We study the microscopical origin of anisotropic ferromagnetism in the van der Waals magnet ${\text{CrI}}_3$. We conclude that the nearest-neighbor exchange is well described by the Heisenberg-Kitaev-$\mathrm{\Gamma }$ ($\mathrm{HK}\mathrm{\Gamma }$) model, and we also find a nonzero Dzyaloshinskii-Moriya interaction (DMI) on next-nearest neighbors. Both Kitaev and DMI are known to generate a nontrivial topology of the magnons in the honeycomb lattice and have been used separately to describe the low-energy regime of this material. We discuss how including one or the other leads to different signs of the Chern number. Furthermore, the topological gap at the $\mathit{K}$ point seems to be mainly produced by the DMI, despite its being one order of magnitude smaller than Kitaev. Finally, we show that, by applying an external electric field perpendicular to the crystal plane, it is possible to induce DMI on nearest neighbors, and this could have consequences in noncollinear spin textures, such as domain walls and skyrmions.

Hopfions are localized and topologically nontrivial magnetic configurations that have received considerable attention in recent years. In this Letter, we use a micromagnetic approach to analyze the scattering of spin waves (SWs) by magnetic hopfions. Our results evidence that SWs experience an electromagnetic field generated by the hopfion and sharing its topological properties. In addition, SWs propagating along the hopfion symmetry axis are deflected by the magnetic texture, which acts as a convergent or divergent lens, depending on the SWs’ propagation direction. Assuming that SWs propagate along the plane perpendicular to the symmetry axis, the scattering is closely related to the Aharonov-Bohm effect, allowing us to identify the magnetic hopfion as a scattering center.

We studied the performance of classical and quantum magnetic Otto cycle with a working substance composed of a single quantum dot using the Fock–Darwin model with the inclusion of the Zeeman interaction. Modulating an external/perpendicular magnetic field, in the classical approach, we found an oscillating behavior in the total work extracted that was not present in the quantum formulation.We found that, in the classical approach, the engine yielded a greater performance in terms of total work extracted and efficiency than when compared with the quantum approach. This is because, in the classical case, the working substance can be in thermal equilibrium at each point of the cycle, which maximizes the energy extracted in the adiabatic strokes.

We show that proper control of magnetization textures can be achieved in noncollinear antiferromagnets. This opens the versatile toolbox of domain-wall manipulation in the context of a different family of materials. In this way, we show that noncollinear antiferromagnets are a good prospect for applications in the context of antiferromagnetic spintronics. As in many noncollinear antiferromagnets, the order parameter field takes values in SO(3). By performing a gradient expansion in the energy functional we derive an effective theory that accounts for the physics of the magnetization of long-wavelength excitations. We apply our formalism to static and dynamic textures such as domain walls and localized oscillations, and identify topologically protected textures that are spatially localized. Our results are applicable to the exchange-bias materials ${\text{Mn}}_{3}X$, with $X=\text{Ir},\text{Rh},\text{Pt}$.

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.

We study the effect of the degeneracy factor in the energy levels of the well-known Landau problem for a magnetic engine. The scheme of the cycle is composed of two adiabatic processes and two isomagnetic processes, driven by a quasi-static modulation of external magnetic field intensity. We derive the analytical expression of the relation between the magnetic field and temperature along the adiabatic process and, in particular, reproduce the expression for the efficiency as a function of the compression ratio.