Magnon polaron formed by selectively coupled coherent magnon and phonon modes of a surface patterned ferromagnet

Strong coupling between two quanta of different excitations leads to the formation of a hybridized state that paves a way for exploiting new degrees of freedom to control phenomena with high efficiency and precision. A magnon polaron is the hybridized state of a phonon and a magnon, the elementary quanta of lattice vibrations and spin waves in a magnetically ordered material. A magnon polaron can be formed at the intersection of the magnon and phonon dispersions, where their frequencies coincide. The observation of magnon polarons in the time domain has remained extremely challenging because the weak interaction of magnons and phonons and their short lifetimes jeopardize the strong coupling required for the formation of a hybridized state. Here, we overcome these limitations by spatial matching of magnons and phonons in a metallic ferromagnet with a nanoscale periodic surface pattern. The spatial overlap of the selected phonon and magnon modes formed in the periodic ferromagnetic structure results in a high coupling strength which, in combination with their long lifetimes, allows us to find clear evidence of an optically excited magnon polaron. We show that the symmetries of the localized magnon and phonon states play a crucial role in the magnon polaron formation and its manifestation in the optically excited magnetic transients.

Figure 1

Phonons and magnons in a galfenol nanograting. (a) Design of the studied sample and its SEM image. (b) Experimental scheme: MO – microscope objective, WP – Wollaston prism, BOR – balanced optical receiver, BS – beam splitter, P – polarizer. (c) Calculated displacements for two phonon modes (exaggerated for clarity) excited by the pump pulse. Black arrows illustrate the used coordinate system. The blue and red arrows indicate the main lattice motions for the two modes. (d) Transient reflectivity signal and its fast Fourier transform (FFT) recorded on the grating at conditions when the interaction between the phonon and magnon modes of the NG is fully suppressed (see the text). The inset shows the close-up of the transient signal after subtraction of the slow background. (e) Transient Kerr rotation (KR) signal measured from an unpatterned part of the studied film and its FFT obtained for $t>1\mathrm{ns}$. The inset shows the zoomed fragment of the transient KR signal, where the fundamental magnon mode solely contributes to the magnetization precession. In both (d) and (e) the transient signals in the insets and their FFTs are shown by symbols, while the fits and their FFT are shown by solid lines. (f) A diagram, which demonstrates the idea of the experiment: the field-dependent magnon mode (oblique line) is tuned into resonance with the field-independent phonon modes (horizontal lines) by an external magnetic field. The crossing points correspond to the FM-QTA and FM-QLA resonance conditions where the magnon-phonon hybridization is expected.

Figure 2

Hybridization of magnon and phonon modes. (a) Color map which shows the spectral density of the measured KR signal as a function of the external magnetic field applied along the NG diagonal when the interaction between the magnon and phonon modes of NG has maximal strength [35]. The anticrossing is observed at $f=13\mathrm{GHz}$ and $B=110\mathrm{mT}$. The inset shows the magnetic field dependence of the spectral peaks in the magnon spectrum around the intersection of the QTA and FM modes. (b) Transient KR signals (left panels) and their FFTs (right panels) at nonresonant $\left(B=30\mathrm{mT}\right)$ and resonant $\left(B=110\mathrm{mT}\right)$ conditions. Symbols show the measured signals and their FFTs; solid lines show respective fits and their FFTs. (c) Zoomed fragments of the FFT spectra shown in (b) around the resonance frequency. The splitting of the line in the resonance at $B=110\mathrm{mT}$ is clearly seen.

Figure 3

Phonon driving of magnons. (a) Kerr rotation signal and its FFT measured at $B=140\mathrm{mT}$ corresponding to the resonance of the FM and QLA phonon modes. (b) FFTs around $f_{\mathrm{QLA}}$ obtained from the KR (left panel) and reflectivity (right panel) signals measured at resonant $\left(B=140\mathrm{mT}\right)$ and nonresonant $\left(B=30\mathrm{mT}\right)$ conditions. (c) Magnetic field dependences of the normalized amplitudes at $f=f_{\mathrm{QLA}}=14.5\mathrm{GHz}$ for the Kerr rotation (lower) and reflectivity (upper) signals (lines are guides for the eye).

Figure 4

Modeling of the magnon polaron spectrum. (a) Spatial distributions of the normalized dynamical magnetization of the fundamental magnon mode and the normalized strain components for the symmetric QTA, antisymmetric $\mathrm{QTA}*$ and symmetric QLA modes. The blue arrows show the pairs, for which the overlap integrals have non-negligible values. (b) The color map shows the calculated magnetic field dependence of the spectral density of the magnon states calculated in the model of three coupled harmonic oscillators. The initial conditions for the calculations are set as following: the lower QTA* mode is not excited (as mentioned in the text), the energy transfer from the pump pulse to the upper QLA mode significantly exceeds the energy transferred to the FM mode. (c) Calculated magnon spectral power density for magnetic fields corresponding to the resonance of the FM mode with the QTA* mode $\left(B=110\mathrm{mT}\right)$ and with the QLA mode $\left(B=140\mathrm{mT}\right)$.