RESUMO
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.
RESUMO
A theory of the dynamics of the Bose-Einstein condensate of magnons is presented. It is shown that, despite magnon decay processes, ongoing during the condensate formation, the system manifests spontaneous quantum coherence with a pseudo-spin degree of freedom originated from the presence of two valleys in momentum space. Finally, a real space description of the condensed state is provided, revealing the condensate state as a spin density wave. The effective dynamics of the spinor condensate wavefunction is characterized, and it is shown to display Josephson-like relations.