Magnonic Floquet Hofstadter Butterfly

TL;DR

This paper introduces the magnonic Floquet Hofstadter butterfly in a honeycomb ferromagnet, revealing fractal spectra, topological properties, and the effects of oscillating electric fields on magnon quasiparticles.

Contribution

It presents the first theoretical framework for the magnonic Floquet Hofstadter butterfly, combining space- and time-dependent electric fields to explore topological phases in insulating honeycomb ferromagnets.

Findings

Magnonic Hofstadter spectrum exhibits fractal structure similar to graphene under magnetic field.

Magnon Chern numbers are odd, leading to quantized magnon Hall conductance.

Floquet formalism reveals topological phase transitions driven by electric field parameters.

Abstract

We introduce the magnonic Floquet Hofstadter butterfly in the two-dimensional insulating honeycomb ferromagnet. We show that when the insulating honeycomb ferromagnet is irradiated by an oscillating space- and time-dependent electric field, the hopping magnetic dipole moment (i.e. magnon quasiparticles) accumulate the Aharonov-Casher phase. In the case of only space-dependent electric field, we realize the magnonic Hofstadter spectrum with similar fractal structure as graphene subject to a perpendicular magnetic field, but with no spin degeneracy due to broken time-reversal symmetry by the ferromagnetic order. In addition, the magnonic Dirac points and Landau levels occur at finite energy as expected in a bosonic system. Remarkably, this discrepancy does not affect the topological invariant of the system. Consequently, the magnonic Chern number assumes odd values and the magnon Hall conductance gets quantized by odd integers. In the case of both space- and time-dependent electric field, the theoretical framework is studied by the Floquet formalism. We show that the magnonic Floquet Hofstadter spectrum emerges entirely from the oscillating space- and time-dependent electric field, which is in stark contrast to electronic Floquet Hofstadter spectrum, where irradiation by circularly polarized light and a perpendicular magnetic field are applied independently. We study the deformation of the fractal structure at different laser frequencies and amplitudes, and analyze the topological phase transitions associated with gap openings in the magnonic Floquet Hofstadter butterfly.