Electronic Thesis and Dissertation Repository


Doctor of Philosophy




Prof. Michael G. Cottam


Motivated by recent experimental developments, we present a theoretical study of some linear and nonlinear properties of spin waves in ferromagnetic nanostructures under conditions of microwave pumping. A microscopic (or Hamiltonian-based) approach is followed including terms for both the short-range exchange and the long-range dipole-dipole interactions, as well as the effects of an external magnetic field, single-ion anisotropy, biquadratic exchange and the Ruderman-KittelKasuya-Yosida interactions, as appropriate. In ultrathin films and nanowires with thickness or lateral dimensions less than about 100 nm, the discreteness of the quantized spin waves (or magnons) and their spatial distributions become modified, making it appropriate to employ a microscopic approach to the nonlinear dynamics based on a lattice model. First an application is made to the magnetization dynamics in trilayer nanowires, consisting of Permalloy layers separated by a nonmagnetic Ru spacer layer. The experimental results for different stripe widths are successfully analyzed using our microscopic theory. Next we investigate the nonlinear spin-wave properties of ultrathin films and ferromagnetic nanowires with rectangular cross sections as well as nanowires and nanotubes with circular cross sections. Numerical results are deduced for the spin-wave frequencies as a function of wave vector, for either parallel or perpendicular external field orientations. Also numerical applications are presented for the dependence of the threshold microwave field amplitudes for instability on the static applied field (the analog of the butterfly curves). Effects due to the discreteness of the spin-wave branches lead to structural features in the butterfly curves that are significantly different, due to edge effects, in nanowires compared with those in the bulk and for ultrathin films. Further, we examine the instability thresholds for nonlinear processes in ferromagnetic stripes and films under perpendicular pumping with an microwave field. Finally the quantum statistical properties are investigated for microwave-driven magnon system in the presence of four-magnon interactions. In particular, collapse-and-revival-phenomena for the time evolution of the average magnon number, squeezing, and super-Poissonian statistics of magnons are studied. Bulk systems are analyzed initially, and then the results are generalized to consider cross correlation and other behavior in two-mode magnon systems.