Origin, criterion, and mechanism of vortex-core reversals in soft magnetic nanodisks under perpendicular bias fields

Abstract

We studied dynamics of vortex-core reversals driven by circular rotating fields along with static perpendicular magnetic fields of different direction and strength. We found that the application of perpendicular fields ${H}_{\text{p}}$ modifies the starting ground state of vortex magnetizations, thereby instigating the development of a magnetization dip ${m}_{\text{z},\text{dip}}$ in the vicinity of the original core up to its threshold value, ${m}_{\text{z},\text{dip}}^{\text{cri}}\ensuremath{\sim}\ensuremath{-}p$, which is necessary for vortex-core reversals, where $p$ is the initial core polarization. We found the relationship of the dynamic evolutions of the ${m}_{\text{z},\text{dip}}$ and the out-of-plane gyrofields ${h}_{\text{z}}$, which was induced, in this case, by vortex-core motion of velocity $\ensuremath{\upsilon}$, thereby their critical value relation ${\ensuremath{\upsilon}}_{\text{cri}}\ensuremath{\propto}{h}_{\text{z}}^{\text{cri}}$. The simulation results indicated that the variation of the critical core velocity ${\ensuremath{\upsilon}}_{\text{cri}}$ with ${H}_{\text{p}}$ can be expressed explicitly as ${\ensuremath{\upsilon}}_{\text{cri}}/{\ensuremath{\upsilon}}_{\text{cri}}^{0}=(\ensuremath{\rho}/{\ensuremath{\rho}}_{0})|\ensuremath{-}p\ensuremath{-}{m}_{\text{z},\text{dip}}^{\text{g}}|$, with the core size $\ensuremath{\rho}$ and the starting ground-state magnetization dip ${m}_{\text{z},\text{dip}}^{\text{g}}$ variable with ${H}_{\text{p}}$, and for the values of ${\ensuremath{\upsilon}}_{\text{cri}}^{0}$ and ${\ensuremath{\rho}}_{0}$ at ${H}_{\text{p}}=0$. This work offers deeper and/or new insights into the origin, criterion and mechanism of vortex-core reversals under application of static perpendicular bias fields.