The Effect of Infrared Light ’ s Power on the Infrared Spectra of Thin Films

There are numerous evidences that a relationship exists between the average power P of electromagnetic waves and the mechanical motion of the objects interacting with them. We investigate the effects of infrared (IR) light’s average power P on the transmission Fourier transform infrared (FTIR) spectra of thin cubic Yb2O3 and rhombohedral LaAlO3 films deposited on silicon via atomic layer deposition. We find that different values of P of the IR light displace the minima of the absorption bands. This effect is reproducible in different sets of experiments and in different spectrometers. To interpret the experimental findings, we use the law of conservation of energy. We find a correlation among the energy of the IR waves and the number, moment of inertia, and vibrational/rotational frequency of the bonds involved in the vibrational or rotational motion. The law of conservation of energy unveils that larger values of P of the IR light and lower wavenumbers of the resonances involve a larger number of crystal bonds. One practical application of our approach is that it suggests a way to improve the sensitivity of the FTIR spectra of thin crystalline films in the far IR region.


Introduction
Absorption of electromagnetic (EM) waves may generate mechanical motion [1] and vibrations [2], at the molecular [1] [2] or nuclear [3] [4] levels.On the other hand, rotating objects can emit EM waves.For example, the magnetic fields on the sun's surface rotate by some angles while generating solar flares with emission at a wavelength, e.g., 656.28 nm, which corresponds to the red Hα line [5].
G. Scarel Rotating galaxies seem to generate the [CII] line at wavelength 157.74 μm, which is in the microwave range of the EM spectrum [6].Neutron star merger events radiate γ-rays plus radio waves [7].Dust grains of variable size in space are expected to emit infrared (IR) light and microwaves in various types of interstellar environments [8].
The magnitude of the average power P of the EM waves seems to play a key role in linking the magnitude of the mechanical motions to the properties of the EM waves generating them or caused by them.For example, in Thomson scattering a precise analytical expression exists between the power over area (i.e. the intensity 0 I ) of the absorbed laser beam with central frequency 0 ω , and the ki- netic energy ( 0 ε ) and emission angle m θ of the scattered electrons such that ( ) ( ) [4], where ( ) m f θ is a function of m θ .In the neu- tron star merger event GW170817 it was recently discovered that the γ-ray plus radio wave afterglow signals and the dynamical ejecta are emitted in the form of a choked jet cocoon [7].Researchers drew this conclusion after studying the flux densities, i.e. the energy versus time profiles or power, of the emitted radio waves [7].On a smaller scale, vibrational spectra enabled the investigation of the absorption of IR light in the formation of urethane and polyurethane.The vibrational spectra unveiled that the addition of a vibrational excitation to thermal energy accelerated the reaction rate of formation [2].From the information that the IR light was emitted with an energy per pulse of 3 μJ, repetition rate of 2 kHz, and wavelength of 2857 nm, we estimated that the average power of the laser was 6 mW P = .At this value of P, approximately 1190 reactions producing urethane and 2976 reactions producing polyurethane were activated within one period 9.5 fs τ = of the illuminating IR light.Finally, at the nanoscale level, a linear relationship was found between the rotational frequency of an optically trapped dielectric particle and the power of the trapping laser [9].According to the authors of Ref. [9], however, the dominating torque transfer mechanism in this experiment is still unknown.
To understand the role of the light's average power P in generating mechanical motion in light-matter interaction involving atoms in crystalline bonds, we consider the wave nature of light.Indeed, for light as a wave, the power over area (i.e. the intensity 0 I ) is the Poynting vector, and the amount of energy conserved in the interaction of light with matter is Pτ , where τ is the period of the of the light wave.These concepts and their consequences in various natural phenomena are discussed in Ref. [10].In this article we specifically investigate the effects of the average power P on the transmission Fourier transform IR (FTIR) [11] spectra of thin crystalline cubic Yb 2 O 3 and rhombohedral LaAlO 3 films deposited on silicon (Si).We first present the method used to grow the thin films via atomic layer deposition (ALD) [12] [13], and report the properties of the thin films.We then describe how we obtained the transmission FTIR spectra [11]  mW ± 4.9 μW).In the Result Section we show that different values of the average power P displace the location (in wavenumber, or frequency in units of THz) of the minima of the absorption bands in the FTIR spectra of the thin films.We ascribe this phenomenon to the fact that the average power P affects the vibrational energy of the crystalline structure of the thin films, vib E , which, in turn, deter- mines the location of the minima of the absorption bands in the FTIR spectra.In the Discussion Section we link the average power P to the location of the minima of the absorption bands observing that the moment of inertia I and the vibrational frequency ω of the vibrating bond depend on vib E .In turn, vib E is correlated to Pτ , the amount of energy conserved in the interaction of light with matter.Since vib E represents the vibrational/rotational energy of the whole crystal structure involved in the interaction with the IR light, this energy depends on the number η of the interested bonds.Therefore, using a model based on the law of conservation of energy [10], and knowing P, τ , vib E , ω and I, we estimate the number η of the bonds involved in the interaction between the IR light and the thin crystalline films.To highlight the significance of our results we report the outcome of our literature search showing that other researchers acknowledged the existence of displacements in the minima of the absorption bands in FTIR spectra [14].These authors, however, were not able to justify such displacements.We also found that the existence of a relationship among P, vib E , ω , and I is acknowledged, e.g., in the motion of a dielectric particle optically trapped by a laser [9].This finding not only supports our approach, but also underlines its innovative character in the field of FTIR spectroscopy.In the Conclusions Section we outline the significance of our study.
First we highlight that η , the number of bonds involved in the interaction be- tween the IR light and the thin crystalline films, might represent a "classical" way (as opposed to the usual "quantum" way) to count the number of the quasi-particles usually called phonons, through the link among P, τ , vib E , ω , I, and η .As far as the practical application of our findings are concerned, our method suggests that, by increasing the power of the IR light, it should be possible to enhance the sensitivity of the FTIR spectra of thin crystalline films in the far IR region.Achieving this goal is possible due to the direct proportionality between moment of inertia and average power, i.e.I P ∝ , as we have found in our study.
Applying our strategy, however, requires keeping in mind that such increase in sensitivity is accompanied by a slight shift in location of the minima of the absorption bands.

Experimental Methods
We analyzed two different types of thin oxide films using transmission FTIR spectroscopy at four average power levels of the IR light using two different spectrometers.In one of the two spectrometers the original power of the source was lowered using a polarizer and a copper mesh.The details of the materials used and measurements performed are as follows.

Thin Films
Uniform thin cubic Yb 2 O 3 (500 nm, thick) and rhombohedral LaAlO 3 films (550 nm thick) on Si were prepared via ALD [12] [13] with growth parameters and precursors described in Ref. [15].The films exhibit remarkable stability [13] as they retain their characteristics over more than the year during which we collected and analyzed their transmission FTIR spectra.We assessed the crystallinity of the thin films using far-IR FTIR spectroscopy, as shown in Appendix 1.

FTIR Spectrometers
We investigated the effects of different levels of the IR light's average power P on transmission FTIR spectra using a N 2 -purged Bruker Vertex 70 spectrometer with a Q301 globar source emitting at On the Bruker Vertex 70 spectrometer we achieved 2 16.4 mW cm P = and 2 7.9 mW cm P = by inserting a copper mesh or polarizer (PIKE Technologies 090-1000 ZnSe polarizer), respectively, in the beam path on the sample holder in front of the thin film.For the measurements with the polarizer we selected p-polarization (or TM-polarization).We investigated the features of the thin cubic Yb 2 O 3 and rhombohedral LaAlO 3 films in the middle IR range (MIR, 350 -7,500 cm −1 wavenumber, 28,600 nm -1300 nm wavelength or 95.33 fs -4.33 fs period).In both spectrometers and in all measurements we selected a resolution of 4 cm −1 and collected the spectra with 100 scans.In both spectrometers, we positioned the thin film on a vertical transmission sample holder perpendicular to the IR beam.We explored only normal incidence transmission spectra because one of the two spectrometers is equipped with neither a reflection nor a rotating transmission accessory.The lack of a reflection accessory on one of the spectrometers prevented us from studying films on metal substrates, which do not enable transmission studies.We measured the spectra with the Bruker Vertex 70 spectrometer two days before measuring them with the Nicolet Magna 6700 spectrometer to allow time for the trip from Harrisonburg (VA) to Raleigh (NC) where the two spectrometers are located.We kept the samples sealed and protected during the transfer from one location to the other, and between all sets of measurements.The collected spectra exhibit excellent reproducibility demonstrating the high stability of the thin crystalline films we used in this research [13].We discuss the effects of the choice of the Si substrate in Appendix 2 and Appendix 3.

Power Measurements
We measured the power of the IR light before all measurements using a power-meter sensor Coherent PowerMax RS PS19, sensitive to wavelength and average power ranges of 300 -11,000 nm and 100 μW to 1 W, respectively.The absorption bands of interest in the examined thin films appear in the 470 -950 cm −1 wavenumber range (or 10,526 -21,276 nm wavelength range).For the ab-World Journal of Condensed Matter Physics sorption bands of the cubic Yb 2 O 3 films, which appear in the 840 -950 cm −1 wavenumber range (10,520 -11,905 nm wavelength range), the IR light's power estimation is within the range of sensitivity of the power sensor.On the other hand, the absorption bands of the rhombohedral LaAlO 3 films appear in the 470 -560 cm −1 wavenumber range (21,276 -17,857 nm wavelength range), which is outside the operating range of the power sensor.Therefore, in the case of the rhombohedral LaAlO 3 films the estimated power is affected by a systematic error.
This systematic error, however, does not prevent us from evaluating the shifts of the minima in the absorption bands observed with either the Bruker Vertex 70 or the Nicolet Magna 6700 spectrometers.

Nomenclature
To simplify reading the Results and Discussion Sections, here we list the meaning of the most significant variables presented: P average power of the IR light, τ period of the IR light, vib E vibrational energy of the crystalline structure of the thin films, ω the vibrational frequency of the vibrating bond, I moment of in- ertia of the vibrating bond, η number of bonds involved in the interaction be- tween the IR light and the thin crystalline films, at m mass of the atoms in- volved in each bond, and l lattice parameter of the film's crystalline structure.2 and in agreement with the trends reported in Figure 1 and Table 1.We thus infer that the location of the minima of the absorption bands is indeed related to the average power P of the IR light.To carefully determine the location of the minima of the absorption bands, in Figure ( )

Results
where off T is the starting transmission level, osc T is the amplitude of the hy- perbolic secant well, c w is the location of the minimum, and c W is the width of the hyperbolic secant well.We selected the hyperbolic secant function to fit the spectra because such a function overlaps the experimental data points and facilitates the process of locating the minimum of the well.The parameter c w , i.e. the location of the minimum of the hyperbolic secant well, is identified as ω and reported in Table 1 and Table 2 for the minima of the significant absorption World Journal of Condensed Matter Physics Table 1.For both the cubic Yb 2 O 3 and the rhombohedral LaAlO 3 lattices, we report the mass at m of the atoms involved in the relevant bonds [16] [17], the lattice parameter l [18] [19], and the vibrational frequency ω at which we find the minima of the absorption bands in Fourier transform infrared (FTIR) spectra obtained at average power P of 12.1 mW and 25 mW.For the rhombohedral LaAlO 3 films we choose an average value of the lattice parameter l to simplify the calculations.The average vibrational frequencies ω , or the parameter c w in Equation ( 1), are determined from the minima in the absorption bands of the FTIR spectra in Figure 1 2. For both the cubic Yb 2 O 3 and the rhombohedral LaAlO 3 lattices, we report the vibrational frequency ω at which we find the minima of the absorption bands in Fourier transform infrared (FTIR) spectra obtained at an average power P of 25 mW, 16.4 mW and 7.9 mW shown in Figure 2 for the Yb 2 O 3 films and in Figure 3 for the LaAlO 3 films.For simplicity, for the Yb 2 O 3 films we display the values for only two out of the three relevant absorption bands.Also here, ω is the parameter c w in Equation (1).bands identified in our thin films.An attentive examination of these tables suggests that the location of the minima of the absorption bands do not exhibit a monotonic trend with the magnitude of the average power P.  In summary, our experimental FTIR spectra highlight two major effects induced by varying the magnitude of the average power P of the IR light: 1) the displacement of the minima of the absorption bands of the crystalline thin films and 2) the lack of a monotonic trend in the extent and direction of the displacements.

Discussion
We argue that the origin of the displacements and of their lack of a monotonic trend in extent and direction is linked to the magnitude of Pτ , where P is the average power and τ the period of the IR light.We start our argument by re- calling that the energy Pτ is the amount of energy conserved in the interaction between the IR light and the thin crystalline films on Si [10].The values of Pτ are labelled in units of keV for the relevant absorption bands in all panels of Figure 1.These values are larger for the absorption bands in the spectra col-lected with 25 mW P = , i.e. for the larger values of P we used, and for the LaAlO 3 films, i.e. for the larger values of the period τ or lower values of the wavenumber at which we detected in the absorption bands.We thus hypothesize that the energy Pτ transfers vibrational energy vib E to the bonds of the thin crystalline films illuminated by the IR light.We correlate Pτ and vib E through the law of conservation of energy as follows: In Equation ( 2), is the moment of inertia of Yb-O [16], La-Al or Al-O bonds [17].The mass of the atoms involved in each bond is at m , and l is the lattice parameter [18] [19].The values of at m and l are displayed in Table 1.
For the rhombohedral LaAlO 3 structure, which is non-cubic, we choose an average value for l, reported in Table 1.The values of the vibrational frequency ω of the bond derived as c w , i.e. the location of the minima of the absorption bands in the FTIR spectra in Figure 1, Figure 2, and Figure 3, appear in Table 1 and Table 2.We claim that Equation (2) explains the change with P of the values of ω , and believe that the complex interaction among the vibrations or rota- tions of the bonds illuminated by the IR light justifies the observation that these changes are not necessarily monotonic.This issue however requires further investigations.
Finally, in Equation ( 2), the number η represents the number of bonds in- volved in a vibration.The need to introduce the number η can be explained as follows.During the absorption of the IR light, when the average power P changes from 7.9 mW, to 12.1 mW, to 16.4 mW or to 25 mW or vice versa, the moment of inertia I does not change.Simultaneously, the magnitude of the vibrational frequency ω of each bond is constrained by the corresponding experimentally measured values.Therefore, a degree of freedom is required to match the energy absorbed from the IR light by the crystalline thin film, to the magnitude of the energy transferred from the IR light.The number η is such a degree of free- dom.Equation (2) suggests that larger values of P and τ increase the energy transferred from the IR light to the thin films and, by doing so, involve a larger number of bonds η .This trend is confirmed by the estimated values of η for both the cubic Yb 2 O 3 and rhombohedral LaAlO 3 films on Si reported in Table 3 and Table 4.
We can extract further consequences from Equation (2).One is that the direct proportionality between the moment of inertia I of each bond and the average power P of the IR light, i.e.I P ∝ , suggests that FTIR spectrometers with larger values of P than the current ones might generate spectra highly sensitive to the features of crystalline films with heavy atoms (low ω ) in the far IR region (smaller τ ).The second consequence is that Equation (2) might foster the un- derstanding of phonon's behavior in crystals.Indeed, the direct proportionality between the number of bonds and the average power, i.e.  of the crystal lattices of cubic Yb 2 O 3 and rhombohedral LaAlO 3 at the minima of the absorption bands at vibrational frequencies ω , and the number of bonds η involved in the vibrations at , 16.4 mW and 7.9 mW of the illuminating IR light over a surface area of ~1 cm 2 .The values of ω , or the parameter c w in Equation ( 1), are extracted from Figure 2 for the Yb 2 O 3 films and from Figure 3 for the LaAlO 3 films.For simplicity for the Yb 2 O 3 films we have chosen only two out of the three relevant absorption bands.the number of phonons involved in the interaction between IR light and a thin crystalline film is constrained by the magnitude of the average power P of the IR light, not just by the scattering events occurring between phonons and imperfec-World Journal of Condensed Matter Physics tions in crystalline thin films.Experimental results of other authors help us to assess the validity of Equation ( 2).We will present two examples: one from Faulkner et al. [20], and another by Reimann et al. [9].Faulkner et al. [20] investigated the effects of a laser beam on the vib E of He nano-droplets at 9 K.These authors used an IR laser with an average power P of ~80 mW, and observed a resonance at 2000 cm −1 (6 × 10 13 Hz or 16.7 fs) with a ro-vibrational transition in a carbonyl sulphide (OCS) molecule accommodated in a He nano-droplet.Furthermore, the transfer of energy from the IR laser to the OCS molecule was observed to lead to the evaporation of ~400 He atoms in the nano-droplet.Using Equation ( 2) we estimate the energy transferred from the IR laser to the OCS molecule to be The OCS molecule uses this energy to initiate a ro-vibrational motion which, in turn, transfers an energy of ~3.3 × 10 −18 J (or 20.8 eV) to each of the 400 He atoms in the nano-droplet for a 2000 cm −1 excited state.The 20.8 eV for each He atom is about 25 × 10 3 times larger than the 0.83 meV energy per atom estimated to enable the evaporation of the He atoms (P.L. Raston, James Madison University, oral communication, 2018).We justify this four orders of magnitude discrepancy between the evaporation energies per atom, 20.8 eV and 0.83 meV, by claiming that 20.8 eV for each He atom are needed to overcome the strong coupling among the He atoms in superfluid He nanoparticles at low temperature (9 K).On the other hand, the evaporation energy per He atom of 0.83 meV, estimated by the authors of Ref. [20], seems very small.Indeed, for comparison, we recall that an energy of ~50 meV transmitted by visible light with P W µ to electrons in semiconductors is sufficient to cause each one of them to jump from shallow donor levels to the conduction band [21].This amount of energy is small but consistent with the fact that the mass of one electron is about four orders of magnitude smaller than the mass of a He atom.
Reimann et al. [9] investigated the relationship between light's power P and the rotational frequency ω of an optically trapped silica nanoparticle [9].In their ex- periment, a laser beam illuminates a nanoparticle, transfers energy to it, and causes the nanoparticle to rotate.From Equation (2), we estimate that, with a laser beam with wavelength 1565 nm ( 5.2 fs τ = ) and average power P of 200 mW [9], the energy transferred to the nanoparticle is  From this value of I, and knowing that the spherical nanoparticle's radius is 50 nm [9], we infer that the mass of one silica nanoparticle is 0.968 × 10 −18 kg, which implies a density of 1.85 × 10 3 kg/m 3 .Such a density is only 3.7 times the published value of 0.49 × 10 3 kg/m 3 [22].This finding suggests that 1.04 fJ Pτ = is a good estimate of the energy transferred from the IR light to the nanoparticle.This finding also enables us to exploit Equation ( 2) to obtain the rotational frequency ω versus average power P in the case of 1 η = at a pressure of ~1.1 × 10 −5 mbar, and  shows that the rotational frequency ω increases almost linearly with the average power P between the two bars with a "slope" of 4.48 × 10 9 J −1 .This finding is in good agreement with the "slope" of 0.3 × 10 9 J −1 at a pressure of 1 × 10 −4 mbar found in Ref. [9].This result reveals the relationship between P and ω of an optically trapped silica nanoparticle [9], and pictures the torque transfer mechanism involved in this experiment as an effect of the law of conservation of energy.

Conclusions
Our work proposes a case in which the magnitude of the average power P of an electromagnetic (EM) wave, together with its period τ , may be correlated with the magnitude of the mechanical motions that either generate the EM waves or are generated by them.Using Fourier transform infrared (IR) spectra of thin films we have shown that the average power P of the IR light affects the mechanical motion, in the form of rotation or vibration, of the bonds involved.We explain the phenomenon by linking, through the law of conservation of energy, the value of the energy Pτ , where τ is the period of the IR light, to the vibra- tional frequency ω , the number η , and the moment of inertia I of the rotating or vibrating bonds affected by the illumination under the IR light.From a practical point of view, this finding highlights the possibility of manufacturing IR spectrometers adopting sources of IR light with larger average power P than those currently used.Such a strategy would enable maximizing the sensitivity of the Fourier transform IR spectra of crystalline films with heavy atoms in the far IR region.The users of spectrometers with higher power IR light sources should however be aware of the shifts in location of the minima of the absorption bands arising with changing P. From a more speculative point of view, our finding highlights that, as the magnitude of Pτ increases, so does the number η of the crystal bonds involved in rotational or vibrational motions.The number η represents a "classical" way (as opposed to the "quantum" way) to count the number of the quasi-particles usually called phonons through the direct relationship between the energy Pτ with the vibrational frequency ω and the moment of inertia I of the rotating or vibrating bonds affected by the illumination under the IR light.Thus, since the number η can be viewed as the number of phonons in a crystal lattice, we conclude that the number η of phonons is constrained by the average power P and the period τ of the IR light impinging on a thin crystalline film, not only by phonon scattering phenomena.Finally, in the context of the current scientific literature our findings are relevant because they either justify results otherwise not explained, or agree with other reports.For instance, our results justify the displacement in the minima of the absorption bands in Fourier transform IR spectra detected but not explained by other authors [14].In addition, our model based on the law of conservation of energy agrees qualitatively and/or quantitatively with results presented in the current literature regarding Thomson scattering [3] [4], neutron star merger events [7], vibrational spectroscopy [2] [20] and optical manipulation of nanoparticles [9].World Journal of Condensed Matter Physics

Figure 1
Figure 1 displays the transmission FTIR spectra of the cubic Yb 2 O 3 films on Si and rhombohedral LaAlO 3 films on Si collected with IR light's average power 12.1 mW P = and 25 mW.First, we observe that the transmission level is about 50 % lower for the spectra acquired with 12.1 mW P = (panels (a) and (c)).Additionally, the absorption bands for both the Yb 2 O 3 and LaAlO 3 films on Si are deeper and better defined when collected with IR light at an average power 25 mW P = (panels (b) and (d)).Furthermore, a careful inspection of Figure 1 indicates that the location of the minima of the absorption bands are different in the spectra obtained with the Bruker Vertex 70 ( 25 mW P = ) and the Nicolet Magna 6700 ( 12.1 mW P =) spectrometers.

Figure 2 and
Figure 2 and Figure 3 compare the effects of different magnitudes of the average power P of the IR light on the FTIR spectra of the cubic Yb 2 O 3 and the rhombohedral LaAlO 3 films on Si, respectively.Differently than in Figure 1, to obtain Figure 2 and Figure 3 we changed the average power P of the IR light only on the Bruker Vertex 70 spectrometer by either inserting or omitting a copper mesh or a polarizer in the IR beam path.This method enabled us to achieve 7.9 mW P = , 16.4 mW P = and 25 mW.First, we note that Figure 2(a), for the cubic Yb 2 O 3 films, and Figure 3(a), for the rhombohedral LaAlO 3 films, show that the transmission levels vary only within 15% for three different average power magnitudes, while the depth of the absorption bands do not exhibit significant variations.We can thus speculate that the large variations in the transmission levels and the depth of the absorption bands in Figure 1 can be ascribed

Figure 1 .
Figure 1.Transmission Fourier transform infrared (FTIR) spectra of cubic Yb 2 O 3 films on Si acquired with infrared (IR) light's power of (a) 12.1 mW and (b) 25 mW.FTIR spectra of rhombohedral LaAlO 3 films on Si collected with IR light's power of (c) 12.1 mW and (d) 25 mW.The values of Pτ are labelled in units of keV for the relevant absorption bands in all panels.These values are approximated for the case of the LaAlO 3 films on Si in panels (c) and (d) since the spectral features appear in a range located at the edge of the sensitivity of the power sensor used in this research.

Figure 2 .
Figure 2. Transmission Fourier transform infrared (FTIR) spectra of cubic Yb 2 O 3 films on Si acquired with infrared (IR) light's power of 7.9 mW, 16.4 mW and 25 mW.Panel (a) shows the original transmission FTIR spectra in the wavenumber range where the relevant absorption bands appear.Panels (b) and (c) zoom into the location where the minima in the absorption bands of the FTIR spectra appear after offsetting the spectra so that they overlap.In panels (b) and (c) the experimental data are fitted by the hyperbolic secant function in Equation (1), which facilitates the precise determination of the location of the minima of the absorption bands, i.e. the parameter c w .

Figure 3 .Figure 3
Figure 3. Transmission Fourier transform infrared (FTIR) spectra of rhombohedral LaAlO 3 films on Si acquired with infrared (IR) light's power of 7.9 mW, 16.4 mW and 25 mW.Panel (a) shows the original transmission FTIR spectra in the wavenumber range where the relevant absorption bands appear.Panels (b) and (c) zoom into the location where the minima in the absorption bands of the FTIR spectra appear after offsetting the spectra so that they overlap.In panels (b) and (c) the experimental data are fitted by the hyperbolic secant function in Equation (1), which facilitates the precise determination of the location of the minima of the absorption bands, i.e. the parameter c w .

Figure 4
Figure 4 reports the FTIR spectra of the cubic Yb 2 O 3 acquired on different days to assess the reproducibility of the location of the minima of the absorption bands.We observe that the location of the absorption bands at 843 cm −1 in Figure 4(a) and Figure 4(b), and 927 cm −1 in Figure 4(c) and Figure 4(d), are consistent in days 1 and 2. This finding enables us to conclude that, at a fixed magnitude of the average power P, the location of the absorption bands does not change, and helps us constraining to P the responsibility of the changes in the

Figure 4 .
Figure 4. Fourier transform infrared (FTIR) spectra of cubic Yb 2 O 3 films on Si acquired with infrared (IR) light's power of 25 mW (panels (a) and (c)) and 7.9 mW (panels (b) and (d)) in two different days (day 1 and day 2) to assess the reproducibility of the location of the minima of the absorption bands.In Appendix 6 we show the same spectra for the rhombohedral LaAlO 3 films on Si.

P
η ∝ , suggests that the number of phonons increases with the average power of the IR light.Thus, G.Scarel, E. C. Stevens DOI: 10.4236/wjcmp.2019.9100111 World Journal of Condensed Matter Physics

33 2 1 .
21 10 kg m I − =× ⋅ .The result is reported in Figure 5, which World Journal of Condensed Matter Physics

Figure 5 .
Figure 5. Rotational frequency ω of a nanoparticle versus average power P of the IR light obtained using Equation (2) with average power 200 mW at a wavelength of 1565 nm ( 5.2 fs τ = ) from Ref. [9], 1.04 fJ Pτ = ,

Table 3 .
Vibrational energy vib E of the crystal lattices of cubic Yb 2 O 3 and rhombohedral LaAlO 3 at the minima of the absorption bands at vibrational frequencies ω , and the number of bonds η involved in the vibrations at 25 mW P = and 12.1 mW of the illuminating IR light over a surface area of ~1 cm 2 .The values of ω are extracted from Figure 1 and are the parameter c w in Equation (1).

Table 4 .
Vibrational energy vib E