Magnon-Polaron

Spin-lattice coupling — magnon-phonon anticrossing & hybridized modes

Parameters

Magnon-polaron:
H = ω_m a†a + ω_ph b†b
+ λ(a†b + ab†)

Anticrossing gap: 2λ
at k where ω_m = ω_ph

Hybridized modes:
ω± = ½(ω_m+ω_ph) ± R
R = √(λ² + δ²/4)