Strongly Coupled Magnon-Plasmon Polaritons in Graphene-Two-Dimensional Ferromagnet Heterostructures

Abstract

Magnons and plasmons are different collective modes, involving the spin and charge degrees of freedom, respectively. Formation of hybrid plasmon-magnon polaritons in heterostructures of plasmonic and magnetic systems faces two challenges, the small interaction of the electromagnetic field of the plasmon with the spins, and the energy mismatch, as in most systems plasmons have energies orders of magnitude larger than those of magnons. We show that graphene plasmons form polaritons with the magnons of two-dimensional ferromagnetic insulators, placed up to to half a micrometer apart, with Rabi splittings in the range of 100 GHz (dramatically larger than cavity magnonics). This is facilitated both by the small energy of graphene plasmons and the cooperative super-radiant nature of the plasmon-magnon coupling afforded by phase matching. We show that the coupling can be modulated both electrically and mechanically, and we propose a ferromagnetic resonance experiment implemented with a two-dimensional ferromagnet driven by graphene plasmons.

Keywords: 2D magnets; FMR; magnons; plasmons; polaritons.

Figure 1

Schematic depiction of the heterostructure where strong plasmon–magnon coupling is predicted to occur. (a) Artistic rendition of the plasmon magnetic field, that emanates from the graphene layer and reaches the magnetic layer, and the precession of the spins in a magnon state, with the same wave vector as the plasmon, in the magnetic layer. (b) Scheme of the structure that would display the effect, including a graphene monolayer, a boron nitride decoupling layer, and a magnetic monolayer. The plasmon–magnon coupling is large for decoupling layers as thick as 5 μm.

Figure 2

Main features of the hybrid plasmon–magnon excitation. (a) Spectral density as a function of frequency and wave vector for fixed graphene doping (E_F = 200 meV) and hBN thickness (10 nm). The magnon gap has been set at 3 meV, corresponding to a frequency of ∼0.73 THz. The dashed blue and red lines correspond to the dispersion relations of the bare magnon and plasmon, respectively. The black dot-dashed lines are the approximate dispersions of the hybrid plasmon–magnon modes given by eq 12. (b) Rabi splitting as a function of hBN thickness for different graphene doping levels (shown in the figure). The magnon gap is the same as in (a). (c) Fermi energy of graphene for which the maximum Rabi splitting is obtained, as a function of the magnon frequency (blue curve, left vertical axes), and the respective maximal splitting (red curve, right vertical axis). (d) Rabi splitting as a function of graphene gating level for different magnon frequencies (shown in the figure), at a fixed hBN thickness of 10 nm.

Figure 3

Attenuated total reflection experiment to probe the plasmon–magnon coupling. (a) Scheme of the setup. (b) Spectral density as a function of wave vector and frequency for a magnon energy of 3 meV and graphene doping corresponding to a Fermi energy of 500 meV. The spectral window probed by this experiment lies between the light dispersion relations within hBN (green dashed line) and germanium (violet dashed line). (c) Spectral density for the wave vector and frequency indicated by the black dot in (b), as a function of and external magnetic field perpendicular to the plane of the heterostructure. The plasmon lifetime has been chosen as ∼5 ns, in line with the intrinsic lifetimes given in ref (36). (d) Effect of experimentally determined plasmon (40 ps) and magnon (2 ns) lifetimes on the optically detected ferromagnetic resonance, as discussed in the main text.