arXiv subjects
Publications and source records attributed to Karin M. Rabe.
We propose a design strategy - based on the coupling of spins, optical phonons, and strain - for systems in which magnetic (electric) phase control can be achieved by an applied electric (magnetic) field. Using first-principles density-functional theory calculations, we present a realization of this strategy for the magnetic perovskite EuTiO$_3$.
Using density functional theory within the local spin density approximation, structural, electronic and magnetic properties of SRO are investigated. We examine the magnitude of the orthorhombic distortion in the ground state and also the effects of applying epitaxial constraints, whereby the influence of large (in the range of $\pm 4%$) in-plane strain resulting from coherent epitaxy, for both [001] and [110] oriented films, have been isolated and investigated. The overall pattern of the structural relaxations reveal coherent distortions of the oxygen octahedra network, which determine stability of the magnetic moment on the Ru ion. The structural and magnetic parameters exhibit substantial changes allowing us to discuss the role of symmetry and possibilities of magneto-structural tuning of \SRO-based thin film structures.
We have studied ferroelectricity in Dion-Jacobson CsBiNb$_2$O$_7$ from first principles. Using group-theoretical analysis and first-principles density functional calculations of the total energy and phonons, we perform a systematic study of the energy surface around a paraelectric prototypic phase. Our results suggest that CsBiNb$_2$O$_7$ is a ferroelectric with a polarization of P$_s$=40$μ$C cm$^{-2}$. We propose further experiments to clarify this point.
We have studied the influence of magnetic order on the optical phonons of the geometrically frustrated spinel ZnCr$_2$O$_4$ from first-principles. By mapping the first-principles phonon calculations onto a Heisenberg-like model, we developed a method to calculate exchange derivatives and subsequently the spin-phonon couping parameter from first-principles. All calculations were performed within LSDA+U.
We have studied the structural phase transition of multiferroic YMnO$_3$ from first principles. Using group-theoretical analysis and first-principles density functional calculations of the total energy and phonons, we perform a systematic study of the energy surface around the prototypic phase. We find a single instability at the zone-boundary which couples strongly to the polarization. This coupling is the mechanism that allows multiferroicity in this class of materials. Our results imply that YMnO$_3$ is an improper ferroelectric. We suggest further experiments to clarify this point.
We have studied the dielectric properties of the ferromagnetic spinel CdCr$_2$S$_4$ from first principles. Zone-center phonons and Born effective charges were calculated by frozen-phonon and Berry phase techniques within LSDA+U. We find that all infrared-active phonons are quite stable within the cubic space group. The calculated static dielectric constant agrees well with previous measurements. These results suggest that the recently observed anomalous dielectric behavior in CdCr$_2$S$_4$ is not due to the softening of a polar mode. We suggest further experiments to clarify this point.
Using an extension of a first-principles method developed by King-Smith and Vanderbilt [Phys. Rev. B {\bf 49}, 5828 (1994)], we investigate the effects of in-plane epitaxial strain on the ground-state structure and polarization of eight perovskite oxides: BaTiO$_3$, SrTiO$_3$, CaTiO$_3$, KNbO$_3$, NaNbO$_3$, PbTiO$_3$, PbZrO$_3$, and BaZrO$_3$. In addition, we investigate the effects of a nonzero normal stress. The results are shown to be useful in predicting the structure and polarization of perovskite oxide thin films and superlattices.
The structure and polarization of the as-yet hypothetical Ruddlesden-Popper compound Pb$_2$TiO$_4$ are investigated within density-functional theory. Zone enter phonons of the high-symmetry K$_2$NiF$_4$-type reference structure, space group $I4/mmm$, were calculated. At the theoretical ground-state lattice constants, there is one unstable infrared-active phonon. This phonon freezes in to give the $I2mm$ ferroelectric state. As a function of epitaxial strain, two additional ferroelectric phases are found, with space groups $I4mm$ and $F2mm$ at compressive and tensile strains, respectively.
The crystal structure and local spontaneous polarization of (BaTiO3)m/(SrTiO3)n superlattices is calculated using a first-principles density functional theory method. The in-plane lattice constant is 1% larger than the SrTiO3 substrate to imitate the relaxed superlattice structure and the symmetry is lowered to monoclinic space group Cm which allows polarization to develop along the [110] and [001] directions. The polarization component in the [110] direction is found to develop only in the SrTiO3 layers and falls to zero in the BaTiO3 layers, whereas the polarization in the [001] direction is approximately uniform throughout the superlattice. These findings are consistent with recent experimental data and first-principles results for epitaxially strained BT and ST.
The direct calculation of the elastic and piezoelectric tensors of solids can be accomplished by treating homogeneous strain within the framework of density-functional perturbation theory. By formulating the energy functional in reduced coordinates, we show that the strain perturbation enters only through metric tensors, and can be treated in a manner exactly paralleling the treatment of other perturbations. We present an analysis of the strain perturbation of the plane-wave pseudopotential functional, including the internal strain terms necessary to treat the atomic-relaxation contributions. Procedures for computationally verifying these expressions by comparison with numerical derivatives of ground-state calculations are described and illustrated.
The effect of in-plane strain on the nonlinear dielectric properties of SrTiO3 epitaxial thin films is calculated using density-functional theory within the local-density approximation. Motivated by recent experiments, the structure, zone-center phonons, and dielectric properties with and without an external electric field are evaluated for several misfit strains within +-3% of the calculated cubic lattice parameter. In these calculations, the in-plane lattice parameters are fixed, and all remaining structural parameters are permitted to relax. The presence of an external bias is treated approximately by applying a force to each ion proportional to the electric field. After obtaining zero-field ground state structures for various strains, the zone-center phonon frequencies and Born effective charges are computed, yielding the zero-field dielectric response. The dielectric response at finite electric field bias is obtained by computing the field dependence of the structure and polarization using an approximate technique. The results are compared with recent experiments and a previous phenomenological theory. The tunability is found to be strongly dependent on the in-plane lattice parameter, showing markedly different behavior for tensile and compressive strains. Our results are expected to be of use for isolating the role of strain in the tunability of real ultrathin epitaxial films.
Using a combination of first-principles and effective-Hamiltonian approaches, we map out the structure of BaTiO3 under epitaxial constraints applicable to growth on perovskite substrates. We obtain a phase diagram in temperature and misfit strain that is qualitatively different from that reported by Pertsev et al. [Phys. Rev. Lett. 80, 1988 (1998)], who based their results on an empirical thermodynamic potential with parameters fitted at temperatures in the vicinity of the bulk phase transitions. In particular, we find a region of `r phase' at low temperature where Pertsev et al. have reported an `ac phase'. We expect our results to be relevant to thin epitaxial films of BaTiO3 at low temperatures and experimentally-achievable strains.
We apply the pseudopotential density functional perturbation theory approach along with the quasiharmonic approximation to calculate the thermal expansion of tungsten and two important metallic alloys, NiAl and PdTi. We derive the theory for anisotropic crystal structures and test the approximation that the anisotropic effects of thermal expansion are equivalent to negative pressure - this simplifies the calculation enormously for complex structures. Throughout, we find excellent agreement with experimental results.
Using a first-principles approach based on density-functional theory, we find that a large tetragonal strain can be induced in PbTiO3 by application of a negative hydrostatic pressure. The structural parameters and the dielectric and dynamical properties are found to change abruptly near a crossover pressure, displaying a ``kinky'' behavior suggestive of proximity to a phase transition. Analogous calculations for BaTiO3 show that the same effect is also present there, but at much higher negative pressure. We investigate this unexpected behavior of PbTiO3 and discuss an interpretation involving a phenomenological description in terms of a reduced set of relevant degrees of freedom.
We have investigated the structural and dielectric properties of Sr$_{2}$TiO$_{4}$,the first member of the Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ Ruddlesden-Popper series, within density functional theory. Motivated by recent work in which thin films of Sr$_{2}$TiO$_{4}$ were grown by molecular beam epitaxy (MBE) on SrTiO$_{3}$ substrates, the in-plane lattice parameter was fixed to the theoretically optimized lattice constant of cubic SrTiO$_{3}$ (n=$\infty$), while the out-of-plane lattice parameter and the internal structural parameters were relaxed. The fully relaxed structure was also investigated. Density functional perturbation theory was used to calculate the zone-center phonon frequencies, Born effective charges, and the electronic dielectric permittivity tensor. A detailed study of the contribution of individual infrared-active modes to the static dielectric permittivity tensor was performed. The calculated Raman and infrared phonon frequencies were found to be in agreement with experiment where available. Comparisons of the calculated static dielectric permittivity with experiments on both ceramic powders and epitaxial thin films are discussed.
The various approximations used in the construction of a first-principles effective Hamiltonian for BaTiO3, and their effects on the calculated transition temperatures, are discussed. An effective Hamiltonian for BaTiO3 is constructed not from first-principles calculations, but from the structural energetics of an atomistic shell model for BaTiO3 of Tinte et al. This allows the elimination of certain uncontrolled approximations that arise in the comparison of first-principles effective Hamiltonian results with experimental values and the quantification of errors associated with the selection of the effective Hamiltonian subspace and subsequent projection. The discrepancies in transition temperatures computed in classical simulations for this effective Hamiltonian and for the atomistic shell model are shown to be associated primarily with a poor description of the thermal expansion in the former case. This leads to specific proposals for refinements to the first-principles effective Hamiltonian method. Our results suggest that there are at least two significant sources of error in the effective-Hamiltonian treatment of BaTiO3 in the literature, i.e., the improper treatment of thermal expansion, and the errors inherent in the first-principles approach itself.
The structural energetics of PdTi and PtTi have been studied using first-principles density-functional theory with pseudopotentials and a plane-wave basis. We predict that in both materials, the experimentally reported orthorhombic $B19$ phase will undergo a low-temperature phase transition to a monoclinic $B19'$ ground state. Within a soft-mode framework, we relate the $B19$ structure to the cubic $B2$ structure, observed at high temperature, and the $B19'$ structure to $B19$ via phonon modes strongly coupled to strain. In contrast to NiTi, the $B19$ structure is extremely close to hcp. We draw on the analogy to the bcc-hcp transition to suggest likely transition mechanisms in the present case.
We have developed and implemented a formalism for computing the structural response of a periodic insulating system to a homogeneous static electric field within density-functional perturbation theory (DFPT). We consider the thermodynamic potentials E(R,eta,e) and F(R,eta,e) whose minimization with respect to the internal structural parameters R and unit cell strain eta yields the equilibrium structure at fixed electric field e and polarization P, respectively. First-order expansion of E(R,eta,e) in e leads to a useful approximation in which R(P) and eta(P) can be obtained by simply minimizing the zero-field internal energy with respect to structural coordinates subject to the constraint of a fixed spontaneous polarization P. To facilitate this minimization, we formulate a modified DFPT scheme such that the computed derivatives of the polarization are consistent with the discretized form of the Berry-phase expression. We then describe the application of this approach to several problems associated with bulk and short-period superlattice structures of ferroelectric materials such as BaTiO3 and PbTiO3. These include the effects of compositionally broken inversion symmetry, the equilibrium structure for high values of polarization, field-induced structural phase transitions, and the lattice contributions to the linear and the non-linear dielectric constants.