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Remote and van der Waals epitaxy are promising approaches for synthesizing single crystalline membranes for flexible electronics and discovery of new properties via extreme strain; however, a fundamental challenge is that most materials do not wet the graphene surface. We develop a cold seed approach for synthesizing smooth intermetallic films on graphene that can be exfoliated to form few nanometer thick single crystalline membranes. Our seeded GdAuGe films have narrow x-ray rocking curve widths of 9-24 arc seconds, which is two orders of magnitude lower than their counterparts grown by typical high temperature methods, and have atomically sharp interfaces observed by transmission electron microscopy. Upon exfoliation and rippling, strain gradients in GdAuGe membranes induce an antiferromagnetic to ferri/ferromagnetic transition. Our smooth, ultrathin membranes provide a clean platform for discovering new flexomagnetic effects in quantum materials.

In the first-principles bulk-layer model the superlattice structure and polarization are determined by first-principles computation of the bulk responses of the constituents to the electrical and mechanical boundary conditions in an insulating superlattice. In this work the model is extended to predict functional properties, specifically dielectric permittivity and piezoelectric response. A detailed comparison between the bulk-layer model and full first-principles calculations for three sets of perovskite oxide superlattices, PbTiO$_3$/BaTiO$_3$, BaTiO$_3$/SrTiO$_3$ and PbTiO$_3$/SrTiO$_3$, is presented. The bulk-layer model is shown to give an excellent first approximation to these important functional properties, and to allow for the identification and investigation of additional physics, including interface reconstruction and finite size effects. Technical issues in the generation of the necessary data for constituent compounds are addressed. These results form the foundation for a powerful data-driven method to facilitate discovery and design of superlattice systems with enhanced and tunable polarization, dielectric permittivity, and piezoelectric response.

Infrared reflectivity spectra of cubic SrMnO$_{3}$ ceramics reveal 18 % stiffening of the lowest-frequency phonon below the antiferromagnetic phase transition occurring at T$_{N}$ = 233 K. Such a large temperature change of the polar phonon frequency is extraordinary and we attribute it to an exceptionally strong spin-phonon coupling in this material. This is consistent with our prediction from first principles calculations. Moreover, polar phonons become Raman active below T$_{N}$, although their activation is forbidden by symmetry in $Pm\bar{3}m$ space group. This gives evidence that the cubic $Pm\bar{3}m$ symmetry is locally broken below T$_{N}$ due to a strong magnetoelectric coupling. Multiphonon and multimagnon scattering is also observed in Raman spectra. Microwave and THz permittivity is strongly influenced by hopping electronic conductivity, which is caused by small non-stoichiometry of the sample. Thermoelectric measurements show room-temperature concentration of free carriers $n_{e}=$3.6 10$^{20}$ cm$^{-3}$ and the sample composition Sr$^{2+}$Mn$_{0.98}^{4+}$Mn$_{0.02}^{3+}$O$_{2.99}^{2-}$. The conductivity exhibits very unusual temperature behavior: THz conductivity increases on cooling, while the static conductivity markedly decreases on cooling. We attribute this to different conductivity of the ceramic grains and grain boundaries., Comment: subm. to PRB

Vibrational properties of iron-chalcogenide superconductor K$_{0.75}$Fe$_{1.75}$Se$_{2}$ with $T_{c}\sim$ 30 K have been measured by Raman and optical spectroscopies over temperature range of 3-300 K. Sample undergoes \textit{I4/m} $\to $ \textit{I4} structural phase transition accompanied by loss of inversion symmetry at $T_{1}$, below 250 K, observed as appearance of new fully-symmetric Raman mode at $\sim$ 165 cm$^{-1}$. Small vibration mode anomalies are also observed at $T_{2}\sim$ 160 K. From first-principles vibrational analysis of antiferromagnetic K$_{0.8}$Fe$_{1.6}$Se$_{2}$ utilizing pseudopotentials all observed Raman and infrared modes have been assigned and the displacement patterns of the new Raman mode identified as involving predominantly the Se atoms.

We present a first principles study of an unusual heterostructure, an atomic-scale checkerboard of BiFeO3-BiMnO3, and compare its properties to the two bulk constituent materials, BiFeO3 and BiMnO3. The "nanocheckerboard" is found to have a multiferroic ground state with the desired properties of each constituent: polar and ferrimagnetic due to BiFeO3 and BiMnO3, respectively. The effect of B-site cation ordering on magnetic ordering in the BiFeO3-BiMnO3 system is studied. The checkerboard geometry is seen to give rise to a a novel magnetostructural effect that is neither present in the bulk constituent materials, nor in the layered BiFeO3-BiMnO3 superlattice., Comment: 15 pages, 14 figures

Using first principles calculations, we present a magnetostructural effect in the BiFeO3-BiMnO3 nanocheckerboard that is not found in either bulk parent compound or in BiFeO3-BiMnO3 superlattices. We also demonstrate that the atomic-scale checkerboard has a multiferroic ground state with the desired properties of each constitutent material: polar and ferrimagnetic due to BiFeO3 and BiMnO3 respectively., Comment: 4 pages, 5 figures

First principles calculations are used to investigate the effects of epitaxial strain on the structure of the perovskite oxide CaTiO$_3$, with particular focus on the stabilization of a ferroelectric phase related to a polar instability hidden in the orthorhombic equilibrium bulk $Pbnm$ structure but found in previous first-principles studies of the ideal cubic perovskite high-symmetry reference structure. At 1.5% strain, we find an epitaxial orientation transition between the $ab$-$ePbnm$ phase, favored for compressive strains, and the $c$-$ePbnm$ phase. For larger tensile strains, a polar instability develops in the $c$-$ePbnm$ phase and an epitaxial-strain-induced ferroelectric phase is obtained with polarization along a $<$110$>$ direction with respect to the primitive perovskite lattice vectors of the square substrate., Comment: 4 pages, 2 figures

We explore the frequency-dependent relative permittivity of Ruddlesden-Popper series Sr(n+1)Ti(n)O(3n+1) (n =1,2,3) thin films as a function of temperature and dc electric field. Interdigitated capacitors and coplanar waveguides were used to extract the frequency response from 500 Hz to 40 GHz. At room temperature, the in-plane relative permittivities obtained for Sr(n+1)Ti(n)O(3n+1) (n =1,2,3) were 42+/-3, 54+/-3, and 77+/-2, respectively, and were independent of frequency. At low temperatures, permittivity increases and electric field tunability develops in Sr(4)Ti(3)O(10).

We present a segregrated strain model that describes the thickness-dependent dielectric properties of ferroelectric films. Using a phenomenological Landau approach, we present results for two specific materials, making comparison with experiment and with first-principles calculations whenever possible. We also suggest a "smoking gun" benchtop probe to test our elastic scenario., Comment: 13 pages, 17 figures

Multiferroicity can be induced in strontium titanate by applying biaxial strain, resulting in the coexistence of both ferroelectric and antiferrodistortive domains. The magnitude and sign of the strain imposed on the lattice by design can be used to tune the phase transitions and interactions between these two phenomena. Using optical second harmonic generation, we report a transition from centrosymmetric 4/mmm phase to ferroelectric mm2, followed by an antiferrodistortive transition to a coupled ferroelastic-ferroelectric mm2 phase in a strontium titanate thin film strained in biaxial tension by 0.94%. The results agree well with theoretical first principles and phase-field predictions. Direct imaging of domains arising from the ferroelectric phase transition, and its switching under electric fields is demonstrated using piezoelectric force microscopy. Nonlinear optics combined with phase-field modeling is used to show that the dominant multiferroic domain switching mechanism is through coupled 90 degree ferroelectric-ferroelastic domain wall motion. More broadly, these studies of coexisting ferroelectric (polar) and antiferrodistortive rotation (axial) phenomena could have relevance to multiferroics with coexisting ferroelectric (polar) and magnetic (axial) phenomena., Comment: 5 pages, 4 figures, In review in Physical Review Letters

In this work, we report on the epitaxial growth of multiferroic YMnO3 on GaN. Both materials are hexagonal with a nominal lattice mismatch of 4%, yet x-ray diffraction reveals an unexpected 30 degree rotation between the unit cells of YMnO3 and GaN that results in a much larger lattice mismatch (10%) compared to the unrotated case. Estimates based on first principles calculations show that the bonding energy gained from the rotated atomic arrangement compensates for the increase in strain energy due to the larger lattice mismatch. Understanding the energy competition between chemical bonding energy and strain energy provides insight into the heteroepitaxial growth mechanisms of complex oxide-semiconductor systems., Comment: 12 pages, 3 figures

We present first-principles density-functional calculations using the local density approximation to investigate the structural instability of cubic perovskite BaBiO_3. This material might exhibit charge disproportionation and some evidence thereof has been linked to the appearance of an additional, fourth peak in the experimental IR spectrum. However, our results suggest that the origin of this additional peak can be understood within the picture of a simple structural instability. While the true instability consists of an oxygen-octahedra breathing distortion and a small octahedra rotation, we find that the breathing alone in a fcc-type cell doubling is sufficient to explain the fourth peak in the IR spectrum. Our results show that the oscillator strength of this particular mode is of the same order of magnitude as the other three modes, in agreement with experiment., Comment: submitted to PRB, completely revised version after referee report

First-principles calculations are used in order to investigate phonon anomalies in non-magnetic and magnetic Heusler alloys. Phonon dispersions for several systems in their cubic L2$\mathrm{_1}$ structure were obtained along the [110] direction. We consider compounds which exhibit phonon instabilities and compare them with their stable counterparts. The analysis of the electronic structure allows us to identify the characteristic features leading to structural instabilities. The phonon dispersions of the unstable compounds show that, while the acoustic modes tend to soften, the optical modes disperse in a way which is significantly different from that of the stable structures. The optical modes that appear to disperse at anomalously low frequencies are Raman active, which is considered an indication of a stronger polarizability of the unstable systems. We show that phonon instability of the TA$_{2}$ mode in Heusler alloys is driven by interaction(repulsion) with the low energy optical vibrations. The optical modes show their unusual behavior due to covalent interactions which are additional bonding features incommensurate with the dominating metallicity in Heusler compounds., Comment: 9 pages, 8 figures

Artificial PbTiO$_{3}$/SrTiO$_{3}$ superlattices were constructed using off-axis RF magnetron sputtering. X-ray diffraction and piezoelectric atomic force microscopy were used to study the evolution of the ferroelectric polarization as the ratio of PbTiO$_{3}$ to SrTiO$_{3}$ was changed. For PbTiO$_{3}$ layer thicknesses larger than the 3-unit cells SrTiO$_{3}$ thickness used in the structure, the polarization is found to be reduced as the PbTiO$_{3}$ thickness is decreased. This observation confirms the primary role of the depolarization field in the polarization reduction in thin films. For the samples with ratios of PbTiO$_{3}$ to SrTiO$_{3}$ of less than one a surprising recovery of ferroelectricity that cannot be explained by electrostatic considerations was observed.

Composition-dependent structural and polar properties of epitaxial short-period CaTiO_3/SrTiO_3/BaTiO_3 superlattices grown on a SrTiO_3 substrate are investigated with first-principles density-functional theory computational techniques. Polarization enhancement with respect to bulk tetragonal BaTiO_3 is found for two- and three-component superlattices with a BaTiO_3 concentration of more than 30%. Individual BaTiO_3 layer thickness is identified as an important factor governing the polarization improvement. In addition, the degree of inversion-symmetry breaking in three-component superlattices can be controlled by varying the thicknesses of the component layers. The flexibility allowed within this large family of structures makes them highly suitable for various applications in modern nano-electro-mechanical devices., Comment: The following article has been submitted to Applied Physics Letters. After it is published, it will be found at http://apl.aip.org/

This review covers the important advances in recent years in the physics of thin film ferroelectric oxides, the strongest emphasis being on those aspects particular to ferroelectrics in thin film form. We introduce the current state of development in the application of ferroelectric thin films for electronic devices and discuss the physics relevant for the performance and failure of these devices. Following this we cover the enormous progress that has been made in the first principles computational approach to understanding ferroelectrics. We then discuss in detail the important role that strain plays in determining the properties of epitaxial thin ferroelectric films. Finally, we look at the emerging possibilities for nanoscale ferroelectrics, with particular emphasis on ferroelectrics in non conventional nanoscale geometries., Comment: This is an invited review for Reviews of Modern Physics. We welcome feedback and will endeavour to incorporate comments received promptly into the final version

The c(2$\times$2) reconstruction of (001) PbTiO$_3$ surfaces is studied by means of first principles calculations for paraelectric (non-polar) and ferroelectric ([001] polarized) films. Analysis of the atomic displacements in the near-surface region shows how the surface modifies the antiferrodistortive (AFD) instability and its interaction with ferroelectric (FE) distortions. The effect of the surface is found to be termination dependent. The AFD instability is suppressed at the TiO$_2$ termination while it is strongly enhanced, relative to the bulk, at the PbO termination resulting in a c(2x2) surface reconstruction which is in excellent agreement with experiments. We find that, in contrast to bulk PbTiO$_3$, in-plane ferroelectricity at the PbO termination does not suppress the AFD instability. The AFD and the in-plane FE distortions are instead concurrently enhanced at the PbO termination. This leads to a novel surface phase with coexisting FE and AFD distortions which is not found in PbTiO$_3$ bulk.

The ground-state structural and electronic properties of ferroelectric BiFeO$_3$ are calculated using density functional theory within the local spin-density approximation and the LSDA+U method. The crystal structure is computed to be rhombohedral with space group $R3c$, and the electronic structure is found to be insulating and antiferromagnetic, both in excellent agreement with available experiments. A large ferroelectric polarization of 90-100 $\mu$C/cm$^2$ is predicted, consistent with the large atomic displacements in the ferroelectric phase and with recent experimental reports, but differing by an order of magnitude from early experiments. One possible explanation is that the latter may have suffered from large leakage currents. However both past and contemporary measurements are shown to be consistent with the modern theory of polarization, suggesting that the range of reported polarizations may instead correspond to distinct switching paths in structural space. Modern measurements on well-characterized bulk samples are required to confirm this interpretation., Comment: (9 pages, 5 figures, 5 tables)

The effect of layer-by-layer heterostructuring and epitaxial strain on lattice instabilities and related ferroelectric properties is investigated from first principles for the [001]-(PbTiO$_3$)$_1$(PbZrO$_3$)$_1$ superlattice and pure PbTiO$_3$ on a cubic substrate. The results for the superlattice show an enhancement of the stability of the monoclinic r-phase with respect to pure PbTiO$_3$. Analysis of the lattice instabilities of the relaxed centrosymmetric reference structure computed within density functional perturbation theory suggests that this results from the presence of two unstable zone-center modes, one confined in the PbTiO$_3$ layer and one in the PbZrO$_3$ layer, which produce in-plane and normal components of the polarization, respectively. The zero-temperature dielectric response is computed and shown to be enhanced not only near the phase boundaries, but throughout the r-phase. Analysis of the analogous calculation for pure PbTiO$_3$ is consistent with this interpretation, and suggests useful approaches to engineering the dielectric properties of artificially structured perovskite oxides., Comment: 8 pages, 5 figures

The phonon dispersion relations and elastic constants for ferromagnetic Ni$_2$MnGa in the cubic and tetragonally distorted Heusler structures are computed using density-functional and density-functional perturbation theory within the spin-polarized generalized-gradient approximation. For $0.9

The spontaneous polarization of epitaxial BaTiO$_3$/SrTiO$_3$ superlattices is studied as a function of composition using first-principles density functional theory within the local density approximation. With the in-plane lattice parameter fixed to that of bulk SrTiO$_3$, the computed superlattice polarization is enhanced above that of bulk BaTiO$_3$ for superlattices with BaTiO$_3$ fraction larger than 40%. In contrast to their bulk paraelectric character, the SrTiO$_3$ layers are found to be {\it tetragonal and polar}, possessing nearly the same polarization as the BaTiO$_3$ layers. General electrostatic arguments elucidate the origin of the polarization in the SrTiO$_3$ layers, with important implications for other ferroelectric nanostructures., Comment: 4 pages, 2 Figures, 1 Table

A first-principles method, based on density functional perturbation theory, is presented for computing the leading order tunability of high-dielectric-constant materials., Comment: 6 pages, MRS Spring 2002 proceedings

The structure, polarization, and zone-center phonons of bulk tetragonal BaTiO$_3$ under compressive epitaxial stress are calculated using density functional theory within the local density approximation. The polarization, computed using the Berry-phase formalism, increases with increasing tetragonality and is found to be enhanced by nearly 70% for the largest compressive misfit strain considered (-2.28%). The results are expected to be useful for the analysis of coherent epitaxial BaTiO$_3$ thin films and heterostructures grown on perovskite substrates having a smaller lattice constant, such as SrTiO$_3$., Comment: MRS Proceedings, Spring 2002

Ab initio phonon calculations for the nonpolar reference structures of the (001), (110), and (111) PbZrO_3/PbTiO_3 [1:1] superlattices are presented. The unstable polar modes in the tetragonal (001) and (110) structures are confined in either the Ti- or the Zr-centered layers and display two-mode behavior, while in the cubic (111) case one-mode behavior is observed. Instabilities with pure oxygen character are observed in all three structures. The implications for the ferroelectric behavior and related properties are discussed., Comment: 12 pages, 2 figures, 7 tables, submitted to PRB

A detailed examination of the energy landscape, density of states and magnetic moment of tetragonally distorted ferromagnetic Ni_2MnGa was performed using first-principles local-spin-density (LSD) pseudopotential calculations, varying V as well as c/a. The energy of tetragonal Ni_2MnGa is found to be nearly constant for values of c/a over a wide range, with shallow minima near c/a = 1 and 1.08 in addition to that near 1.2. This flat energy surface is consistent with the wide range of observed values of c/a. It also explains the observation of pseudomorphic growth of Ni_2MnGa on GaAs, despite a nominal 3% lattice mismatch. The related materials Ni_2MnAl, Ni_2MnIn and ferromagnetic NiMn were examined for similar behavior, but all are seen to have a single well-defined minimum at c/a near 1, consistent with available experimental information. For NiMn, the ground state antiferromagnetic ordering and structural parameters are correctly predicted within the LSD approach., Comment: 6 pages, 7 figures

Using first-principles calculations based on a variational density functional perturbation theory, we investigate the lattice dynamics of solid solutions of barium and strontium titanates. Averaging the information available for the related pure compounds yields results equivalent to those obtained within the virtual crystal approximation, providing frequencies which are a good approximation to those computed for a (111) ordered supercell. Using the same averaging technique we report the evolution of the ferroelectric and antiferrodistortive instabilities with composition., Comment: 9 pages, 2 figures, Proceedings for Fundamental Physics of Ferroelectrics, Aspen (CO), Feb. 13-20, 2000

The ground-state polarization of PbTiO3 thin films is studied using a microscopic effective Hamiltonian with parameters obtained from first-principles calculations. Under short-circuit electrical boundary conditions, (001) films with thickness as low as three unit cells are found to have a perpendicularly polarized ferroelectric ground state with significant enhancement of the polarization at the surface., Comment: 4 pages, 1 figure (revised version)

The full phonon dispersion relations of lead titanate and lead zirconate in the cubic perovskite structure are computed using first-principles variational density-functional perturbation theory, with ab initio pseudopotentials and a plane-wave basis set. Comparison with the results previously obtained for barium titanate shows that the change of a single constituent (Ba to Pb, Ti to Zr) has profound effects on the character and dispersion of unstable modes, with significant implications for the nature of the phase transitions and the dielectric and piezoelectric responses of the compounds. Examination of the interatomic force constants in real space, obtained by a transformation which correctly treats the long-range dipolar contribution, shows that most are strikingly similar, while it is the differences in a few key interactions which produce the observed changes in the phonon dispersions. These trends suggest the possibility of the transferability of force constants to predict the lattice dynamics of perovskite solid solutions., Comment: 9 pages, 2 figures (one in colors), revised version (small changes essentially in Sec. III)

Molecular-dynamics simulations of KNbO$_3$ reveal preformed dynamic chain-like structures, present even in the paraelectric phase, that are related to the softening of phonon branches over large regions of the Brillouin zone. The phase sequence of ferroelectric transitions is correctly reproduced, showing that the first-principles effective Hamiltonian used in the simulations captures the essential behavior of the microscopic fluctuations driving the transitions. Real space chains provide a framework for understanding both the displacive and order-disorder characteristics of these phase transitions., Comment: 4 pages, REVTeX, three eps figures

The fcc-based structure of Yb2.75C60 is unique among metal-doped fullerene compounds, exhibiting long-range-ordered vacancies, significantly off-centered divalent Yb cations, and distorted, crystallographically inequivalent, orientationally ordered C60 anions. A simple electrostatic-energy analysis, which models the constituents using point charges, is shown to provide insight into how each of these features stabilizes this unusual crystal structure. The results have general implications for a variety of other intercalated metal fullerides., Comment: 4 pages, REVTeX, two eps figures

An effective Hamiltonian for the ferroelectric transition in PbTiO3 is constructed from first-principles density-functional-theory total-energy and linear-response calculations through the use of a localized, symmetrized basis set of ``lattice Wannier functions.'' Explicit parametrization of the polar lattice Wannier functions is used for subspace projection, addressing the issues of LO-TO splitting and coupling to the complementary subspace. In contrast with ferroelectric BaTiO3 and KNbO3, we find significant involvement of the Pb atom in the lattice instability. Monte Carlo simulations for this Hamiltonian show a first-order cubic-tetragonal transition at 660 K. Resulting temperature dependence of spontaneous polarization, c/a ratio and unit-cell volume near the transition are in good agreement with experiment. Comparison of Monte Carlo results with mean field theory analysis shows that both strain and fluctuations are necessary to produce the first order character of this transition., Comment: LateX file, 32 pages, 10 figures

An effective Hamiltonian for the ferroelectric transition in $PbTiO_3$ is constructed from first-principles density-functional-theory total-energy and linear-response calculations through the use of a localized, symmetrized basis set of ``lattice Wannier functions.'' Preliminary results of Monte Carlo simulations for this system show a first-order cubic-tetragonal transition at 660 K. The involvement of the Pb atom in the lattice instability and the coupling of local distortions to strain are found to be particularly important in producing the behavior characteristic of the $PbTiO_3$ transition. A tentative explanation for the presence of local distortions experimentally observed above $T_c$ is suggested. Further applications of this method to a variety of systems and structures are proposed for first-principles study of finite-temperature structural properties in individual materials., Comment: 14 pages, harvmac, 4 uuencoded figures

We use ab initio pseudopotential total energy calculations with a plane wave basis set to investigate the structural energetics of various phases of polymorphic NbN. Particular attention is given to its recently discovered superconducting phase with a $T_c$ of 16.4 K, reported to have the NbO structure type. Results of total energy calculations show that it is in fact energetically unfavorable for NbN to form in this cubic structure, and its predicted theoretical lattice constant is significantly smaller than the experimental value. Various approaches to the identification of an alternative structure are discussed. In preliminary investigations, we have found two new structures that are energetically more favorable than the NbO structure., Comment: 11 pages, in RevTex, 3 uuencoded figures

We carry out a completely first-principles study of the ferroelectric phase transitions in BaTiO$_3$. Our approach takes advantage of two features of these transitions: the structural changes are small, and only low-energy distortions are important. Based on these observations, we make systematically improvable approximations which enable the parameterization of the complicated energy surface. The parameters are determined from first-principles total-energy calculations using ultra-soft pseudopotentials and a preconditioned conjugate-gradient scheme. The resulting effective Hamiltonian is then solved by Monte Carlo simulation. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. We find the transitions to be intermediate between order-disorder and displacive character. We find all three phase transitions to be of first order. The roles of different interactions are discussed., Comment: 33 pages latex file, 9 figures

A systematic method is presented for constructing effective Hamiltonians for general phonon-related structural transitions. The key feature is the application of group theoretical methods to identify the subspace in which the effective Hamiltonian acts and construct for it localized basis vectors, which are the analogue of electronic Wannier functions. The results of the symmetry analysis for the perovskite, rocksalt, fluorite and A15 structures and the forms of effective Hamiltonians for the ferroelectric transition in $PbTiO_3$ and $BaTiO_3$, the oxygen-octahedron rotation transition in $SrTiO_3$, the Jahn-Teller instability in $La_{1-x}(Ca,Sr,Ba)_xMnO_3$ and the antiferroelectric transition in $PbZrO_3$ are discussed. For the oxygen- octahedron rotation transition in $SrTiO_3$, this method provides an alternative to the rotational variable approach which is well behaved throughout the Brillouin zone. The parameters appearing in the Wannier basis vectors and in the effective Hamiltonian, given by the corresponding invariant energy expansion, can be obtained for individual materials using first- principles density-functional-theory total energy and linear response techniques, or any technique that can reliably calculate force constants and distortion energies. A practical approach to the determination of these parameters is presented and the application to ferroelectric $PbTiO_3$ discussed., Comment: extensive revisions in presentation, 32 pages, Revtex, 7 Postscript figures

The structural stability and electronic properties of the ternary intermetallic compounds NiSnM (M = Ti, Zr, Hf) and the closely related Heusler compounds Ni$_2$SnM are discussed using the results of ab initio pseudopotential total energy and band-structure calculations performed with a plane wave basis set using the conjugate gradients algorithm. The results characterize the lowest energy phase of NiSnM compounds, with a SnM rocksalt structure sublattice, as narrow gap semiconductors with indirect gaps near 0.5 eV. Two other atomic arrangements for NiSnM in the MgAgAs structure result in energetically unfavorable compounds that are metallic. The gap formation in the lowest energy structure of NiSnZr and relative stability of the three atomic arrangements are investigated within a tight-binding framework and by considering the decompositions of each ternary compound into a binary substructure plus a third element sublattice. The stabilization of the lowest energy phase of NiSnZr is found to be mainly due to the relative stability of the SnZr rocksalt substructure, while the opening of the gap induced by the addition of the symmetry-breaking Ni sublattice makes a relatively minor contribution. From analysis of structural and chemical trends, CoVSn is predicted to be a new semiconducting intermetallic in the MgAgAs structure with a 0.8 eV indirect gap., Comment: 27 pages (Sections IVB, IVE rewritten; PRB April 15 II 1995 issue)

We develop a first-principles scheme to study ferroelectric phase transitions for perovskite compounds. We obtain an effective Hamiltonian which is fully specified by first-principles ultra-soft pseudopotential calculations. This approach is applied to BaTiO$_3$, and the resulting Hamiltonian is studied using Monte Carlo simulations. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. The order-disorder vs.\ displacive character of the transitions and the roles played by different interactions are discussed., Comment: 13 pages