Magnon-phonon Fermi resonance in antiferromagnetic CoF2

Abstract

Understanding spin-lattice interactions in antiferromagnets is a critical element of the fields of antiferromagnetic spintronics and magnonics. Recently, coherent nonlinear phonon dynamics mediated by a magnon state were discovered in an antiferromagnet. Here, we suggest that a strongly coupled two-magnon-one phonon state in this prototypical system opens a novel pathway to coherently control magnon-phonon dynamics. Utilizing intense narrow-band terahertz (THz) pulses and tunable magnetic fields up to μ₀H_ext = 7 T, we experimentally realize the conditions of magnon-phonon Fermi resonance in antiferromagnetic CoF₂. These conditions imply that both the spin and the lattice anharmonicities harvest energy from the transfer between the subsystems if the magnon eigenfrequency f_m is half the frequency of the phonon 2f_m = f_ph. Performing THz pump-infrared probe spectroscopy in conjunction with simulations, we explore the coupled magnon-phonon dynamics in the vicinity of the Fermi-resonance and reveal the corresponding fingerprints of nonlinear interaction facilitating energy exchange between these subsystems.

Fig. 1. The pathway to magnon-phonon Fermi resonance.

a Frequency tuning of the fundamental magnon frequency f₀ and double frequency 2f₀ by an external magnetic field μ₀H_ext applied along the antiferromagnetic easy axis of CoF₂. The Fermi resonance matching condition 2f_m = f_ph at the crossing of the double magnon frequency (red) and the phonon frequency (blue) is marked by a black star. Blue dots and red rectangles correspond to real experimental data points. b Graphical illustration of the nonlinear magnon-phonon dynamics. If the magnon frequency is f₀, a THz pump pulse exclusively populates the magnon state. However, by tuning the resonance condition by an external magnetic field, for 2f_m = f_ph, the magnon-phonon Fermi resonance condition is fulfilled and a channel of nonlinear energy transfer opens. c Feynman diagrams illustrating the processes of energy transfer involving two magnons and one phonon. Two magnon-phonon confluence (left) and phonon-two magnon splitting (right).

Fig. 2. Experimental setup and results.

a THz pump—IR probe spectroscopy with external magnetic field applied perpendicular to the sample plane, along the c-axis. The changes of THz-induced probe polarization rotation α_F are measured by a balanced photodetector. Electro-optical sampling of the THz pulse (with nitrogen purge) is shown in both the time and frequency domains. b Time domain data for polarization rotation α_F for a series of external magnetic field values measured at T = 6 K.

Fig. 3. Fingerprints of the magnon-phonon Fermi resonance.

a Fourier transformation of the time domain signals in Fig. 2b plotted with equidistant offset in the vicinity of the magnon (left) and phonon (right) resonance frequencies. To compensate for the THz power change of the TELBE source, magnon (phonon) spectral amplitudes are normalized by the square root of THz power (the THz power). b Phonon spectral weight (blue spheres) extracted as an integral value from the shaded frequency interval in (a). The phonon weight from our numerical calculation is shown as solid blue line. The vertical dotted line emphasizes the drop in the phonon spectral weight at H_ext= 3.5 T for both simulation and experiment. Excluding effects which can additionally contribute to our signal on the time scale of our THz pump pulse, i.e., nonlinear electro-optical Kerr effect, we demonstrate even better agreement of experiment and simulation in Supplementary Section A.

Fig. 4. Theoretically modeled effect of the nonlinear coupling strength on the observation of magnon-phonon Fermi resonance.

a Fourier transformation centered around the phonon resonance for the case of weak coupling with α = 0.07. b Fourier transformation centered around the phonon resonance for the case of strong coupling with α = 7. c Phonon weight extracted as an integral value in the shaded frequency region of 1.9–2.0 THz for the weak coupling case (purple line) and the strong coupling case (blue line), respectively. The evident difference for FFT line shapes in the range of μ₀H_ext = 3–4 T (a, b) and extracted phonon weight (c) clearly emphasizes the mutual coupling between the two magnons and the phonon state.