We calculate the effects of the spin-lattice coupling on the magnon spectrum of thin ferromagnetic films consisting of the magnetic insulator yttrium-iron garnet. The magnon-phonon hybridisation generates a characteristic minimum in the spin dynamic structure factor which quantitatively agrees with recent Brillouin light scattering experiments. We also show that at room temperature the phonon contribution to the magnon damping exhibits a rather complicated momentum dependence: In the exchange regime the magnon damping is dominated by Cherenkov type scattering processes, while in the long-wavelength dipolar regime these processes are subdominant and the magnon damping is two orders of magnitude smaller. We supplement our calculations by actual measurements of the magnon relaxation in the dipolar regime. Our theory provides a simple explanation of a recent experiment probing the different temperatures of the magnon and phonon gases in yttrium-iron garnet.

We investigate the spin transport properties of a topological magnon insulator, a magnetic insulator characterized by topologically nontrivial bulk magnon bands and protected magnon edge modes located in the bulk band gaps. Employing the Landau-Lifshitz-Gilbert phenomenology, we calculate the spin current driven through a normal metal|topological magnon insulator|normal metal heterostructure by a spin accumulation imbalance between the metals, with and without random lattice defects. We show that bulk and edge transport are characterized by different length scales. This results in a characteristic system size where the magnon transport crosses over from being bulk-dominated for small systems to edge-dominated for larger systems. These findings are generic and relevant for topological transport in systems of nonconserved bosons.

We show that the formation of a magnon condensate in thin ferromagnetic films can be explained within the framework of a classical stochastic non-Markovian Landau-Lifshitz-Gilbert equation where the properties of the random magnetic field and the dissipation are determined by the underlying phonon dynamics. We have numerically solved this equation for a tangentially magnetized yttrium-iron garnet film in the presence of a parallel parametric pumping field. We obtain a complete description of all stages of the nonequilibrium time evolution of the magnon gas which is in excellent agreement with experiments. Our calculation proves that the experimentally observed condensation of magnons in yttrium-iron garnet at room temperature is a purely classical phenomenon which should be called Rayleigh-Jeans rather than Bose-Einstein condensation.PACS numbers: 75.30. Ds, 75.10.Hk, 05.30.Jp In the past decade the nonequilibrium dynamics of parametrically pumped magnons in thin yttrium-iron garnet (YIG) films has been investigated by many experimental studies [1][2][3][4][5][6][7][8][9]. Very rich physics was found, including the overpopulation of the lowest energy state, which was interpreted as Bose-Einstein condensation (BEC) of magnons at room temperature and finite momentum. Using the technique of Brillouin light scattering it is even possible to measure the magnon distribution with momentum and time resolution [10]. This allows an observation of the parametric resonance and of the subsequent thermalization leading to the formation of the condensate in detail [6,7]. Unfortunately, a complete theoretical understanding of this phenomenon is still lacking and there is no theory that can simultaneously describe all stages of the experiment. While the so-called S-theory [11][12][13][14][15][16][17][18] is able to describe the parametric resonance used to populate certain magnon states, it does not properly take magnon-magnon scattering into account and therefore cannot describe the cascade of relaxation processes leading to the formation of a magnon condensate. On the other hand, theories that focus on the condensate usually do not take the pumping dynamics into account and start with some given quasiequilibrium state which can be identified with the ground state of some effective quantum mechanical Hamiltonian [19][20][21]. Phenomenological approaches of the Ginzburg-Landau type also have been used to study the condensation dynamics [22]. Finally, theories dealing with the relaxation processes and kinetics of excited magnons did not include the possibility of magnon condensation [23][24][25][26].Since BEC is a manifestation of quantum mechanics, it seems at the first sight reasonable that quantized magnons obeying Bose statistics are essential to obtain a satisfactory theoretical description of magnon condensation in YIG. However, since the experiments are performed at room temperature, which is large compared with the relevant magnon energies, the equilibrium distribution of the magnons is the Rayleigh-Jeans rather than t...

We develop a microscopic theory of spin-lattice interactions in magnetic insulators, separating rigid-body rotations and the internal angular momentum, or spin, of the phonons, while conserving the total angular momentum. In the low-energy limit, the microscopic couplings are mapped onto experimentally accessible magnetoelastic constants. We show that the transient phonon spin contribution of the excited system can dominate over the magnon spin, leading to nontrivial Einstein-de Haas physics.