Rigorous ESR spectroscopy of $F{e}^{3+}$ impurity ion with oxygen vacancy in ferroelectric $SrTi{O}_3$ crystal at 20 mK

Impurity $F{e}^{3+}$ ion electron spin resonance (ESR) spectroscopy using multiple dielectric modes in a $SrTi{O}_3$ dielectric resonator has been performed with a tuneable DC magnetic field of up to $1.6T$. The $T{i}^{4+}(d^0)$ ion is substituted by $F{e}^{3+}$ ion forming $Fe{O}_6$ octahedral complex with an iron-oxygen-vacancy $(F{e}^{3+}-V_O)$. In such a metal-ligand complex, a giant g-factor of $g_{\parallel F}=5.51$ was observed in the ferroelectric phase at $20mK$. The the change of $F{e}^{3+}$ ion center-symmetry in the $Fe{O}_6$ complex as a soft-mode characteristics of ferroelectric phase transition and the influences of iron-oxygen-vacancy $(F{e}^{3+}-V_O)$, interactively sensitive to asymmetry in the octahedral rotational parameter $\mathrm{\Phi }$ in $SrTi{0}_3$.