Spin Dynamics Of Magnetic Vortex Under Perpendicular Resonant Magnetic Fields

Magnetic vortex is the common ground state in low-dimensional magnetic nanomaterials.The polarity of a magnetic vortex can be coded as the logical units "0" and"1" for information storage devices.Precise control of the polarity of vortex core(VC)is key to fabricate magnetic vortex random access memory.Using a perpendicular magnetic field,the VC polarity can be reversed in situ,which is advantageous to read the VC polarity.Therefore,it is of great significance to study the mechanism of speeding up the VC reversal under a perpendicular magnetic field.Our first exploration thrust is to design a geometrically non-uniform magnetic nanodisk and utilize the abrupt structural change to manipulate the spin wave property.We designed a cylindrical cavity in the center of a magnetic nanodisk in expecting that the boundary of the cavity would confine the spin wave inside.Our micromagnetic simulations confirmed that the radial spin waves excited by alternating perpendicular magnetic field were confined inside the cavity which led to much stronger magnetization oscillations and greatly enhanced VC reversal speed.The spin wave potential well created by the cylindrical cavity can be attributed to the large gradient of exchange field at the cavity boundary.In addition to speeding up the VC reversal,the cylindrical cavity also extends the frequency range in which the alternating perpendicular magnetic field can switch the VC polarity.Our second thrust is to design spatially non-uniform magnetic field in order to raise the efficiency of stimulating spin wave.Previous studies have shown that using a spatially uniform magnetic field,the vortex can only be effectively reversed using the fundamental spin wave mode.The higher order modes are much less able to switch the VC.It is noteworthy that the non-fundamental radial-spin-wave modes are characterized by annular alternating phase regions where adjacent regions are in antiphase.Our micromagnetic simulations show that the spinwaves excited by fields exerted in the in-phase regions are also in phase,therefore generate strong magnetization oscillations due to constructive spinwave interference.Comparing with the spatially uniform field,the annular magnetic fields significantly speed up the VC reversal by exciting non-fundamental radial-spin-wave modes.The fact of much stronger radial-spin-wave excited by perpendicular annular magnetic leads us to guess that,to generate spin-wave resonance in a magnetic nanodisk,not only the frequency of external field should match one of the resonance frequencies but also the spatial distribution of external field must meet a certain requirement.Thus we make further exploration by making the spatial distribution of external field to agree with the phase distribution of a radial-spin-wave mode,and the oscillation phases of external field in adjacent phase regions are 180-degree out-of-phase.Such "phase-matched"external magnetic field is composed of multiple annular regions,and our micromagnetic calculations demonstrate that the spin-waves stimulated by such annular field sources are always in-phase.This leads to much higher efficiency of exciting spin-wave by the"phase matched" field,in comparison to the spatially uniform external field.Our numerical calculations show that,under non-fundamental mode,the "phase matched"field greatly increases the VC reversal speed.In addition to phase-matching,we found that matching the spatial distribution of field amplitude with the amplitude distribution of a radial-spin-wave mode can further increase the efficiency in stimulating spin-wave.Moreover,when the external field is confined at the antinodes of a radial-spin-wave mode,the spin-wave excited by field is even stronger.These result clearly demonstrate that,complete resonance requires not only the matchness of the stimulus frequency with the resonance frequency,but also the matchness of spatial distribution of the stimulus with that of the resonance mode.We therefore call such resonance,created by stimulus which matches the resonance mode both in the time domain and space domain,the multidimensional resonance.Our analytical calculations on boundary fixed circular membrane and string proof that multidimensional resonance exists in mechanical systems as well.Since the superposition of wave does not depend on the materials,our results demonstrate that multidimensional resonance is a general principle of oscillation.Our work opens an uncharted region in the study of oscillation.