Berry Phase Theory Research Articles

First-principles study on the electronic structure of bismuth transition-metaloxides

The electronic structure, magnetic and electric properties, and lattice stability of multiferroicBiMnO3 as a typical system in perovskite Bi transition-metal oxides(BiMO3) are studied from first principles. It is demonstrated theoreticallyfor the first time that the orbital ordering within the Mneg orbitals isactually realized in BiMnO3, being consistent with crystallographic data, and plays a crucial rolein the appearance of ferromagnetism. Total-energy calculation showsthe ferromagnetic state is indeed stabilized. Electrical polarization ofBiMnO3 is also estimated based on the Berry phase theory. Lattice instability tooff-centred displacement, which is driven by strong covalent bondingbetween Bi 6p and O 2p states, is found to be rather common in theBiMO3 series.

The spin chirality induced anomalous Hall effect in pyrochlore ferromagnets

Temperature and magnetic field dependences of the anomalous Hall effect have been investigatedfor single crystals of Mo-based ferromagnets with pyrochlore structure. The Hall resistivity ofNd2Mo2O7 compound shows unconventional temperature dependence whereasGd2Mo2O7 exhibits rather normal behaviour. The Berry phase model can explain thedifference well; it is attributed to the difference in nature of the anisotropy ofthe rare-earth moment and the resultant Mo spin state. The Hall resistivity ofNd2Mo2O7 changes its sign with increasing field applied along the [111] direction, while itmonotonically approaches zero with the field applied along the [100] or [110] direction.This behaviour is also in accord with the prediction of the Berry phase theory.

Contribution of Pb to Ferroelectricity in Perovskite-Type Oxides

We have studied the nature of the covalent bond between Pb 6p and O 2p orbitals in perovskites based on first-principles calculations with Berry phase theory. We compared the electric polarization and Young's modulus between PbTiO3 and BaTiO3. We found that PbTiO3 has higher electric polarization and softness than BaTiO3 because of the cooperation mode of both Ti—O(2) and Pb—O(1) covalent bonds. We propose that in the structural phase transition the system with the lower symmetry avoids ion repulsion through the additional degree of freedom available from atom displacement.

Magnetic field induced sign reversal of the anomalous Hall effect in a pyrochlore ferromagnet Nd2Mo2O7: evidence for a spin chirality mechanism.

The anisotropic Hall effect and magnetization have been investigated for single crystals of Nd2Mo2O7 under high magnetic fields up to 27 T and at low temperatures down to 50 mK. The magnetization curves indicate that the Nd moments with strong Ising anisotropy are coupled antiferromagnetically with the Mo spins and show field-induced flipping on the respective sites. The Hall resistivity changes its sign with increasing field applied along the [111] direction, while it monotonously approaches zero with the field applied along the [100] or [110] direction. This behavior is in accord with the prediction by the Berry phase theory and is interpreted in terms of the field-induced reversal of spin chirality on the pyrochlore lattice.

Anharmonic Raman spectra in high-pressure ice from ab initio simulations.

We calculate from ab initio molecular dynamics the Raman scattering of high-pressure ice. To this effect we apply a new method based on the Berry phase theory of polarization. Our results are in agreement with recent and difficult experiments and are compatible with a picture in which ice VII is a proton-disordered system and in ice X the hydrogen bond is symmetric.

Contribution of Pb to Ferroelectricity in Perovskite-type Oxides

ABSTRACTWe have studied the nature of the covalent bond between Pb 6s, 6p and O 2p orbitals in perovskites based on first-principles calculations. We conclude that the Pb 6p - O 2p covalent bond, not a bond involving Pb 6s, is crucial for the large ferroelectric effect in PbTiO3. The Pb 6s states behave like a shallow core level. To examine the effect of a Pb atom at the A site in the perovskite-type structure, we compared several calculated properties of PbTiO3 and BaTiO3 - the electric polarization, piezoelectric stress tensor and Young's modulus. The piezoelectric stress tensor e33 was calculated through Berry phase theory. BaTiO3 was found to have a larger e33 value than PbTiO3. In the case of BaTiO3, the response of Ti-O(2) to c-axis distortion is larger than in PbTiO3. We found that PbTiO3 is softer than BaTiO3 because of the cooperation of both Ti-O(2) and Pb-O(1) covalent bonds. We also found that the ferroelectric state is much softer than the paraelectric state. We propose that in the structural phase transition the system with the lower symmetry avoids ion repulsion through the additional degree of freedom available from atom displacement.

First-Principles Calculation of Spontaneous Polarization and Phase Stability in NaNO2

Ferroelectricity in sodium nitrite NaNO 2 has been studied from first principles. The spontaneous polarization calculated with Berry-phase theory is 0.116 C/m 2 , being in excellent agreement with experimental values, 0.117 C/m 2 and 0.119 C/m 2 . In order to discuss the phase transitions, we have estimated coupling parameters J 1 and J 2 in the axial next-nearest-neighbor Ising model from total-energy and force calculations. As results, J 1 and J 2 are quite sensitive to relative displacement of NO 2 molecules. The transition temperature and a role of molecular displacement in the phase transitions are discussed in detail.

Relationship between Lattice Deformation and Polarization in BaTiO3

The relationship between lattice deformation and electrical polarization in tetragonal BaTiO3 is investigated. The density functional theory within the local density approximation using the full-potential-linear-augmented-plane-wave (FLAPW) method is adopted to obtain internal atom positions and one-electron wave functions. Electric polarization is calculated using the Berry-phase theory. We have found that a lattice strain of the order of 1% along the c-axis enhances polarization considerably. However, for that of the order of 0.1%, polarization hardly changes. We assume that these responses of the polarization to lattice strain are related to the stress sensitivity of the polarization in ferroelectric-thin films through nanoscale domains, especially ferroelectric-90-degree domains. We have also found that the polarization of BaTiO3 can be scaled linearly by the distance between Ti and its nearest-neighbor oxygen (apical site in oxygen octahedron). This indicates that the covalency between Ti and the apical oxygen is the only driving force for the ferroelectricity in BaTiO3. We suggest that this covalency softens Young's modulus of BaTiO3 in the ferroelectric states compared to the paraelectric states through the increase of the degree of freedom for atomic displacements in a unit cell.

Berry-phase theory of proper piezoelectric response

Recent theoretical advances have established that the electric polarization in an insulating crystal can be viewed as a multivalued quantity that is determined by certain Berry phases associated with the occupied Bloch bands. The application of this approach to the computation of piezoelectric coefficients is not entirely straightforward, since a naive determination of the (“improper”) piezoelectric coefficients from finite differences of the polarization at nearby strain states leads to a dependence upon the choice of “branch” of the polarization. The purpose of the present paper is to clarify that if one calculates instead the “proper” piezoelectric response, the branch dependence is eliminated. From this analysis, a simplified recipe for the direct finite-difference computation of the proper piezoelectric coefficients emerges naturally.

Berry Phase Theory of the Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites

We show that the anomalous Hall effect (AHE) observed in colossal magnetoresistance manganites is a manifestation of Berry phase effects caused by carrier hopping in a nontrivial spin background. We determine the magnitude and temperature dependence of the Berry phase contribution to the AHE, finding that it increases rapidly in magnitude as the temperature is raised from zero through the magnetic transition temperature ${T}_{c}$, peaks at a temperature ${T}_{\mathrm{max}}>{T}_{c}$, and decays as a power of $T$, in agreement with experimental data. We suggest that our theory may be relevant to the anomalous Hall effect in conventional ferromagnets as well.

Quantum-Mechanical Position Operator in Extended Systems

The position operator (defined within the Schr\"odinger representation in the standard way) becomes meaningless when periodic boundary conditions are adopted for the wave function, as usual in condensed matter physics. I show how to define the position expectation value by means of a simple many-body operator acting on the wave function of the extended system. The relationships of the present findings to the Berry-phase theory of polarization are discussed.