5 T$_{N}$ , it is not sufficient for phonon behavior in BiFeO$_{3}$. In this case it is necessary to go to fourth order in L. The reasons are explained by Nugroho et al . [33] in their work on YbMnO$_{3}$. In this case the key term in the free energy is of the form gP $^{2}$L$^{2}$, which for weak coupling gives an explicit interaction of electric field to L that results in a magnetocapacitance of tion by our group [43] that 140K is a spin-reorientation transition temperature is not confirmed by very recent neutron scattering studies [44] and spin-glass effects[45] have also been suggested but are unproven. Although this fourth-order term is higher order than the terms in g < L $^{2}$> considered by Fox et al . [48], it is sin- gular at T$_{N}$ , because it is proportional to the cube of the correlation length ( η ) that diverges at T$_{N}$ . ( g $^{2}$P $^{2}$/kT ) ∫ [ < L $^{2}$( x ) L $^{2}$(0) > − < L 2 > $^{2}$] dx. (2) D. Weak phonon-magnon coupling: In our Raman spectra (Figs. 1c and d) we observed small (1 or 2 cm − $^{1}$) increases or decreases in phonon frequencies very near T$_{N}$ . Note that this is observed for several different phonon symmetries. The symmetry- independence of the phonon-magnon coupling implies an interaction of form P $^{2}$M2 (where P and M are the po- larization and magnetization, respectively) in the free en- ergy, as first suggested for magnetoelectrics by Smolen- skii and Chupis [13]. In general the coupling of phonons and magnons can occur through several different micro- scopic physical models: The Torrance-Slonczewski model [46] involves modulation of the crystal field at the spin site by the optical phonon and is significant for ions with unquenched orbital angular momenta, such as Co +2 or Fe $^{+2}$; the model of Buyers et al . [47] is an angular mo- mentum coupling of spins in octahedra where the opti- cal phonon eigenvector is rotation-like as viewed from the magnetic ion. However, such models do not give frequency anomalies near T$_{N}$ like those we observed in BiFeO$_{3}$. A rather detailed model of magneto-capacitance was given by Fox et al . [48] for BaMnF$_{4}$ near T$_{N}$ , and related models by Scott [49] and by Glass et al . [50] for the BaMF$_{4}$ family near T(2D), the two-dimensional spin ordering temperature [typically ca. 3 T$_{N}$ in that family]. The free energy of Fox et al . can be defined as: The result is that the phonons in Raman effect in BiFeO$_{3}$ of any symmetry will be expected to have small anomalies in their frequencies at T$_{N}$ . These small dips or jumps will be proportional to temperature t ( α − 1) [33] [51], where t is reduced temperature, t = [ T$_{N}$ - T ]/ T$_{N}$ and α is the critical exponent describing divergence of the spe- cific heat [52]. Since the α is typically small, the phonon frequencies should vary approximately as T$_{N}$ /[ T$_{N}$ -T] near T$_{N}$ and in principle could be used to evaluate critical ex- ponent α . However in the present work the data are too imprecise for this chore, and even higher resolution would by insufficient due to phonon damping. The bump in phonon frequencies and linewidth are qualitatively pre- dicted from the non-mean field theory of Nugroho et al . [33]. However, their model does not predict magnitudes for the height (increase in frequency) or width (how near the transition the increase occurs) of the bump. No anomaly at all is predicted by the mean-field theory of Fox et al . [48], which does not consider terms in the free energy introduced by Nugroho et al . [33]. A similar behavior has been observed at 150 K (Figs. 3b and c) could be due to the change in magnetic ordering [36]. As matter of coincidence the bottom electrode SRO has a ferromagnetic phase transition at 150 K. Note that none of these peaks is related to SRO and a modulated effect is highly unlikely, but not impossible. In summary, our Raman frequencies near T$_{N}$ and 150 K show small peaks or dips for all phonon modes that are qualitatively similar to those predicted by Nugroho et al . [33], implying a general interaction of form P $^{2}$L$^{2}$, and the need for a fluctuation term neglected in the mean-field, weak ferromagnetism model of Fox et al [48]. G = f ( L $^{2}$, L2 $_{z}$)+ BM $^{2}$+ ( b$_{0}$ + b$_{1}$p + b$_{2}$p $^{2}$) M$_{x}$L$_{z}$ + ..., (1) where P is along y , the polar axis and z is the sublat- tice magnetization direction; L is (1/2)g µ S 1 / 2 (S+1) 1 / 2 [ ∑ (Sj up - Sj down)] and M is the weak magnetization M = g µ S 1 / 2 (S+1) 1 / 2 [ ∑ (Sj up + Sj down)]. Note that p is not the total polarization P but only the part induced by the magnetoelectric coupling: P = P$_{r}$ + p and it was carried out to second order in polarization P , sublattice magnetization M , and weak ferromagneti- zation L , with the result that the magneto-capacitance varies with temperature as (b$_{0}$ - b$_{1}$b$_{2}$)L$_{2}$(T), where b$_{0}$, b$_{1}$, and b$_{2}$ are respectively the coefficients of magneto- electric free energy terms independent of, linear in, and quadratic in polarization P. The authors noted that the mean-field theory, although generally not satisfactory for magnetic transitions, works well for weakly canted fer- romagnets because the expansion parameter L is small at all temperatures. Note that the sign of the magneto- capacitance term can be positive or negative depending upon the magnitude of (b$_{0}$ - b$_{1}$b$_{2}$). Because they used mean field theory, their work neglected the small term near T$_{N}$ due to fluctuations considered below. In conclusion, high quality epitaxial (001)BFO films have been grown on (100) STO substrates using PLD. The XRD studies showed that films are c -axis oriented with high degree of crystallinity. The RT polarized Raman scattering of (001)BFO films showed pseudo- orthorhombic monoclinic crystal structure contrary to the rhombohedral and tetragonal symmetries reported earlier. We observed the ferroelectric phase transition Although the second-order theory of Fox et al . [48] was satisfactory for describing all the data in BaMnF$_{4}$ near IV. CONCLUSION