Abstract
We have investigated the optical and electrical properties of polycrystalline DyM synthesized by sol-gel method. Analysis of the reflectivity spectrum has led to the observation of 18 infrared (IR) active phonon modes out of 36 predicted ones. We discuss the results in terms of different phonon bands originated as a result of atomic vibrations. Moreover, the optical energy band gap of eV has been estimated from optical conductivity spectrum. The energy band gap and optical transitions were also determined from UV-visible absorption spectrum and band gap of eV was estimated. Moreover, DC electrical resistivity shows the p-type polaronic conduction above room temperature.
1. Introduction
Manganites M, typical type-II multiferroics, usually show large coupling between spin (magnetism), charge (ferroelectricity), and lattice (structure). M compounds show cascade of phase transitions with characteristic temperature at Néel transition = 40–45 K and ferroelectric transition at = 28–39 K and ordering of rare-earth moments occurs below 10 K [1]. Until recently, it is well known that M crystallize in the orthorhombic structure with Pbam space group at room temperature [2]. However, very recently it is proposed that M crystallize in two possible monoclinic space groups and depending on the existence of polarization in plane and along axis, respectively [3].
Among the family of M, DyM exhibits remarkable magnetodielectric behavior as compared to other M compounds [4]. An unconventional behavior of phonon anomalies in M ( = Bi, Eu, Dy) has been observed in the paramagnetic phase [5]. They have suggested that these anomalies at new characteristics temperature ~ 1.5 are related to the spin-phonon coupling and signaling a transition between states. Moreover, spin-phonon coupling has been observed slightly above indicating the drastic change in phonon frequency due to magnetic field and temperature [6, 7]. Remarkably, recently we have observed an unconventional magnetodielectric effect in DyM above , where the infrared and Raman phonons have shown spin-phonon coupling and confirm the strong correlation between spin, charge, and lattice degree of freedom [8]. Such a strong interplay between many degrees of freedom in the paramagnetic phase is a special characteristic of M family [5–9]. The knowledge of lattice vibrations and their correlation to different conduction mechanisms is of crucial importance for engineering the materials for various technological applications. However, currently there is no report on the correlation between IR active phonon and the conduction mechanism for DyM.
In this work, we have measured the IR reflectivity spectrum of DyM and assign the IR active phonon modes with theoretically calculated modes. In addition, we have performed UV-visible spectroscopy and temperature dependent electrical response to observe the microscopic conduction mechanism. The main objective of this paper is to investigate the lattice vibration in DyM and the possible correlation to electronic transport mechanism through energy band gap and activation energy.
2. Experiment
The sample was synthesized by using the sol-gel technique as described previously [9]. Stoichiometric amounts of Gd and Mn nitrates were dissolved into distilled water and stirred for 2 h along with heating at 80°C until viscous gel was formed. The obtained gel was dried at 150°C for 2 h and finally the obtained black powder was sintered at 1000°C for 6 h. Single phase character of prepared sample has been checked by using X-ray diffraction (XRD) pattern. The measurements were performed with the help of Bruker D8 Advance diffractometer with Cu-K source having wavelength 1.5405 Å. Microstructure was observed by using the scanning electron microscopy (SEM) and image was taken at accelerating voltage of 10 KV and magnification of 80 K. The powder was uniaxially pressed into pellets of 13 mm diameter under the pressure of 30 KN by using the Paul-Otto Weber hydraulic press to obtain high density ceramics for the reflectivity measurement. One of the surfaces of the disc shaped sample was made smooth prior to spectroscopic measurements. Room temperature infrared reflectivity has been measured using Fourier transform infrared spectrometer (Vertex 80v) at near-normal incidence mode. The frequency measurements in the mid-range (550–7500 cm−1) and far (30–680 cm−1) infrared regions were performed using KBR-DLaTGS and Mylar 6 m DLaTGS beam splitter-detector combinations, respectively. Mid and far infrared spectra were obtained under vacuum purges, by averaging 100 scans, with spectral resolution of 2 cm−1. A gold mirror was initially used as reference spectrum. The reflectivity spectra in the mid and far infrared regions matched well in the superposition region (550–680 cm−1). The absorption spectra in the 200–1000 nm wavelength region have been obtained using Perkin Elmer Lambda 950 UV/vis/NIR spectrophotometer. The electrical measurements were made by using Keithley source meter 2400, while applying the voltage range of 0–20 V in the temperature range 300–475 K.
3. Results and Discussion
3.1. Structural Analysis
X-ray diffraction (XRD) was performed to check the single phase character of the prepared sample at room temperature and the obtained XRD pattern of DyM is shown in Figure 1. JANA2006 program was used for the Rietveld refinement of the XRD pattern assuming orthorhombic structure with space group (Figure 2). All the XRD peaks were well fitted confirming the single phase formation and no trace of any impurity peak was found. The obtained unit cell parameters are = 7.251 Å, = 8.445 Å, and = 5.647 Å, which are in good agreement with theoretically calculated values (7.270, 8.518, and 5.600 Å, resp.) as well as experimentally observed values (7.285, 8.487, and 5.668 Å, resp.) [10].
In addition, we have also calculated the strain present in the material and crystallite size by using the Williamson-Hall (W-H) model considering the uniform isotropic crystal for the total peak broadening using the relation [11]where is the crystallite size, is the shape factor (), is the wavelength of X-rays, and is the strain induced line broadening. It is easy to calculate the strain and crystallite size by extracting the slope and the intercept of the linear fit as shown in Figure 3. The obtained values of strain and crystallite size are and 50 nm, respectively.
Figure 4 shows the SEM micrograph of DyM. Large grains with less grain boundaries can be clearly seen from micrograph. However, grains show no perfect alignment, which is a typical characteristic of polycrystalline sample. The individual grains shown are of the round shape with an average grain size ~40 nm, which is consistent with crystallite size of ~38 nm obtained from XRD analysis by using the well-known Debye-Scherrer formula.
3.2. Infrared Reflectivity
Figure 5 shows the near-normal reflectivity of DyM in frequency range 30–1000 cm−1 at room temperature. Considering the quasi-normal incidence angle, the optical reflectivity spectrum () is related to the dielectric function by Fresnel’s formula
To quantify the infrared phonon contribution to the dielectric function is defined aswhere is the high frequency dielectric constant indicating the contribution to the electronic polarization. , , and are the optical phonon frequency, oscillator strength, and damping factor of th phonon, respectively. Both (2) and (3) together can give the measured reflectivity spectrum. Following above relations, the well-known Lyddane-Sachs-Teller (LST) relation becomes as , used to calculate the longitudinal optical phonon modes ().
According to group theoretical analysis, there are 36 infrared active vibrational phonon modes in the paraelectric phase of M at the point () [7, 12]. These modes are classified into different phonon bands which correspond to relative motion of rare-earth, manganese, and oxygen ions. The observed phonon frequencies obtained from the fit are assigned via comparison with those found in lattice dynamics calculations (Table 1) and are in agreement with reported data [7, 12]. Among the 36 theoretically predicted infrared active modes, we are able to observe only 18 modes. The origin of this discrepancy will be discussed later.
As far as the microscopic motion of the active phonon modes is concerned, the phonon modes at 151, 167, 194, 217, and 251 cm−1 involve the relative motion of Dy ions with respect to manganese ions of Mn and Mn polyhedra and assigned to the calculated modes between 95 and 245 cm−1, respectively, as can be seen in Figures 6(a)–6(d). Moreover, high frequency modes between 260 and 684 cm−1 are attributed to Mn-O bending and stretching motion of the distorted octahedra and square pyramidal building block units. These modes may correspond to the calculated modes between 283 and 728 cm−1 and mainly arise from the Mn-O stretching motion within the equatorial plan of the Mn octahedra and Mn-O stretching motion in the axial direction of Mn square pyramids as shown in Figures 6(e)–6(i) [12]. Similar stretching and bending vibration of oxygen atoms at >300 cm−1 has also been observed through Raman spectra in M ( = Bi, Tb, Eu, Dy, Ho) [5, 13].
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
As mentioned previously, out of 36 theoretically predicted modes, we have only observed 18 modes. The origin of this discrepancy is due to the polycrystalline nature of our sample which has mixed -plane and axis response. For example, let us consider the infrared modes of and that occur in close pair such that at least 10 of them have wavenumber difference less than 10 cm−1, which is due to the typical damping value. This clearly reflects that they can not be resolved separately by using unpolarized light in polycrystal and that they have been considered together in the fitting procedure.
For quantitative analysis of phonon contribution to the infrared spectrum of DyM, we have calculated real part of optical conductivity spectrum by using Kramers-Krönig transformation, as shown in Figure 7. is zero suggesting no contribution from free carriers at low frequency range and suggesting the charge carriers are rather localized. Moreover, the optical energy band gap has been calculated from the spectrum of optical conductivity [see inset of Figure 7]. An optical band gap can be observed as a gradual onset of the spectral intensity showing a sharp rise, as determined by the crossing point of the energy axis [14, 15]. The band gap distinctly seen at eV arises due to lowest energy oscillator, close to the band gap (~1.70 eV) observed for TbM through ellipsometry technique [16].
3.3. UV-Visible Spectroscopy
We have measured UV-visible absorption spectrum of DyM in the wavelength range 200–1000 nm as shown in Figure 8. The diffuse reflectance spectrum has been transformed into Kubelka-Munk function or absorption by using the Kubelka-Munk theory [17, 18]. Such strong absorption with cutoff wavelength at 1000 nm indicates that DyM can efficiently absorb light over a broad range of wavelengths including the complete visible range (390–780 nm). Moreover, we have observed two strong absorption peaks at about 485 nm and 525 nm which reflects that there is a probability of electrons from () ions tunnel to () ions, giving rise to the local distortion near these ions [19]. These strong absorption peaks may be attributed to the 3-electronic transitions of /.
In order to verify the energy band gap estimated from optical conductivity, we have calculated the energy band gap by using the relation [20]where is the energy of the incident photon, is the K-M function, is a characteristic parameter, and is the band gap. Exponent specifies the type of transition and it may be 1/2 or 2 for the direct forbidden or indirect transition, respectively. Here, we have estimated the indirect band gap from the plot of versus energy () by extrapolating the linear portion to the energy axis (i.e., ) to determine the energy band gap of about eV as shown in Figure 9. We have observed a comparable energy band gap estimated through optical conductivity ( eV) and UV-visible ( eV). Despite the slight difference in energy band gap ( = 0.21 eV), DyM exhibits a semiconducting behavior. The obtained value of band gap is close to the band gap observed for similar compounds such as TbM eV, YM eV [16, 21].
3.4. Electrical Properties
In order to study the conduction mechanism, we have performed temperature dependent characteristics of DyM which demonstrate a smooth increase in current with increase in applied voltage (0–20 V) as shown in Figure 10. Moreover, at a certain voltage (i.e., = 15 V) current increases with increase in temperature supporting a semiconducting nature of the material [see inset of Figure 10]. Temperature dependent DC electrical resistivity of DyM system has been measured in the temperature range (300–473 K), as shown in Figure 11. The logarithmic variation of resistivity with temperature is also shown [see inset of Figure 11]. It follows the Arrhenius rule with positive slope as shown in Figure 12. The plot in Figure 12 is extracted from the given equation where is activation energy, is absolute temperature, and is Boltzmann constant.
The activation energy ~0.759 eV for DyM is calculated from slope of versus 1/. This may be explained in terms of dominant character of grain boundaries to find out the resistive properties of this system. Generally, activation energies for the oxide ionic conductors are >0.9 eV. It is usually <0.2 eV for n-type polaronic conduction of electrons and 0.2 eV for the polaronic conduction of holes [22]. In our case, observed value of activation energy suggests a p-type polaronic conduction of holes above room temperature in DyM. Moreover, the temperature dependent DC resistivity (see Figure 11) shows decrease in resistivity with the increase in temperature reflecting the role of thermally activated charge carriers according to the hopping conduction mechanism [23–25]. We have tested the validity of this polaronic hopping conduction mechanism in the same temperature range (300–473 K) by Mott’s variable-range-hopping (VRH) conduction rule [26–28]It is observed that variation of with is a straight line as depicted in inset of Figure 12. The linear dependence in our case confirms the presence of hopping type conduction in given temperature range [29–31]. Moreover, the obtained value of is almost equal to half of the optical energy band gap (1.78 eV), confirming the correlation between thermally activated charge carriers with localized free-carrier response. The obtained value of activation energy (0.759 eV) of DyM in our investigated compound is comparable with Mn based compound such as SmM for which activation energy is 0.59 eV [32].
4. Conclusion
We have investigated the infrared reflectivity, UV-visible absorption spectra, and electrical conduction mechanism of polycrystalline DyM. The experimentally observed phonon modes have been assigned to the different lattice dynamics and crystal symmetry. In addition, we have calculated optical conductivity, and no contribution of free carriers has been observed at low frequency. On comparison, an agreement found between energy band gap estimated through UV-visible measurement and optical conductivity and is associated with the semiconducting behavior of DyM. Indeed, the semiconducting mechanism has also been confirmed from existence of p-type polaronic conduction above room temperature. The results conclude DyM as a typical semiconductor.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.