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We combine a wide variety of experimental techniques to analyze two heretofore mysterious phase transitions in multiferroic bismuth ferrite at low temperature. Raman spectroscopy, resonant ultrasound spectroscopy, EPR, X-ray lattice constant measurements, conductivity and dielectric response, specific heat and pyroelectric data have been collected for two different types of samples: single crystals and, in order to maximize surface/volume ratio to enhance surface phase transition effects, BiFeO3 nanotubes were also studied. The transition at T=140.3K is shown to be a surface phase transition, with an associated sharp change in lattice parameter and charge density at the surface. Meanwhile, the 201K anomaly appears to signal the onset of glassy behaviour., Comment: submitted to PRB

Using the symmetry theory we analyze of the flexomagnetic effect in all 90 magnetic classes and showed that 69 of them are flexomagnetic. Then we explore how the symmetry breaking, inevitably present in the vicinity of the surface, changes the local symmetry and thus the form of the flexomagnetic tensors. All possible surface magnetic classes (in the number of 19) were obtained from the 90 bulk magnetic classes for the surface cuts 001, 010 and 100 types. It appeared that all 90 bulk magnetic classes become flexomagnetic, piezomagnetic and piezoelectric in the vicinity of surface. Using the free energy approach, we show that the flexomagnetic effect leads to a new type of flexo-magnetoelectric (FME) coupling in nanosized and bulk materials, in all spatial regions, where the polarization and (anti)magnetization vectors are spatially inhomogeneous due to external or internal forces. The linear FME coupling, proportional to the product of the gradients of (anti)magnetization and polarization, flexoelectric and flexomagnetic tensors, is significant in nanosized ferroelectrics-(anti)ferromagnetics, where gradients of the polarization and magnetization obligatory exist. The spontaneous FME coupling induced by the spatial confinement give rise to the size-dependent linear magnetoelectric coupling in nanosized ferroelectrics-(anti)ferromagnetics. We show that the flexomagnetic effect may lead to improper ferroelectricity in bulk (anti)ferromagnetics via the linear and nonlinear FME coupling. Inhomogeneous spontaneous polarization is induced by the (anti)magnetization gradient, which exists in all spatial regions, where polarization varies and (anti)magnetization vector changes its direction. The gradient can be induced by the surface influence as well as by external strain via e.g. the sample bending., Comment: 29 pages, 6 figures, 5 tables

Based on our analytical results [http://arxiv.org/abs/1006.3670], we predict that undoped nanoparticles (size <10-100nm) of incipient ferroelectrics without any magnetic ions can become ferromagnetic even at room temperatures due to the inherent presence of a new type of magnetic defects with spin S=1, namely oxygen vacancies, where the magnetic triplet state is the ground state in the vicinity of the surface (magnetic shell), while the nonmagnetic singlet is the ground state in the bulk material (nonmagnetic core). Consideration of randomly distributed magnetic spins (S=1) had shown that magnetic properties of incipient ferroelectric nanoparticles are strongly size and temperature dependent due to the size and temperature dependence of their dielectric permittivity and the effective Bohr radius proportional to permittivity. The phase diagrams in coordinates temperature - particle radius are considered. In particular, for particle radii less that the critical radius ferromagnetic long-range order appears in a shell region of thickness 5 - 50 nm once the concentration of magnetic defects exceeds the magnetic percolation threshold. The critical radius is calculated in the mean field theory from the condition of the magnetic defects exchange energy equality to thermal energy. For particle radii higher than critical value only the paramagnetic phase is possible. The conditions of the super-paramagnetic state appearance in the assembly of nanoparticles with narrow distribution function of their sizes are discussed also., Comment: 33 pages, 7 figures, 2 appendices

The electrocaloric effect (ECE) in normal and relaxor ferroelectrics is investigated in the framework of a thermodynamic approach based on the Maxwell relation and a Landau-type free energy model. The static dielectric response of relaxors is described by the spherical random bond--random field model, yielding the first Landau coefficient a=a(T), which differs from the usual expression for ferroelectrics. The fourth-order coefficient b is treated as a phenomenological parameter, which is either positive or negative due to the anisotropy of the stress-mediated coupling between the polar nanoregions. When b<0, the maximum ECE in a relaxor is predicted near the critical point in the temperature-field phase diagram, whereas in a ferroelectric it occurs at the first order phase transition. The theoretical upper bound on the ECE temperature change is estimated from the values of saturated polarization, effective Curie constant, and specific heat of the material., Comment: 20 pages, 4 figures

Using the quantum-mechanical approach combined with the image charge method we calculated the lowest energy levels of the impurities and neutral vacancies with two electrons or holes located in the vicinity of flat surface of different solids. We obtained that the magnetic triplet state is the ground state of the impurities and neutral vacancies in the vicinity of surface, while the nonmagnetic singlet is the ground state in the bulk for e.g. He atom, Li+, Be++, etc. ions. The energy difference between the lowest triplet and singlet states strongly depends on the electron (hole) effective mass, dielectric permittivity of the solid and the distance from the surface. Pair interaction of the identical surface defects (two doubly charged impurities or vacancies with two electrons or holes) reveals the ferromagnetic spin state with the maximal exchange energy at the definite distance between the defects (~5-25 nm). We obtained that the nonmagnetic singlet state is the lowest one for a molecule with two electrons formed by a pair of identical surface impurities (like surface hydrogen), while its next state with deep enough negative energy minimum is the magnetic triplet. The metastable magnetic triplet state appeared for such molecule at the surface indicates the possibility of metastable orto-states of the hydrogen-like molecules, while they are absent in the bulk of material. We hope that obtained results could provide an alternative mechanism of the room temperature ferromagnetism observed in TiO2, HfO2, and In2O3 thin films with contribution of the oxygen vacancies., Comment: 59 pages, 11 figures, 5 appendices

The symmetry breaking inevitably present in the vicinity of any surface, namely an inversion center disappears in surface normal direction and only axes and planes normal to the surface conserve, gives rise to the spontaneous piezomagnetic, piezoelectric and magnetoelectric effects in nanosystems, while the effects can be absent in a bulk material. All these phenomena are inherent to nanos made of materials belonging to all ninety bulk magnetic classes. Therefore the new linear magnetoelectrics should appear among nanomaterials, nonpiezomagnetic and nonpiezoelectric in the bulk. To demonstrate this we consider the typical cases of ultra-thin films, nanowires and nanospheres. Coupled with a surface stress for nanoparticles and a mismatch strains for thin films on substrates the surface piezomagnetic and piezoelectric effects lead to the appearance of built-in magnetic and electric fields respectively. The built-in fields play an important role in the appearance of self-magnetization and self-polarization in the nanosystems paramagnetic and paraelectric in the bulk and can lead to the appearance of some other interesting properties absent in the bulk. We obtained analytical dependencies on sizes for the built-in fields and magnetoelectric coupling coefficients. The values of the built-in fields increase with the decrease of film thickness h or nanoparticles radii R as ~1/h or 1/R2 respectively, while the magnetoelectric coupling is inversely proportional to the sizes in both cases. This shows the strong influence of sizes on the considered properties of nanos and so opens the ways to govern the properties by the choice of the sizes and to create new multifunctional nanomaterials., Comment: 12 pages, 2 Tables, 1 Appendix

We present electric and magnetic properties of 0.8Pb(Fe1/2Nb1/2)O3-0.2Pb(Mg1/2W1/2)O3 films epitaxially grown on (001) SrTiO3 substrates using pulsed laser deposition. A narrow deposition window around 710 oC and 0.2 mbar has been identified to achieve epitaxial single-phase thin films. A typical Vogel-Fulcher relaxor-like dielectric and magnetic susceptibility dispersion is observed, suggesting magnetoelectric relaxor behavior in these films similar to the bulk. We determine a magnetic cluster freezing temperature of 36 K, while observing weak ferromagnetism via magnetic hysteresis loops up to 300 K., Comment: 12 pages, 4 figures

We have made magnetization and x-ray diffraction measurements on an epitaxial Pb(Fe1/2Nb1/2)O3 200 nm film. From the temperature dependence of the out-of-plane lattice parameter we can assign a Burns' temperature at Td ~ 640 K, a temperature at T* ~ 510 K, related to the appearance of static polar nanoregions, and an anomaly occurring at 200 K. The latter is precisely the N\'eel temperature TN determined from magnetization and points to spin-lattice coupling at TN ~ 200 K. We also observe "weak ferromagnetism" up to 300K and propose superantiferromagnetic clusters as a plausible scenario to explain this hysteresis above TN., Comment: 12 pages, 4 figures

We have grown lead iron niobate thin films with composition Pb(Fe1/2Nb1/2)O3 (PFN) on (0 0 1) SrTiO3 substrates by pulsed laser deposition. The influence of the deposition conditions on the phase purity was studied. Due to similar thermodynamic stability spaces, a pyrochlore phase often coexists with the PFN perovskite phase. By optimizing the kinetic parameters, we succeeded in identifying a deposition window which resulted in epitaxial perovskite-phase PFN thin films with no identifiable trace of impurity phases appearing in the X-ray diffractograms. PFN films having thicknesses between 20 and 200 nm were smooth and epitaxially oriented with the substrate and as demonstrated by RHEED streaks which were aligned with the substrate axes. X-ray diffraction showed that the films were completely c-axis oriented and of excellent crystalline quality with low mosaicity (X-ray rocking curve FWHM<0.09). The surface roughness of thin films was also investigated by atomic force microscopy. The root-mean-square roughness varies between 0.9 nm for 50-nm-thick films to 16 nm for 100-nm-thick films. We also observe a correlation between grain size, surface roughness and film thickness., Comment: 13 Pages, 6 figures. To be published in J. Mag. Mag Mater. proceedings of EMRS2008

Within the Landau-Ginsburg-Devonshire phenomenological approach we study the ferroic nanosystems properties changes caused by the flexo-effect (flexoelectric, flexomagnetic, flexoelastic) existing spontaneously due to the inhomogeneity of order parameters. Exact solution for the spatially inhomogeneous mechanical displacement vector allowing for flexo-coupling contribution was found for nanowires and thin pills. Strong influence of flexo-effect in nanorods and thin pills leads to the displacements of the atoms resulting into the unit cell symmetry changes, which lead to the phase transition temperature shift, as well as the flat geometry in radial direction transforms into the saucer-like one. The new phenomena can be considered as true manifestation of the spontaneous flexo-effect existence. It was shown that flexo-effect leads to (a) the appearance of new linear and nonlinear contribution and renormalization of coefficients before the order parameter gradient, (b) essentially influences the transition temperature, piezoelectric response and the spatial distribution of the order parameter, (c) results in renormalization of extrapolation length in the boundary conditions., Comment: 35 pages, 7 figures, 4 Appendices, to be submitted to Phys. Rev. B

We show that misfit strain originated from the film-substrate lattice mismatch strongly increases the value of the quadratic magnetoelectric coupling. The giant magnetoelectric coupling, size effects and misfit strain cause strong changes of ferroic films phase diagrams at zero external magnetic and electric fields, in particular, the transformation of antiferromagnetic phase into ferromagnetic or ferrimagnetic ones for compressive or tensile misfit strains correspondingly as well as thickness induced paramagnetic or/and paraelectric phases appearance. Ferromagnetism appearance and magnetoelectric coupling increase in thin ferroelectric-antiferromagnetic films is in agreement with available experimental data and opens the way for tailoring of ferroic films magnetic and electric properties., Comment: 25 pages, 3 Figures, 1 Table, 2 Appendices

We show that the presence of free carriers in a substance can generate the multiferroic behavior. Namely, if the substance has mixed-valence ions, which can supply free carriers and have electric dipole and spin moments, all three types of long-range order (ferromagnetic, ferroelectric and magnetoelectric (ME)) can occur at low temperature. The physical origin of the effect is that charge carriers can mediate the multiferroic behavior via spin - spin (RKKY), dipole-dipole and dipole - spin interactions. Our estimate of the interaction magnitude shows that there exist an optimal carrier concentration, at which the strength of ME interaction is maximal and comparable to that of spin-spin RKKY interaction. This permits to conclude that in substances, where RKKY interaction between local spins is not small, a substantial value of free carriers mediated ME interaction can occur. Our analysis shows that disorder in the above substances does not suppress multiferroic effects., Comment: 4 pages, 1 figure

The general approach for the consideration of the magnetoelectric effects in ferroic nanorods is proposed in the framework of the phenomenological theory. The intrinsic surface stress, magneto- and electrostriction as well as piezoelectric and piezomagnetic effects are included into the free energy. The intrinsic surface stress under the curved nanoparticle surface is shown to play an important role in the shift of ferroelectric and ferromagnetic transition temperatures and built-in magnetic and electric fields appearance, which are inversely proportional to the nanorod radius. We consider the case of quadratic and linear magnetoelectric coupling coefficients. The linear coupling coefficient is radius independent, whereas the quadratic ones include terms inversely proportional to the nanorod radius and thus strongly increase with decrease of the radius. The predicted giant relative dielectric tunability in the vicinity of ferromagnetic and ferroelectric phase transition points induced by quadratic magnetoelectric coupling increases by 2-50 times. The quadratic magnetoelectric coupling dramatically changes the phase diagrams of ferroic nanorods when the radius decreases. In particular the second order phase transition may become a first one, the triple point state characterized by continuous set of order parameters appears at zero external electric and magnetic fields and the tricritical points appear under external fields., Comment: 36 pages, 11 figures, 3 Appendices

A physical mechanism for the freezing of polar nanoregions (PNRs) in relaxor ferroelectrics is presented. Assuming that the activation energy for the reorientation of a cluster of PNRs scales with the mean volume of the cluster, the characteristic relaxation time $\tau$ is found to diverge as the cluster volume reaches the percolation limit. Applying the mean field theory of continuum percolation, the familiar Vogel-Fulcher equation for the temperature dependence of $\tau$ is derived.

Born-Oppenheimer (BO) potential in any material. The proton potential surfaces in the hydrogen bonded superprotonic conductor Rb3H(SO4)2 are extracted from the momentum distribution measured using Deep Inelastic Neutron Scattering(DINS). The potential has a single minimum along the bond direction, which accounts for the absence of the antiferroelectric transition seen in the deuterated material, and a saddle point off the bond direction for tunneling into the next well with a barrier height of 350 meV. The measured potential is in qualitative agreement with phenomenological double Morse potentials that have been used to describe hydrogen bonds in other systems.

It has been recently established by NMR techniques that in the high temperature cubic phase of BaTiO$_3$ the Ti ions are not confined to the high symmetry cubic sites, but rather occupy one of the eight off-center positions along the $[111]$ directions. The off-center Ti picture is in apparent contrast with most soft-mode type theoretical descriptions of this classical perovskite ferroelectric. Here we apply a mesoscopic model of BaTiO$_3$, assuming that the symmetrized occupation operators for the Ti off-center sites are linearly coupled to the normal coordinates for lattice vibrations. On the time scale of Ti intersite jumps, most phonon modes are fast and thus merely contribute to an effective static Ti-Ti interaction. Close to the stability limit for the soft TO optic modes, however, the phonon time scale becomes comparable to the relaxation time for the Ti occupational states of $T_{1u}$ symmetry, and a hybrid vibrational-orientational soft mode appears. The frequency of the hybrid soft mode is calculated as a function of temperature and coupling strength, and its its role in the ferroelectric phase transition is discussed., Comment: Revtex4, 8 pages, 3 figures

The 93Nb and 45Sc NMR spectra in PbSc_1/2Nb_1/2O_3 (PSN) and PbMg_1/3Nb_2/3O_3 (PMN) disordered relaxor ferroelectrics at the temperature T > T_0 (T_0 is the temperature of the dielectric susceptibility maximum) have been studied. Spectra analysis was performed on the base both of the analytical description of NMR lines shapes, allowing for homogeneous and inhomogeneous broadening related to a random distribution of the electric field gradients and numerical Monte Carlo method taking into account electric field gradients originated from random distribution of Mg, Sc and Nb ions (which may be shifted or not) over B-type cation sites. The observed 1/2 -1/2 transition spectrum both of the 93Nb and 45Sc nuclei in the PSN was shown to contain a narrow (3-4 kHz) almost isotropic part and a broad strongly anisotropic part. These two components of NMR spectra are related to 1:1 Sc/Nb ordered and compositionally disordered regions of the crystal, respectively. It was shown that in the disordered regions Sc^3+, Nb^5+ and O^2- ions are shifted from their cubic lattice sites at one of three possible directions: <100>, <110> or <111>. In PMN the NMR spectrum of 93Nb contains practically only the broad component. The portion of unbroadened spectrum that may correspond to ideal 1:2 regions accounts only for 1-2 percent of the total integral intensity. No evidance was obtained about existence of the 1:1 regions in PMN. The NMR data demonstrate that in PMN the cubic symmetry at T > T_0 is locally broken due to ions shifts similar to that in disordered PSN. The values of the ion shifts were estimated in the point charges point dipoles approximation of the electric field gradients calculation both in the PSN and PMN.

We study a dynamic model of relaxor ferroelectrics based on the spherical random-bond---random-field model and the Langevin equations of motion. The solution to these equations is obtained in the long-time limit where the system reaches an equilibrium state in the presence of random local electric fields. The complex dynamic linear and third-order nonlinear susceptibilities $\chi_1(\omega)$ and $\chi_3(\omega)$, respectively, are calculated as functions of frequency and temperature. In analogy with the static case, the dynamic model predicts a narrow frequency dependent peak in $\chi_3(T,\omega)$, which mimics a transition into a glass-like state., Comment: 15 pages, Revtex plus 5 eps figures

The static behavior of orientational glasses is discussed in terms of a replica theory based on the infinite range random bond--random field model. A general version of the model applicable to dipolar and quadrupolar glasses is presented using a symmetry-adapted representation for the order parameter fields. Numerical results for the $<100>$ quadrupolar glass are obtained and compared with the Ising and $<111>$ orientational glass models., Comment: 10 pages, PostScript file with 3 figures included, Z-compressed . Latex + sty files available upon request