X-ray absorption near-edge, terahertz and Raman spectroscopies evidence growth-orientation dependent cation order, phase transitions and spin–phonon coupling in half-metallic Ca2FeMoO6 thin films

The disorder due to anti-site cation distribution is intrinsic to the double perovskites wherein the crystal orientations of the substrate template are predicted to offer different degrees of cation order in thin film form. To demonstrate this effect, epitaxial thin films of half-metallic double perovskite Ca2FeMoO6 (CFMO) were prepared on (100) and (111) oriented LaAlO3 substrates in vacuum and nitrogen atmospheres. The findings using X-ray absorption near-edge structure, Terahertz (THz) and Raman spectroscopies, in combination with magnetization show that (111) epitaxial template effectively restricts the Fe–Mo anti-site cation disorder. A resultantly enhanced cation order in (111) films induces dramatic transformations in its properties as follows: (i) significantly enhanced ferromagnetic exchange interactions and saturation magnetization, (ii) a significant increase in the Curie temperatures, (iii) a metallic behavior down to much lower temperature (∼75 K) compared to that down to 200 K for (100) film, (iv) an enhanced spin–phonon coupling. The complex THz optical conductivity spectra evaluated in the framework of Drude and Drude–Smith phenomenological models and the temperature-dependent Raman data fitted to the Balkanski model corroborate well to indicate an enhanced cation order in (111) films. While this study establishes a dominant role of crystallographic orientation in the much-desired control of cation order in double perovskites, a demonstration of the same in room temperature half-metallic CFMO system could reinforce its technological utility both as active and passive components in emergent spintronic functionalities.


Introduction
Half-metallic oxides, having an unbalanced spin population at the Fermi level, facilitate the spin-polarized charge transport, making them promising materials for advanced spintronics.In this regard, half-metallic A 2 BB ′ O 6 (A = Ca, Sr, and Ba, B = Fe, B ′ = Mo) double perovskites have gained tremendous attention owing to the relevance of high Curie temperature (T C ), 100% spin polarization at room temperature (RT) and the spin control of transport properties which help in realizing spintronic applications at RT or above [1,2].The impetus in research on these compounds was imparted by the discovery of low-field magnetoresistance at RT in Sr 2 FeMoO 6 (SFMO) [3].In A 2 FeMoO 6 (AFMO) compounds, a high Curie temperature of 360 K, 415 K, and 380 K for A = Ca, Sr, and Ba, respectively, makes them more promising vis-à-vis mixed-valent manganites with both lower T C and smaller spin polarization [4,5].Despite such promising attributes of all

Experimental
We synthesized two sets of CFMO thin films (∼65 nm) on LaAlO 3 (LAO) single crystal substrate with two different orientations, i.e. (100) and (111), using the PLD technique.For each set of films, one film was deposited in vacuum and the other in nitrogen atmosphere.For the sake of clarity, the indexing is done as CFMO-Vac (100), CFMO-N 2 (100) for the CFMO films deposited on LAO (100), and CFMO-Vac (111), CFMO-N 2 (111) for the other set deposited on LAO (111).The bulk pellet of CFMO, used as the target material in the PLD chamber, was synthesized via conventional solid-state reaction method.For that purpose, high-purity (>99.99%)powders of CaCO 3 , Fe 2 O 3, and MoO 3 (Sigma Aldrich), in proper stoichiometric amounts, were ground and calcined at 900 • C for 12 h.The resulting mixture was reground and pressed into pellets (15 mm) using a hydraulic press, and then sintering was carried out at 1150 • C for 12 h in Ar + 5% H 2 atmosphere.This pellet was used for the deposition in the PLD chamber.A KrF excimer laser (λ = 248 nm, Coherent Compex Pro) with laser energy 350 mJ operating at a frequency of 5 Hz was used to ablate the target material in the PLD chamber (Excel Instruments).The substrate temperature was maintained at 770 • C, and the target to substrate distance was 4 cm.For one set, vacuum (∼10 −4 Pa) was maintained during deposition, while 0.5 Pa nitrogen partial pressure was maintained for the other set.After deposition, the samples were cooled to RT in the same atmosphere at 10 • C min −1 .The dimension of prepared CFMO films is 10 mm * 6 mm with 65 nm thickness.
The phase-purity and growth orientation of the synthesized thin films have been investigated by X-ray diffraction (XRD) measurements in Bruker D8 Diffractometer in Bragg-Brantano geometry using Cu k α radiations.The Fe K-edge x-ray absorption near edge structure (XANES) spectra were recorded at BL-9, Scanning EXAFS Beamline of Indus-2 at RRCAT, Indore.The measurements were carried out in fluorescence mode using an energy-dispersive detector.The beamline consists of an Rh/Pt coated meridional cylindrical mirror for collimation and a Si (111) double crystal monochromator (DCM) to select the excitation energy of Fe (7112 eV) K-edge.The second crystal of the DCM is a sagittal cylinder that provides a beam focused in the horizontal direction.The thickness of the films has been decided by x-ray reflectivity (XRR) measurements.The electrical properties of the thin films have been studied by performing dc electrical resistivity measurements in a temperature range of 300-10 K using the four-point probe method.For this purpose, Keithley (2612 A) made source and measurement meters were used.To understand the variation in charge carrier dynamics with anti-site disorder, Terahertz time-domain spectroscopic (THz-TDS) measurement has been performed in a temperature range from 300 to 5 K and frequency range from 0.2 to 1.2 THz.For this purpose, an LT-GaAs photoconductive antenna-based THz spectrometer has been used.A careful substrate signal background subtraction has been employed to accurately determine the optical constants.Vibrational characteristics of the thin films have been understood by Raman spectroscopy measurements using a Horiba LabRAM-made HR-Evolution Raman microscope consisting of a charge coupled device detector.Micro-Raman signals were recorded in back-scattering mode using a HeNe laser with excitation light 632.8 nm and a laser power of 1 mW.Temperature-dependent Raman measurements were carried out by placing the sample on a commercial Linkam stage and varying the temperature using temperature controllers and the LN 2 module.The Magnetization measurements for all the samples were performed using SQUID-VSM (Quantum Design) magnetometer in the temperature range of 1.8-300 K and in a magnetic field ranging from −5 T to 5 T.

Structural properties
Figures 2(a) and 3(a) show the full-scale XRD patterns of the CFMO thin films grown on LAO (100) and LAO (111) substrates, respectively, suggesting that the films are grown single-phase, impurity-free, and highly oriented toward the crystallographic orientation of the substrates.Figures 2(b) and 3(b) show the magnified view of the second-order Bragg's reflection of the CFMO films oriented along (100) and (111) directions, respectively.The c-axis lattice parameter of (100) oriented CFMO films derived from XRD data is ∼3.92 Å, while it is ∼3.81 Å for (111) oriented films.The CFMO films oriented along the (111) axis have narrower peaks, indicating more crystalline structure as compared to (100) films.LAO (100) [3.79 Å] and LAO (111) [3.82 Å] impart lattice mismatch of −3.6% and −0.49% to CFMO [3.86 Å] films, respectively.Further, this lattice mismatch and the FWHM of the XRD peaks increase for nitrogen-grown films.The thickness of the films has been estimated by the number of laser shots required for the deposition.Earlier, XRR measurements were carried out for an SFMO film grown in exactly the same deposition conditions and laser parameters, in the same deposition chamber.The exact growth rate has been obtained from XRR and hence thickness of CFMO films is estimated to be ∼65 nm.
Depending upon the preparation conditions, the Fe and Mo ions in the A 2 FeMoO 6 family can arrange in a random or ordered fashion at their respective sites [4][5][6][7].Previous x-ray absorption spectroscopy data of polycrystalline SFMO at the Fe L-edge conclude that Fe is either in +3 oxidation state or intermediate valence Fe 2+ /Fe 3+ [14].Furthermore, Mössbauer data were also interpreted for either Fe 3+ or Fe 2+ /Fe 3+ valence states in these compounds [15].Many efforts are made to resolve the oxidation state of Fe ions in these compounds, but this is not understood clearly.Therefore, to investigate the valence state and cation ordering in the present films, we carried out XANES spectroscopy on the set of CFMO films grown in vacuum.Figure 4(a) shows the Fe K-edge XANES spectra of the CFMO films and standard references of Fe 2+ and Fe 3+ .To quantify the amount of Fe 2+ and Fe 3+ , Fe XANES data were calculated using linear combination fitting (LCF) with Athena software [16] within an energy range of −20 eV below to +20 eV above the edge (figure 4).The LCF method is used to quantify the relative percentage of mixed oxidation state present in a material.LCF of CFMO-Vac (100) (figure 4(b)) and CFMO-Vac (111) (figure 4(c) were done using a combination of Fe 2+ and Fe 3+ standard spectra and goodness of fit parameters (reduced χ 2 ) along with the percent that contributes to each fit.The accuracy of this method depends on how well the    spectra of the chosen reference compounds represent the components in the samples [16].The relative percentage of Fe 2+ /Fe 3+ extracted from LCF fitting is presented in table 1.The obtained reduced χ 2 for best-fit χ 2 = 0.011 for all the samples.It is clear from the table that for both the CFMO films, Fe ions are present in divalent and trivalent states with the majority being in the trivalent state.However, it should be noted that the concentration of Fe 2+ ions is higher in (111) oriented films than in (100) oriented films.

Magnetic properties
The effect of substrate orientation and background gas atmosphere on the magnetic properties of CFMO thin films has been investigated by magnetic field and temperature-dependent magnetization measurements.The diamagnetic contribution from the LAO substrate has been eliminated from the data to present the actual sample contribution.The temperature-dependent magnetizations of the vacuum-grown CFMO thin films of different orientations are shown in figures 5(a) and (b).Both films exhibit qualitatively similar magnetization curves, and the Curie temperature (T C ) is assigned as the onset temperature of the rapid increase in magnetization.The T C for (100) and (111) oriented CFMO films is found to be 320 K and 340 K, respectively.The magnetic hystereses have been recorded at 300 K, 150 K, 10 K, and 2 K for all the CFMO films.For a comparison, figure 6(a) shows the magnetic hysteresis loops for all the films at 150 K.It can be noted here that CFMO-Vac (111) film possesses the highest saturation magnetization of 3.2 µ B /f.u., while the CFMO-N 2 (100) film shows the least saturation magnetization of 2.4 µ B /f.u.For the brevity of the presentation, the hysteresis plots recorded at different constant temperatures only for CFMO-Vac (111) film are shown in figure 6(b).It can be seen from the figure that the maximum saturation magnetization of 3.5 µ B /f.u. is achieved at 2 K, which is quite close to the theoretically predicted value of 4 µ B /f.u. for a perfectly ordered system.As expected, the saturation magnetization decreases with an increase in temperature.
It is imperative from the data that the saturation magnetization of CFMO films is quite lower than the theoretically predicted value of 4 µ B /f.u., which could be attributed to the finite amount of anti-site disorder in CFMO thin films.As described earlier in a perfectly ordered CFMO system, the alternate arrangement of Fe and Mo gives rise to ferrimagnetic interactions with a predominant contribution from Fe ions with a spin-up state.In the present case, a higher degree of anti-site disorder in (100) oriented CFMO films affects the Fe-O-Mo alternate arrangement and causes paramagnetic and antiferromagnetic contributions, which finally decreases the magnetization and Curie temperature compared to those of (111) oriented films.The strength of anti-site disorder present in these A 2 FeMoO 6 type samples can be quantified as [17]: where χ is the concentration of anti-site disorder and M S is the saturation magnetization.The anti-site disorder is found to be 17.2% and 22.8% for the CFMO films grown on LAO (111) and LAO (100) substrates, respectively, confirming higher cation ordering in CFMO (111) films.

Electrical properties
The electrical properties of the Fe-Mo based double perovskites, whether in bulk or thin film forms, are highly dependent on the synthesis conditions [5,12].In AFMO films, a variation in deposition temperature or background gas atmosphere brings only a moderate change in the electronic transport [2,18].CFMO may show metallic, semiconducting, or insulating behavior based on the degree of anti-site disorder [12].However, the B-site ordered bulk CFMO exhibits metallicity below the Curie temperature of 350 K. Figure 7 shows the dc resistivity of all the CFMO films.The (100) oriented CFMO films grown in vacuum and nitrogen atmospheres display semiconducting behavior below 210 K and 225 K, respectively.In contrast, the CFMO (111) films grown in vacuum and nitrogen exhibit a semiconducting to metallic transition at 45 K and 65 K, respectively.The appearance of the majority of the metallic state in (111) oriented CFMO films is attributed to a large enhancement in the B-site cation ordering of the system by changing the underneath substrate orientation to (111) direction.This proves to be an alternate method to improve the cation ordering in CFMO films by the PLD method at optimum deposition temperature and pressure, without the requirement of the growth parameters which are difficult to achieve.
In the present half-metallic CFMO system, two spin channels act parallel to each other [19,20].Here, the spin-up channel with a band-gap at the Fermi level is semiconducting; while the spin-down channel without any gap has a metallic nature.The half-metallicity is preserved in the ordered CFMO; however, the introduction of anti-site disorder reduces the half-metallic character and a large amount of anti-site disorder gives rise to a semiconducting state.The band structure calculations show that the majority spin band mainly separates the Fe e g states from Mo t 2g states finally creating a gap, while the minority band consists of strongly hybridized Fe t 2g and Mo t 2g states [3,[21][22][23], giving rise to metallicity, in an overall half-metallic system.In general, the Fe 3+ -O-Mo 5+ arrangement is predominantly present in CFMO facilitating the spin-up charge conduction with a semiconducting nature as well as the spin-down charge conduction with a metallic nature as schematically presented in figure 8.However, the conduction channel through Fe 2+ -O-Mo 6+ arrangement can support only spin-down metallic type conduction.
In the metallic state, the resistivity as a function of temperature can be described as [24,25]: where ρ 0 is residual resistivity which is a temperature-independent term, existing due to lattice imperfections, impurities, grain boundary contributions, etc, ρ n governs the strength of electron-electron interactions, and n is an adjustable parameter.According to the classical Fermi liquid model, the value of exponent n remains 2, which explains the quadratic dependence of resistivity over temperature [21].However, in case of strong electronic correlation, two other values of n are often reported i.e., 1.6 and 1.3 which define the non-Fermi liquid (NFL) state.This model describes the electrical conduction mechanism in the spin-down metallic state only.On the other hand, the resistivity of the spin-up semiconducting band can be described as [19]: where ρ 0 is temperature-independent term, ρ SC d is a constant governing electrical charge density and E g is the band-gap of the material in spin-up channel.In this context, the total resistivity for CFMO films, which takes into account the resistivity from spin-up semiconducting band (ρ SC ), spin-down metallic band (ρ m ) and the temperature-independent term (ρ 0 ), can be described by parallel spin channel given as [19,26]: For the present data analysis, this parallel spin-channel model is applied to CFMO thin films where the anti-site disorder, oxygen vacancies and strain play a dominating role in deciding the transport properties and temperature dependent band-gap.The equation ( 4) was fitted to the resistivity data of all the CFMO films as shown in figure 7 in red line.The one-to-one correspondence of the experimental data with the model fitting shows that the resistivity is absolutely defined by the parallel spin channel model.A small upturn in the resistivity at low temperatures indicates that the semiconducting channel is rather more actively contributing for charge transport.The contributions of spin-down and spin-up channels towards the total resistivity of the samples have been separately estimated from the extracted parameters as presented in table 2. It is worth mentioning here that the residual resistivity in spin-down channel (ρ 0 ) is quite low for all the CFMO films as compared to that in spin-up channel (ρ SC d ) due to the ease of conduction in the metallic channel.The values of residual resistivities in both channels increase with rise in anti-site disorder, showing the minimum value for CFMO-Vac (111) film and the maximum value for CFMO-N 2 (100) film.From table 2, it can be seen that the spin-down channel is rather more active in (111) oriented films.As shown  earlier by XANES results too, a higher concentration of Fe 2+ -O-Mo 6+ channels are available for spin-down conduction.Hence, the resistivity and XANES data analyses, in a combined way, show that Fe 2+ -O-Mo 6+ channels in (111) oriented films facilitate a dominant metallic conductivity.The NFL exponent as described in equation ( 2) is n = 1.3 for (111) oriented films and n = 1.6 for (100) oriented CFMO films, suggesting a NFL behavior for metallic state in all the films.The parameter governing electron-electron scattering strength (ρ n ), increases abruptly with change in the substrate orientation, which indicates an increase in the defect concentration or the anti-site disorder.The CFMO (111) films have a smaller band-gap as compared to the CFMO (100) films.In this context, CFMO-Vac (111) film exhibits the lowest band gap of 0.13 meV and CFMO-N 2 (111) film has the highest band gap of 4.3 meV.

Terahertz spectroscopy
Terahertz (THz) spectroscopy is a potential tool to investigate various intriguing phenomena such as charge or spin density waves, orbital ordering, topological phases, phase transitions etc [27,28].For the present investigations, the set of CFMO films grown in vacuum show highest cation ordering and hence the effects have also been studied by temperature-dependent THz spectroscopy.Figures 9 and 10(a), (b) show the real (σ 1 ) and imaginary (σ 2 ) parts of the complex optical conductivity (σ * ) in the investigated frequency (0.2-1.2 THz) and temperature (5-300 K) ranges for both the vacuum grown CFMO films.It is worth noting here that for (111) oriented CFMO film, both (σ 1 and σ 2 ) exhibit positive values.Further, σ 2 increases with increasing THz frequency, while σ 1 decreases.These are characteristic features of Drude type of optical conductivity which describes the free carrier dynamics of nearly disorder-free systems.According to the Drude model, the complex conductivity as a function of frequency (ω) can be written as follows [27]: where ε 0 is the permittivity of vacuum, ω p is the plasma frequency, ε ∞ is the permittivity of the medium at higher frequencies, and Γ is the scattering rate of charge carriers.The optical conductivity of CFMO-Vac (111) film has been fitted to the Drude model (equation ( 5)).Here, the real and imaginary parts are fitted simultaneously at all temperatures.The fittings for maximum (300 K) and minimum (10 K) temperatures of the measured range are presented in figures 9(c) and (d).
The optical conductivity of CFMO-Vac (100) film (figure 10) shows that the values of imaginary conductivity remain negative in the investigated ranges of frequency and temperature.These features defy the Drude type of carrier dynamics.Rather, such features are often observed in disordered systems and can be described well using the Drude-Smith model.This model has been successfully applied to explain non-Drude like conductivity of many nanostructured metals, semiconductors, oxides, disordered materials so far [29].It is an extension of Drude model which takes account of the backscattering of charge carries due to the disorder present in the system.As discussed in magnetization results, (100) orientated films have larger anti-site disorder in the system.Therefore, it creates irregularity at B and B ′ sites causing a larger scattering of the charge carriers.In other words, the anti-site disorder disrupts the charge transport network connected through B and B ′ site ions and increases back-scattering of carriers.The Drude-Smith model is expressed as [29]: where, c is the disorder parameter accounting charge carrier backscattering.In general, the more negative value of c suggests larger backscattering of charge carriers which, in turn, highlights more amount of disorder present in CFMO-Vac (100) film.
As shown in figure 10, the THz conductivity data of (100) oriented CFMO film fits well with the Drude-Smith model.Again, the data is fitted simultaneously to both σ 1 and σ 2 of the film.Here, the value of disorder parameter c varies weakly with temperature, i.e. it varies from −0.99 at RT to −0.95 ± 0.05 at 10 K.This feature indicates a static disorder in the film.Any static disorder is inherent to the film and depends on the sample fabrication process.Unlike this, the disorder in RNiO 3 systems is dynamic in nature which brings strong dependency of parameter c on the temperature [28].The derived values of ω p and Γ for both the CFMO-Vac films are presented in figure 11.For CFMO-Vac (111) film, the ω p increases with rising temperature suggesting strong electron-electron correlation in the metallic state.Also, Γ increases with increasing temperature.Both ω p and Γ show variations presenting metallic conductivity in CFMO-Vac (111) film throughout the temperature range.These results of CFMO-Vac (111) agree well with the resistivity data.In contrast to this, for CFMO-Vac (100) film, ω p first decreases from low temperature to T MI and then it continues increasing up to RT (figure 11(c)).Γ also exhibits similar temperature-dependence as ω p (figure 11(d)).These features also corroborate well with the dc resistivity data as described earlier.

Vibrational properties
Earlier, Raman spectroscopy has been used to study the impact of cation ordering and spin-phonon coupling in La 2 CoMnO 6 thin films [30,31].In the present case, Raman spectroscopy measurements have been performed on the CFMO films to explore the B-site ordering and spin-phonon interactions in the films.Figure 12 displays the room-temperature Raman spectra of all the CFMO thin films.The Raman modes are observed at 258, 294, 315, 422 and 450 cm −1 .The curves are de-convoluted, and the corresponding peak position and FWHM of the Raman modes are presented in table 3. The Raman spectra show that (111) oriented CFMO films show sharp and well-defined Raman modes.These intense and  well-defined Raman modes indicate B-site ordering due to the Brillouin zone folding [31].In a disordered double perovskite, the B and B ′ ions are randomly distributed in the lattice.However, the B and B ′ are alternatively arranged in a long-range cation-ordered double perovskite system, which gives rise to doubling of the pseudocubic unit cell lattice parameter with respect to the primitive cell.It eventually causes Brillouin-zone folding and changing of symmetry.The present results suggest that CFMO-Vac (111) film has the highest degree of B-site ordering, while CFMO-N 2 (100) film exhibits the lowest B-site ordering.Here, we emphasize the point that although all the CFMO films are phase-pure, as observed by XRD, a significant difference in the cation ordering has been probed by Raman spectroscopy.
It is imperative to mention that any thermal perturbation in the lattice, spin or orbital degrees of freedom of a system can be sensed by temperature-dependent Raman spectroscopy [30][31][32].Bulk polycrystalline CFMO exhibits Curie transition at ∼350 K [12].However, in thin films, variation in lattice strain and anti-site order significantly modifies the transition temperature of the system.The thermal evolution of vibrational properties of the CFMO system has been understood by temperature-dependent Raman spectroscopy from 90 K to 400 K. Figures 13(a  CFMO-Vac (100) and CFMO-Vac (111) films, respectively.The temperature-induced thermal expansion of the lattice produces red-shift of the Raman modes as expected.For a magnetic material, the red-shift of Raman modes can be attributed to various factors such as [24,32,33]: ω (T) = ω 0 + ∆ω ph−ph + ∆ω sp−ph + ∆ω anharmonic (7) where ω 0 is the Raman shift corresponding to 0 K, ∆ω ph-ph is the cell volume contribution, ∆ω sp-ph is the spin-phonon coupling contribution and ∆ω anharmonic signifies the contribution of anharmonic terms in the system.Here, ∆ω sp-ph arises because of modulation of spin exchange integral by a change in the lattice vibrational frequencies and hence signifies contribution from spin-phonon interactions.In the present case, the term ∆ω ph-ph represents the isotropic variation in volume which is found negligible here.Thus, the observed red-shifts of the Raman modes are mainly contributed by higher-order anharmonicity and spin-phonon coupling in the system.Balkanski model [34] is valid in the absence of any structural phase change and can quantify the ∆ω anharmonic contribution for the phonon behavior with temperature variation.To estimate the contribution due to anharmonic terms in the Raman shift, the temperature-dependent variations in the Raman shift and FWHM are fitted by Balkanski model (equations ( 8) and ( 9)) as shown in figures 14(a) and (b): where, ω 0 is the Raman shift at 0 K, Υ(0) is the FWHM at 0 K, parameter A is the anharmonic constant which describes the contribution from higher order terms for three phonon processes, and [e hω 2k β T ] −1 corresponds to the thermal population factor of Raman modes.In a three-phonon process, three phonons interact such that both energy and momentum are collectively transferred between lattice vibrations.
The Balkanski model fits to the data in both the temperature regions i.e. above and below Curie temperature, as shown in figure 14.The solid lines represent the Balkanski fit for the Raman shift plot (equation ( 8)), and the dashed lines show the fits to FWHM (equation ( 9)) plots.As this model purely defines the contributions from anharmonic phonon vibrations, the deviation from the fits at Curie  temperature strongly suggests the presence of spin-phonon coupling.At the vicinity of magnetic phase transition, the phonon renormalization takes place which influences the spin-lattice coupling and gives rise to an anomaly in the plot of anharmonicity.
Here, the difference in anharmonic coefficients (∆ω 0 ) is the difference between ω 0 in both the fitted curves (red and pink fitted lines in figure 14).The value of ∆ω 0 is 79 cm −1 and 44 cm −1 for (111) and (100) oriented CFMO films, respectively (table 4).Literature reports suggest that the higher value of ∆ω 0 implies higher spin-phonon coupling strength in the system [33].Thus, the temperature-dependent Raman data suggest that the CFMO (111) films with higher cation ordering exhibit stronger spin-phonon coupling with higher ∆ω 0 .Similar studies of enhanced spin-phonon coupling by chemical doping at A-site in ordered manganese-based double perovskites such as A 2 BMnO 6 (A = La, Pr, Nd, Sm, Gd; B = Co, Ni) has been reported earlier [35,36].
The spin-phonon coupling arises from the phonon modulation of the superexchange integral which depends on the net amplitude of spin-spin correlation <S i .S j > functions where S i and S j are the localized spins at the ith and jth sites, respectively.Under the mean-field approximation, the phonon renormalization function δω (T) is related to the magnetization as follows [35]: where M(T) and M 0 are the magnetization of the sample at temperature T and 0 K, respectively.Hence, the amplitude of the spin-spin correlation function and the strength of the spin-phonon coupling depends on the level of cation ordering in double perovskites.This discussion clearly indicates that higher cation ordering in CFMO (111) films gives rise to stronger spin-phonon coupling in the films.Additionally, enhanced ferrimagnetic interactions and hence higher magnetization in cation-ordered Fe-Mo system give rise to higher spin-phonon coupling.Additionally, the deviation from normal anharmonic behavior takes place is exactly at the transition, T C .The deviation appears at 325 K and 350 K for the CFMO-Vac (100) and CFMO-Vac (111) thin films, respectively.The estimated value of T C from Raman data matches well with that observed from the temperature-dependent magnetization measurements shown earlier.For example in [37], a detailed study of temperature-dependent Raman spectroscopy is reported on SFMO and CFMO bulk samples by other researchers, where they have discarded the possibility of spin-phonon coupling in their bulk samples.The absence of spin-phonon coupling in bulk samples suggests that the spin-phonon coupling in the present case of 65 nm CFMO thin films appears because of the substrate-induced strain.Consecutively, the coupled spin and lattice degrees of freedom in these thin films manifest in the temperature-dependent Raman results.

Conclusions
In summary, a successful effort has been made to achieve a state of significantly improved cation order in half-metallic Ca 2 FeMoO 6 (CFMO) thin films by precisely choosing the substrate-orientation and deposition condition.XANES spectroscopy suggests that the CFMO films contain both the divalent and the trivalent Fe ions with a dominating presence of Fe 3+ .In spite of overall dominant present of Fe 3+ ions in all films, CFMO (111) films show slightly higher concentration of Fe 2+ ions as compared to that in CFMO (100) films.As anti-site disorder disturbs the alternate Fe-O-Mo arrangement, it results to weakened ferrimagnetic interactions in (100) films.Thus, a reduced saturation magnetization and lower T C observed for CFMO (100) films indirectly show a higher anti-site disorder in these films.This indirect observation of higher anti-site disorder in CFMO(100) films have also been supported by other measurements, namely, (i) a drastic change from insulating to metallic state takes place by changing the growth orientation from (100) to (111), respectively; (ii) terahertz spectroscopy suggests that (111) oriented CFMO film follows Drude conductivity, however, Drude-Smith model is followed by CFMO-Vac (100) film due to higher degree of cation disorder; (iii) well-defined and intense Raman modes are observed for CFMO films grown on LAO (111).The spin-up and spin-down channel contributions to the resistivity have been distinguished by data analysis which is further supported by XANES data too.The Curie temperatures and the parameter indicating spin-phonon coupling strength have been derived for CFMO films using temperature-dependent Raman spectroscopy.The T C derived using Raman data agrees very well with the magnetization.The spin-phonon coupling occurs in CFMO films in spite of its absence in the bulk counterpart.Spin-phonon coupling is stronger in CFMO (111) films than in CFMO (100) films.As shown in the present study, the substrate orientation plays a key role in modifying the structural, electronic, magnetic, vibrational, and optical properties of this half-metallic double perovskite system.

Figure 1 .
Figure 1.Schematic showing the FeO6 and MoO6 octahedra containing anti-phase rotations in double perovskite CFMO films for; (a) (100) orientation and (b) (111) orientation.The zig-zag pattern of Fe-O-Mo chains is shown by black dashed line.

Figure 2 .
Figure 2. (a) XRD patterns of CFMO films deposited on LAO (100) substrates in vacuum and nitrogen atmospheres.The label 's' represents peaks from substrate having reflections other than (100).(b) Magnified view of the (400) Bragg's reflection of these films.

Figure 3 .
Figure 3. (a) XRD patterns of CFMO films deposited on LAO (111) substrates in vacuum and nitrogen atmospheres.The label 's' represents peaks from substrate having reflections other than (111).(b) Magnified view of the (444) Bragg's reflection of these films.

Figure 6 .
Figure 6.(a) Magnetization versus magnetic field curves for all CFMO films recorded at 150 K. (b) Magnetization versus magnetic field curves of CFMO-Vac (111) thin film recorded at 300 K, 150 K, 10 K and 2 K.

Figure
Figure The complex conductivity i.e.(a) real and (b) imaginary THz conductivity spectra of CFMO-Vac (111) film.(c), (d): Drude model fitted to the complex conductivity data at 300 K, and 10 K.
) and (b) shows the temperature-dependent Raman spectra of

Figure 14 .
Figure 14.(a), (b) Raman shift and FWHM plots as a function of temperature for CFMO-Vac (111) and CFMO-Vac (100) thin films.Red and pink lines show the Balkanski fit to the Raman shift and FWHM plots.

Table 1 .
Relative percentage of the mixed oxidation state of Fe ions obtained from the linear combination fitting (LCF) done on XANES spectra of CFMO films.

Table 2 .
Parameters extracted from the parallel spin model fitting to the temperature-dependent resistivity plots of all the CFMO films.

Table 3 .
Raman peak position and FWHM extracted from the deconvolution of the room-temperature data of CFMO thin films.

Table 4 .
Parameters derived from the Balkanski model fitted to temperature-dependent Raman spectra of CFMO thin films.