Study of magnon–phonon non-equilibrium in a magnetic insulator—Thulium iron garnet

The non-equilibrium state between magnons and phonons is the key to understand the spin-caloric phenomena. We developed a unique optical reflectometry technique to spatially resolve Kerr angle ( θK) and optical reflectance ( R) in a magnetic insulator—thulium iron garnet (TmIG). The TmIG was subjected to a thermal gradient to estimate populations of thermally excited magnons and phonons through the variation of θK and R. The results showed that the spatial gradient of θK is different from that of R, indicating the non-equilibrium state between magnons and phonons. Particularly, the characteristic decay length of θK was significantly influenced by the heating power and the magnetic field, suggesting non-linear magnon scattering in a high magnon density regime. Our work not only provides a scheme to investigate the spatial profiles of magnons and phonons but also reveals the magnon–phonon non-equilibrium in TmIG. Hence, this report will stimulate further studies based on magnon–phonon non-equilibrium such as a transverse spin Seebeck effect and Bose–Einstein condensation.