Coherent strong-coupling of terahertz magnons and phonons in a Van der Waals antiferromagnetic insulator

Emergent cooperative motions of individual degrees of freedom, i.e. collective excitations, govern the low-energy response of system ground states under external stimulations, and play essential roles for understanding many-body phenomena in lowdimensional materials1-3. The hybridization of distinct collective modes provides a route towards coherent manipulation of coupled degrees of freedom and quantum phases3,4. In magnets, strong-coupling between collective spin and lattice excitations, i.e., magnons and phonons, can lead to coherent quasi-particle magnon polarons5-11. Here, we report the direct observation of a series of terahertz magnon polarons in a layered zigzag antiferromagnet FePS3 via far-infrared (FIR) transmission measurements. The characteristic avoidedcrossing behavior is clearly seen as the magnon-phonon detuning is continuously changed via Zeeman shift of the magnon mode. The coupling strength g is giant, achieving 120 GHz (0.5 meV), the largest value reported so far. Such a strong coupling leads to large ratio of g to the resonance frequency (g/ω) of 4.5%, and a value of 29 in cooperativity (gg22 γγppppγγmmmmgg � ). Experimental results are well reproduced by first-principle calculations, where the strong coupling is identified to arise from phonon-modulated anisotropic magnetic interactions due to spin-orbit coupling. These findings establish FePS3 as an ideal testbed for exploring hybridization-induced topological magnonics in two-dimensions and the coherent control of spin and lattice degrees of freedom in the terahertz regime. Magnons and phonons are the quanta of collective spin and lattice vibration, respectively. Besides their similarities in bosonic statistics and energy scales, the acoustic branches of magnons and phonons are the Goldstone modes of the system, with the spontaneous breaking of the spin rotational symmetry for the former and translational symmetry for the latter. The hybridization of magnons and phonons represents the coherent and dynamical coupling between the spin and lattice degrees of freedom. In the strong coupling regime, a new type of quasiparticles known as magnon polarons (MP) is formed. As shown in Fig. 1a, the coherent hybridization leads to the avoided crossing of the upper (UMP) and lower (LMP) magnon-polaron bands, whose energy difference is determined by the coupling strength g, in analogy to the vacuum Rabi splitting of light-matter interactions. The magnon polaron has recently attracted intense research attensions5-10,12,13. Theoretical studies suggested such hybridization enable Berry curvatures in the avoid-crossing regions of the magnon bands, and lead to nontrivial magnonic topology5-7,9,10, as well as magnon mediated thermal Hall effects in two-dimensional magnets9. Besides intense theoretical investigations, signatures of magnon-phonon interaction have been identified via spin Seebeck measurements in ferromagnetic YIG12, antiferromagnetic Cr2O3, and via inelastic neutron scattering in CuCrO2 and CuTeO6. However, realization of magnonphonon interactions in the strongly coupled regime is challenging, since it requires the coupling strength g to be larger than the decay rate of individual modes. Hybrid structures, such as cavities16,17 and surface patterning18 have been utilized to create strongly coupled magnons and phonons. The avoided-crossing behavior, illustrated in Fig. 1a, is rarely seen in intrinsic materials19. In addition, previous studies mainly focus on magnon-acoustic phonon coupling via the Kitteltype magnetoelastic coupling with moderate coupling strength typically less than μeV20 (or GHz regime). The hybridization of antiferromagnetic (AFM) magnons and optical phonons in the terahertz regime remains largely unexplored21. Recently, the emergence of van der Waals materials offer a new platform for studying and engineering coherent coupling between distinct degrees of freedom3. Examples include exciton polaritons up to room temperature22,23, highly tunable phonon polaritons24, and Dirac plasmon polariton25,26. However, the coupling between spin waves and collective excitations of other degrees of freedom remains to be explored. In this work, we report the observation of coherent strong-coupling between a series of magnons and phonons in the THz regime in a van der Waals antiferromagnetic insulator FePS3. Remarkably, a giant coupling strength of 0.5 meV (~120 GHz) is achieved, 5 times larger than the MP linewidth. This giant coupling leads to the observation of clear avoided crossing of magnon and phonon branches, as well as the brightening of the IRinactive Raman modes. These observations imply the long lifetime of THz magnons in FePS3. Our first principle calculations well reproduce the observed MP dispersion curve, revealing its origin from the optical phonon-modulated anisotropic magnetic interactions due to spin-orbit coupling. At high magnetic field, we further observed a hysteretic spin-flip transition with the emergence of two ferromagnetic (FM) magnon branches, which yields a precise measurement of single ion anisotropy and interlayer exchange interactions. The antiferromagnetic insulator of interest, FePS3, belongs to a class of transition metal phosphorous trichalcogenides (MPX3, M = Fe, Mn, Ni and X = S, Se). Magnetic moments mainly come from the Fe atoms, arranged in a honeycomb spin lattice structure27-32. It has a zigzag AFM ground state with strong magnetic anisotropy, and is considered as a 2D Ising spin system30,31. We performed far-infrared magnetospectroscopy (FIRMS) measurements on single crystal FePS3 flakes of ~ 50 μm in thickness (methods). The magnetic field is applied out-of-plane, parallel with the spin directions (Faraday geometry). The measurement was performed at 4.2 K, well below the antiferromagnetic transition temperature (TN ~ 117K). Normalized FIR transmission spectra as a function of magnetic fields are presented in Fig. 1b (See Supplementary Figure S1 for raw data). At zero field, a prominence mode at 3.67 THz (122 cm-1) is the doubly degenerated acoustic AFM magnons, which is consistent with previous Raman study33. The optical AFM magnons have also been observed at 9.6 THz (320 cm-1) (See Supplementary Figure S2). When an external magnetic field was applied, the degeneracy of the AFM magnons with opposite angular momenta was lifted, and the AFM magnon modes exhibit Zeeman splitting with a g-factor of 2.1. As the field increasing, the low-energy AFM magnon branch approaches a nearby phonon mode (Ph3) located at 3.25 THz. This mode is a zone-folded optical phonon at the Г-point with its atomic motions shown in Fig. 1a, bottom panel. In the paramagnetic phase of FePS3, it corresponds to an acoustic mode at M-point (see Supplementary Figs. S3 and S4 for temperature and polarization resolved study of the Raman modes).30 In the case of no interaction, these two modes will cross around 13 T (zero-detuning). Experimentally, however, a clear avoided-crossing behavior is observed, which is the signature of coherent magnon-phonon interaction in the strongcoupling regime. The top-panel of Fig. 1b shows the FIR spectrum at 13 T, which is close to the zero detuning. The separation between UMP and LMP peaks is about 170 GHz. The magnon-phonon coupling strength g was further extracted to be 85 GHz (see supplement Text S1), which is much larger than the linewidth of both the UMP (26 GHz) and LMP (24 GHz). The small dip next to the LMP is due to the coupling between the magnon and a phonon at 3.15 THz with a coupling strength (~10 GHz) slightly smaller than the MP linewidth. Figure 1c shows the extracted MP linewidth as a function of detuning. As the detuning is decreased, the linewidths of UMP and LMP modes approach each other, and finally cross at the zero detuning, evidencing the coherent hybridization of magnons and phonons. Multiple magnon polarons are also observed in high-field FIR transmission measurements up to 35 T, as shown in Fig. 2a. As the magnetic field increases above 20T, the low-energy branch of the AFM magnon exhibits a series of avoided crossing with nearby phonon modes. Similar to Ph3 mode (3.25 THz), Ph1 (2.63 THz) and Ph2 (2.83 THz) are also Brillouin zone-folded phonons (from M point to Г point) due to the formation of the zigzag spin order. It is revealed by the temperature dependent Raman scattering and supported by first principle calculations (Supplement Fig. S3). The atomic motions of Ph1, Ph2 and Ph3 phonons are illustrated in Supplement Fig.S5. The avoided crossing and the MP branches are fitted with a theoretical model discussed below (Eq.2) for coupled magnon/phonon modes (also see Supplement Text S1). As shown in Fig. 2b, experimental magnon/phonon peak positions are well described by the fitting. The fitting lines are color-coded, which indicates the percentage of magnon/phonon components in each hybridized MP branch. The greenish regions represent nearly 50%/50% hybridization of magnons and phonons. The composition of MP branch is shown in Fig.2c, where MP is decomposed into uncoupled magnons and phonons with their percentage given by the normalized amplitude square of each mode (see Supplement Text S1). Uncoupled magnon/phonon frequencies and the coupling strength g for each magnon-phonon pair are extracted and listed in Table 1. A g value of 120 GHz was obtained between the magnon and Ph1 phonon, which is the largest value reported so far. The ratio of coupling strength and resonance frequencies (g/ω) reaches 4.5%. The cooperativity, defined as gg2 γγpphγγmmmmmm � , is a dimensionless merit of quantifying the efficiency of energy circulation between the coupled modes. It reaches a value of 29 in our measurements, which is remarkable for coherent magnon-phonon coupling systems. Now we consider the symmetry requirements for the magnon-phonon strong coupling. Monolayer FePS3 has the point group of D3d. The symmetry reduces to the space group C2/m due to the formation of the zigzag s