Abstract
We present infrared (IR) reflectivity of with = 0, 0.2, 0.4, 0.6, 0.8, and 1 in the frequency range 30–1000 cm−1. A total of 18 IR active phonons were observed for Gd () and three additional phonons have been observed with increasing , marking a total of 21 phonons in (). A systematic investigation was performed to map out the structural distortion through the lattice vibration and discuss the consequences of frequency shifts in phonon modes. In addition, we have calculated the real part of optical conductivity () which reflects the semiconducting nature of .
1. Introduction
Multiferroic materials are promising for future technology due to the simultaneous existence of electric and magnetic orders [1, 2]. Multiferroic received much attention due to strong coupling between magnetic and ferroelectric orders, puzzling magnetic structure, large ferroelectric polarization, and interesting physics [3–5]. At ambient condition, has an orthorhombic structure with space group for a broad range of R ions as shown in Figure 1 [6, 7]. The octahedra are linked in the form of an infinite chain parallel to -axis. However, the chains of are cross-linked with pyramidal with an edge-sharing. The R atoms form an eightfold coordination to oxygen atoms. From high resolution diffraction method it has been found that lattice parameters of system show no significant effect on field or temperature variation [8]. However, the low temperature (below K) behavior is quite complex, originating from magnetic interaction between 4 and 3 magnetic moment of and / ions, respectively. Below , shows various phase transitions upon temperature variation [5, 9].
In the family of , is a unique multiferroic with largest polarization under strong magnetic field among the known multiferroics [3]. Very recently, we have observed a magnetodielectric effect in the paramagnetic phase of [10] as well as in [11]. This unusual magnetodielectric behavior in is consistent with the softening of Raman active phonons, indicating a distinct magnetic correlation slightly above [12]. Moreover, the softening of infrared active modes has also been observed in above [13]. In case of , magnetoelectric effect and spin-lattice coupling are commonly acknowledged in several investigations [4, 10, 12, 14]; little is known about the correlations between structural distortion and lattice dynamics. Infrared spectroscopy demonstrates the local lattice distortion and provides the information about the flexible crystalline lattice. Several investigations on IR reflectivity of (R=Tb [15, 16], Dy [13, 17], Ho [18], and Bi [19]) have been performed. In this regard, we are motivated to conduct a systematic investigation of and probe the structural distortion through IR phonons. This system is interesting due to many aspects: (i) large difference in ionic radius of Y ( Å) and Gd ( = 1.05 Å), (ii) large difference in ionic mass of Y ( amu) and Gd ( = 157 amu), and (iii) Gd having strongest magnetic moment (4) and Y being nonmagnetic. It is noteworthy to mention that the intermediate members ( = 0.2, 0.4, 0.6, and 0.8) of are prepared for the first time, to the best of our knowledge, and are expected to have the same crystal structure as the end members. A detailed investigation of Raman and infrared measurements on system has shown increase in structural distortion from orthorhombic to hexagonal with increasing () [20]. As majority of vibrational modes are sensitive to structural distortion induced in both Mn polyhedra and with respect to R centers, thus a significant change in the ionic mass and radii at R site would be interesting.
The question whether the continuous substitution of Y into Gd site may lead to any kind of disorder effect due to large difference in mass and ionic radius has not been addressed yet. Therefore, we present lattice dynamics study of using the IR reflectivity spectroscopy. The study of optical phonons and their correlation to distortion allows us to have closer look on structural evolution in .
2. Experiment
ceramic samples have been synthesized by using sol-gel method, similar to other compounds [10, 11, 21]. Fourier transform infrared (FTIR) spectrometer (Vertex 80v) has been used to measure the IR reflectivity. Pellets of 13 mm diameter were made smooth prior to spectroscopic measurements. IR reflectivity has been measured in the frequency range of far (30–680 cm−1) and mid (550–7500 cm−1) infrared regions at room temperature under vacuum purge. Detail of measurements can be seen elsewhere [22].
3. Results and Discussion
Figure 2 demonstrates X-ray diffraction (XRD) patterns for the composition which exhibit the quite similar phase sequences for all concentration . The obtained XRD patterns have been analyzed by using the Rietveld refinement and the calculated lattice parameters are given in Table 1. A peak at has been identified only for intermediate member of ( = 0.2, 0.4, 0.6, and 0.8) and is attributed to an additional peak as it was not fitted with the Rietveld refinement (Figure 2). In addition, the peaks at were only found in and and well fitted with the Rietveld refinement which remain absent for the intermediate (Figure 2). However, crystal structure of all members of was found to be orthorhombic and the obtained lattice parameters for end members ( and ) of the series are in excellent agreement with reported values [23]. As observed, the peak positions slightly shift towards low values with increasing . Moreover, lattice parameters show a nonmonotonic dependence on which may be caused by the substitution of small ionic radius of Y into Gd ions which leads to affecting the bond length and bond angle of Mn-O-Mn [9]. These facts are manifesting a structural distortion, which will be of particular focus through IR spectroscopic analysis.
Figure 3 demonstrates the IR reflectivity spectra obtained for at room temperature. The experimental spectra were fitted by using Lorentz oscillator model that correlates the optical reflectivity (R) with the dielectric function by Fresnel’s formula as
To quantify the infrared phonon contribution, 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 (1) and (2) together can give the measured reflectivity spectra. The dispersion parameters (, , and ) obtained from the best fit to the experimental curve of are summarized in Tables 2 and 3. According to lattice dynamic calculations there are 36 IR active modes in system; however we were able to observe maximum 21 phonons in . The origin of this discrepancy simply lies in the polycrystalline nature of our samples having mixed response of all crystallographic axes.
In order to elucidate the lattice dynamics of individual phonon, we have analyzed the ionic displacement within the crystal. Vibrational properties are better understood in the limits of harmonic oscillator , where denotes force constant and is the reduced mass of the ions involved in the corresponding phonon mode. Thus it is natural to expect that low frequency phonons (200 cm−1) are attributed to the vibrations of Gd(Y) and Mn ions, while the intermediate phonon modes are due to the bending and twisting motion of Mn-O polyhedra. At higher frequencies (450 cm−1), stretching of the octahedra (including the bending motion of equatorial planes) will contribute to the vibration of phonons [13]. Thus it is expected that substitution of Y into Gd sites always leads to increase in frequency of phonon modes at low frequency due to decrease in reduced mass.
Figure 4 shows a closer look of the low frequency phonon modes dynamics as indicated by arrows. Interestingly, there is a significant increase in frequency for the two most prominent phonon modes and . Moreover, the mode was only observed for at 167 and almost disappeared and reappeared for at 176 cm. Although it shows an increase in the frequency as expected the absence of for the intermediate is quite surprising. One possible explanation is some structural changes that totally damped these mode and is quite reasonable as we have observed some new peaks in XRD patterns at that is only present for intermediate and thus may be responsible for the absence of . The substitution of Y at Gd site takes the system in combined effect of Y/Gd ions that may vibrate in opposite direction relative to Mn polyhedra results in damping the vibration as observed. Moreover, small ionic radius of Y directly affects the Mn-Mn interaction which leads to affecting the relative motion of Y/Gd ions with respect to Mn polyhedral. Thus, a consistent change in both rare-earth ionic radius and Mn-Mn bond distance may result in damped and discontinuous evolution of frequencies. Thus, we have observed strong lattice dynamics in low frequency range (200 cm−1) as expected.
With a further insight into lattice dynamics of intermediate frequency modes, one can see that the mode shows no obvious frequency shift (Figure 4). Interestingly, a new phonon mode () has been observed only for and (Figure 4). Moreover, the phonon modes from to that lies in the intermediate frequency range have shown no significant frequency shift as can be seen from Table 2. More interestingly, corresponding values of and ( = 5–12) remain almost the same for the complete series (Table 3). This simply reflects that Y substitution into Gd sites does not disturb much at higher frequencies. The effect of Y substitution can also be observed in high frequency region as a result of two new phonons. One new phonon () has been observed for at a frequency of 380 cm−1 and remains almost unchanged with increasing . The second new phonon is that has been observed only for at frequency of about 486 cm−1. Thus the origin of three new phonon modes (, , and ) after the substitution indicates the strong structural distortion produced, which is difficult to observe in XRD patterns.
In contrast, the high frequency modes to exhibit strong frequency hardening as shown in Figure 5. These modes represent the stretching and bending motion of octahedra, as in this frequency range, oxygen atoms vibrate as per harmonic oscillator limitation due to its reduced mass as compared to Gd, Y, and Mn ions. While increasing Y content, the whole crystal reduces its volume due to the substitution of lighter element Y into heavy ion Gd. The phonon dynamics is also a function of volume that ultimately gives rise to the change in frequency of phonon modes [24]. Hence, the modes to harden with decrease in volume, giving rise to stretching of octahedra to vibrate at higher frequency (Figure 5).
We have also calculated the static dielectric constant, which is given by
represents the static dielectric response obtained from the sum of all the oscillator dielectric strength () and the electronic polarizability (). It is important to note that we have observed less number of phonons as compared to those theoretically predicted and thus the dielectric strength of the missing modes must be relatively weaker than those observed. The decrease in with , similar to the trend of , is clearly reflecting the small values of the , which mainly decreases with (see Figure 6). However, an overall decrease in the value of means that energy band gap expands with increasing Y content [24].
We have calculated the real part of optical conductivity () through the measured reflectivity spectra by using the relation . Here, and are wavenumber and complex part of the dielectric function obtained from measured reflectivity spectra [24]. As a representative, the obtained for is shown in Figure 7. It is noteworthy that the spectra have strong absorption peaks, indicating semiconducting behavior of . In addition, spectra are structureless below 100 cm−1 and have shown no conduction mechanism reflecting the absence of free charge carriers, which is a typical semiconducting nature, in contrast to the Drude-type metallic behavior [25, 26]. Similar behavior has been observed for all samples.
4. Conclusion
We have performed a systematic investigation on structural distortion through lattice dynamics of the phonon modes in . By utilizing the discriminative sensitivity of IR reflectivity technique, we explicitly observed different types of phonon modes in depending upon their symmetry and participating ions. The substitution of Y ion in leads to hardening of phonons caused by the difference in mass and thus decrease in cell volume. Strong movements of Gd(Y) ions exhibit disorder induced effects through low frequency phonons shifts. The Mn sites remain almost unchanged upon increasing , as reflected through almost constant frequency of the intermediate phonon modes. However, O-ions contribute at higher frequency modes inducing the stretching motion in octahedra caused by change in cell volume. Moreover, optical conductivity indicates the semiconducting nature of the prepared compounds.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.