Magnonic Floquet Hofstadter butterfly

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. arXiv:1809.09102v1 [cond-mat.str-el]

Photo-induced Floquet Weyl magnons in noncollinear antiferromagnets

“…Therefore for an experimentally feasible light wavelength λ of order 10 −8 m, the spin magnetic dipole moment gµ B carried by magnon in the periodically driven insulating magnets is comparable to the electron charge e. This shows that the electronic Floquet topological systems [1][2][3][4][5] are indeed similar to the magnetic bosonic Floquet topological systems recently studied in insulating ferromagnets with finite magnetization [24,[26][27][28]. In magnetic systems, however, the Floquet physics can reshape the underlying spin Hamiltonian to stabilize magnetic phases and provides a promising avenue for inducing and tuning topological spin excitations in trivial quantum magnets [24,26,27], as well as photoinduced topological phase transitions in intrinsic topological magnon insulators [28]. This formalism provides a direct avenue of generating and manipulating ultrafast spin current using terahertz radiation [29].…”

Laser control of magnonic topological phases in antiferromagnets

“…[14]. Therefore by applying this mapping to Floquet TIs established in Dirac electron systems [63,64], the magnonic analog of the Floquet TIs can be derived theoretically [103][104][105][106]. Moreover, while it is outside the scope of this work since we focus on the magnon dynamics away from the adiabatic limit Ω ω c , the laser-induced resonance across the Landau energy gap of magnons is expected to be generated, in the same way as the ac fielddriven resonance across the band gap [20,21], by tuning the laser frequency to the cyclotron frequency of magnons Ω ≈ ω c , which we leave for the further study [99].…”

Laser-controlled real- and reciprocal-space topology in multiferroic insulators

“…Previously, Floquet topological magnons were discussed in collinear ferromagnets and antiferromagnets driven by a laser field which couples to the magnetic order via the Aharonov-Casher effect [48,[59][60][61][62]. However, this approach is unsuitable for noncollinear magnetic textures whose magnetic unit cell, of paramount importance for the proper description of magnons, may itself become time-dependent [63].…”