Magnetostatic interaction between Bloch point nanospheres

Abstract

Three-dimensional topological textures have become a topic of intense interest in recent years. This work uses analytical and numerical calculations to determine the magnetostatic field produced by a Bloch point (BP) singularity confined in a magnetic nanosphere. It is observed that BPs hosted in a nanosphere generate magnetic fields with quadrupolar nature. This finding is interesting because it shows the possibility of obtaining quadrupole magnetic fields with just one magnetic particle, unlike other propositions considering arrays of magnetic elements to generate this kind of field. The obtained magnetostatic field allows us to determine the interaction between two BPs as a function of the relative orientation of their polarities and the distance between them. It is shown that depending on the rotation of one BP related to the other, the magnetostatic interaction varies in strength and character, being attractive or repulsive. The obtained results reveal that the BP interaction has a complex behavior beyond topological charge-mediated interaction.

Symmetry Breaking-Induced Resonance Dynamics in Bloch Point Nanospheres: Unveiling Magnetic Volume Effects and Geometric Parameters for Advanced Applications in Magnetic Sensing and Spintronics

“…For our calculations, we use an exchange stiffness A = 11 × 10 −12 J m −1 and a saturation magnetization M s = 800 × 10 3 Am −1 , corresponding to Permalloy. 42 We introduce asymmetries in these spheres by cutting specific sections characterized by the parameter δ = r/R, as illustrated in Figure 1a. A symmetric sphere is characterized by δ = 1.0, while a hemisphere is represented by δ = 0.0.…”

“…M denotes the magnetization vector, and H eff refers to the effective field obtained from the exchange and dipolar and anisotropy contributions to the energy. For our calculations, we use an exchange stiffness A = 11 × 10 –12 J m –1 and a saturation magnetization M s = 800 × 10 3 Am –1 , corresponding to Permalloy . We introduce asymmetries in these spheres by cutting specific sections characterized by the parameter δ = r / R , as illustrated in Figure a.…”

“…We specifically introduced geometric asymmetries by exploring BPs confined in magnetic nanospheres from which we extracted sections (planes) of the sphere, as depicted in Figure . The choice of such geometry is manifold: first, several reports on BP stabilization in spherical geometries allow us to safely establish a BP as (at least) a metastable state. ,,,,, Second, asymmetric nanospheres are likely easier to synthesize experimentally than perfectly symmetric ones, thus approaching a more feasible experimental realization of our system. Also, there is experimental evidence of BP-like structures in spherical nanoparticles .…”

“…For example, the switching of vortex cores in nanodisks has been demonstrated to be mediated by the nucleation of BPs. ,− Similarly, the annihilation of skyrmions during the contraction of their cores is also accompanied by the appearance of BPs. − The magnetization reversal process of a cylindrical nanowire with specific geometric and magnetic parameters is mediated by a vortex domain wall containing a BP at its center (referred to as the BP domain wall). ,, Furthermore, recent reports include proposals for different methods to nucleate and stabilize BPs. For instance, the nucleation and stabilization of BPs in bilayer-like systems with opposite signs of Dzyaloshinskii–Moriya interaction have been studied through micromagnetic simulations. ,, Similarly, some of us have studied the demagnetizing field generated by a BP nanosphere and explored its consequences on the interaction with other BPs and potential applications. Specifically, it was demonstrated that utilizing the demagnetizing field originating from an ordered array of BP nanospheres has significant applications in designing nanoscale magnetic traps .…”

Magnetic characterization techniques and micromagnetic simulations of magnetic nanostructures: from zero to three dimensions

“…, Bloch point) would exist within 0D MNs, but they have not yet been explicitly observed. 80 This is likely constrained by the spatial resolution of the nanosample preparation and transfer. X-ray tomographic mapping techniques with spatial resolution close to the nanometre range may help us acquire insight into these exotic 3D magnetic textures.…”