Title: Rigorous ESR spectroscopy of $Fe^{3+}$ impurity ion with oxygen vacancy in ferroelectric $SrTiO_3$ crystal at 20 mK

Abstract: Impurity $Fe^{3+}$ ion electron spin resonance (ESR) spectroscopy using multiple dielectric modes in a $SrTiO_3$ dielectric resonator has been performed with a tuneable DC magnetic field of up to $1.6~T$. The $Ti^{4+}(d^0)$ ion is substituted by $Fe^{3+}$ ion forming $FeO_6$ octahedral complex with an iron-oxygen-vacancy $(Fe^{3+}-V_O)$. In such a metal-ligand complex, a giant g-factor of $g_{\scriptscriptstyle\parallel F} = 5.51$ was observed in the ferroelectric phase at $20~mK$. The the change of $Fe^{3+}$ ion center-symmetry in the $FeO_6$ complex as a soft-mode characteristics of ferroelectric phase transition and the influences of iron-oxygen-vacancy $(Fe^{3+}-V_O)$, interactively sensitive to asymmetry in the octahedral rotational parameter $\Phi$ in $SrTi0_3$.