Double-exchange theory of ferroelectric polarization in orthorhombic manganites with twofold periodic magnetic texture

We argue that many aspects of improper ferroelectric activity in orthorhombic manganites can be rationalized by considering the limit of infinite intra-atomic splitting between the majority- and minority-spin states (or the double exchange limit), which reduces the problem to the analysis of a spinless double exchange (DE) Hamiltonian. We apply this strategy to the low-energy model, derived from the first-principles calculations, and combine it with the Berry-phase theory of electric polarization. We start with the simplest two-orbital model, describing the behavior of the eg bands, and apply it to the E-type antiferromagnetic (AFM) phase, which in the DE limit effectively breaks up into one-dimensional zigzag chains. We derive an analytical expression for the electronic polarization (Pel) and explain how it depends on the orbital ordering and the energy splitting Delta between eg states. Then, we evaluate parameters of this model, starting from a more general five-orbital model for all Mn 3d bands and constructing a new downfolded model for the eg bands. From the analysis of these parameters, we conclude that the behavior of Pel in realistic manganites corresponds to the limit of large Delta. We further utilize this property in order to derive an analytical expression for Pel in a general two-fold periodic magnetic texture, based on the five-orbital model and the perturbation-theory expansion for the Wannier functions in the first order of 1/Delta. This expression explains the functional dependence of Pel on the relative directions of spins. Furthermore, it suggests that Pel is related to the asymmetry of the transfer integrals, which should simultaneously have symmetric and antisymmetric components. Finally, we explain how the polarization can be switched between orthorhombic directions a and c by inverting the zigzag AFM texture in every second ab plane.Comment: 41 page, 10 figure

Spin dependence of ferroelectric polarization in the double exchange model for manganites

The double exchange (DE) model is systematically applied for studying the coupling between ferroelectric (FE) and magnetic orders in several prototypical types of multiferroic manganites. The model was constructed for the magnetically active Mn $3d$ bands in the basis of Wannier functions and include the effect of screened on-site Coulomb interactions. The essence of our approach for the FE polarization is to use the Berry phase theory, formulated in terms of occupied Wannier functions, and to evaluate the asymmetric spin-dependent change of these functions in the framework of the DE model. This enables us to quantify the effect of the magnetic symmetry breaking and derive several useful expressions for the electronic polarization ${\bf P}$, depending on the relative directions of spins. The proposed theory is applied to the solution of three major problems: (i) The magnetic-state dependence of ${\bf P}$ in hexagonal manganites; (ii) The microscopic relationship between canted ferromagnetism and ${\bf P}$ in monoclinic BiMnO$_3$; (iii) The origin of FE activity in orthorhombic manganites. We show that for an arbitrary noncollinear magnetic structure, propagating along the orthorhombic $\boldsymbol{b}$ axis and antiferromagnetically coupled $\boldsymbol{c}$, ${\bf P}$ can be obtained by scaling the one of the E-phase with the prefactor depending only on the relative directions of spins and being the measure of the spin inhomogeneity. This picture works equally well for the twofold (HoMnO$_3$) and fourfold (TbMnO$_3$) periodic manganites. The basic difference is that the twofold periodic magnetic structure is strongly inhomogeneous, that leads to large ${\bf P}$. On the contrary, the fourfold periodic magnetic structure can be viewed as a moderately distorted homogeneous spin spiral, which corresponds to weaker ${\bf P}$.Comment: 32 pages, 7 figure

Unitarity cutting rules for the nucleus excitation and topological cross sections in hard production off nuclei from nonlinear k_t-factorization

At the partonic level, a typical final state in small-x deep inelastic scattering off nuclei and hard proton-nucleus collisions can be characterized by the multiplicity of color-excited nucleons. Within reggeon field theory, each color-excited nucleon is associated with the unitarity cut of the pomeron exchanged between the projectile and nucleus. In this communication we derive the unitarity rules for the multiplicity of excited nucleons, alias cut pomerons, alias topological cross sections, for typical hard dijet production processes. We demonstrate how the coupled-channel non-Abelian intranuclear evolution of color dipoles, inherent to pQCD, gives rise to the reggeon field theory diagrams for final states in terms of the uncut, and two kinds of cut, pomerons. Upon the proper identification of the uncut and cut pomeron exchanges, the topological cross sections for dijet production follow in a straightforward way from the earlier derived nonlinear k_t - factorization quadratures for the inclusive dijet cross sections. The concept of a coherent (collective) nuclear glue proves extremely useful for the formulation of reggeon field theory vertices of multipomeron - cut and uncut - couplings to particles and between themselves. A departure of our unitarity cutting rules from the ones suggested by the pre-QCD Abramovsky-Kancheli-Gribov rules, stems from the coupled-channel features of intranuclear pQCD. We propose a multiplicity re-summation as a tool for the isolation of topological cross sections for single-jet production.Comment: 53 pages, 16 eps-figures, to appear in Phys. Rev.

Cosmic ray acceleration by stellar wind. Simulation for heliosphere

The solar wind deceleration by the interstellar medium may result in the existence of the solar wind terminal shock. In this case a certain fraction of thermal particles after being heated at the shock would obtain enough energy to be injected to the regular acceleration process. An analytical solution for the spectrum in the frame of a simplified model that includes particle acceleration at the shock front and adiabatic cooling inside the stellar wind cavity has been derived. It is shown that the acceleration of the solar wind particles at the solar wind terminal shock is capable of providing the total flux, spectrum and radial gradients of the low-energy protons close to one observed in the interplanetary space

Realization of anisotropic compass model on the diamond lattice of Cu2+^{2+} in CuAl2_2O4_4

Spin-orbit (SO) Mott insulators are regarded as a new paradigm of magnetic materials, whose properties are largely influenced by SO coupling and featured by highly anisotropic bond-dependent exchange interactions between the spin-orbital entangled Kramers doublets, as typically manifested in $5d$ iridates. Here, we propose that a very similar situation can be realized in cuprates when the Cu$^{2+}$ ions reside in a tetrahedral environment, like in spinel compounds. Using first-principles electronic structure calculations, we construct a realistic model for the diamond lattice of the Cu$^{2+}$ ions in CuAl$_2$O$_4$ and show that the magnetic properties of this compound are largely controlled by anisotropic compass-type exchange interactions that dramatically modify the magnetic ground state by lifting the spiral spin-liquid degeneracy and stabilizing a commensurate single-$\boldsymbol{q}$ spiral

Kinetic Scalar Curvature Extended f(R)f(R) Gravity

In this work we study a modified version of vacuum $f(R)$ gravity with a kinetic term which consists of the first derivatives of the Ricci scalar. We develop the general formalism of this kinetic Ricci modified $f(R)$ gravity and we emphasize on cosmological applications for a spatially flat cosmological background. By using the formalism of this theory, we investigate how it is possible to realize various cosmological scenarios. Also we demonstrate that this theoretical framework can be treated as a reconstruction method, in the context of which it is possible to realize various exotic cosmologies for ordinary Einstein-Hilbert action. Finally, we derive the scalar-tensor counterpart theory of this kinetic Ricci modified $f(R)$ gravity, and we show the mathematical equivalence of the two theories.Comment: NPB Accepte