Small polaron migration in LixMn2O4: From first principles calculations

Migration of small polarons in λ-MnO₂, Li_0.5Mn₂O₄ and LiMn₂O₄ is studied via first principles calculations. Migration energy barriers of single small polaron migrations in λ-MnO₂, Li_0.5Mn₂O₄ and LiMn₂O₄ are 0.22 eV, 0.45 eV and 0.35 eV, respectively. The energy level changes of Mn-3d states along the polaron migration path are analyzed in detail. Results indicate that the activation energy barrier of polaron migration is strongly associated with the energy level shift of Mn-3dz² orbital, which is dependent on the short range structural arrangement of Mn³⁺/Mn⁴⁺ in the crystal. The electrical conduction properties of Li_xMn₂O₄ at room temperature are then discussed.     

Infrared reflectivity of Cox(SiO2)1−x (x∼0.85, 0.55, 0.38) granular films on SiO2 glass substrates

We report the infrared specular reflectivity of Co_x(SiO₂)_1−x (x∼0.85, 0.55, 0.38) films on SiO₂ glass spanning from a metal-like to insulating behavior. While films for x∼0.85 show carrier metallic shielding and hopping conductivity, for x∼0.65 and lower concentrations, the nanoparticles’ number and size promote a localization edge near the highest longitudinal optical frequency. Such an edge is associated with a reflectivity minimum and a higher frequency band connoting strong electron-phonon interactions, carrier phonon assisted hopping, and polaron formation. Optical conductivity fits with current polaron models provide grounds toward a microscopic understanding of transport properties in these as-prepared granular films.     

Small polaron electron transport in reduced CeO2 single crystals

An investigation of the electrical properties of reduced ceria, CeO_2?x, carried out on single crystals, shows that CeO_2?x provides one of the clearest examples of hopping conduction and the small polaron mechanism. Included are conductivity and Seebeck coefficient measurements at constant x, obtained by sealing off the specimen chamber after reduction. The Seebeck coefficient is independent of temperature, suggesting that the number of carriers is constant. On the other hand, the mobility is activated, with activation energy E_h = 0.40 eV at small x and increasing to 0.52 eV at x = 0.25. The results for the mobility preexponential are consistent with the adiabatic theory of small polaron behavior. A puzzling feature of the Seebeck data as a function of x is that, for low x, the data fit the well-known Heikes formula, without a degeneracy factor of 2 for spin. Nevertheless, these data are interpreted to show that the proportion of mobile carriers decreases as x increases, presumably because of the presence of short-range ordered configurations which immobilize some carriers.     

Excitonic polaron and phonon assisted photoluminescence of ZnO nanowires

The coupling strength of the radiative transition of hexagonal ZnO nanowires to the longitudinal optic (LO) phonon polarization field is deduced from temperature dependent photoluminescence spectra. An excitonic polaron formation is discussed to explain why the interaction of free excitons with LO phonons in ZnO nanowires is much stronger than that of bound excitons with LO phonons. The strong exciton-phonon coupling in ZnO nanowires affects not only the Haung-Ray S factor but also the FXA-1LO phonon energy spacing, which can be explained by the excitonic polaron formation.     

Influence of vacancies on the electrical properties of the ZnCr2−xNixSe4 spinels

The effect of vacancies on the electronic transport in the ZnCr_2−xNi_xSe₄ paramagnetic single crystals is considered. For this purpose, the structure refinements, the high temperature electrical conductivity and the thermoelectric power measurements as well as the calculations of the vacancy model parameters were used. The electrical measurements have been done in the temperature range from 290 to 520 K for single crystals with x=0.001, 0.05, and 0.065. The above investigations provide evidence for polaron conduction in defective spinel materials. In particular: (1) at high temperatures a linear dependence between thermopower S and the electrical resistivity (ln ρ), a characteristic of small polarons, was observed, (2) an origin of small polarons in this case could be associated with a crystalline distortion, which is characterized by larger values of the anion parameter than u=0.375, which describes an ideal spinel structure, and (3) a large defectiveness, which is identified by the large value of the vacancy parameter of about β=11.5%. These effects are explained in terms of a polaron mechanism of the electrical conductivity including structural defects.     

Characterization and electrical properties of V2O5-CuO-P2O5 glasses

Characterization and electrical properties of vanadium-copper-phosphate glasses of compositions xV₂O₅-(40−x)CuO-60P₂O₅ have been reported. X-ray diffraction (XRD) confirms the amorphous nature of these glasses. It was observed that, the density (d) decreases gradually while the molar volume (V_m) increases with the increase of the vanadium oxide content in such glasses. This may be due to the effect of the polarizing power strength, PPS, which is a measure of ratio of the cation valance to its diameter. The dc conductivity increases while the activation energy decreases with the increase of the V₂O₅ content. The dc conductivity in the present glasses is electronic and depends strongly upon the average distance, R, between the vanadium ions. Analysis of the electrical properties has been made in the light of small polaron hopping model. The parameters obtained from the fits of the experimental data to this model are reasonable and consistent with glass composition. The conduction is attributed to non-adiabatic hopping of small polaron.     

Non-adiabatic polaron hopping conduction in CaMn1−xCrxO3 (0?x?0.3)

DC electrical conductivity (σ_dc) of electron-doped antiferromagnetic CaMn_1−xCr_xO₃ (0?x?0.3) has been discussed elaborately in the light of polaron hopping conduction. The increase in Cr doping concentration increases the conductivity and decreases the activation energy. Non-adiabatic polaron hopping conduction is observed in all the manganites at high temperatures. The analysis of σ_dc data shows that small polarons are formed at lower concentrations (?5%) of Cr doping and undoped samples. However, large polarons are materialized at higher doping (?10%) concentrations. This is consistent with the fact that doped Cr³⁺ has larger ionic size compared to that of Mn⁴⁺. Again, strong electron-phonon (e-ph) interaction is perceived in undoped and 5% Cr-doped samples but not in manganites with larger doping concentration. This also confirms the formation of larger polarons with the increase of x. Mott's variable range hopping (VRH) model can elucidate the dc conductivity at very low temperatures. It has been detected that single phonon-assisted hopping is responsible for the dc conduction in the Cr-doped CaMnO₃ manganites.     

On the structure of wave fields in the region of linear interaction between ordinary and extraordinary waves in two-dimensionally inhomogeneous magnetoactive plasmas

The spectra of the low-temperature photodissociation (photoionization) of Landau-Pekar polarons are calculated using the theory of quantum-coherent states and a new method of variation with respect to the parameters of phonon vacuum deformation. It is shown that the final polaron states upon photodissociation may have different numbers of phonons produced in a single dissociation event and different momenta of charge carriers. The spectrum of optical absorption related to the photodissociation of polarons exhibits a superposition of bands corresponding to various numbers of phonons formed as a result of dissociation of a single polaron. Due to a large width of the energy region corresponding to the final states of charge carriers, the halfwidth of each band is on the order of the energy of polaron coupling and is much greater than the phonon energy. For this reason, the individual phonon bands exhibit strong overlap. The very broad and, probably, structureless band formed as a result of the superposition of all these components begins at an energy equal to the sum of the polaron coupling energy (E _p) and the phonon energy. This band has a maximum at a frequency of about 5.6E _p/? and a halfwidth on the order of 5.6E _p/? at a unit effective mass (m* = m _e) of band electrons. For an effective charge carrier mass within m* = (1–3)m _e, the energy of the polaron band maximum can be estimated as 5E _p with an error of about 10%, and the halfwidth falls within 3.4E _p < ?Ω_1/2 < 5.6E _p. The multiphonon character of this band is related to a decay of the phonon condensate after the escape of charge carrier from a polaron. Such polarons are likely to be observed in the spectra of complex metal oxides, including high-temperature superconductors. Examples of such polaron bands in the reported absorption and photoconductivity spectra of nonstoichiometric cuprates, manganites, nickelates, and titanates are presented. A theory of the formation of Landau-Pekar polarons with the participation of branches of the polarization oscillations of the medium is developed. It is shown that, under certain conditions, such a multiphonon-dressed polaron can possess a coupling energy on the order of 0.2–0.3 eV, so that the maximum of the corresponding absorption band may occur at 1–1.5 eV.     

Ground state energy of a polaron in a superlattice

The ground state energy of a polaron in a superlattice was calculated using the double-time Green functions. The effective mass of the polaron along the planes perpendicular to the superlattice axis was also calculated. The dependence of the ground state energy and the effective mass along the planes perpendicular to the superlattice axis on the electron–phonon coupling constant α and on the superlattice parameters (i.e. the superlattice periodd and the bandwidth Δ) were studied. It was observed that if an infinite square-well potential is assumed, the ground state energy of the polaron decreases (i.e. becomes more negative) with increasing α and d, but increases with increasing Δ. For small values of α, the polaron ground state energy varies slowly with Δ, becoming approximately constant for large Δ. The effective mass along the planes perpendicular to the superlattice axis was found to be approximately equal to the mass of an electron for all typical values ofα , d and Δ.     

On the coexistence of spin and lattice polarons in the La0.67−xEuxCa0.33MnO3 CMR system

The electrical and magnetic transport properties of the La_0.67−xEu_xCa_0.33MnO₃ system exhibit lowering of insulator to metal and paramagnetic to ferromagnetic transition temperature (T_C) with the increase of Eu concentration in addition to possessing CMR property. The temperature variation of electrical resistivity and magnetic susceptibility for x=0.21 is found to have two distinct regions in the paramagnetic state for T>T_P; one with the localization of lattice polaron in the high-temperature region (T>1.5T_P) satisfying the dynamics of variable range hopping (VRH) model and the other being the combination of the spin and lattice polarons in the region T_P<T<1.5T_P. The resistivity variation with temperature and magnetic field, the cusp in the resistivity peak and CMR phenomenon are interpreted in terms of coexistence of spin and lattice small polarons in the intermediate region (T_P<T<1.5T_P). The spin polaron energy in the La_0.46Eu_0.21Ca_0.33MnO₃ system is estimated to be 106.73±0.90 meV and this energy decreases with the increase of external magnetic field. The MR ratio is maximal with a value of 99.99% around the transition temperature and this maximum persists till T→0 K, at the field of 8 T.     

Thermoelectric power of potassium doped lanthanum manganites at low temperatures

The temperature-dependent resistivity and thermoelectric power of monovalent (K) doped La_1−xK_xMnO₃ polycrystalline pellets (x=0.05, 0.10 and 0.15) between 50 and 300 K are reported. K substitution enhances the conductivity of this system. Curie temperature (T_C) also increases from 260 to 309 K with increasing K content. In the paramagnetic region (T>T_C), the electrical resistivity is well represented by adiabatic polaron hopping, while in the ferromagnetic region (T<T_C), the resistivity data show a nearly perfect fit for all the samples to an expression containing, the residual resistivity, spin-wave and two-magnon scattering and the term associated with small-polaron metallic conduction, which involves a relaxation time due to a soft optical phonon mode. Small polaron hopping mechanism is found to fit well to the thermoelectric power (S) data for T>T_C whereas at low temperatures (T<T_C) in ferromagnetic region (S_FM), S_FM is well explained with the spin-wave fluctuation and electron–magnon scattering. Both, resistivity and thermopower data over the entire temperature range (50–300 K) are also examined in light of a two-phase model based on an effective medium approximation.     

Positron annihilation lifetime studies on La0.5Pb0.5Mn1−yCryO3

Concentration dependent positron annihilation lifetime (PAL) measurements on Cr doped La_0.5Pb_0.5Mn_1−yCr_yO₃ (y=0.075, 0.15, 0.3, 0.35, 0.45) samples showing metal-insulator transitions (MIT) between 178 and 276 K (depending on y) reveal anomalous variation of average and bulk PAL, τ_av and τ_B, respectively, around y=0.35. Such anomaly has not, however, been observed from the corresponding magnetic susceptibility and resistivity data. Interestingly, the model parameters (polaron radius, number of ion sites per unit volume) obtained from fitting the high temperature (above MIT, T_p) resistivity data with small polaron hopping model show the signature of the said anomaly around the same concentration. Nonlinear variations of τ_av and τ_B support the existence of small polarons (T>T_p) which act as defect centers in such rare-earth manganites. Analysis of X-ray diffraction pattern confirms a change of lattice parameters indicating a structural transformation from rhombohedral (for y≤0.30) to orthorhombic (for y≥0.35) in the present system.     

Contribution of polaron hopping to the electron paramagnetic resonance linewidth in La1−xCaxMnO3 and related materials

We analyze the contribution of polaron hopping to the electron paramagnetic resonance linewidth in La_1−xCa_xMnO₃ and related materials. The material is assumed to be in the paramagnetic phase and the conductivity is associated with the activated polaron hopping. It is also assumed that the adiabatic, small polaron picture is appropriate so that the conductivity varies as exp[−E_a/T]/T, where E_a denotes the polaron activation energy. The polaron contribution to the linewidth is given by the expression C[χ₀(T)/χ(T)]exp[−E_a/T] where χ₀(T) is the Curie susceptibility (∼1/T), χ(T) is the measured susceptibility and C is a material-dependent parameter. Various experimental studies reporting polaron contributions to the linewidth are discussed. It is pointed out that fitting the linewidth to the functional form ΔH₀+(A/T)exp[−E_a/T] is not physically justified. In the high temperature–mean field regime, the exchange narrowed width, (1−Θ/T)k(∞), where Θ is the paramagnetic Curie temperature, replicates the exponential functional form with reasonable values for the activation energy. From previous measurements of the conductivity that showed activated polaron hopping as the leading transport mechanism, we concluded that the linewidth in La_0.7Ca_0.3MnO₃ is a sum of exchange narrowing and one-phonon spin–lattice terms with no evidence of a contribution from polaron hopping or band transport as had been previously proposed. A similar conclusion is reached for La_0.8Ca_0.2MnO₃, nanometer-sized La_0.9Ca_0.1MnO₃, and La_0.9Te_0.1MnO₃.     

Energy of a Polaron in a Wurtzite Nitride Finite Parabolic Quantum Well

The effects of electron-phonon interaction on energy levels of a polaron in a wurtzite nitride finite parabolic quantum well （PQW） are studied by using a modified Lee-Low-Pines variational method. The ground state, first excited state, and transition energy of the polaron in the GaN/Al0.3Ga0.7N wurtzite PQW are calculated by taking account of the influence of confined LO（TO）-like phonon modes and the half-spaee LO（TO）-like phonon modes and considering the anisotropy of all kinds of phonon modes. The numerical results are given and discussed. The results show that the electron-phonon interaction strongly affects the energy levels of the polaron, and the contributions from phonons to the energy of a polaron in a wurtzite nitride PQW are greater than that in an A1GaAs PQW. This indicates that ehe electron-phonon interaction in a wurtzite nitride PQW is not negligible.     

Effects of Cr doping in electron-doped manganites La0.9Te0.1MnO3

The effects of Cr doping on Mn sites in the electron-doped manganites La_0.9Te_0.1MnO₃ have been studied by preparing the series La_0.9Te_0.1Mn_1−xCr_xO₃ (0.05≤x≤0.20). Upon Cr doping, both the Curie temperature T_C and magnetization M are suppressed. The resistivity measurements indicate that there exists a weak metal-insulator (M-I) transition for the sample with x=0.05, with an increase in the doping level, the M-I transition disappears and the resistivity increases. Thermopower S(T) exhibits a maximum near T_C for all samples. By fitting the S(T) and ρ(T) curves, it is found that the temperature dependences of both S(T) and ρ(T) in the high temperature paramagnetic (PM) region follow the small polaron conduction (SPC) mechanism for all samples. The fitting parameters obtained imply changes of both the average-hopping distance of the polarons and the polaron concentration with Cr doping in our studied samples. In the case of the thermal conductivity κ(T), the variation of κ(T) is analyzed based on the combined effects due to the suppression of the local Mn³⁺O₆ Jahn-Teller (JT) lattice distortion because of the substitution of Cr³⁺ for Mn³⁺ ions, which results in the increase in κ, and the introduction of the disorder due to Cr-doping, which contributes to the decrease in κ.     

Magnetic properties of electron-doped Y1−xCexMnO3 compounds

Cerium-doped Y_1−xCe_xMnO₃ compounds have been prepared in single-phase form for x=0 to 0.10. X-ray diffraction (XRD) patterns could be analyzed by using P6₃cm space group. Temperature variations of ac susceptibility and magnetization measurements show that these Ce-doped materials exhibit weak ferromagnetic transition. The observed ferromagnetic transition is attributed to the double exchange ferromagnetic interaction between Mn²⁺ and Mn³⁺ ions due to electron doping. The M–H loops exhibit hysteresis along with linear contribution and were analyzed based on bound magnetic polaron (BMP) model. Increase in saturation magnetization and decrease in BMP concentrations have been observed with increase in Ce doping.     

Magnetic transition and polaron crossover in a two-site single polaron model including double exchange interaction

A two-site double exchange model with a single polaron is studied using a perturbation expansion based on the modified Lang-Firsov transformation. The antiferromagnetic to ferromagnetic transition and the crossover from small to large polaron are investigated for different values of the antiferromagnetic interaction (J) between the core spins and the hopping (t) of the itinerant electron. Effect of the external magnetic field on the small to large polaron crossover and on the polaronic kinetic energy are studied. When the magnetic transition and the small to large polaron crossover coincide for some suitable range of J/t, the magnetic field has very pronounced effect on the dynamics of polarons. Received 1 June 2000     

Dynamic process of self-trapped polaron in photoexcited SrTiO3

Relaxation process of self-trapped polaron is investigated by a nonadiabatic molecular dynamic method. We show localized disorder due to lattice fluctuations can give rise to a tightly-bound electronic state in ultraviolet illuminated SrTiO₃ crystal. This bound state is actually a self-trapped polaron in accordance with the experimentally observed large Stokes-shift. The formation of the self-trapped polaron is shown to be an ultrafast process.     

Exciton and polaron properties in GaxIn1−xAs ternary mixed crystals

Based on the pseudopotential method under the virtual crystal approximation that takes into account the effect of compositional disorder, the electron and heavy-hole effective masses and the dielectric constants in Ga_xIn_1−xAs (0≤x≤1) have been calculated. The results are firstly used in the Wannier equation, which allowed the determination of the exciton reduced mass, binding energy and Bohr radius; then, the polaron properties have been investigated. In this respect, the Fröhlich coupling parameter, Debye temperature and polaron effective mass are calculated and their dependence on the Ga concentration is examined. For InAs and GaAs, our results are generally in reasonable agreement with the known data in the literature, while for compositions x in the range 0-1, our treatment represents the first theoretical predictions. It is found that the exciton and polaron properties for compositions 0<x<1 differ from those of the parent compounds suggesting thus more diverse opportunities to describe most exciton and polaron properties in ternary mixed crystals of interest.     

Fractal dimension study of polaron effects in cylindrical GaAs/Al<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>1-<Emphasis Type="Italic">x</Emphasis></Subscript>As core–shell nanowires

Polaron effects in cylindrical GaAs/Al _x Ga_1-xAs core–shell nanowires are studied by applying the fractal dimension method. In this paper, the polaron properties of GaAs/Al _x Ga_1-xAs core–shell nanowires with different core radii and aluminum concentrations are discussed. The polaron binding energy, polaron mass shift, and fractal dimension parameter are numerically determined as functions of shell width. The calculation results reveal that the binding energy and mass shift of the polaron first increase and then decrease as the shell width increases. A maximum value appears at a certain shell width for different aluminum concentrations and a given core radius. By using the fractal dimension method, polaron problems in cylindrical GaAs/Al _x Ga_1-xAs core–shell nanowires are solved in a simple manner that avoids complex and lengthy calculations.