Amplification of Spin Waves in the Antiferromagnet through the Spin Hall Effect

Presently, the field of magnonics attracts more and more interest from scientists. This circumstance is because, unlike conventional electronics, in which an electric current carries information, in magnonics, the magnon current is the means of transmitting the information. Because of the development of this area, it is possible to create new storage devices and batteries. In this regard, an important direction is the study of spin-waves in magnetic materials, especially in antiferromagnets, whose dynamics, which is more complex than ferromagnets, opens the way to the terahertz range devices. A spin wave propagating in the magnetic material is damped, so there is a need for spin current amplifiers.The purpose of this work is to model amplification of a spin-wave in a ferromagnetic Yttrium Iron Garnet (YIG) strip using transport equation and to compare linear and nonlinear cases. Complexity of solving this equation analytically leads to consideration of solving it with semi-analytical method of characteristics and second-order Runge-Kutta method. This work demonstrates process of normalization of the equation, semi-analytical solution and dependence of amplitude of a spin-wave and its real and imaginary parts in the linear and nonlinear cases. As a result, amplitude increases for all of the integration time in linear case and tends to the constant value in nonlinear one. Constant amplitude value depends on the absolute value of nonlinearity coefficient.