Abstract:
Derivative structural polytypes coexisting with the rhombohedral A7 structure of elemental bismuth (Bi) have been discovered at ambient condition, based on microstructure analyses of pure Bi samples treated under high pressure and high temperature conditions. Three structures with atomic positions close to those of the A7 structure have been identi?ed through ?rst-principles calculations, showing these polytypes energetically comparable to the A7 structure under ambient condition. Simulated di?raction data are in excellent agreement with the experimental observations. We argue that previously reported variations in physical properties (e.g., density, melting point, electrical conductivity, and magnetism) in bismuth could be due to the formation of these polytypes. The coexistence of metastable derivative structural polytypes may be a widely occurring phenomenon in other elemental materials

Abstract:
A new investigation of the coexistence and competition of ferroelectricity and superconductivity is reported. In particular we show that the starting Hamiltonian of a previous study by Birman and Weger (2001) can be exactly diagonalized. The result differs significantly from mean-field theory. A Hamiltonian with a different realization of the coupling between ferroelectricity and superconductivity is proposed. We report the results for mean-field theory applied to this Hamiltonian. We find that the order parameters are strongly affected by this coupling.

Abstract:
Ferroelectricity has been found to occur in several insulating systems, such as TbMnO$_3$ (TMO) and Ni$_3$V$_2$O$_8$ (NVO) which have more than one phase with incommensurately modulated long-range magnetic order. Here we give a phenomenological model which relates the symmetries of the magnetic structure as obtained from neutron diffraction to the development and orientation of a spontaneous ferroelectric moment induced by the magnetic ordering. This model leads directly to the formulation of a microscopic spin-phonon interaction which gives explains the observed phenomena. The results are given in terms of gradients of the exchange tensor with respect to generalized displacements for the specific example of NVO. It is assumed that these gradients will now be the target of first-principles calculations using the LDA or related schemes.

Abstract:
The competitions between ferroelectric and rotational instabilities in rhombohedral PZT near x = 0.5 are investigated using first principles density functional supercell calculations. As expected, we find a strong ferroelectric instability. However, we also find a substantial R-point rotational instability, close to but not as deep as the ferroelectric one. This is similar to the situation in pure PbZrO_3. These two instabilities are both strongly pressure dependent, but in opposite directions so that lattice compression of less than 1% is sufficient to change their ordering. Because of this, local stress fields due to B-site cation disorder may lead to coexistence of both types of instability are likely present in the alloy near the morphotropic phase boundary.

Abstract:
The origin of both the Ising chain magnetism and ferroelectricity in Ca$_3$CoMnO$_6$ is studied by $ab$ $initio$ electronic structure calculations and x-ray absorption spectroscopy. We find that Ca$_3$CoMnO$_6$ has the alternate trigonal prismatic Co$^{2+}$ and octahedral Mn$^{4+}$ sites in the spin chain. Both the Co$^{2+}$ and Mn$^{4+}$ are in the high spin state. In addition, the Co$^{2+}$ has a huge orbital moment of 1.7 $\mu_B$ which is responsible for the significant Ising magnetism. The centrosymmetric crystal structure known so far is calculated to be unstable with respect to exchange striction in the experimentally observed $\uparrow\uparrow\downarrow\downarrow$ antiferromagnetic structure for the Ising chain. The calculated inequivalence of the Co-Mn distances accounts for the ferroelectricity.

Abstract:
We study the strong coupling limit of a two-band Hubbard Hamiltonian that also includes an inter-orbital on-site repulsive interaction $U_{ab}$. When the two bands have opposite parity and are quarter filled, we prove that the ground state is simultaneously ferromagnetic and ferroelectric for infinite intra-orbital Coulomb interactions $U_{aa}$ and $U_{bb}$. We also show that this coexistence leads to a singular magnetoelectric effect.

Abstract:
Multiferroics - materials which are simultaneously (ferro)magnetic and ferroelectric, and often also ferroelastic, attract now considerable attention, both because of the interesting physics involved and as they promise important practical applications. In this paper I give a survey of microscopic factors determining the coexistence of these properties, and discuss different possible routes to combine them in one material. In particular the role of the occupation of d-states in transition metal perovskites is discussed, possible role of spiral magnetic structures is stressed and the novel mechanism of ferroelectricity in magnetic systems due to combination of site-centred and bond-centred charge ordering is presented. Microscopic nature of multiferroic behaviour in several particular materials, including magnetite Fe3O4, is discussed.

Abstract:
We report the magnetic and electrical characteristics of a polycrystalline specimen of FeTiO3 synthesized at high pressure that is isostructural with acentric LiNbO3 (LBO). Piezoresponse force microscopy, optical second harmonic generation, and magnetometry demonstrate that FeTiO3-II is ferroelectric at and below room temperature and weakly ferromagnetic below ~120 K. These results validate symmetry-based materials design criteria and first principles calculations of coexistence between ferroelectricity and weak ferromagnetism in a series of transition metal titanates crystallizing in the LBO structure. The high-pressure form of FeTiO3 stands out as a rare example of a ferroelectric exhibiting weak ferromagnetism generated by a Dzyaloshinskii-Moriya interaction.

Abstract:
A model for the coexistence of p-wave superconductivity (SC) and ferroelectricity (FE) is presented. The Hamiltonian of SC sector and FE sector can be diagonalized by using the $so(5)$ and $h(4)$ algebraic coherent states respectively. We assume a minimal symmetry-allow coupling and simplify the total Hamiltonian through a double mean-field approximation (DMFA). A variational coherent-state (VCS) trial wave-function is applied for the ground state. It is found that the ferroelectricity gives rise to the magnetic field effect of p-wave superconductivity.

Abstract:
Multiferroics, where two or more ferroic order parameters coexist, is one of the hottest fields in condensed matter physics and materials science[1-9]. However, the coexistence of magnetism and conventional ferroelectricity is physically unfavoured[10]. Recently several remedies have been proposed, e.g., improper ferroelectricity induced by specific magnetic[6] or charge orders[2]. Guiding by these theories, currently most research is focused on frustrated magnets, which usually have complicated magnetic structure and low magnetic ordering temperature, consequently far from the practical application. Simple collinear magnets, which can have high magnetic transition temperature, have never been considered seriously as the candidates for multiferroics. Here, we argue that actually simple interatomic magnetic exchange interaction already contains a driving force for ferroelectricity, thus providing a new microscopic mechanism for the coexistence and strong coupling between ferroelectricity and magnetism. We demonstrate this mechanism by showing that even the simplest antiferromagnetic (AFM) insulator MnO, can display a magnetically induced ferroelectricity under a biaxial strain.