Diagram for vortex formation in quasi-two-dimensional magnetic dots

Abstract

The existence of nonlinear objects of the vortex type in two-dimensional magnetic systems presents itself as one of the most promising candidates for the construction of nanodevices, useful for storing data, and for the construction of reading and writing magnetic heads. The vortex appears as the ground state of a magnetic nanodisk whose magnetic moments interact via dipole-dipole potential?. In this work it is investigated the conditions for the formation of vortices in nanodisks in triangular, square, and hexagonal lattices as a function of the size of the lattice and of the strength of the dipole interaction D. Our results show that there is a "transition" line separating the vortex state from a capacitor like state. This line has a finite size scaling form depending on the size, L, of the system as Dc=D0 +1/A(?1+B*L^2)?. This behavior is obeyed by the three types of lattices. Inside the vortex phase it is possible to identify two types of vortices separated by a constant, D=Dc, line: An in-plane and an out-of-plane vortex. We observed that the out-of-plane phase does not appear for the triangular lattice. In a two layer system the extra layer of dipoles works as an effective out-of-plane anisotropy inducing a large S^z component at the center of the vortex. Also, we analyzed the mechanism for switching the out-of-plane vortex component. Contrary to some reported results, we found evidences that the mechanism is not a creation-annihilation vortex anti-vortex process.Comment: 5 page

Spin-Wave Dynamics in the Presence of Magnetic Vortices

“…Our results obtained for circular dots are consistent with this observation: in-plane vortex is stable in such a system for very weak exchange interaction, much weaker than in usual ferromagnets. We obtain the critical dipolar-to-exchange interaction ratio d 1 ¼ 0:1115 (which corresponds to the exchange integral J ¼ 0:058 eV) and this value is the same as received from Monte Carlo simulations in reference [37]. This critical value does not depend on the size of a dot which is also in agreement with simulations [37].…”

“…On the other hand, in comparison with time-domain simulations, the time of calculations is very short, and the spin-wave spectrum is obtained directly from diagonalization of the dynamic matrix (without the usage of the Fourier transformation). For simple magnetic configurations, our results are in perfect agreement with simulations [37,13,44]. In the case of more complicated systems, the simulations should be used for finding the stable magnetic configuration and for the simulated configuration the dynamical matrix method can be used to obtain the spin-wave spectrum.…”

“…Surprisingly, for the exchange-driven reorientation the critical value d 1 ¼ 0:1115 and is constant in the whole range of the dot size, i.e., from 60 to 8000 spins (L ¼ 9−101). (The same value and behavior of d 1 is reported in reference [37] where circular dots are studied by means of Monte Carlo simulations. )…”

Manipulation of magnetic state in nanostructures by perpendicular anisotropy and magnetic field

“…5,26 This state can be approximately assumed as the ground state. 5,27,28 Then, we track the evolution of the lattice at different K z . Following earlier reports, 5,26 the lattice is allowed to evolve in a ladder protocol, i.e., K z is varied following the linear protocol…”

The influence of magnetic impurities in the vortex core dynamics in magnetic nano-disks

“…We consider the magnetic nano-disks modeled by magnetic moments with dipole-dipole and exchange interactions [26] and we follow Ref. [27] to build the simulated nano-disks.…”