Cavity magnon polaritons with lithium ferrite and three-dimensional microwave resonators at millikelvin 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 quasiparticles) 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 the 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 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.

Figure 1

(a) Double post re-entrant cavity (without top lid) with a LiFe sphere in external magnetic field, with cross-section in (b). This cavity supports a dark $\uparrow \uparrow$ and a bright mode $\downarrow \uparrow$ as shown in (c).

Figure 2

Frequency response of the LiFe sphere-cavity system as a function of external dc field for the HF case: (a) close to the bright mode $\downarrow \uparrow$, (b) near dark mode $\uparrow \uparrow$.

Figure 3

Frequency response of the LiFe sphere-cavity system as a function of external dc field for the LF case: (a) close to the bright mode, (b) close to the dark mode $\uparrow \uparrow$, which has been fitted with a two-mode model, with the coupled (uncoupled) solutions in dashed purple (white) and showing two mode crossings. The lower crossing in (b) is not in the strongly coupled regime due to excess magnon losses at low magnetic field, while the upper crossing is strongly coupled.

Figure 4

(a) Magnetization loops for LeFe spheres at 300 K and 3 K with the external field scaled to the saturation field. (b) Curve fits to resonance peaks at low frequencies.

Figure 5

Modeled interaction of mode crossing shown in Fig. 3, lowered from its ${\mathrm{LF}}_{\uparrow \uparrow }$ frequency of $f_{\uparrow \uparrow }^{\left(0\right)}=5.96\mathrm{GHz}$ (a), to $f_{\uparrow \uparrow }^{\left(1\right)}=5.76\mathrm{GHz}$ (b), and, finally, $f_{\uparrow \uparrow }^{\left(2\right)}=f_s=5.56\mathrm{GHz}$ (c). The white and yellow curves represent the uncoupled magnon and cavity modes' magnetic-field dependences, respectively, whilst the dark lines represent the behavior when the two are coupled at a rate of $g=68\mathrm{MHz}$. The frequency difference between the higher frequency branch and lower frequency branch (the transition frequency, $f_{\text{CMP}}=f_{+}-f_{-}$) is then plotted for each of these three cases in (d). The red stars represent the location where the photon and magnon maximally hybridize.

Figure 6

First (a) and second (b) derivatives of the frequency of the CMP quasiparticle transition with respect to magnetic field for the same values of detuning as shown in Fig. 5.