Skyrmions in thin films with easy-plane magnetocrystalline anisotropy

Abstract

We demonstrate that chiral skyrmionic magnetization configurations can be found as the minimum energy state in B20 thin film materials with easy-plane magnetocrystalline anisotropy with an applied magnetic field perpendicular to the film plane. Our observations contradict results from prior analytical work, but are compatible with recent experimental investigations. The size of the observed skyrmions increases with the easy-plane magnetocrystalline anisotropy. We use a full micromagnetic model including demagnetization and a three-dimensional geometry to find local energy minimum (metastable) magnetization configurations using numerical damped time integration. We explore the phase space of the system and start simulations from a variety of initial magnetization configurations to present a systematic overview of anisotropy and magnetic field parameters for which skyrmions are metastable and global energy minimum (stable) states. Skyrmions are topological defects1 that can be observed in the magnetization configuration of materials that lack inversion symmetry, 2 either due to a noncentrosymmetric crystal lattice, 3,4 or at interfaces between different materials.5 This lack of inversion symmetry results in a chiral interaction known as the Dzyaloshinskii-Moriya (DM) interaction.3,4 The DM interaction results in a rich variety of chiral magnetization configurations, including helical, conical, and skyrmionic magnetization configurations. Skyrmionic configurations were predicted 6 and later observed in helimagnetic materials, 7-10 and materials with an interfacial DM interaction. 11-15Skyrmions demonstrate potential for applications in data storage and processing devices. Skyrmions have been observed with diameters of the order of atom spacings in mono-atomic Fe layers, 16 which is significantly smaller than the magnetic domains proposed for the racetrack memory design.17 This results in a greater storage density. The movement of skyrmions has also been demonstrated 18,19 using spin-polarized current densities of the order 10 6 Am −2 , which is orders of magnitude less than what is required to move magnetic domain walls.17,20 These observations demonstrate potential for skyrmion-based racetrack memory technology 21 and other data storage and processing devices. 22Certain material restrictions need to be overcome before skyrmions can be used in such technologies. While skyrmions can be stabilized, they are only stable in a limited region of the parameter space defined by an applied magnetic field and the temperature. This region is narrow in bulk materials, 7 larger in thin film materials, 9and further stabilized in laterally confined geometries 23 and materials with pinning defects. 24 Analytical analysis of helimagnetic thin film material models find that skyrmion lattice states are ground states in helimagnetic thin films with an applied magnetic field only in systems with easy-axis magnetocrystalline anisotropy, 2,25where the easy axis and the applied field are perpendicular to the plane of the film. However, si...

Chopping skyrmions from magnetic chiral domains with uniaxial stress in magnetic nanowire

“…29, we use the following parameters: the non-adiabaticity factor 0 .1 , and the degree of spin polarization is P=0.5.It should be mentioned that the demagnetization energy or the magnetic dipole interaction is neglected in our model. In thin-plate magnets, magnetic skyrmions is often realized by competition among the magnetostatic energy, the exchange interaction, and the uniaxial magnetic anisotropy[44][45][46][47]. For our model, comparing the results of with and without including the demagnetization energy, the influence of the demagnetization energy approximately reduces to a perpendicular uniaxial anisotropy with anisotropy constant , the demagnetization energy only quantitatively affects our results without any qualitative changes.…”

Exotic skyrmion crystals in chiral magnets with compass anisotropy

“…B20-type helimagnets with another type of easy-plane anisotropy A s ( S i z ) 2 ( A s > 0) were also studied by MC simulation, which shows that this anisotropy may lead to the alternating HSk and HASk crystal structures on a square lattice at proper A too 40 . In addition, skyrmions in B20-type helimagnet thin films with easy-plane anisotropy A s ( S i z ) 2 ( A s > 0) were recently studied using a micromagnetic model including demagnetization and a three-dimensional geometry 41 . This work showed the demagnetization effects and/or the finite thickness effects on the skyrmion energetics and stability, which were explicitly demonstrated in earlier studies 42 43 .…”

Antiferromagnetism Emerging in a Ferromagnet with Gain

“…While the physical meaning of a negative dipolar interaction −H DDI n i is not so transparent, we find that the dipole-dipole interaction effectively renormalizes the exchange constant as J → J − µ 0 M 2 s a 3 /(4π) when the stabilized magnetizations are aligned in an antiparallel manner, by expanding the Hamiltonian for nearest neighbors. This correction, however, usually is negligibly small: In Fe 0.7 Co 0.3 Si [36], for example, the ratio µ 0 M 2 s a 3 /(4πJ) ∼ 10 −4 . We thus conclude that a ferromagnet with gain is equivalent to an antiferromagnet with an equal amount of loss.…”