Synchrotron infrared measurements were conducted over the range 100 to 8000 cm-1 on a self-doped LaxMnO3-d (x~~0.8) film. From these measurements we determined the conductivity, the effective number of free carriers, and the specific phonon modes as a function of frequency. While the metal-insulator transition temperature (TMI) and the magnetic ordering temperature (TC) approximately coincide, the free carrier density onset occurs at a significantly lower temperature (~~45 K below). This suggests that local distortions exist below TMI and TC which trap the eg conduction electrons. These regions with local distortions constitute an insulating phase which persists for temperatures significantly below TMI and TC. The initial large drop in resistivity is due to the enhanced magnetic ordering while further drops correspond to reductions in the insulating phase which increase the number of free carriers.
It is suggested that extrinsic inhomogeneities in mixed-valence manganites deserve more attention and they should be taking into account on equal footing with hypothetical phase separation while examinating experimental data and developing the theoretical models of influence of stoichiometric and other types of inhomogeneities on properties of these and other transition-metal oxides.
The possible redox (oxidation reduction) chemical methods for precisely determining the oxygen content in the perovskite manganites including hole-doped La1-xCaxMnOy and electron-doped La1-xTexMnOy compounds are described. For manganites annealed at different temperatures, the oxygen content of the samples was determined by a redox back titration in which the powder samples taken in a quartz crucible were dissolved in (1+1) sulfuric acid containing an excess of sodium oxalate, and the excess sodium oxalate was titrated with permanganate standard solution. The results indicate that the method i…
The mixed-valence perovskitelike manganites are characterized by unique interrelation of Jahn-Teller distortions, electric and magnetic properties. The Jahn-Teller distortion follows the Mn(3+)->Mn(4+) charge transfer with some delay. Its development depends on the lifetime of Mn in (3+) state, governed by the Mn(4+)/Mn(3+) ratio and magnetic correlation. The non-coherence of Jahn-Teller distortions in orthorhombic mixed-valence manganites and rhombohedral RMnO3 (R = rare earth) results in oxygen disorder. We demonstrate that the Raman spectra in this case are dominated by disorder-induced ban…
We report on temperature dependent measurements of the Longitudinal Spin Seebeck Effect (LSSE) in the mixed valent manganite La$_{0.7}$Ca$_{0.3}$MnO$_3$. By disentangling the contribution arising due to the Anisotropic Nernst effect, we observe that these two thermally driven phenomena vary disparately with temperature. In a narrow low temperature regime, the LSSE exhibits a $T^{0.55}$ dependence, which matches well with that predicted by the magnon-driven spin current model. Across the double exchange driven paramagnetic-ferromagnetic transition, the LSSE exponent is significantly higher than…
The effect of cationic size mismatch at the A site at constant manganese valence on the structural and magnetic properties of a perovskite-type rare-earth manganate was investigated in the Pr0.9(Na1-xKx)0.1MnO3 solid solution system (0 <= x < 1). All members of this solid solution series are orthorhombic at room temperature, space group Pbnm. Structural refinements using the Rietveld method show that the cell volume increases and the static Jahn-Teller distortion decreases with increasing potassium content x. Magnetic properties are characterized by strong positive θp values, and are ascribed …
The frequency and temperature dependence of the optical conductivity of ferromagnetic manganites is explained within the framework of the bipolaron theory. As these materials are cooled below the Curie temperature, the colossal magnetoressitance (CMR) is accompanied by a massive transfer of the spectral weight of the optical conductivity to lower frequencies. As with the CMR itself, this change in the optical conductivity is explained by the dissociation of bipolarons into small polarons by exchange interaction with the localized Mn spins during the transition to the low temperature ferromagne…
We investigated electrical and magnetic properties of the electron-doped manganites Ca1-xSmxMnO3 (0<x<0.2). Our results indicate the possibility of phase separation in electron doped manganites. The compounds with x = 0.13-0.15 show unusual difference between zero-field cooled and field-cooled resistivities which are not observed in lower compositions. Our results suggest that electronic phase separation alone is insufficient to understand the origin of the resistivity irreversibilities.
Using frequency dependent complex capacitance measurements on thin films of the mixed-valence manganite (La$_{1-y}$Pr$_{y}$)$_{1-x}$Ca$_{x}$MnO$_{3}$, we identify and resolve the individual dielectric responses of two competing dielectric phases. We characterize their competition over a large temperature range, revealing they are in dynamic competition both spatially and temporally. The phase competition is shown to be governed by the thermodynamic constraints imposed by detailed balance. The consequences of the detailed balance model strongly support the notion of an `electronically soft' mat…
We have performed electrical resistivity and DC magnetization measurements as a function of temperature, on polycrystalline samples of phase separated LaPrCaMnO. We have used the General Effective Medium Theory to obtain theoretical resistivity vs. temperature curves corresponding to different fixed ferromagnetic volume fraction values, assuming that the sample is a mixture of typical metallic like and insulating manganites. By comparing this data with our experimental resistivity curves we have obtained the relative ferromagnetic volume fraction of our sample as a function of temperature. Thi…
Recent experimental study reveals the optical conductivity of La$_{1-x}$Ca$_x$MnO$_3$ over a wide range of energy and the occurrence of spectral weight transfer as the system transforms from paramagnetic insulating to ferromagnetic metallic phase [Rusydi {\it et al.}, Phys. Rev. B {\bf 78}, 125110 (2008)]. We propose a model and calculation within the Dynamical Mean Field Theory to explain this phenomenon. We find the role of oxygens in mediating the hopping of electrons between manganeses as the key that determines the structures of the optical conductivity. In addition, by parametrizing the …
Ferroelectric materials possess a spontaneous electric polarization and may be utilized in various technological applications ranging from non-volatile memories to solar cells and light polarizers. Recently, hexagonal rare-earth manganites, h-RMnO$_3$ (R is a rare-earth ion) have attracted considerable interest due to their intricate multiferroic properties and improper ferroelectricity characterized by a sizable remnant polarization and high Curie temperature. Here, we demonstrate that these compounds can serve as very efficient photovoltaic materials and, in addition, possess remarkable opti…
Optical conductivity spectra of a cleaved ab-plane of a La_{1.2}Sr_{1.8}Mn_2O_7 single crystal exhibit a small polaron absorption band in the mid-infrared region at overall temperatures. With decreasing temperature (T) to Curie temperature (T_C), the center frequency of the small polaron band moves to a higher frequency, resulting in a gap-like feature, and that it collapses to a lower frequency below T_C. Interestingly, with decreasing T, the stretching phonon mode hardens above T_C and softens below T_C. These concurring changes of lattice and electronic structure indicate that short range p…
By using the dark-field real-space imaging technique of transmission electron microscopy (TEM), we have observed slow 200 A-scale fluctuations of charge-ordered (CO) phase in mixed-valent manganites under a strong electron beam irradiation. In addition to these unusual fluctuations of the CO phase, we observed the switching-type fluctuations of electrical resistivity in the same sample, which were found to be as large as several percents. Systematic analysis indicates that these two different types of fluctuations with a similar time scale of the order of seconds are interconnected through a m…
We present a thorough and quantitative comparison of double-exchange models to experimental data on the colossal magnetoresistance manganese perovskites. Our results settle a controversy by showing that physics beyond double-exchange is important even in La$_{0.7}$Sr$_{0.3}$MnO$_3$, which has been regarded as a conventional double-exchange system. We show that the crucial quantity for comparisons of different calculations to each other and to data is the conduction band kinetic energy $K$, which is insensitive to the details of the band structure and can be experimentally determined from optic…
This is an informal paper that contains a list of ``things we know'' and ``things we do not know'' in manganites. It is adapted from the conclusions chapter of a recent book by the author, {\it Nanoscale Phase Separation and Colossal Magnetoresistance. The Physics of Manganites and Related Compounds}, Springer-Verlag, Berlin, November 2002. The main new result of recent manganite investigations is the discovery of tendencies toward inhomogeneous states, both in experiments and in simulations of models. The colossal magnetoresistance effect appears to be closely linked to these mixed-phase tend…
We have performed both theoretical and experimental study of optical response of parent perovskite manganites RMnO_3 with a main goal to elucidate nature of clearly visible optical features. Starting with a simple cluster model approach we addressed the both one-center (p-d) and two-center (d-d) charge transfer (CT) transitions, their polarization properties, the role played by structural parameters, orbital mixing, and spin degree of freedom. Optical complex dielectric function of single crystalline samples of RMnO_3 (R=La, Pr, Nd, Sm, Eu) was measured by ellipsometric technique at room tempe…
The ferromagnetic phase in La0.7Sr0.3MnO3 manganite is completely spin polarized (100%) at room temperature. This is demonstrated on high quality epitaxial films by Spin-Polarized Scanning Tunneling Microscopy. The films consist of a highly homogeneous ferromagnetic (FM) phase in which minority paramagnetic (PM) defects are embedded (less than 1% for best films). PM defects exhibit featureless tunneling spectroscopic characteristics and an insulating-like conductance. FM phase exhibit metallic behavior and strongly nonlinear characteristics. Deconvolution of the spectroscopic curves for the FM…
We calculate the value of the Fröhlich electron-phonon interaction in manganites, cuprates, and some other charge-transfer insulators and show that this interaction is much stronger than any relevant magnetic interaction. A polaron shift due to the Fröhlich interaction, which is about 1 eV, suggests that carriers in those systems are small (bi)polarons at all temperatures and doping levels, in agreement with the oxygen isotope effect and other data. An opposite conclusion, recently suggested in the literature, is shown to be incorrect. The frequency and temperature dependence of the optical co…
We show that the current carrier density collapse in doped manganites, which results from bipolaron formation in the paramagnetic phase, leads to a colossal change of the optical conductivity in an external magnetic field at temperatures close to the ferromagnetic transition. As with the colossal magnetoresistance (CMR) itself, the corresponding magnetooptical effect is explained by the dissociation of localized bipolarons into mobile polarons owing to the exchange interaction with the localized Mn spins in the ferromagnetic phase. The effect is positive at low frequencies and negative in the …
We report on non-volatile memory devices based on multifunctional manganites. The electric field induced resistive switching of Ti/$La_{1/3}$$Ca_{2/3}$Mn$O_3$/n-Si devices is explored using different measurement protocols. We show that using current as the electrical stimulus (instead of standard voltage-controlled protocols) improves the electrical performance of our devices and unveils an intermediate resistance state. We observe three discrete resistance levels (low, intermediate and high), which can be set either by the application of current-voltage ramps or by means of single pulses. The…
Temperature dependent optical conductivity spectra of a La0.7Ca0.3MnO3 (LCMO) sample were measured. In the metallic regime at very low temperatures, they clearly showed two types of absorption features, i.e., a sharp Drude peak and a broad mid-infrared absorption band, which could be explained as coherent and incoherent bands of a large lattice polaron. This elementary excitation in LCMO was found to be in a strong coupling regime and to have interactions with the spin degree of freedom.
In the optical conductivity of four different manganites with commensurate charge order (CO), strong peaks appear in the meV range below the ordering temperature T_{CO}. They are similar to those reported for one-dimensional charge density waves (CDW) and are assigned to pinned phasons. The peaks and their overtones allow one to obtain, for La{1-n/8}Ca{n/8}$MnO{3} with n = 5, 6, the electron-phonon coupling, the effective mass of the CO system, and its contribution to the dielectric constant. These results support a description of the CO in La-Ca manganites in terms of moderately weak-coupling…
We show evidence that the competition between the antiferromagetic metallic phase and the charge- and orbital-ordered insulating phase at the reentrant phase boundary of a layered manganite, LaSr2Mn2O7, can be manipulated using ultrafast optical excitation. The time-dependent evolution of the Jahn-Teller superlattice reflection, which indicates the formation of the charge and orbital order, was measured at different laser fluences. The laser-induced enhancement and reduction the Jahn-Teller reflection intensity shows a reversal of sign between earlier (~10 ns) and later (~150 ns) time delays d…
Calculations of one-electron spectral functions, optical conductivity and spin-wave energy in the Holstein double-exchange model are made using the many-body coherent potential approximation. Satisfactory agreement is obtained with angle-resolved photoemission results on La_1.2Sr_1.8Mn_2O_7 and optical measurements on Nd_0.7Sr_0.3MnO_3. A pseudogap in the one-electron spectrum at the Fermi level plays an important role in both systems, but a small-polaron band is only predicted to exist in the La system. A rigorous upper bound on spin-wave energies at T=0 is derived. The spin-wave stiffness co…
We report a comprehensive investigation of La0.2Pr0.4Ca0.4MnO3 to clarify the micrometre scale phase separation phenomenon in the mixed valent manganite (La,Pr,Ca)MnO3. The compound shows multiple magnetic transitions, in which the charge-ordered state is converted into a ferromagnetic state in steps with the application of a magnetic field. The ac susceptibility measurements show that the glassy transition at low temperatures does not depend on the frequency, thus indicating the absence of any spin glass behaviour. Magnetization as well as heat capacity measurements indicate that this low tem…
In the mixed-valence manganites, a near-infrared laser typically melts the orbital and spin order simultaneously, corresponding to the photoinduced $d^{1}d^{0}$ $\xrightarrow{}$ $d^{0}d^{1}$ excitations in the Mott-Hubbard bands of manganese. Here, we use ultrafast methods -- both femtosecond resonant x-ray diffraction and optical reflectivity -- to demonstrate that the orbital response in the layered manganite Nd$_{1-x}$Sr$_{1+x}$MnO$_{4}$ ($\it{x}$ = 2/3) does not follow this scheme. At the photoexcitation saturation fluence, the orbital order is only diminished by a few percent in the trans…
A major challenge in condensed matter physics is active control of quantum phases. Dynamic control with pulsed electromagnetic fields can overcome energetic barriers enabling access to transient or metastable states that are not thermally accessible. Here we demonstrate strain-engineered tuning of La2/3Ca1/3MnO3 into an emergent charge-ordered insulating phase with extreme photo-susceptibility where even a single optical pulse can initiate a transition to a long-lived metastable hidden metallic phase. Comprehensive single-shot pulsed excitation measurements demonstrate that the transition is c…
Nominally pure undoped parent manganite LaMnO_3 exhibits a puzzling behavior inconsistent with a simple picture of an A-type antiferromagnetic insulator (A-AFI) with a cooperative Jahn-Teller ordering. We do assign its anomalous properties to charge transfer instabilities and competition between insulating A-AFI phase and metallic-like dynamically disproportionated phase formally separated by a first-order phase transition at T_{disp}=T_{JT}\approx 750 K. The unconventional high-temperature phase is addressed to be a specific electron-hole Bose liquid (EHBL) rather than a simple "chemically" d…
In the charge-ordered phase of strongly doped manganites La$_{1-x}$Ca$_x$MnO$_3$ ($x \geq 0.5$) absorption lines appear in the terahertz spectral range for commensurate $x$ values right below the charge-ordering temperature. They are connected to acoustic phonons that become optically active by folding of the Brillouin zone. At lower temperatures a strongly asymmetric extra absorption band develops at frequencies corresponding to the position of the lowest-energy van Hove singularity in the reduced Brillouin zone. The band is assigned to the boson peak, i.e. to the excess of lattice vibrationa…
The effect of 16O-18O isotope exchange on the electric resistivity was studied for (La(1-y)Pr(y))0.7Ca0.3MnO3 ceramic samples. Depending on y, this mixed perovskite exhibited different types of low-temperature behavior ranging from ferromagnetic metal (FM) to charge ordered (CO) antiferromagnetic insulator. It was found that at y=0.75, the substitution of 16O by 18O results in the reversible transition from a FM to a CO insulator at zero magnetic field. The applied magnetic field (H >= 2 T) transformed the sample with 18O again to the metallic state and caused the increase in the FM transition…
Optical conductivity spectra of La_{0.7-y}Pr_{y}Ca_{0.3}MnO_3 were systematically investigated. For metallic samples, the spectral weight below 0.5 eV, whose magnitude can be represented by the effective carrier number N_{eff}(0.5 eV), increases as temperature becomes lower. Regardless of the Pr doping, all the measured values of N_{eff}(0.5 eV)/T_C fall into one scaling curve. This scaling behavior could be explained by the theoretical model by Roeder et al. [Phys. Rev. Lett. 76, 1356 (1996)], which includes spin double exchange and Jahn-Teller lattice coupling to holes. With the Pr doping, f…
Heterostructures of mixed-valence manganites are still under intense scrutiny, due to the occurrence of exotic quantum phenomena linked to electronic correlation and interfacial composition. For instance, if two anti-ferromagnetic insulators as LaMnO$_3$ and SrMnO$_3$ are grown in a (001)-oriented superlattice, a half-metallic ferromagnet may form, provided that the thickness is sufficiently small to allow tunneling across interfaces. In this article, we employ electronic structure calculations to show that all the layers of a (111)-oriented LaMnO$_3$|SrMnO$_3$ superlattice retain a half-metal…
In frames of a rather conventional cluster approach, which combines the crystal field and the ligand field models we have considered different charge transfer (CT) states and O 2p-Mn 3d CT transitions in MnO$_{6}^{9-}$ octahedra. The many-electron dipole transition matrix elements were calculated using the Racah algebra for the cubic point group. Simple "local" approximation allowed to calculate the relative intensity for all dipole-allowed $π-π$ and $σ-σ$ CT transitions. We present a self-consistent description of the CT bands in insulating stoichiometric LaMn$^{3+}$O$_3$ compound with the on…
We investigate the evolution of spin and orbital order in undoped LaMnO$_3$ under increasing temperature with a model including both superexchange and Jahn-Teller interactions. We used several cluster mean field calculation schemes and find coexisting $A$-type antiferromagnetic ($A$-AF) and $C$-type alternating orbital order at low temperature. The value of the Jahn-Teller coupling between strongly correlated $e_g$ orbitals is estimated from the orbital transition temperature at $T_{\rm OO}\simeq 780$ K. By a careful analysis of on-site and on-bond correlations we demonstrate that spin-orbital…
Presently, cerium-doped LaMnO$_3$ is vividly discussed as an electron-doped counterpart prototype to the well-established hole-doped mixed-valence manganites. Here, La$_{0.7}$Ce$_{0.3}$MnO$_3$ thin films of different thicknesses, degrees of CeO$_2$ phase segregation, and oxygen deficiency, grown on SrTiO$_3$ single crystal substrates, are compared with respect to their resistance-vs.-temperature (R vs. T) behavior from 300~K down to 90~K. While the variation of the film thickness (and thus the degree of epitaxial strain) in the range between 10~nm and 100~nm has only a weak impact on the elect…
Spin dynamics of excitons and carriers in mixed-cation MA$_{x}$FA$_{1-x}$PbI$_{3}$ perovskite crystals: alloy fluctuations probed by optical orientation
The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalisation yields exact results in the thermodynamic limit, whereas at finite carrier density analytical approximations based on previous work on single-particle spectral functions are obtained. Particular emphasis is put on deviations from weak-coupling, small-polaron or one-electron theories occurring at intermediate coupling and/or finite carrier density. The analytical results are in surprisingly good agreement…
Optical reflectivity spectra were measured on cleaved surfaces of La1-xSrxMnO3 single crystals (x=0.175, T_C=283 K) over a temperature range 10-295 K. The optical conductivity $sigma(ω)$ shows, keeping single-component nature, incoherent-to-coherent crossover with increase of electrical conductivity. The $σ(ω)$ spectrum of low-temperature ferromagnetic-metallic phase (10 K) exhibits a pronounced Drude-like component with large spectral weight, contrary to the previous result. The present result indicates that the optical spectrum of the manganites is sensitive to condition of sample surfaces.
In this work we report on the controlled fabrication of a self-assembled line network in highly epitaxial BiFeO3 thin films on top of LaAlO3 in the kinetically limited grown region by RF sputtering. As previously shown in the case of manganite thin films, the remarkable degree of ordering is achieved using vicinal substrates with well-defined step-terrace morphology. Nanostructured BiFeO3 thin films show mixed-phase morphology. Besides typical formation following (100) and (010) axes, some mixed phase nanodomains are detected also in-between the regular line network. These particular microstru…
Temperature and current dependences of resistivity of bulk La$_{0.75}$Ca$_{0.25}$MnO$_{3}$ sample grown by the floating-zone method were studied using single ramp pulses of current. It is found that near the Curie temperature $T_C$ the sample resistance depends substantially on current magnitude. The observed features can be determined by inhomogeneous Joule overheating due to mixed phase state of manganites near the ferromagnetic-paramagnetic transition and percolation character of this transition.
We show that mixed-phase titanium dioxide (TiO2) can be effectively employed as an unconventional, inorganic, dual-emitting and ratiometric optical sensor of O2. Simultaneous availability of rutile and anatase TiO2 PL and their peculiar anti-correlated PL responses to O2 allow using their ratio as measurement parameter associated to O2 concentration, leading to an experimental responsivity being by construction larger than the one obtainable for single-phase PL detection. A proof of this concept in given, showing a two-fold enhancement of the optical responsivity provided by the ratiometric ap…
Bottom-up assembly of optically nonlinear and magnetically anisotropic lanthanide materials involving precisely placed spin carriers and optimized metal-ligand coordination offers a potential route to developing electronic architectures for coherent radiation generation and spin-based technologies, but the chemical design historically has been extremely hard to achieve. To address this, we developed a worthwhile avenue for creating new noncentrosymmetric chiral Ln3+ materials Ln2(SeO3)2(SO4)(H2O)2 (Ln = Sm, Dy, Yb) by mixed-ligand design. The materials exhibit phase-matching nonlinear optical …
We present optical absorption spectra of mixed films of pentacene (PEN) and perfluoropentacene (PFP) grown on SiO2. We investigated the influence of intermolecular coupling between PEN and PFP on the optical spectra by analyzing samples with five different mixing ratios of PFP:PEN with variable angle spectroscopic ellipsometry (VASE) and differential reflectance spectroscopy (DRS). The data show how the spectral shape is influenced by changes in the volume ratio of the two components. By comparison with the pure film spectra an attempt is made to distinguish transitions due to intermolecular c…
The effect of quantum lattice fluctuations on the optical-absorption spectra in the ground state of halogen-bridged mixed-valence transition-metal linear-chain complexes is studied by using a one-dimensional extended Peierls-Hubbard model. The nonadiabatic effects due to finite phonon frequency $ω_π>0$ are treated through an energy-dependent electron-phonon scattering function $δ(k^{\prime},k)$ introduced by means of an unitary transformation. The calculated optical-absorption spectra do not have the inverse-square-root singularity, but they have a peak above the gap edge and there exists a si…
Transport, magnetic, magneto-optical (Kerr effect) and optical (light absorption) properties have been studied in an oriented polycrystalline La_{0.67}Ca_{0.33}MnO_{3} film which shows colossal magneto-resistance. The correlations between these properties are presented. A giant change in IR light transmission (more than a 1000-fold decrease) is observed on crossing the Curie temperature (about 270 K) from high to low temperature. Large changes in transmittance in a magnetic field were observed as well. The giant changes in transmittance and the large magneto-transmittance can be used for devel…
The optical spectra in the family of multiferroic manganites RMnO3 is a great puzzle. Current models can not explain the fact that two strong electromagnons are present in the non-collinear spin cycloidal phase, with only one electromagnon surviving the transition into the collinear spin sinusoidal phase. We show that this is a signature of the presence of anomalous magnetoelectric coupling that breaks rotational invariance in spin space and generates oscillatory polarization in the ground state.
We investigate the structural, electronic and optical properties of mixed bromide-iodide lead perovskite solar cell CH$_3$NH$_3$Pb(I$_{1-x}$Br$_x$)$_3$ by means of the virtual crystal approximation (VCA) within density functional theory (DFT). Optimizing the atomic positions and lattice parameters increasing the bromide content $x$ from 0.0 to 1.0, we fit the calculated lattice parameter and energy band gap to the linear and quadratic function of Br content, respectively, which are in good agreement with the experiment, respecting the Vegard's law. With the calculated exciton binding energy an…
The possibility of using mixed crystals highly doped with rare earth ions (REIs) as physical systems for creating fast quantum computers with a sampling time of nanoseconds is discussed. The electronic 4f states of rare earth ions with small values of the diagonal elements of the Judd-Ofelt matrix U(2) are proposed as optical frequency qubit levels. CNOT and other conditional gate operations are performed by exciting the rare earth ion into the 4f state with a large diagonal element of U(2), causing a Stark blockade. It is found that the main interaction responsible for this blockade is the qu…
We report detailed temperature dependent photoluminescence (PL) spectra of pentacene (PEN), perfluoropentacene (PFP), and PEN:PFP mixed thin films grown on SiO2. PEN and PFP are particularly suitable for this study, since they are structurally compatible for good intermixing and form a model donor/acceptor system. The PL spectra of PEN are discussed in the context of existing literature and compared to the new findings for PFP. We analyze the optical transitions observed in the spectra of PEN and PFP using time-dependent density functional theory (TD-DFT) calculations. Importantly, for the mix…
