Magnetically tuned continuous transition from weak to strong coupling in terahertz magnon polaritons

Depending on the relative rates of coupling and dissipation, a light-matter coupled system is either in the weak- or strong-coupling regime. Here, we present a unique system where the coupling rate continuously increases with an externally applied magnetic field while the dissipation rate remains constant, allowing us to monitor a weak-to-strong coupling transition as a function of magnetic field. We observed a Rabi splitting of a terahertz magnon mode in yttrium orthoferrite above a threshold magnetic field of $\sim 14$ T. Based on a microscopic theoretical model, we show that with increasing magnetic field the magnons transition into magnon polaritons through an exceptional point, which will open up new opportunities for in situ control of non-Hermitian systems.

Figure 1

(a) Schematic of the experimental setup, showing a tabletop minicoil pulse magnet with optical access (RAMBO). (b) Spin motion of the quasiferromagnetic (qFM) magnon mode in ${\mathrm{YFeO}}_3$. ${\vec{S}}_1$ and ${\vec{S}}_2$ are spins in the two respective sublattices with a small canting angle, which produces a net magnetization $\vec{M}$. (c) Experimental geometry. The two sublattice spins lie in the $a-c$ plane with a canting angle $\beta$. The Cartesian coordinates, $x, y$, and $z$, are parallel to the crystal $a, b$, and $c$ axes, respectively. The electric (magnetic) field component of the THz radiation, ${\vec{E}}_{\mathrm{THz}}$ (${\vec{H}}_{\mathrm{THz}}$), was parallel to the $b$ axis ($a$ axis). The black arrow on the right shows the external millimeter-long pulsed magnetic field produced by the RAMBO magnet, which can be considered to be a dc field ${\vec{H}}_{\mathrm{dc}}$, during the picosecond-long THz pulse. In this configuration, only the qFM mode is excited through the Zeeman torque.

Figure 2

(a) Magnetic-field-induced changes in the transmitted THz electric field as a function of time at various magnetic fields from 9.2 to 26.6 T. (b) Fourier transforms of the time-domain waveforms in (a). The traces are vertically offset for clarity both in (a) and in (b).

Figure 3

(a) The frequency $\omega$ of the qFM mode, normalized by the center frequency ${\omega }_0$, as a function of magnetic field. At high fields, the qFM resonance splits into two, which is attributed to the formation of a bulk magnon polariton. The color map is our simulated spectra. The open circles are obtained from experimental data, and the dashed lines are square-root function fits. (b) Calculated magnon polariton spectra for three values of magnetic field –0, 15, and 30 T. (c) Calculated coupling strength $g$ as a function of magnetic field. The dashed line indicates the loss $\sqrt{\kappa \gamma }/2$. (d) The magnitude of splitting $\mathrm{\Delta }\omega$ versus sample thickness.