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. 
W.G. Farr, M. Goryachev, J.M. le Floch, P. Bushev and M.E. Tobar
cond-mat.mtrl-sci quant-ph