Evidence of dilute ferromagnetism in rare-earth doped yttrium aluminium garnet

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 106 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.