Raman scattering measurement

Raman scattering was first observed by Raman and Krishnan in 1928 [59], although the Raman effect had been predicted by Smekal in 1923 [60]. Raman spectra are established by analyzing inelastically scattered light. Raman scattering originates from a change in the polarizability of molecules or susceptibility of crystals by quasi-particles [61]. Fig. 3-2 shows the schematic of Rayleigh and Raman scattering processes. The frequency of the incident light is i, and the frequency of the scattered light is s. The

Ei = hi ， (3.2.1) Ei = hs ， (3.2.2) The scattered photon has an energy that is less than the incident photon called Stokes Raman scattering, and the energy that is greater than the incident photon called anti-Stokes Raman scattering. The difference between the inverse of these two wavelengths is known as the Raman shift, a value that is directly related to the energy. The Raman shift depends on the scattering media, demonstrating that the Raman spectrum is strongly related to the properties of the scattering materials. Raman scattering measurements yield information on lattice vibration and the excitations of the charge, spin, and orbital degrees of freedom [61].

Fig. 3-3 shows the sketch map of micro-Raman spectroscopy. The first laser light wavelength is 785 nm with the input power of 0, 1, 10, 25, 50, and 100 mW. The second laser light wavelength is 532 nm with the output power of 0, 0.2, 2, 5, 10, and 20 mW. The third laser light wavelength is 488 nm with the output power of 0, 0.4, 4, 10, 20, and 40 mW. The laser is in conjunction with the grating density of 400 grooves/mm or 1200 grooves/mm. The laser light is focused by the 50× microscope objective with NA = 0.5 and directed perpendicular to the surface of the sample, with the spatial resolution of 4 μm.

Then, the scattering light is collected at 180° and compared with the incident light.

Alternatively, the laser light is focused on the 100× microscope objective with NA = 0.9 and directed perpendicular to the surface of the sample, with the spatial resolution of 1 μm.

The charge-coupled detector with the model DU 420A-OE-152 can reduce lower the temperature to −60 ℃ to −65 ℃ with a 1024 × 256 resolution. The spectral resolution of these instruments is typically less than 0.5 cm⁻¹. Fig. 3-4 shows a mechanical cross-sectional device. The sample was clamped on the gap for cross-cross-sectional measurement. A cryostat is used for temperature-dependent measurements. The continuous liquid helium flow into the cryostat allows measurements to be conducted in the temperature range of

10–300 K. Fig. 3-5 illustrates the setup for temperature-dependent Raman scattering measurements. The sample was mounted inside the cryostat. Coaxial shield flow liquid helium transfer line, flow meter panel for helium gas flow control, silicon diode sensor, and temperature controller were used to monitor the sample’s temperature.

Fig. 3-1: Spectroscopic ellipsometer with the focusing optics.

Fig. 3-2: Schematic of Rayleigh, anti-Stokes, and Stokes scattering.

Focusing optics coupled tube

Sample

Fig. 3-3: Sketch map of the setup of the micro-Raman scattering spectroscopy.

Fig. 3-4: The cross-sectional mechanical setup.

Sample position

Fig. 3-5: Temperature-dependent Raman scattering experimental setup.

LHe transfer line

LHe dewar

Vacuum pump

Temperature controller Flow meter

Cryostat on the stage of optical microscopy

Chapter 4

Results and discussion

4.1 Optical properties of SrFeO

single crystals

In this section, we present the spectroscopic ellipsometry and Raman scattering measurements of SrFeO2.86 and SrFeO2.75 single crystals. These samples were acquired from Prof. C. H. Du’s research group at the Department of Physics, Tamkang University.

We used spectroscopic ellipsometry to investigate the dielectric function and optical constants. Fig. 4-1 displays the ellipsometric parameters  and  of SrFeO2.86 and SrFeO2.75 single crystal at 70°angles of incidence. Optical constants can be derived from these ellipsometric parameters using Eqs. 3.1.17 and 3.1.18. Fig. 4-2 reveals the refractive index n and extinction coefficient k of SrFeO2.86 and SrFeO2.75 single crystals. We observed that the shapes of the refraction index dispersion of SrFeO2.86 and SrFeO2.75 single crystal were similar despite the different oxygen contents. As displayed in Fig. 4-2(a), when the photon energy increased from 2.1 to 3.8 eV and from 4.7 to 5.4 eV, the refractive index decreased, which indicates anomalous dispersion. As illustrated in Fig. 4-2(b), when the photon energy increased from 2.3 to 3.9 eV and from 4.6 to 5.3 eV, the refractive index decreased, which displays anomalous dispersion. Fig. 4-3 illustrates the optical absorption coefficient spectra of SrFeO2.86 and SrFeO2.75 single crystals measured at room temperature.

We fitted these absorption spectra by using a standard Lorentzian model [62]. The background was fitted using the Lorentzian functions [62]. The absorption was resolved into two peaks. An increase in the photon energy resulted in a progressive increase in the absorption. Two absorption bands were observed at approximately 2.98, and 5.05 eV for

the SrFeO2.86 single crystal. Galakhov et al. [63] presented the valence band region of the XPS spectra, showing the similar absorption bands. Similar absorption bands were also observed for the SrFeO2.75 single crystal. The first-principles calculations [31,33,64]

indicated that 2.98 and 5.05 eV peaks were associated with the charge transfer transitions between oxygen 2p states to the iron 3d states.

The absorption coefficient included contributions from the direct and indirect bandgap transitions in the typical solid state and is expressed as follows [65,66]:

(5.1)

where Eg,dir is the magnitude of the direct bandgap, Eg,ind is the magnitude of the indirect bandgap, Eph means the absorbed (emitted) phonon energy, and A and B are constants. The model described above, which supposes a simple band shape, causes the extraction of the direct energy gap when (·E)² is plotted as a function of photon energy. Fig. 4-4 (a) displays the direct bandgap analysis of SrFeO2.86 and SrFeO2.75 single crystals. Plotting (α．E)^0.5 as a function of photon energyled to an indirect band gap shown in Fig. 4-4(b) and (c). The values of band gap of both samples are 2.00 ± 0.01 and 1.98 ± 0.01 eV at 300 K, respectively.

Rothschild et al. [52] performed the four-point probe conductivity measurements and demonstrated the band gap of SrFeO3- at approximately 1.9 ± 0.1 eV. Ghaffari et al. [53]

employed the ultraviolet photoelectron spectroscopy and determined the band gap of SrFeO3- at approximately 1.8 eV. L. Wang et al. [67] measured the spectroscopic ellipsometry spectra of SrFeO2.5, SrFeO2.5+ and SrFeO3 thin films. The decrease in band gap from 2.05 to 0 eV indicated that thin films transitioned from semiconductor to metal.

Our experimental results are comparable to these previous studies [52,53,67].

Fig. 4-5 demonstrates the room-temperature Raman scattering spectra of SrFeO2.86

and SrFeO2.75 single crystals. We fitted these Raman scattering spectra using the standard Lorentzian functions [62]. The factor group analysis indicated that SrFeO2.86 has a

tetragonal structure (space group I4/mmm), with atoms located in the 8f(Fe), 16m(O), 8i(Sr), phonon modes. Our spectrum consists of 15 first-order phonon modes at approximately 83, 94, 107, 117, 123, 135, 175, 226, 267, 320, 332, 414, 428, 478, and 626 cm^-1 and four second-order phonon modes at approximately 800, 988, 1234, and 1363 cm⁻¹. The numbers of observed phonon modes are less than the predicted result because of the weak intensity of some phonon modes. The phonon modes at approximately 84, 94, 107, 117, 123, 135, 175, 226, and 267 cm^-1 modes were associated with the Sr atoms movements and the rotation of FeO6. The phonon modes at approximately 320, 332, 414, 428, and 478 cm⁻¹ were assigned to the bending vibrations of oxygen ions in the FeO6 octahedra. The phonon mode near 626 cm⁻¹ was related with the stretching vibrations of oxygen ions in the FeO6

octahedra [68-70].

Factor group analysis indicated that SrFeO2.75 has an orthorhombic structure (space group Cmmm) [19] including one formula unit per primitive cell, with atoms located in the 4f(Fe), 4h(O), 2d(Sr), 4g(Sr), 4i(Fe), 16r(O), 2c(Sr), and 2b(O) Wyckoff sites. Sr = Ag + B1g + 3B1u + B2g + 3B2u + 3B3u + B3g represent the motion of Sr. The motion of Fe is represented as Fe = Ag + Au + B1g + 2B1u + 3B3u + B3g. The motion of O is represented as

of the phonon modes of SrFeO2.75 at the center of the Brillouin zone are expressed as total

= 7Ag + 6B1g + 5B2g +4B3g + 9B1u + 10B2u + 10B3u + B1u + B2u + B3u + 4Au. The modes Ag, B1g, B2g, and B3g are Raman active; B1u, B2u, and B3u modes are infrared active; Au mode is neither Raman nor infrared active. The SrFeO2.75 structure with the Cmmm space group contains 22 Raman-active modes. Our spectrum is composed of 12 first-order phonon modes at approximately 84, 92, 107, 116, 130, 138, 175, 321, 333, 416, 479, and 624 cm^-1 and two second-order phonon modes at approximately 800 and 1380 cm^-1. The phonon modes at approximately 84, 92, 017, 116, 130, 138, and 175 cm^-1 were assigned to the displacement of Sr atoms and the rotations of FeO6 octahedra. The phonon modes at approximately 321, 333, 416, and 479 cm⁻¹ were attributed to the bending vibrations of oxygen ions in the FeO6 octahedra. The phonon mode near 624 cm⁻¹ was associated with the stretching vibrations of oxygen ions in the FeO6 octahedra [68-70]. Fig. 4-6 (a) and (b) reveals the room-temperature polarized Raman scattering spectra of SrFeO2.86 single crystal between the different frequency ranges. The inset displays the optical image of the SrFeO2.86 single crystal. Fig. 4-7 displays the room-temperature cross sectional polarized Raman scattering spectra.

Table 4-1 summarizes the symmetry of Raman-active phonon modes observed in different scattering configurations for SrFeO2.86 single crystals. According to the selection rule, the A1g and B1g symmetry phonon modes appear in the parallel configurations of the ab plane. The B2g symmetry phonon mode only appears in the cross configurations of the ab plane. The Eg symmetry phonon mode appears in the cross configurations of the ac or bc plane [71-76].

The modes at approximately 320, 332, and 428 cm⁻¹ displayed a larger intensity in the parallel configuration (YY) than in the perpendicular configuration (YX) and did not appear in the cross sectional parallel configuration (ZZ), thus revealed to be B1g symmetry.

The mode at 626 cm⁻¹ displayed a larger intensity in the parallel configuration (YY) than in the perpendicular configuration (YX) and displayed a larger intensity in the cross-section parallel configuration (XX) and (ZZ) than in the perpendicular configuration (YX), thus revealed to be A1g symmetry.

Table 4-1: Symmetry of Raman-active phonon modes observed in different scattering configurations for SrFeO2.86 single crystals.

Symmetry A1g B1g B2g Eg

X(YY)X̅

○ ○

X(YZ) X̅

○

X(ZZ) X̅

○

Y(XX)Y̅

○ ○

Y(XZ)Y̅

○

Y(ZZ) Y̅

○

Z(XX) Z̅

○ ○

Z(YX) Z̅

○

Z(YY) Z̅

○ ○

Fig. 4-8 illustrates the room-temperature polarized Raman scattering spectra and optical image of SrFeO2.75 single crystals. Table 4-2 summarizes symmetry of Raman-active phonon modes observed in different scattering configurations for SrFeO2.75 single crystals. According to the selection rule, the Ag symmetry phonon mode appears in the parallel configurations of the ab plane. The B1g symmetry phonon mode appear in the cross configurations of the ab plane. The B2g and B3g symmetry phonon modes appear in the cross configurations of the ac or bc plane. The modes at 320, 333, 416, and 624 cm⁻¹ displayed

a larger intensity in the parallel configuration (YY) than in the cross configuration (YX), thus revealed to be Ag symmetry [71-76].

Table 4-2: Symmetry of Raman-active phonon modes observed in different scattering configurations for SrFeO2.75 single crystal.

Symmetry Ag B1g B2g B3g SrFeO2.86 single crystal at different frequency ranges. When the temperature decreased, no obvious changes in the phonon modes were observed. This indicated that the crystal structure of SrFeO2.86 single crystal was unchanged at low temperatures. Fig. 4-11 (a)-(d) displays the temperature-dependent phonon parameters (frequency, linewidth, and normalized intensity) of the 320, 332, 428, and 626 cm⁻¹ modes of SrFeO2.86 single crystal.

When the temperature was decreased, the phonon frequency revealed a blueshift.

Anharmonic interactions are relevant to the high-order terms of atomic vibrations beyond the conventional harmonic terms. The temperature dependence of the phonon frequency and linewidth can be denoted as follows [77]:

, (5.2)

, (5.3)

where 0 and γ0 are the intrinsic frequency of the optical phonon mode and the linewidth broadening that results from defects. The anharmonic coefficient of parameter A with negative value represents blueshift. The anharmonic coefficient of B with positive value indicates the linewidth decreased with temperature.

1

Table 4-3: The anharmonic parameters of SrFeO2.86 phonon modes.

Phonon frequency (cm⁻¹) 0(cm⁻¹) A( cm⁻¹) (0) (cm⁻¹)

320 332.9 -11.3 331.6

332 355.3 -19.4 335.9

428 440.9 -9.6 431.3

626 654.8 -20.0 634.8

For the analysis of the anharmonic contributions to the 320 cm⁻¹ phonon mode, the value of 0 (approximately 332.9 cm⁻¹ ), the parameter A (approximately −11.3 cm⁻¹) and the value of (0) (approximately 331.6 cm⁻¹) were determined. For the analysis of the anharmonic contribution of the 332 cm⁻¹ phonon mode, the value of 0 (approximately 355.3 cm⁻¹) , the parameter A (approximately −19.4 cm⁻¹), and the value of (0) (approximately 335.9 cm⁻¹) were determined. For the analysis of the anharmonic

contribution of the 428 cm⁻¹ phonon mode, the value of 0 (approximately 440.9 cm⁻¹), the parameter A (approximately −9.6 cm⁻¹), and the value of (0) (approximately 431.3 cm⁻¹) were determined. For the analysis of the anharmonic contribution of the 626 cm⁻¹ phonon mode, the value of 0 (approximately 654.8 cm⁻¹), the parameter A (approximately −20 cm⁻¹), and the value of (0) (approximately 634.8 cm⁻¹) were determined. The frequency, linewidth, and normalized intensity of all phonon modes did not display anomalies when the temperature decreased to 70 K.

Fig. 4-12 reveals the temperature-dependent Raman scattering spectra of the SrFeO2.75

single crystal. With a decrease in temperature, no obvious changes in the phonon modes were observed, which indicated that the crystal structure of SrFeO2.75 single crystal did not change at low temperatures. Fig. 4-13(a) ~ (c) displays the temperature-dependent phonon parameters of frequency, linewidth, and normalized intensity of the 321, 333, and 429 cm⁻¹ modes When the temperature decreased from room temperature, the phonon frequency exhibited a blueshift. Below 230 K, the phonon frequency did not display anomalies. The values of the fitting parameters are summarized in Table 4-4.

Table 4-4: The anharmonic parameters of SrFeO2.75 phonon modes.

Phonon frequency(cm⁻¹) 0(cm⁻¹) A( cm⁻¹) (0)(cm⁻¹)

321 323.5 -2.2 321.3

333 336.9 0 336.9

429 450.0 -18.36 431.6

For the analysis of the anharmonic contributions to the 321 cm⁻¹ phonon mode, the value of 0 (approximately 323.5 cm⁻¹), the parameter A (approximately −2.2 cm⁻¹), and the value of (0) (approximately 321.3 cm⁻¹) were determined. For the analysis of the anharmonic contributions to the 333 cm⁻¹ phonon mode, the value of 0 (approximately

336.9 cm⁻¹), the parameter A (approximately 0 cm⁻¹) and the value of (0) (approximately 336.9 cm⁻¹) were determined. For the analysis of the anharmonic contribution of the 429 cm⁻¹ phonon mode, the value of 0 (approximately 450.0 cm⁻¹), the parameter A (approximately −18.36 cm⁻¹), and the value of (0) (approximately 431.6 cm⁻¹) were determined.

4.2 Optical studies of Ba

CuTeO

single crystals

In this section, we employ the spectroscopic ellipsometry and Raman scattering spectroscopy to investigate the electronic structure and lattice dynamics of Ba2CuTeO6

single crystals. These samples were acquired from Prof. F. C. Chou’s research group at the Center for Condensed Matter Sciences, National Taiwan University.

Fig. 4-14 reveals the psi () and delta () ellipsometric parameters of Ba2CuTeO6 at room temperature. Optical constants can be derived from these ellipsometric parameters using Eqs. 3.1.17 and 3.1.18. Fig. 4-15 presents the real (1) and imaginary (2) parts of the dielectric function() of Ba2CuTeO6. The dispersive response of 1 had a positive value, which was similar to the typical behavior of a semiconductor. The peak of 2 at approximately 4.0 eV leveled off at higher energies, which revealed that electromagnetic radiation was absorbed by Ba2CuTeO6 near 4.0 eV. Fig. 4-16 illustrates the optical absorption coefficient spectrum of Ba2CuTeO6 measured atroom temperature. The inset illustrates the optical absorption coefficient in the low-energy region (0.5 ~ 3.5 eV) of Ba2CuTeO6. We fitted this absorption spectrum by using standard Lorentzian functions [62].

With an increase in photon energy, absorption increased progressively and four absorption bands were observed at approximately 1.45, 3.43, 4.65, and 5.79 eV. According to the previous first-principles calculations, the first absorption peak shown in the low-energy

attributed to charge-transfer transitions from the oxygen 2p states to the tellurium 5p states [29]. In a typical solid, the absorption coefficient includes contributions from the direct and indirect band gap transitions and is expressed as Eq. 5.1 [65,66]. Fig. 4-17 presents a direct band gap of 1.04 ± 0.01 eV at 300 K. Plotting (α．E)^0.5 as a function of photon energy led to an indirect band gap of about 0.24 eV, shown in

Fig. 4-18. Our experimental result in the direct band gap analysis is in good agreement with the theoretical band structure calculations of Ba2CuTeO6, which yield a direct band gap energy of 1.0 eV [29].

Fig. 4-19 depicts the unpolarized room-temperature Raman scattering spectrum of Ba2CuTeO6. We fitted these phonon peaks using standard Lorentzian functions [62]. We observed a total of 16 Raman-active phonon modes at approximately 85, 97, 104, 119, 160, 194, 380, 396, 404, 409, 492, 568, 574, 606, 679, and 751 cm⁻¹. Fig. 4-19 illustrates the polarized Raman scattering spectra of Ba2CuTeO6 at room temperature in four configurations. The modes at 85, 97, 104, 119, 160, 194, 380, 396, 404, 409, 492, 568, 574, 606, 679, and 751 cm⁻¹ exhibited a higher intensity in the parallel configuration (YY) than in the cross configuration (YX). This satisfies the selection rule for C2/m in which A1g and B1g modes should appear in the YY configuration and no peaks are expected for the YX configuration. On the other hand, the primed spectra Y′Y′ was different from its unprimed counterpart YY, which shows that the sample is a single crystal [71-76]. The Y′Y′ spectrum showed the suppressed intensity of the modes approximately 160 and 606 cm⁻¹. We deduced that the 85, 97, 104, 119, 194, 380, 396, 404, 409, 492, 568, 574, 679, and 751 cm⁻¹ phonon modes exhibited Ag symmetry, whereas the 160 and 606 cm⁻¹ phonon modes exhibited Bg symmetry. According to factor group analysis, Ba2CuTeO6 has a monoclinic structure (space group C2/m) [36]. It contains one formula unit per primitive cell at room temperature. The irreducible representation of the phonon modes at the center of the Brillouin zone is presented as follows: = 16Ag + 11Bg [36]. In accordance with previous

report [36], the phonon peaks at approximately 85, 97, 104, 119, 160 and 194 cm⁻¹ were assigned to the displacement of Ba atoms and the rotations of CuO6 and the TeO6 octahedra.

The phonon peaks at approximately 380, 396, 404, 409, and 492 cm⁻¹ were associated with the bending vibrations of CuO6 and TeO6 octahedra. The phonon peaks at approximately 568, 574, 606, 679, and 751 cm⁻¹ were attributed to the stretching vibration of TeO6 and CuO6 octahedra.

The temperature-dependent Raman scattering spectra of Ba2CuTeO6 are depicted in Fig. 4-21. At the center of the Brillouin zone, the irreducible representation of the phonon modes is given as follows:  = 27Ag at low temperature. In our investigation, we observed 20 phonon modes. New peaks appeared at approximately 124, 128, 152, and 601 cm⁻¹ at low temperature. Fig. 4-22 illustrates the new peaks that appeared between 75 and 150 cm⁻¹ at low temperatures. The new peaks indicate that a weak crystal phase change occurred from the monoclinic state to the triclinic state [30,36]. With a decrease in temperature, these new phonon modes exhibited softening at temperatures lower than 75 K.

Fig. 4-23 to 4-27 exhibit the temperature-dependent phonon parameters (frequency, linewidth, and normalized intensity) of all phonon modes. We focus on the stretching vibrations of TeO6 and CuO6 octahedra near 606 and 679 cm⁻¹. They exhibited a blueshift when the temperature decreased to 200 K. When the temperature decreased to 75 K, which is the short-range AF phase transition temperature, the redshift and normalized intensities of the phonon modes increased. Our results differed from those of previous measurements [36]. Glamazda et al. [36] did not observe the phonon anomalies at temperatures lower than the magnetic phase transition temperatures. One possibility that could account for this difference is due to the different growth processes [30,78], resulting in different quality of single crystals.

The temperature dependence of the phonon frequency can be expressed as Eq. 5.2 [77].

For the analysis of anharmonic contributions to the 606 cm^-1 phonon modes, the values of

0 (approximately 615 cm⁻¹) and parameter A (approximately −6.8 cm^-1) were determined.

For the 679 cm^-1 phonon mode, the values of 0 (approximately 690 cm⁻¹) and parameter

In a magnetic material, the temperature-dependent frequency change of the phonon mode can be expressed as follows [79]:

(T) =0 +latt(T) +anh (T) +e-ph (T) +s-ph (T) , (5.4) where 0 is the harmonic frequency of the phonon; latt(T) is the contribution of lattice expansion and contraction to the phonon frequency;anh (T) is the intrinsic anharmonic contribution;e-ph(T) is the contribution due to the renormalization effect of the phonon frequency that results from electron–phonon coupling, which could be negligible in Ba2CuTeO6;ands-ph (T) is the spin-phonon coupling contribution caused by lattice vibrations due to the modulation of the exchange integral. The magnetic coupling among Cu spins is expected to be established through the Cu–O–Te–O–Cu superexchange path.

Spin correlations develop when the temperature decreases to 75 K. We calculated s-ph

from the frequency-shift data by using the following expression [80]:

s-ph = ²

magnetic magnetization. We used the magnetic susceptibility [78] to estimate the spin-phonon coupling constant for all redshifted spin-phonon modes. The spin-spin-phonon coupling constants are listed in Table 4-5.

Table 4-5: The spin-phonon coupling constant for 14 phonon modes in Ba2CuTeO6. Mode frequency (cm^-1) Spin-phonon coupling constant (mRy/Ų)

97 0.39

These values were one order of magnitude lower than those obtained for perovskite oxides [81-85], thus reflecting a weak spin-phonon coupling in Ba2CuTeO6.

4.3 Electronic structure and lattice dynamics of Li

Ni(WO

)

In this section, we investigate the electronic structure and lattice dynamics of Li2Ni(WO4)2 using spectroscopic ellipsometry and Raman scattering spectroscopy. The samples were acquired from Prof. F. C. Chou’s research group at the Center for Condensed Matter Sciences, National Taiwan University.

Fig. 4-29 shows the the psi () and delta () ellipsometric parameters of Li2Ni(WO4)2

at room temperature. Optical constants can be derived from these ellipsometric parameters.

We adopted the Bruggeman effective-medium [86] to fit the raw ellipsometry data and

We adopted the Bruggeman effective-medium [86] to fit the raw ellipsometry data and