Field-dependence of magnon decay in yttrium iron garnet thin films

We discuss threshold field-dependence of the decay rate of the uniform magnon mode in yttrium iron garnet (YIG) thin films. We demonstrate that decays must cease to exist in YIG films of thickness less than 1 \mu m, the lengthscale defined by the exchange length. We show that due to the symmetry of the three-magnon coupling the decay rate is linear in \Delta H=(Hc-H) in the vicinity of the threshold field Hc instead of the step-like \Gamma \Theta(\Delta H) expected from the two-dimensional character of magnon excitations in such films. For thicker films, the decay rate should exhibit multiple steps due to thresholds for decays into a sequence of the two-dimensional magnon bands. For yet thicker films, such thresholds merge and crossover to the three-dimensional single-mode behavior: \Gamma |\Delta H|^{3/2}.