TY - JOUR
T1 - Tunable Mode Coupling in Nanocontact Spin-Torque Oscillators
AU - Zhang, Steven S. -L.
AU - Iacocca, Ezio
AU - Heinonen, Olle
PY - 2017/7/27
Y1 - 2017/7/27
N2 - Recent experiments on spin-torque oscillators have revealed interactions between multiple magnetodynamic modes, including mode coexistence, mode hopping, and temperature-driven crossover between modes. The initial multimode theory indicates that a linear coupling between several dominant modes, arising from the interaction of the subdynamic system with a magnon bath, plays an essential role in the generation of various multimode behaviors, such as mode hopping and mode coexistence. In this work, we derive a set of rate equations to describe the dynamics of coupled magnetodynamic modes in a nanocontact spin-torque oscillator. Expressions for both linear and nonlinear coupling terms are obtained, which allow us to analyze the dependence of the coupled dynamic behaviors of modes on external experimental conditions as well as intrinsic magnetic properties. For a minimal two-mode system, we further map the energy and phase difference of the two modes onto a two-dimensional phase space and demonstrate in the phase portraits how the manifolds of periodic orbits and fixed points vary with an external magnetic field as well as with the temperature.
AB - Recent experiments on spin-torque oscillators have revealed interactions between multiple magnetodynamic modes, including mode coexistence, mode hopping, and temperature-driven crossover between modes. The initial multimode theory indicates that a linear coupling between several dominant modes, arising from the interaction of the subdynamic system with a magnon bath, plays an essential role in the generation of various multimode behaviors, such as mode hopping and mode coexistence. In this work, we derive a set of rate equations to describe the dynamics of coupled magnetodynamic modes in a nanocontact spin-torque oscillator. Expressions for both linear and nonlinear coupling terms are obtained, which allow us to analyze the dependence of the coupled dynamic behaviors of modes on external experimental conditions as well as intrinsic magnetic properties. For a minimal two-mode system, we further map the energy and phase difference of the two modes onto a two-dimensional phase space and demonstrate in the phase portraits how the manifolds of periodic orbits and fixed points vary with an external magnetic field as well as with the temperature.
KW - spin transfer torque
KW - spin waves
KW - spintronics
KW - spin valves
KW - Landau-Lifschitz-Gilbert equation
U2 - 10.1103/PhysRevApplied.8.014034
DO - 10.1103/PhysRevApplied.8.014034
M3 - Article
VL - 8
JO - Physical Review Applied
JF - Physical Review Applied
SN - 2331-7019
IS - 1
M1 - 014034
ER -