We theoretically study field-induced domain wall motion in an electrically insulating ferromagnet with hard-and easy-axis anisotropies. Domain walls can propagate along a dissipationless wire through spin wave emission locked into the known soliton velocity at low fields. In the presence of damping, the usual Walker rigid-body propagation mode can become unstable for a magnetic field smaller than the Walker breakdown field. DOI: 10.1103/PhysRevLett.109.167209 PACS numbers: 75.60.Jk, 75.30.Ds, 75.60.Ch, 85.75.Àd Magnetic domain wall (DW) propagation in nanowires has attracted attention because of the academic interest of a unique nonlinear system [1][2][3][4] and potential applications in data storage and logic devices [4][5][6]. The field-driven DW dynamics is governed by the Landau-Lifshitz-Gilbert (LLG) equation [1], which has analytical solutions in limiting cases [1,7], such as the soliton solution [8] in the absence of both dissipations and external magnetic fields. The interplay between spin waves (SWs) and DWs has also received attention, including DW propagation driven by externally generated SWs [9][10][11] and SW generation by a moving DW [12,13]. Our understanding of the fieldinduced DW motion is nevertheless far from complete. According to conventional wisdom, DWs move under a static magnetic field only in the presence of energy dissipation [1,14]. Numerical evidence against this view therefore came as a surprise [12,15].We report here a physical picture for the SW emissioninduced domain wall motion for a head-to-head DW in a magnetic nanowire with the easy axis along the wire (z direction) as shown in Fig. 1. Let K k and K ? be anisotropy coefficients of the easy and hard axis (along the x direction), respectively. An external field along the wire rotates the DW out of the yz plane. The DW structure thereby experiences an internal field in the x direction twisting the DW plane and generating a nonuniform internal field along the wire. This field causes periodic deformations of the DW structure, such as ''breathing'' [1] by which the entire DW precesses around the wire axis while its width shrinks and expands periodically. The local modulation of the magnetization texture generates SWs (wavy lines with arrows in Fig. 1) that radiate away from the DW center. The energy needed to generate the SWs has to come from the Zeeman energy [14] that is released by propagating the DW. The DW velocity of a dissipationless ferromagnet in the steady state may then be expected to be proportional to the SW emission rate.In this Letter, we numerically solve the LLG equation, initially without damping in order to confirm the above mentioned relation between spin wave emission and DW propagation. Depending on K ? and the magnetic field, breathing or more complicated periodic transformations of the DW emit spin waves. The DW propagation at low fields tends to lock into a particular soliton mode in which the energy dissipation rate due to the SW emission is balanced by the Zeeman energy gain. We predict robust spin wa...

Spin current injection and spin accumulation near a ferromagnetic insulator (FI)/nonmagnetic metal (NM) bilayer film under a thermal gradient is investigated theoretically. Using the Fermi golden rule and the Boltzmann equations, we find that FI and NM can exchange spins via interfacial electron-magnon scattering because of the imbalance between magnon emission and absorption caused by either non-equilibrium distribution of magnons or non-equilibrium between magnons and electrons. A temperature gradient in FI and/or a temperature difference across the FI/NM interface generates a spin current which carries angular momenta parallel to the magnetization of FI from the hotter side to the colder one. Interestingly, the spin current induced by a temperature gradient in NM is negligibly small due to the nonmagnetic nature of the non-equilibrium electron distributions. The results agree well with all existing experiments.