Lattice Dynamics of Gd1−xYxMn2O5 Investigated by Infrared Spectroscopy

We present infrared (IR) reflectivity of Gd1−xYxMn2O5 with x = 0, 0.2, 0.4, 0.6, 0.8, and 1 in the frequency range 30–1000 cm . A total of 18 IR active phonons were observed for GdMn2O5 (x = 0) and three additional phonons have been observedwith increasing x, marking a total of 21 phonons in YMn2O5 (x = 1). A systematic investigation was performed tomap 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 (σ1(ω)) which reflects the semiconducting nature of Gd1−xYxMn2O5.


Introduction
Multiferroic materials are promising for future technology due to the simultaneous existence of electric and magnetic orders [1,2].Multiferroic Mn 2 O 5 received much attention due to strong coupling between magnetic and ferroelectric orders, puzzling magnetic structure, large ferroelectric polarization, and interesting physics [3][4][5].At ambient condition, Mn 2 O 5 has an orthorhombic structure with  space group for a broad range of R ions as shown in Figure 1 [6,7].The MnO 6 octahedra are linked in the form of an infinite chain parallel to -axis.However, the chains of MnO 6 are cross-linked with pyramidal MnO 5 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 Mn 2 O 5 system show no significant effect on field or temperature variation [8].However, the low temperature (below   ∼ 40-45 K) behavior is quite complex, originating from magnetic interaction between 4 and 3 magnetic moment of  and Mn 3+ /Mn 4+ ions, respectively.Below   , Mn 2 O 5 shows various phase transitions upon temperature variation [5,9].
In the family of Mn 2 O 5 , GdMn 2 O 5 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 GdMn 2 O 5 [10] as well as in DyMn 2 O 5 [11].This unusual magnetodielectric behavior in GdMn 2 O 5 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 DyMn 2 O 5 above   [13].In case of GdMn 2 O 5 , 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 Mn 2 O 5 (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 Gd 1− Y  Mn 2 O 5 and probe the structural distortion through IR phonons.This system is interesting due to many aspects: (i) large difference in ionic radius of Y ( Y = 1.019Å) and Gd ( Gd = 1.05 Å), (ii) large difference in ionic mass of Y ( Y = 89 amu) and Gd ( 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 Gd 1− Y  Mn 2 O 5 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 Eu 1− Y  MnO 3 system has shown increase in structural distortion from orthorhombic to hexagonal with increasing  ( > 0.5) [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 Gd 1− Y  Mn 2 O 5 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 Gd 1− Y  Mn 2 O 5 .

Experiment
Gd 1− Y  Mn 2 O 5 ceramic samples have been synthesized by using sol-gel method, similar to other Mn 2 O 5 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].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 2 ∼ 28 has been identified only for intermediate member of Gd 1− Y  Mn 2 O 5 ( = 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 2 ∼ 32 were only found in  = 0 and  = 1 and well fitted with the Rietveld refinement which remain absent for the intermediate  (Figure 2).However, crystal structure of all members of Gd 1− Y  Mn 2 O 5 was found to be orthorhombic and the obtained lattice parameters for end members (GdMn 2 O 5 and YMn 2 O 5 ) of the series Gd 1− Y  Mn 2 O 5 are in excellent agreement with reported values [23].As observed, the peak positions slightly shift  towards low 2 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 Gd 1− Y  Mn 2 O 5 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

Results and Discussion
To quantify the infrared phonon contribution, the dielectric function () is defined as where  ∞ is the high frequency dielectric constant indicating the contribution to the electronic polarization. TO() ,   , 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 ( TO() ,   , and   ) obtained from the best fit to the experimental curve of Gd 1− Y  Mn 2 O 5 are summarized in Tables 2 and 3.According to lattice dynamic calculations there are 36 IR active modes in Mn 2 O 5 system; however we were able to observe maximum 21 phonons in YMn 2 O 5 .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  = (/) 1/2 , 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 MnO 6 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  TO1 and  TO3 .Moreover, the mode  TO2 was only observed for GdMn 2 O 5 at 167 cm −1 and almost disappeared and reappeared for YMn 2 O 5 at 176 cm −1 .Although it shows an increase in the frequency as expected the absence of  TO2 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 2 ∼ 28 that is only present for intermediate  and thus may be responsible for the absence of  O2 .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  TO4 shows no obvious frequency shift (Figure 4).Interestingly, a new phonon mode ( TO4  ) has been observed only for  = 0.2 and  = 1 (Figure 4).Moreover, the phonon modes from  TO5 to  TO12 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 Gd 1− Y  Mn 2 O 5 (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 ( TO9  ) has been observed for  = 0.2 at a frequency of 380 cm −1 and remains almost unchanged with increasing .The second new phonon is  TO12  that has been observed only for YMn 2 O 5 at frequency of about 486 cm −1 .Thus the origin of three new phonon modes ( TO4  ,  TO9  , and  TO12  ) after the substitution indicates the strong structural distortion produced, which is difficult to observe in XRD patterns.
In contrast, the high frequency modes  TO13 to  TO18 exhibit strong frequency hardening as shown in Figure 5.These modes represent the stretching and bending motion of MnO 6 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  TO13 to  TO18 harden with decrease in volume, giving rise to stretching of MnO 6 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 ( 1 ) through the measured reflectivity spectra by using the relation  1 () =  2 /4.Here,  and  2 are wavenumber and complex part of the dielectric function obtained from measured reflectivity spectra [24].As a representative, the obtained  1 for GdMn 2 O 5 is shown in Figure 7.It is noteworthy that the spectra have strong absorption peaks, indicating semiconducting behavior of GdMn 2 O 5 .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.

Conclusion
We have performed a systematic investigation on structural distortion through lattice dynamics of the phonon modes in Gd

Figure 2 Figure 2 :
Figure 2 demonstrates X-ray diffraction (XRD) patterns for the composition Gd 1− Y  Mn 2 O 5 which exhibit the quite

Figure 3 :
Figure 3: Infrared reflectivity of Gd 1− Y  Mn 2 O 5 ( = 0, 0.2, 0.4, 0.6, 0.8, and 1) at room temperature.The black open circle shows the experimental curve and the red line shows the fitted data.The spectra are vertically shifted for clarity.

Figure 4 :
Figure 4: Detailed view of the low frequency (<250 cm −1 ) for Gd 1− Y  Mn 2 O 5 ( = 0, 0.2, 0.4, 0.6, 0.8, and 1).The black open circle shows the experimental curve and the red line shows the fitted data.Arrows shows the mode evolution with  and the spectra are vertically shifted for clarity.
1− Y  Mn 2 O 5 .By utilizing the discriminative sensitivity of IR reflectivity technique, we explicitly observed different types of phonon modes in Gd 1− Y  Mn 2 O 5 depending upon their symmetry and participating ions.The substitution of Y ion in GdMn 2 O 5 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 MnO 6 octahedra caused by change in cell volume.Moreover, optical conductivity indicates the semiconducting nature of the prepared compounds.

Figure 5 :Figure 6 :
Figure 5: Transverse optical frequency ( TO ) of the high frequency phonon mode  TO13 to  TO18 as a function of concentration .

Table 1 :
Summary of lattice parameters and refinement data for Gd 1− Y  Mn 2 O 5 .