Coherent oscillation between phonons and magnons

Two different waves with the same frequency and wavelengths can be coupled, so that the amplitude alternates periodically between the two to form a phenomenon known as a coherent beating oscillation. The process can be observed ...

In a new report now published in Nature Communications Physics , Tomosato Hioki and a team of scientists in materials research and applied physics at the Tohoku University and the University of Tokyo in Japan, described coherent beating observed between different excitation species in a solid, namely phonons —quantum vibrational mechanical energy, and magnons —a quasiparticle representing the collective excitation of the electron's spin structure. The team used time-resolved magneto-optical microscopy to show how magnons generated in a compound gradually disappeared by transferring to phonons, to then return to the form of magnons after a while. The oscillation period was consistent with magnon -phonon beating. The scientists envision the experimental outcomes will pave way to coherently control magnon-phonon systems in solids.

Phonon-magnon interactions in lutetium iron garnet Phonons are vibrational waves of a solid crystal lattice responsible for the elasticity and thermal properties of solids. Magnons or spin waves are conversely representative of a wavy motion of magnetization, present in magnets responsible for their magnetic and thermal properties. These two particles can interact within solids via magneto-elastic and magneto-static couplings . The dynamics of the particles are provided in the dispersion curves of each system to show the relationship between the wave number and frequency. Scientists have recorded the dispersion curves of transverse acoustic phonons and magnons in a film of a typical insulator such as lutetium iron garnet . Such dispersion curves of the phonon and magnon particles maintain an intersection around which a magnon-phonon hybridized state can be formed. Researchers have found this state, to exhibit an extremely long lifetime, far greater than pure magnons due to hybridization with phonons that maintain a long lifetime .

Concept of coherent oscillation between phonons and magnons, and time-resolved magneto-optical microscopy. (a) A schematic illustration of phonons and magnons, (b) A schematic illustration of coherent oscillation between phonons and magnons. (c) The dispersion curves of phonon and magnon in lutetium iron garnet (LuIG). (d) A magnified view around A in Fig. 1c. The black curves represent the dispersion relation of hybridized magnon-phonon polaron, while the red and blue dashed curves represents dispersion relation of pure magnons and transverse acoustic phonons, respectively. (e) Optical setup for the time-resolved magneto-optical microscopy with the extended delay time. The excited magnetization dynamics is detected via the polarization rotation angle of the probe laser pulse induced by the magneto-optical Faraday effect in the sample. The detection is performed by an charge-coupled device (CCD) camera. (f) Magneto-optical image observed 3.5 ns after the pump pulse irradiation under the external magnetic field B = 11.5 mT parallel to the wavevector of the excited magnons. g, Wavenumber spectrum of the obtained magneto-optical images observed 3.5 ns after the excitation (B = 11.5 mT). The inset shows a magnified view. Credit: Communications Physics (2022). DOI: 10.1038/s42005-022-00888-1 Read more

Observation of magnon-phonon coherent oscillation. (a) Temporal evolution of the real part of F~k(t) at kx = kTA under the magnetic field B = 11.5 mT parallel to k, where kTA 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 F~k(t) at kx = kTA. 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 kx = kTA and ky = 0, where we use the crystalline anisotropy energy Kc = 73.0 [J ⋅ m−3], uniaxial anisotropy energy Ku = −767.5 [J ⋅ m−3], saturation magnetization Ms = 14.8 [kA ⋅ m−1], velocity of LA phonons vLA = 6.51 [km ⋅ s−1], velocity of TA phonons vTA = 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 F~k(t) at kx = kLA under the magnetic field B = 11.5 mT parallel to k, where kLA refers to the wavenumber of the intersection point between dispersion relations of longitudinal acoustic (LA) phonons and magnons. (e) A frequency power spectrum of F~k(t) at kx = kLA. 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 kx = kLA. The gray line and red curve represent the dispersion curves of LA phonons and magnons, respectively. (g) Temporal evolution of the real part of F~k(t) at kx = kTA under the magnetic field B = 11.5 mT perpendicular to k. (h) Temporal evolution of real part of F~k(t) at kx = kLA under the magnetic field B = 11.5 mT perpendicular to k. (i), Magneto-optical images taken at different delay times. Credit: Communications Physics (2022). DOI: 10.1038/s42005-022-00888-1 Read more

Wavenumber and field dependence of magnon-phonon coherent oscillation. (a) Frequency spectrum Fk(ω) observed at B = 11.5 mT around the intersection of the magnon and transverse acoustic (TA) phonon dispersion curves. (b) Comparison between experimentally obtained gap between the upper branch and lower branch of the spectrum at B = 11.5 mT and the theoretical calculation of the gap frequency. Error bars represent standard deviation. (c) Frequency spectrum Fk(ω) observed at B = 13.0 mT around the intersection of the magnon and TA-phonon dispersion curves. (d) Comparison between experimentally obtained gap between the upper branch and lower branch of the frequency spectrum at B = 13.0 mT and the theoretical calculation of the gap frequency. Credit: Communications Physics (2022). DOI: 10.1038/s42005-022-00888-1 Read more

Parameter fitting of coherent oscillation. (a) Experimentally obtained temporal evolution of |F~k(t)|2 at B = 11.5 mT. (b) Calculated temporal evolution of magnon amplitude |a~k(t)|2. (c) Temporal evolution of |F~k(t)|2 at different wavenumbers. Gray curves represents fitting curves according to Eq. (3) described in the study. Errors of the data are evaluated as a standard deviation, which is smaller than the data plot. Credit: Communications Physics (2022). DOI: 10.1038/s42005-022-00888-1 Read more

Numerical calculation of magnon excitation intensity. (a) Heat map of G(r). σx and σy are set to realize plane-wave excitation of magnon polaron (σx = 40 nm, σy = 40 nm). (b) Time evolution of excitation intensity f(t). (c) Heat map of spectrum intensity calculated according to Eq. (ts = 1.5 ns, te = 1.6 ns, σt = 0.3 ns). The spectrum intensity takes peak at the dispersion crossing between transverse acoustic (TA) phonon and magnon, reproducing the experimental results. Credit: Communications Physics (2022). DOI: 10.1038/s42005-022-00888-1 Read more