We studied the structural and magnetic properties of \FeC~thin films deposited by co-sputtering of Fe and C targets in a direct current magnetron sputtering (dcMS) process at a substrate temperature (\Ts) of 300, 523 and 773\,K. The structure and morphology was measured using x-ray diffraction (XRD), x-ray absorption near edge spectroscopy (XANES) at Fe $L$ and C $K$-edges and atomic/magnetic force microscopy (AFM, MFM), respectively. An ultrathin (3\,nm) $^{57}$\FeC~layer, placed between relatively thick \FeC~layers was used to estimate Fe self-diffusion taking place during growth at different \Ts~using depth profiling measurements. Such $^{57}$\FeC~layer was also used for $^{57}$Fe conversion electron M\"{o}ssbauer spectroscopy (CEMS) and nuclear resonance scattering (NRS) measurements, yielding the magnetic structure of this ultrathin layer. We found from XRD measurements that the structure formed at low \Ts~(300\,K) is analogous to Fe-based amorphous alloy and at high \Ts~(773\,K), pre-dominantly a \tifc~phase has been formed. Interestingly, at an intermediate \Ts~(523\,K), a clear presence of \tefc~(along with \tifc~and Fe) can be seen from the NRS spectra. The microstructure obtained from AFM images was found to be in agreement with XRD results. MFM images also agrees well with NRS results as the presence of multi-magnetic components can be clearly seen in the sample grown at \Ts~= 523\,K. The information about the hybridization between Fe and C, obtained from Fe $L$ and C $K$-edges XANES also supports the results obtained from other measurements. In essence, from this work, experimental realization of \tefc~has been demonstrated. It can be anticipated that by further fine-tuning the deposition conditions, even single phase \tefc~phase can be realized which hitherto remains an experimental challenge.