Strong Coupling of Antiferromagnetic Resonance with Subterahertz Cavity Fields

Strong coupling of electromagnetic cavity fields with antiferromagnetic spin waves in hematite ($\alpha$-${\mathrm{Fe}}_2{\mathrm{O}}_3$) is achieved above room temperature. A cube of hematite is placed in a metallic tube and the transmission is measured, using a continuous-wave terahertz spectrometer. The spectra, collected as a function of the temperature, reveal the formation of magnetic polaritons.

Figure 1

A plane electromagnetic wave (blue wiggles) is focused into a cylinder cavity containing a hematite cube. The cavity magnetic field (blue curve) interacts with the resonance (violet circles) of two antiferromagnetic sublattices (red arrows). The transmitted linear polarization is measured parallel to that of the incident beam.

Figure 2

The normalized transmission magnitude at polarization angle $\delta ={30}^{\circ }$. (a) The measured spectra (violet lines) and fit using Eq. (1) (green lines). (b) A map of the spectra: the green dashed lines show interacting and noninteracting modes fitted using Eq. (3). (c) A map of the spectra fitted using Eq. (1).

Figure 3

(a),(b) The angular dependence of $a_1$ [Eq. (1)] in two configurations of the experiment. (c) The normalized $|S_{21}|$ at $\delta =-{75}^{\circ }$ in configuration (a). (e) The normalized $|S_{21}|$ at $\delta =-{60}^{\circ }$ and (g) $\delta ={70}^{\circ }$, both in configuration (b). (d),(f),(h) Fits using Eq. (1).

Figure 4

The temperature-derivative spectra: (a) magnitude and (c) phase. (b),(d) Corresponding fits using Eq. (7).

Figure 5

A model of the cavity, drawn to scale, in cross section. The arrows show the strength and the direction of the magnetic field of the first cavity mode on the $x$ plane.

Figure 6

The temperature-derivative spectra over a broad temperature range. The arrows mark the expected frequencies of the cavity modes and the circles mark the observed interactions.

Figure 7

A close-up of the first cavity mode in an oversaturated scale. The green line shows the assumed linear temperature dependence of the first mode frequency.

Figure 8

The dependence of the mode frequencies on (a) the displacement of the cube from the center of the tube, (b) the rotation of the cube about the $y$ axis, (c) the length of the tube, (d) the diameter of the tube, (e) the cube edge length, and (f) the dielectric constant of the cube. In (a), (c), (d), (e), and (f), the vertical lines mark nominal values of these parameters.

Figure 9

(a) A model of the cavity, drawn to scale, in cross section. The cube is rotated about the $y$ axis by an angle $\beta ={45}^{\circ }$. Rotation about the $x$ axis is bound by the condition of the cube touching the tube by its three corners. The arrows show the direction and strength of the magnetic field of the first cavity mode on the $x$ plane. Statistics of the magnetic field of the first five modes are presented in Table 2. (b) The strength and the direction of the magnetic field in the second mode the cavity on the $x$ plane.