Cavity Magnon Polaritons with Lithium Ferrite and 3D Microwave Resonators at milli-Kelvin Temperatures

Single crystal Lithium Ferrite (LiFe) spheres of sub-mm dimension are examined at mK temperatures, microwave frequencies and variable DC magnetic field, for use in hybrid quantum systems and condensed matter and fundamental physics experiments. Strong coupling regimes of the photon-magnon interaction (cavity magnon polariton quasi-particles) were observed with coupling strength of up to 250 MHz at 9.5 GHz (2.6\%) with magnon linewidths of order 4 MHz (with potential improvement to sub-MHz values). We show that the photon-magnon coupling can be significantly improved and exceed that of the widely used Yttrium Iron Garnet crystal, due to the small unit cell of LiFe, allowing twice more spins per unit volume. Magnon mode softening was observed at low DC fields and combined with the normal Zeeman effect creates magnon spin wave modes that are insensitive to first order order magnetic field fluctuations. This effect is observed in the Kittel mode at 5.5 GHz (and another higher order mode at 6.5 GHz) with a DC magnetic field close to 0.19 Tesla. We show that if the cavity is tuned close to this frequency, the magnon polariton particles exhibit an enhanced range of strong coupling and insensitivity to magnetic field fluctuations with both first order and second order insensitivity to magnetic field as a function of frequency (double magic point clock transition), which could potentially be exploited in cavity QED experiments.