Cavity-Mediated Coupling of Terahertz Antiferromagnetic Resonators

Coupling of space-separated resonators is interesting for quantum and communication technologies. In this work, we show that antiferromagnetic resonance in separated parallel-plane slabs of hematite ($\alpha$-${\mathrm{Fe}}_2{\mathrm{O}}_3$) couple cooperatively to terahertz electromagnetic cavity modes formed by the slabs themselves. We demonstrate control of these hybridized magnon-polariton modes either by tuning the distance between the slabs in the range of up to a few millimters or by scanning their temperatures in a range above room temperature. Analysis of measured spectra with three distinct theoretical models shows that the best approximations can be obtained with a model based on classical electromagnetism. Cavity-mediated coupling allows the engineering of resonators at millimeter-range frequencies (millielectronvolts).

Figure 1

The measured system comprises a hematite crystal of thickness $h_M$ placed on a copper mirror and a second hematite crystal of thickness $h_W$ placed at the end of the oversized copper waveguide. We measure reflection in the frequency range from 0.2 to 0.28 THz as a function of the gap $d$ between the crystals, imposing a temperature difference $\mathrm{\Delta }T=T_M-T_W$, while keeping $T_M+T_W$ constant.

Figure 2

Normalized reflection magnitude at three different values of the gap $d$ between the crystals, obtained for $(T_M+T_W)/2=336\mathrm{K}$, for which the crossing point is at $f\approx 227\mathrm{GHz}$.

Figure 3

Normalized reflection magnitude at three temperature differences $\mathrm{\Delta }T$, as a function of the gap $d$ between the crystals. Green rectangles mark strong couplings of AFMR modes with cavity modes. This result comes from the same set of data as the results in Fig. 2.

Figure 4

(a) Enlargement of the observed interaction region, (b) fit with the input-output model [Eq. (1)], and (c) predicted reflection obtained with the electrodynamics model.

Figure 5

(a)–(d) Measured interactions at four selected distances between the crystals, which are equal to integer numbers of half wavelengths. (e)–(h) Reflection simulated with use of the electrodynamics model. (i) Splitting between the upper and lower magnon-polariton modes as a function of the gap $d$ between the crystals; the solid green line is a fit obtained with Eq. (4).

Figure 6

The system simulated in the electrodynamics model.

Figure 7

(a) Experimental reflection for $=11.71\mathrm{mm}$ as in Fig. 5, (b) simulated transmission spectrum, and (c) simulated reflection spectrum.