A phenomenological theory for polarization flop in spiral multiferroic TbMnO<Subscript>3</Subscript>

A phenomenological Landau theory has been used to explain magnetic field-driven polarization flop in TbMnO ₃. The Néel wall-like magnetic structure in spiral multiferroics induces a space-dependent internal magnetic field which exerts a torque on spins to rotate bc-spiral to ab-spiral. The external magnetic field is argued to be competing with easy axis anisotropy and the system stabilizes when anisotropy is minimum. With the help of Landau free energy with DM magnetoelectric coupling and a general ansatz for magnetization, the phenomenon of polarization flop has been explained. Relation between T_flop and critical magnetic field has been established and found to be in good agreement with the experiment. This could be an indication that anisotropy of the system is temperature- and magnetic field-dependent.     

First-principles theory of magnetically induced ferroelectricity in TbMnO<Subscript>3</Subscript>

We study the polarization induced via spin-orbit interaction by a magnetic cycloidal order in orthorhombic TbMnO₃ using first-principle methods. The case of magnetic spiral lying in the b-c plane is analyzed, in which the pure electronic contribution to the polarization is shown to be small. We focus our attention on the lattice-mediated contribution, and study it’s dependence on the Coulomb interaction parameter U in the LDA+U method and on the wave-vector of the spin spiral. The role of the spin-orbit interaction on different sites is also analyzed.     

Features of the low-frequency polarization response in the region of the ferroelectric phase transition in multiferroic TbMnO<Subscript>3</Subscript>

The unusual behavior of the low-frequency (10 Hz–1 MHz) permittivity in single crystals of ferroelectric multiferroic TbMnO₃ has been experimentally and theoretically studied in detail in the region of the narrow temperature peak of the permittivity, associated with the ferroelectric phase transition (T_C ~ 27.4 K). It has been found that the ε_c^′(ω, T) maximum sharply decreases with increasing measured field frequency, while the temperature position of the maximum is independent of frequency. It has been shown that the observed features of the polarization response can be satisfactorily described within the Landau–Khalatnikov polarization relaxation theory.     

Colossal magnetodielectric effect in SmFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

The colossal (more than threefold) decrease in the dielectric constant ɛ in the easy-plane SmFe₃(BO₃)₄ ferroborate in a magnetic field of ∼5 kOe applied in the basal ab plane of the crystal has been found. A close relation of this effect to anomalies in the field dependence of the electric polarization has been established. It has been shown that this magnetodielectric effect is due to the contribution to ɛ from the electric susceptibility, which is related to the rotation of spins in the ab plane, arises in the region of the antiferromagnetic ordering T < T _N = 33 K, and is suppressed by the magnetic field. A theoretical model describing the main features of the behavior of ɛ and electric polarization in the magnetic field has been proposed, taking into account the additional anisotropy in the basal plane induced by the magnetoelastic stresses.     

Suppression of ferroelectricity and quantum fluctuations in Ru-doped TbMnO<Subscript>3</Subscript>

We investigate the effects of Ru-doping in polycrystalline TbMn_1−x Ru _x O₃ (x≤0.10) on the multiferroicity. It is observed that the Ru substitution gradually melts away the dielectric anomaly at the ferroelectric transition point and the ferroelectricity by suppressing the polarization, accompanied with a surprising low-temperature dielectric plateau. While it is reasonable to observe the significant suppression of ferroelectricity, owing to the fact that the Ru-doping disrupts the Mn spiral spin ordering and reduces the Mn–Mn spin angle, quantum fluctuations associated with the Ru substitution, responsible for the low-temperature dielectric plateau, seems to be significant.     

Anomalously strong relaxation of the polarization of muons in the magnetically ordered and paramagnetic states of the TbMnO<Subscript>3</Subscript> multiferroic

An anomalously strong relaxation of the muon polarization in a magnetically ordered state in the TbMnO₃ multiferroic has been revealed by the method below the μSR Néel temperature (42 K). Such a relaxation is due to the muon channel of relaxation of the polarization and the interaction of the magnetic moment of the muon with inhomogeneities of the internal magnetic field of an ordered state in the form of a cycloid. Above the Néel temperature, beginning with temperatures depending on the applied magnetic field, a two-phase state has been revealed where one phase has an anomalously strong relaxation of the muon polarization for a paramagnetic state. These features of the paramagnetic state are due to short-range magnetic order domains that appear in strongly frustrated TbMnO₃. A true paramagnetic state has been observed only at T ≥ 150 K.     

Neutron scattering investigations of multiferroic YMnO<Subscript>3</Subscript>

Multiferroic materials are the materials that show several cooperative ordering phenomena simultaneously. Here we consider only those materials that show both antiferromagnetism and ferroelectricity and in which the ordering parameters are coupled to each other. I shall review our recent neutron scattering investigations on multiferroic hexagonal manganites YMnO₃. We have determined the spin wave dispersions in YMnO₃ in symmetry directions by inelastic neutron scattering and have fitted the results with a simple nearest-neighbour anisotropic Heisenberg model. We have investigated the spin dynamics of YMnO₃ above T _N ∼ 70 K and have shown the existence of persistent albeit heavily damped spin waves.      

Phase transition in Bi<Subscript>8</Subscript>Fe<Subscript>6</Subscript>Ti<Subscript>3</Subscript>O<Subscript>27</Subscript> multiferroic ceramics

The polycrystalline Bi₈Fe₆Ti₃O₂₇ compound was prepared by a high-temperature solid-state reaction technique. Preliminary structural analysis by X-ray diffraction (XRD) confirms the formation of a single-phase compound in an orthorhombic crystal system at room temperature. The elemental content of the compound was analyzed by EDAX microanalysis. Microstructural analysis by scanning electron microscopy (SEM) shows that the compound has well defined grains, which are distributed uniformly throughout the surface of the pellet sample. Detailed studies of temperature-dependent dielectric response at various frequencies show dielectric anomalies at 380, 389 and 403°C for 10 kHz, 100 kHz, and 1 MHz respectively. The hysteresis loop observed by applying an electric field of 12 kV/cm on the poled sample with smaller remanent polarization supports the existence of ferroelectricity in this material. The value of d₃₃ of the compound was found to be 19 pC/N.      

Electronic excitations and defects in nanostructural Al<Subscript>2</Subscript>O<Subscript>3</Subscript>

A time-resolved cathodo-and photoluminescence study of nanostructural modifications of Al₂O₃ (powders and ceramics) excited by heavy-current electron beams, as well as by pulsed synchrotron radiation, is reported. It was found that Al₂O₃ nanopowders probed before and after Fe⁺ ion irradiation have the same phase composition (the γ-phase/δ-phase ratio is equal to 1), an average grain size equal to ～17 nm, and practically the same set of broad cathodoluminescence (CL) bands peaking at 2.4, 3.2, and 3.8 eV. It was established that Al₂O₃ nanopowders exhibit fast photoluminescence (PL) (a band at 3.2 eV), whose decay kinetics is described by two exponential stages (τ₁ = 0.5 ns, τ₂ = 5.5 ns). Three bands, at 5.24, 6.13, and 7.44 eV, were isolated in the excitation spectrum of the fast PL. Two alternate models of PL centers were considered, according to which the 3.2-eV luminescence either originates from radiative relaxation of the P^? centers (anion-cation vacancy pairs) or is due to the formation of surface analogs of the F⁺ center (F _S ⁺ -type centers). In addition to the fast luminescence, nano-Al₂O₃ was found to produce slow luminescence in the form of a broad band peaking at 3.5 eV. The excitation spectrum of the 3.5-eV luminescence obtained at T = 13 K exhibits two doublet bands with maxima at 7.8 and 8.3 eV. An analysis of the luminescent properties of nanostructural and single-crystal Al₂O₃ suggests that the slow luminescence of nanopowders at 3.5 eV is due to radiative annihilation of excitons localized near structural defects.     

Double-exchange model study of multiferroic RMnO<Subscript>3</Subscript> perovskites

In this proceeding, recent theoretical investigations by the authors on the multiferroic RMnO₃ perovskites are briefly reviewed at first. Using the double-exchange model, the realistic spiral spin order in undoped manganites such as TbMnO₃ and DyMnO₃ is well reproduced by incorporating a weak next-nearest neighbor superexchange (~10% of nearest neighbor superexchange) and moderate Jahn-Teller distortion. The phase transitions from the A-type antiferromagnet (as in LaMnO₃), to the spiral phase (as in TbMnO₃), and finally to the E-type antiferromagnet (as in HoMnO₃), with decreasing size of the R ions, were also explained. Moreover, new results of phase diagram of the three-dimensional lattice are also included. The ferromagnetic tendency recently discovered in the LaMnO₃ and TbMnO₃ thin films is explained by considering the substrate stress. Finally, the relationship between our double-exchange model and a previously used J₁-J₂-J₃ model is further discussed from the perspective of spin wave excitations.     

Nanostructured multiferroic PbFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> and its physical properties

Polycrystalline multiferroic PbFe_0.5Nb_0.5O3 (PFN) fabricated by a solid-phase method is studied. Before sintering, a synthesized PFN powder is processed in Bridgman anvils via a force action in combination with shear deformation (FASD) at room temperature. The electrophysical properties and structural parameters of processed samples and a reference sample are compared. Point defects are shown to play a key role in the formation of the physical properties beginning from an FASD of 200 MPa.     

<Superscript>57</Superscript>Fe NMR study of multiferroic BiFeO<Subscript>3</Subscript>

The effects of the ⁵⁷Fe isotope content and high-frequency magnetic field amplitude h ₁ on the shape of the NMR spectrum of multiferroic BiFeO₃ at T = 4.2 K are studied by pulsed nuclear magnetic resonance. The NMR spectrum shape and transverse relaxation time T ₂ are found to depend strongly on the ⁵⁷Fe isotope content and h ₁ in multiferroic BiFeO₃ in the presence of a spatial spin-modulated structure of a cycloid type. In a sample with a high ⁵⁷Fe isotope content, the Suhl-Nakamura interaction contributes substantially to T ₂. When these dynamic effects are taken into account for analysis of the NMR spectrum shape, an undisturbed (without an anharmonicity effect) spatial spin-modulated structure of a cycloid type is shown to exist in BiFeO₃.     

Luminescence and electronic excitations in KBe<Subscript>2</Subscript>BO<Subscript>3</Subscript>F<Subscript>2</Subscript> crystals

This paper reports on a study of the dynamics of electronic excitations in KBe₂BO₃F₂ (KBBF) crystals by low-temperature luminescent vacuum ultraviolet spectroscopy with nanosecond time resolution under photoexcitation by synchrotron radiation. The first data have been obtained on the kinetics of photoluminescence (PL) decay, time-resolved PL spectra, time-resolved PL excitation spectra, and reflection spectra at 7 K; the estimation has been performed for the band gap E _g = 10.6−11.0 eV; the predominantly excitonic mechanism for PL excitation at 3.88 eV has been identified; and defect luminescence bands at 3.03 and 4.30 eV have been revealed. The channels of generation and decay of electronic excitations in KBBF crystals have been discussed.     

Peculiarities in the magnetic,magnetoelectric, and magnetoelastic properties of SmFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

Results of a complex investigation of the magnetic, magnetoelectric, and magnetoelastic properties of a SmFe₃(BO₃)₄ single crystal are presented. Samarium iron borate is similar to another easy-plane iron borate, NdFe₃(BO₃)₄, in that it possesses a large value of the magnetic-field-induced polarization (about 500 μC/m²), the sign of which changes when the field direction is changed between axes a and b of the crystal. However, the temperature dependence of the magnetic susceptibility and the field dependence of polarization and magnetostriction of the two compounds are significantly different, which is explained by the weak effect of external magnetic field on the ground-state multiplet of samarium ion, which is characterized by an extremely small value of its g-factor.     

Luminescence and electronic excitations in Li<Subscript>6</Subscript>Gd(BO<Subscript>3</Subscript>)<Subscript>3</Subscript>: Ce<Superscript>3+</Superscript> crystals

This paper reports on a study of the luminescence emitted by Li₆Gd(BO₃)₃: Ce³⁺ crystals under selective photoexcitation to lower excited states of the host ion Gd³⁺ and impurity ion Ce³⁺ within the 100–500-K temperature interval, where the mechanisms of migration and relaxation of electronic excitation energy have been shown to undergo noticeable changes. The monotonic 10–15-fold increase in intensity of the luminescence band at 3.97 eV has been explained within a model describing two competing processes, namely, migration of electronic excitation energy over chains of Gd³⁺ ions and vibrational energy relaxation between the ⁶ I _j and ⁶ P _j levels. It has been shown that radiative transitions in Ce³⁺ ions from the lower excited state 5d ¹ to ² F _5/2 and ² F _7/2 levels of the ground state produce two photoluminescence bands, at 2.08 and 2.38 eV (Ce1 center) and 2.88 and 3.13 eV (Ce2 center). Possible models of the Ce1 and Ce2 luminescence centers have been discussed.     

Multiphonon relaxation of optical excitations in CsCdBr<Subscript>3</Subscript>:Pr<Superscript>3+</Superscript> and LiYF<Subscript>4</Subscript>:Nd<Superscript>3+</Superscript> crystals

The technique of calculation of the n-phonon transition rates between electronic sublevels of impurity rare earth ions in dielectric crystals is developed in the case when n>2. The n-phonon transition probabilities are calculated according to the 1st and 2nd orders of perturbation theory. The Hamiltonian of the electron-phonon interaction is constructed in the framework of the exchange charge model and developed as series in relative displacements of the rare earth ion and ligands. The contribution of the lattice anharmonicity on the probabilities of n-phonon transitions is taken into account. On the basis of the developed technique, the nonradiative relaxation rates of ⁴ G _7/2 multiplet of Nd³⁺ ions in LiYF₄:Nd³⁺crystal and ³P₁ multiplet of Pr³⁺ ions in CsCdBr₃:Pr³⁺ crystal were computed. The results of our calculations show that the 2nd order terms in the expressions for the probabilities studied here are comparable with, and in some cases prevail over the 1st order terms. An account of lattice anharmonicity in case of LiYF₄:Nd³⁺ crystal substantially modifies the corresponding multiphonon relaxation rates. The calculated nonradiative relaxation rates for both crystals agree well with the experimental data.     

Magnetic circular dichroism and optical absorption in TmAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The polarized spectra of absorption and magnetic circular dichroism in a TmAl₃(BO₃)₄ single crystal are studied in the region of ³ H ₆ → ³ F ₄, ³ H ₆ → ³ F ₃, and ³ H ₆ → ³ F ₂ electronic transitions in the Tm³⁺ ion. The structure of the spectra is interpreted qualitatively. It is shown that the magnetic circular dichroism of the ³ H ₆ → ³ F ₄ transition is determined by the contribution from the splitting of the ground state, whereas the magnetic circular dichroism of the ³ H ₆ → ³ F ₃ transition is governed by the contribution from the splitting of an excited state in a trigonal crystal field.     

Transient hole-polaron optical absorption in Li<Subscript>6</Subscript>Gd(BO<Subscript>3</Subscript>)<Subscript>3</Subscript> crystals

Results of a study of transient optical absorption (TOA) and luminescence of lithium gadolinium orthoborate Li₆Gd(BO₃)₃ (LGBO) in the visible and UV spectral regions are presented. As revealed by absorption optical spectroscopy with nanosecond time resolution, the LGBO TOA derives from optical transitions in hole centers, with the optical density relaxation kinetics being mediated by interdefect tunneling recombination involving these centers and neutral lithium atoms acting as electronic Li⁰ centers. At 290 K, the Li⁰ centers are involved in thermostimulated migration, which is not accompanied by carrier transfer to the conduction or valence band. The slow components of the TOA decay kinetics, with characteristic times ranging from a few milliseconds to seconds, have been assigned to diffusion-limited annihilation of lithium interstitials with vacancies. The mechanisms responsible for the creation and relaxation of short-lived Frenkel defect pairs in the LGBO cation sublattice have been analyzed.     

Polarization modes in the Ba<Subscript>2</Subscript>Mg<Subscript>2</Subscript>Fe1<Subscript>2</Subscript>O<Subscript>22</Subscript> multiferroic

The spectra of complex permittivity of a Ba₂Mg₂Fe₁₂O₂₂ single crystal belonging to the family of Y-type hexaferrites have been measured over a wide temperature range (10–300 K) with the aim of determining the dynamic parameters of the phonon and magnetic subsystems in the terahertz and infrared frequency ranges (3–4500 cm⁻¹). A factor-group analysis of the vibrational modes has been performed, and the results obtained have been compared with the experimentally observed resonances. The oscillator parameters of all nineteen phonon modes of E _u symmetry, which are allowed by the symmetry of the Ba₂Mg₂Fe₁₂O₂₂ crystal lattice, have been calculated. It has been found that, at temperatures below 195 and 50 K, the spectral response exhibits new absorption lines due to magnetic excitations.     

Switching of spontaneous electric polarization in the DyMnO<Subscript>3</Subscript> multiferroic

For the DyMnO₃ multiferroic with a modulated magnetic structure, switching of its spontaneous electric polarization (P ‖ c axis) near the ferroelectric transition (T < T _FE ～ 20 K) is revealed by measuring the dielectric hysteresis loops. It is found that the coercive field strongly increases as the temperature decreases (up to 2.6 kV/mm at 17.6 K). The values obtained for the spontaneous polarization are found to agree well with the data obtained from pyroelectric measurements. In addition, anomalies are observed in the temperature dependences of the spontaneous polarization P _c , dielectric constant ? _c , and magnetic susceptibility x _b at T ～ 6 K; these anomalies are attributed to the antiferromagnetic ordering of the Dy³⁺ ions.