Fig. 2: Observation of magnon-phonon coherent oscillation.

a Temporal evolution of the real part of \({\tilde{F}}_{{{{{{{{\bf{k}}}}}}}}}(t)\) at k_x = k_TA under the magnetic field B = 11.5 mT parallel to k, where k_TA refers to the wavenumber of the intersection point between dispersion relations of transverse acoustic (TA) phonons and magnons. Red inverted triangles indicates t = 15 ns, 20 ns, and 25 ns after the pump pulse irradiation. b A frequency power spectrum of \({\tilde{F}}_{{{{{{{{\bf{k}}}}}}}}}(t)\) at k_x = k_TA. The blue filled circles represents experimentally obtained spectrum intensity, while the gray curve represents fitting curve. Inverted red triangle highlights peaks. Errors of the data are evaluated as a standard deviation, which is smaller than the data plot. c Theoretically calculated dispersion curves of magnon polarons around k_x = k_TA and k_y = 0, where we use the crystalline anisotropy energy K_c = 73.0 [J ⋅ m⁻³], uniaxial anisotropy energy K_u = −767.5 [J ⋅ m⁻³], saturation magnetization M_s = 14.8 [kA ⋅ m⁻¹], velocity of LA phonons v_LA = 6.51 [km ⋅ s⁻¹], velocity of TA phonons v_TA = 3.06 [km ⋅ s⁻¹] and magnon-phonon coupling constant b₂ = 1.8 × 10⁵ [J ⋅ m⁻³]. The black solid curves represent the dispersion curves of magnon polarons, while the blue and red dashed curves represent pure TA phonons and magnons, respectively. d Temporal evolution of the real part of \({\tilde{F}}_{{{{{{{{\bf{k}}}}}}}}}(t)\) at k_x = k_LA under the magnetic field B = 11.5 mT parallel to k, where k_LA refers to the wavenumber of the intersection point between dispersion relations of longitudinal acoustic (LA) phonons and magnons. e A frequency power spectrum of \({\tilde{F}}_{{{{{{{{\bf{k}}}}}}}}}(t)\) at k_x = k_LA. The black filled circles represents experimentally obtained spectrum intensity, while the gray curve represents fitting curve. Errors of the data are evaluated as a standard deviation, which is smaller than the data plot. f Theoretically calculated dispersion curves of magnon polarons around k_x = k_LA. The gray line and red curve represent the dispersion curves of LA phonons and magnons, respectively. g Temporal evolution of the real part of \({\tilde{F}}_{{{{{{{{\bf{k}}}}}}}}}(t)\) at k_x = k_TA under the magnetic field B = 11.5 mT perpendicular to k. h Temporal evolution of real part of \({\tilde{F}}_{{{{{{{{\bf{k}}}}}}}}}(t)\) at k_x = k_LA under the magnetic field B = 11.5 mT perpendicular to k. i, Magneto-optical images taken at different delay times.