Anomalous low-temperature magnetic ordering and spin-phonon coupling in BiFeO$_{3}$ thin films

Low-temperature magnetic properties and Raman spectra of epitaxal BiFeO$_{3}$ (BFO) thin films grown on (111) SrTiO$_{3}$ substrates have been studied. Zero-field-cooled (ZFC) and field-cooled (FC) magnetization curves showed a large discrepancy beginning at a characteristic temperature which did depend on the magnetic-field strength, suggesting a spin-glass-like behavior of the epitaxial BFO film with R3c symmetry. For all three major A$_{1}$-symmetry Raman modes (138, 170, and 214 cm$^{-1})$, there was a good linear correlation between the mode-frequency softening and the square of the in-plane magnetization in the temperature range between 80 and 300 K. These observations were ascribed to the spin-phonon coupling below the N\'{e}el temperature (T$_{N }$= 643 K).