry curvature tensors in terms of both phonon and spin degrees of freedom, and describe a first-principles methodology for calculating these. We then solve Lagrange’s equations of motion to determine the energies and characters of the mixed excitations, allowing us to quantify, for example, the energy splittings between chiral pairs of phonons in some cases, and the degree of magnetically induced mixing between infrared and Raman modes in others. The approach is general and can be applied to determine the adiabatic dynamics of any mixed set of slow variables. Published by the American Physical Society 2024

Phase transitions in HfO2 probed by first-principles computations

Ever since ferroelectricity was discovered in HfO2, the question of its origin remains controversial. Here, we probe this question using a combination of Landau theory of phase transitions and first-principles computations. In such an approach, the energy landscape associated with the phase transition between cubic and different experimentally demonstrated phases of HfO2 (tetragonal, monoclinic, orthorhombic Pbca, orthorhombic Pnma, and orthorhombic Pca21) is explored using density functional theory calculations. Computations revealed that stabilization of all but orthorhombic Pbca phase is driven by a single unstable zone-boundary antipolar mode X2−. When coupled with zone-center modes (Γ1+ and Γ3+), it stabilizes the tetragonal phase. Coupling with four additional modes (Γ5+, X3−, X5−, X5+) results in the monoclinic phase, which is the ground state of the material. If, however, Γ5+ mode is replaced with Γ4− mode, orthorhombic polar phase Pca21 is stabilized. The application of this framework to examine the effect of electric field on the ferroelectric phase of hafnia reveals that the field of 5 MV/cm is capable of stabilizing ferroelectric phase over the monoclinic one at 0 K.

Frequency Splitting of Chiral Phonons from Broken Time-Reversal Symmetry in CrI_{3}.

Conventional approaches for lattice dynamics based on static interatomic forces do not fully account for the effects of time-reversal-symmetry breaking in magnetic systems. Recent approaches to rectify this involve incorporating the first-order change in forces with atomic velocities under the assumption of adiabatic separation of electronic and nuclear degrees of freedom. In this Letter, we develop a first-principles method to calculate this velocity-force coupling in extended solids and show via the example of ferromagnetic CrI_{3} that, due to the slow dynamics of the spins in the system, the assumption of adiabatic separation can result in large errors for splittings of zone-center chiral modes. We demonstrate that an accurate description of the lattice dynamics requires treating magnons and phonons on the same footing.

The effect of spin–orbit coupling on the physical and superconducting properties of the Ir-rich cubic Laves superconductors AIr[formula omitted] (A = Y, Lu, and Th)

We have examined the impact of spin–orbit coupling (SOC) in cubic Laves superconductors AIr2 (A = Y, Lu, and Th) by realizing ab initio pseudopotential calculations of their physical and electron–phonon interaction properties. The inclusion of SOC removes the degeneracy of the electronic states and moderately influences the elastic and mechanical properties of all the compounds investigated. A critical examination of the elastic and mechanical properties reveals that all the compounds studied are soft (ductile) because of significant metallic bonding. The SOC effect on the phonon and electron–phonon interaction properties depends on the type of A element. This coupling has little influence on the phonon properties of YIr2. However, differently from YIr2, three optical phonon branches of LuIr2 and ThIr2 originating from the triply degenerate zone-center T2u mode are significantly affected by the inclusion of SOC. Although the effect of SOC on the electron–phonon interaction properties changes with the type of A atom, the presence of this coupling improves the agreement with experiment for the superconducting transition temperatures of all the cubic Laves superconductors investigated.

Electron-phonon coupling strength from ab initio frozen-phonon approach

We propose a fast method for high-throughput screening of potential superconducting materials. The method is based on calculating metallic screening of zone-center phonon modes, which provides an accurate estimate for the electron-phonon coupling strength. This method is complementary to the recently proposed Rigid Muffin Tin (RMT) method, which amounts to integrating the electron-phonon coupling over the entire Brillouin zone (as opposed to the zone center), but in a relatively inferior approximation. We illustrate the use of this method by applying it to MgB$_\text{2}$, where the high-temperature superconductivity is known to be driven largely by the zone-center modes, and compare it to a sister compound AlB$_\text{2}$. We further illustrate the usage of this descriptor by screening a large number of binary hydrides, for which accurate first-principle calculations of electron-phonon coupling have been recently published. Together with the RMT descriptor, this method opens a way to perform initial high-throughput screening in search of conventional superconductors via machine learning or data mining.

Study of phase transitions and lattice dynamics, elastic and electronic properties, bonding and weak interactions analysis of YCuS2 in P212121, [formula omitted] and [formula omitted] space group structures

The present work shows several physical behaviors of YCuS2 that are still unknown, such as electronic properties, phase transitions, mechanical properties and several dynamical behaviors. This study has shown that YCuS2 is elastically stable in the three studied structures (P212121, P-421m and I-42d), while it is dynamically stable in P212121 structure only, which shows that this latter is that of the ground state and the rest (P-421m and I-42d) are those of phase transitions. For P212121 structure, the found lattice parameters are very close to those of experimental and theoretical ones. Electronic properties have shown that YCuS2 is a semiconductor in all three studied structures with a slightly wider band-gap for P212121 structure. These results highlight the optoelectronic importance of this compound. The dynamical study of YCuS2 has been carried out taking into consideration the LO/TO splitting. The zone-center modes have been presented. Bonding analysis using QTAIM has shown the presence of an intermediate bonding type between the different atoms, while the different weak interactions have been identified and located by NCI method.

Calculated phonon modes, infrared and Raman spectra in orthorhombic α − MoO3 and monolayer MoO3

Orthorhombic α−MoO3 is a layered oxide with various applications and with excellent potential to be exfoliated as a 2D ultra-thin film or monolayer. In this paper, we present a first-principles computational study of its vibrational properties. Our focus is on the zone center modes, which can be measured by a combination of infrared and Raman spectroscopy. The polarization dependent spectra are simulated. Calculations are also performed for a monolayer form in which “double layers” of Mo2O6, which are weakly van der Waals bonded in the α-structure, are isolated. Shifts in phonon frequencies are analyzed.

Anharmonic lattice dynamics of SnS across phase transition: A study using high-dimensional neural network potential

SnS that exhibits strong lattice anharmonicity and a structural phase transition between the Pnma and Cmcm phases has emerged as a high-performance thermoelectric material. Herein, the lattice dynamics of SnS have been investigated by molecular dynamics to reveal the soft mode mechanisms across the phase transition. We construct a first-principles-based machine-learning potential, which is capable of reproducing the dynamical nature of the structural phase transition of SnS. We reproduce an explicit softening of the zone-center phonon mode and unveil a similar behavior at the zone boundary U = (0.5, 0.0, 0.5) of SnS, which are attributed to the large anharmonicity induced by the phase transition. Our results reveal a non-monotonic temperature dependence of the linewidth of the soft modes beyond the perturbative regime. The zone-center optical soft mode collapses across the structural phase transition, corresponding to a second-order nature. These results pave the way for further phonon engineering of SnS and the related IV–VI thermoelectrics.

Strong trilinear coupling of phonon instabilities drives the avalanche-like hybrid improper ferroelectric transition in SrBi2Nb2O9

Improper and hybrid-improper ferroelectrics (FEs) host spontaneous polarization ($P$) owing to the anharmonic coupling between polar and nonpolar modes. In general, the unstable zone-boundary nonpolar mode is a primary order parameter that couples to the stable zone-center polar mode to induce $P$. However, in certain FEs, such as the Aurivillius family, the polar mode is also unstable. In such cases, the strength of coupling between polar and nonpolar modes governs whether FE phase transition is a single or double step. Here we investigate a single-step avalanche-like transition in ${\mathrm{SrBi}}_{2}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$, an Aurivillius family compound, using inelastic neutron scattering and Raman spectroscopy combined with group theory and first-principles simulations. We find that a strong trilinear coupling constant $\ensuremath{\lambda}$ between the two nonpolar and one polar instabilities enables their single-step condensation at the FE transition temperature ${T}_{FE}$ and overcomes the effect of the positive bi-quadratic coupling that works against it. The ratio of $\ensuremath{\lambda}$ to the leading-order term in the energy invariant polynomial is two to six times larger than in iso-structural ${\mathrm{SrBi}}_{2}{\mathrm{Ta}}_{2}{\mathrm{O}}_{9}$, which undergoes a double-step transition. We identify and track polar and nonpolar instabilities and find their temperature dependence consistent with the theoretical prediction based on the strong trilinear coupling mechanism. From the sign ($\ifmmode\pm\else\textpm\fi{}$) of bi-quadratic coupling constants in the energy invariant polynomial, we further rule out the triggering mechanism to drive the FE transition. Moreover, we observe little change in phonons across ${T}_{FE}$ despite a first-order transition. However, a significant phonon broadening occurs even at 300 K, which we rationalize based on a large anharmonic vibrational amplitude of O atoms in the ${\mathrm{NbO}}_{6}$ octahedra.

Electron\u2013phonon coupling in superconducting 1T-PdTe2

We have determined the electron–phonon interaction in type II Dirac semimetallic 1T-PdTe2 by means of helium atom scattering. While 1T-PdTe2 is isostructural with 1T-PtTe2, only the former is superconductor. The difference can be traced to the substantially larger value of the electron–phonon coupling in 1T-PdTe2, λ = 0.58, obtained from the Debye-Waller attenuation of the He specular peak. With this value and the surface Debye temperature, ΘD = 106.2 K, we have figured out the superconducting critical temperature, Tc = 1.83 K given by the BCS theory, which is in good agreement with Tc = (1.95 ± 0.03) K obtained with low-temperature scanning tunneling microscopy. The value of the effective mass related to ΘD indicates that the large electron–phonon coupling in 1T-PdTe2 is due to coupling, not only with the zone-center optical mode O2 at 9.2 meV, as proposed in a recent theoretical study, but also with the zone-boundary acoustic mode LA. Our results suggest that the topological states of a Dirac cone play a negligible role on the onset of superconductivity.

Symmetry-Resolved Two-Magnon Excitations in a Strong Spin-Orbit-Coupled Bilayer Antiferromagnet.

We used a combination of polarized Raman spectroscopy and spin wave calculations to study magnetic excitations in the strong spin-orbit-coupled bilayer perovskite antiferromagnet Sr_{3}Ir_{2}O_{7}. We observed two broad Raman features at ∼800 and ∼1400 cm^{-1} arising from magnetic excitations. Unconventionally, the ∼800 cm^{-1} feature is fully symmetric (A_{1g}) with respect to the underlying tetragonal (D_{4h}) crystal lattice which, together with its broad line shape, definitively rules out the possibility of a single magnon excitation as its origin. In contrast, the ∼1400 cm^{-1} feature shows up in both the A_{1g} and B_{2g} channels. From spin wave and two-magnon scattering cross-section calculations of a tetragonal bilayer antiferromagnet, we identified the ∼800 cm^{-1} (1400 cm^{-1}) feature as two-magnon excitations with pairs of magnons from the zone-center Γ point (zone-boundary van Hove singularity X point). We further found that this zone-center two-magnon scattering is unique to bilayer perovskite magnets which host an optical branch in addition to the acoustic branch, as compared to their single layer counterparts. This zone-center two-magnon mode is distinct in symmetry from the time-reversal symmetry broken "spin wave gap" and "phase mode" proposed to explain the ∼92 meV (742 cm^{-1}) gap in resonant inelastic x-ray spectroscopy magnetic excitation spectra of Sr_{3}Ir_{2}O_{7}.

Brillouin zone center phonon modes in ZnGa2O4

Infrared-active lattice mode properties of melt-grown high-quality single bulk crystals of ZnGa2O4 are investigated by combined spectroscopic ellipsometry and density functional theory computation analysis. The normal spinel structure crystals are measured by spectroscopic ellipsometry at room temperature in the range of 100 cm–1–1200 cm–1. The complex-valued dielectric function is determined from a wavenumber-by-wavenumber approach, which is then analyzed by the four-parameter semi-quantum model dielectric function approach augmented by impurity mode contributions. We determine four infrared-active transverse and longitudinal optical mode pairs, five localized impurity mode pairs, and the high frequency dielectric constant. All four infrared-active transverse and longitudinal optical mode pairs are in excellent agreement with results from our density functional theory computations. With the Lyddane–Sachs–Teller relationship, we determine the static dielectric constant, which agrees well with electrical capacitance measurements performed on similarly grown samples. We also provide calculated parameters for all Raman-active and for all silent modes and, thereby, provide a complete set of all symmetry predicted Brillouin zone center modes.

Structural dynamics of incommensurate charge-density waves tracked by ultrafast low-energy electron diffraction.

We study the non-equilibrium structural dynamics of the incommensurate and nearly commensurate charge-density wave (CDW) phases in 1T-. Employing ultrafast low-energy electron diffraction with 1 ps temporal resolution, we investigate the ultrafast quench and recovery of the CDW-coupled periodic lattice distortion (PLD). Sequential structural relaxation processes are observed by tracking the intensities of main lattice as well as satellite diffraction peaks and the diffuse scattering background. Comparing distinct groups of diffraction peaks, we disentangle the ultrafast quench of the PLD amplitude from phonon-related reductions of the diffraction intensity. Fluence-dependent relaxation cycles reveal a long-lived partial suppression of the order parameter for up to 60 ps, far outlasting the initial amplitude recovery and electron-phonon scattering times. This delayed return to a quasi-thermal level is controlled by lattice thermalization and coincides with the population of zone-center acoustic modes, as evidenced by a structured diffuse background. The long-lived non-equilibrium order parameter suppression suggests hot populations of CDW-coupled lattice modes. Finally, a broadening of the superlattice peaks is observed at high fluences, pointing to a non-linear generation of phase fluctuations.

Magnetically driven phonon instability enables the metal–insulator transition in h-FeS

Hexagonal iron sulfide exhibits a fascinating coexistence of metal–insulator, structural and magnetic transitions, reflecting an intimate interplay of its spin, phonon and charge degrees of freedom. Here, we show how a subtle competition of energetic and entropic free-energy components governs its thermodynamics and the sequence of phase transitions it undergoes upon cooling. By means of comprehensive neutron and X-ray scattering measurements, and supported by first-principles electronic structure simulations, we identify the critical role of the coupling between antiferromagnetic ordering and instabilities of anharmonic phonons in the metallic phase in driving the metal–insulator transition. The antiferromagnetic ordering enables the emergence of two zone-boundary soft phonons, whose coupling to a zone-centre mode drives the lattice distortion opening the electronic bandgap. Simultaneously, spin–lattice coupling opens a gap in the magnon spectrum that controls the entropy component of the metal–insulator transition free energy. These results reveal the importance of spin–phonon coupling to tune anharmonic effects, thus opening new avenues to design novel technologically important materials harbouring the metal–insulator transition and magnetoelectric behaviours. A detailed and systematic X-ray and neutron scattering study of hexagonal iron sulfide uncovers the critical role of spin–phonon coupling in promoting the metal–insulator transition in this system.

Electronic and Phonon Instabilities in Bilayer Graphene under Applied External Bias

Abstract We have performed electronic-structure and lattice-dynamics calculations on the AB and AA structures of bilayer graphene. We study the effect of external electric fields and compare results obtained with different levels of theory to existing theoretical and experimental results. Application of an external field to the AB bilayer alters the electronic spectrum, with the bands changing under bias from a parabolic to a “Mexican hat” structure. This results in a semi-metal-to-semiconductor phase transition, with the size of the induced electronic band-gap being tuneable through the field strength. A reduction of continuous symmetry from a hexagonal to a triangular lattice is also evidenced through in-plane electronic charge inhomogeneities between the sublattices. When spin-orbit coupling is turned on for the AB system, we find that the bulk gap decreases, gradually increasing for larger intensities of the bias. Under large bias the energy dispersion recovers the Mexican hat structure, since the energy interaction between the layers balances the coupling interaction. We find that external bias perturbs the harmonic phonon spectra and leads to anomalous behaviour of the out-of-plane flexural ZA and layer-breathing ZO' modes. For the AA system, the electronic and phonon dispersions both remain stable under bias, but the phonon spectrum exhibits zone-center imaginary modes due to layer-sliding dynamical instabilities.

First-principles investigation of the ferroelectric, piezoelectric and nonlinear optical properties of LiNbO3-type ZnTiO3

The newly synthesized LN-type ZnTiO3 (J. Am. Chem. Soc. 2014, 136, 2748) contains cations with the electronic configurations nd10 (Zn2+: 3d10) along with second-order Jahn-Teller (SOJT) nd0 (Ti4+: 3d0) cations. This is different from traditional ferroelectrics with the electric configurations of d0 transition metal ions or/and lone pair electrons of ns2. Using a first-principles approach based on density functional theory, we investigate the electronic structure, zone-center phonon modes, piezoelectric and nonlinear optical properties of the LiNbO3-type ZnTiO3. The electronic structure indicates that this compound is a wide direct-band-gap insulator. The results reveal that this compound is a good ferroelectric material with a large spontaneous polarization of 90.43μC/cm2. The Raman scattering peaks of A1 and E modes are assigned to their zone-center optical modes. Additionally, the large piezoelectric and nonlinear optical susceptibilities reveal that LiNbO3-type ZnTiO3 is a high-performance lead-free piezoelectric and nonlinear optical crystal.

Discrete modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling**Project supported by the National Natural Science Foundation of China (Grant Nos. 11604121 and 11875126), the Natural Science Fund Project of Hunan Province, China (Grant No. 2017JJ3255), the National College Students’ Innovation Entrepreneurship Training Program, China (Grant No. 201810531014), and the Scientific

We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor couplings. With a linear stability analysis, we calculate the growth rates of the modulational instability, and plot the instability regions. When the strength of the next-nearest-neighbor coupling is large enough, two new asymmetric modulational instability regions appear near the boundary of the first Brillouin zone. Furthermore, analytical forms of the bright nonlinear localized modes are constructed by means of a quasi-discreteness approach. The influence of the next-nearest-neighbor coupling on the Brillouin zone center mode and boundary mode are discussed. In particular, we discover a reversal phenomenon of the propagation direction of the Brillouin zone boundary mode.

(Invited) Limits to Phonon Thermal Boundary Resistance across GaN Interfaces

As material length scales decrease below typical vibrational heat carrier (e.g., phonon) mean free paths, the thermal boundary resistances (TBR) at heterogeneous material interfaces become the dominant thermal resistances that dictate temperature rises, thermal runaway, and power density at failure in a wide array of devices. In this work, I will discuss the phonon scattering processes that dictate the thermal boundary conductance (TBC, the inverse of TBR, so TBC = 1/TBR) across GaN-based interfaces, including the maximum limits to TBC at GaN interfaces and the roles of point defect scattering and interfacial layers on GaN TBC. I will first present experimental measurements of the TBC from 78−500 K across isolated heteroepitaxially grown ZnO films on GaN substrates. This data provides an assessment of the underlying assumptions driving phonon gas-based models, such as the diffuse mismatch model (DMM), and atomistic Green’s function (AGF) formalisms used to predict TBC. Our measurements, when compared to previous experimental data, suggest that TBC can be influenced by long wavelength, zone center modes in a material on one side of the interface as opposed to the “vibrational mismatch” concept assumed in the DMM; this disagreement is pronounced at high temperatures. At room temperature, we measure the ZnO/GaN TBC as 490[+150,−110] MW m-2 K-1. The disagreement among the DMM and AGF, and the experimental data at elevated temperatures, suggests a non-negligible contribution from other types of modes that are not accounted for in the fundamental assumptions of these harmonic based formalisms, which may rely on anharmonicity. Given the high quality of these ZnO/GaN interfaces, these results provide an invaluable, critical, and quantitative assessment of the accuracy of assumptions in the current state of the art computational approaches used to predict phonon TBC across interfaces. I will then turn my discussion to focus on the role that interfacial imperfections, such as point defects and continuous films at the interface, have on GaN TBC. These results demonstrate the large variability that can occur in TBC at GaN-based interfaces based on interfacial non-idealities. 1. J. T. Gaskins, et al. "Thermal boundary conductance across heteroepitaxial zno/gan interfaces: Assessment of the phonon gas model," Nano Letters, 18, 7469–7477 (2018). 2. B. F. Donovan, et al. "Thermal boundary conductance across metal-gallium nitride interfaces from 80 - 450 K," Applied Physics Letters, 105, 203502 (2014).

Thermal Boundary Conductance Across Heteroepitaxial ZnO/GaN Interfaces: Assessment of the Phonon Gas Model.

We present experimental measurements of the thermal boundary conductance (TBC) from 78-500 K across isolated heteroepitaxially grown ZnO films on GaN substrates. This data provides an assessment of the underlying assumptions driving phonon gas-based models, such as the diffuse mismatch model (DMM), and atomistic Green's function (AGF) formalisms used to predict TBC. Our measurements, when compared to previous experimental data, suggest that TBC can be influenced by long wavelength, zone center modes in a material on one side of the interface as opposed to the '"vibrational mismatch"' concept assumed in the DMM; this disagreement is pronounced at high temperatures. At room temperature, we measure the ZnO/GaN TBC as 490[+150,-110] MW m-2 K-1. The disagreement among the DMM and AGF, and the experimental data at elevated temperatures, suggests a non-negligible contribution from other types of modes that are not accounted for in the fundamental assumptions of these harmonic based formalisms, which may rely on anharmonicity. Given the high quality of these ZnO/GaN interfaces, these results provide an invaluable, critical, and quantitative assessment of the accuracy of assumptions in the current state of the art computational approaches used to predict phonon TBC across interfaces.

Inelastic light scattering from plasmons tunneling between Wannier-Stark states

Using inelastic light scattering, we measure the zone-center electronic excitation modes in a set of multiple quantum wells. The width of the wavefunction barriers was chosen such that it prevents significant coupling of the electron ground states between wells yet is transparent to electron tunneling under an electric field. Under these conditions, we find charge-density-like and spin-density-like plasmons whose energies do not correspond to the excitations calculated for either a single well or a set of Coulomb-coupled wells. The observed energies are proportional to the electric field strength and the lower energy modes agree with predictions for plasmons tunneling between the Wannier-Stark ladder states.Using inelastic light scattering, we measure the zone-center electronic excitation modes in a set of multiple quantum wells. The width of the wavefunction barriers was chosen such that it prevents significant coupling of the electron ground states between wells yet is transparent to electron tunneling under an electric field. Under these conditions, we find charge-density-like and spin-density-like plasmons whose energies do not correspond to the excitations calculated for either a single well or a set of Coulomb-coupled wells. The observed energies are proportional to the electric field strength and the lower energy modes agree with predictions for plasmons tunneling between the Wannier-Stark ladder states.