Evidence of Dilute Ferromagnetism in Rare-Earth doped YAG

This work demonstrates strong coupling regime between an Erbium ion spin ensemble and microwave Hybrid Cavity-Whispering Gallery Modes in a Yttrium Aluminium Garnet dielectric crystal. Coupling strengths of $220$~MHz and mode quality factors in excess of $10^6$ are demonstrated. Moreover, the magnetic response of high-Q modes demonstrates behaviour which is unusual for paramagnetic systems. This behaviour includes hysteresis and memory effects. Such qualitative change of the system's magnetic field response is interpreted as a phase transition of Rare Earth ion impurities. This phenomenon is similar to the phenomenon of dilute ferromagnetism in semiconductors. The clear temperature dependence of the phenomenon is demonstrated.