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 length scale defined by the exchange length. We show that due to the symmetry of the three-magnon coupling, the decay rate is linear in $\Delta H=(H_c-H)$ in the vicinity of the threshold field $H_c$ instead of the steplike ${\Gamma }_{\mathbf{k}=0}\propto \Theta \left(\Delta H\right)$ 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: ${\Gamma }_{\mathbf{k}=0}\propto {\left|\Delta H\right|}^{3/2}$.

Figure 1

(a) 2D plot of magnon dispersion in YIG in the lowest-mode approximation, Eq. (1), for $H=1000$ Oe, $d=5$ $\mu$m, and in $k_z>0$ sector. Inset: axes conventions relative to the film and the field/magnetization direction. (b) 2D magnon density of states (DOS) for several representative field values, $E$ is in GHz.

Figure 2

$d$-$H$ decay diagram for YIG, shaded area is where decays are allowed. Solid (dashed) boundary is the numerical (analytical) solution for the threshold boundary, see text. $H_{\max }$ and $d_{\min }$ are shown. Inset: $2E_{\min }/E_0$ vs $H$ for several $d$'s, upper threshold fields are indicated.

Figure 3

The $T=0$ decay rate ${\Gamma }_{\mathbf{k}=0}$ vs $H$ for $d=2$, 5, and 10 $\mu$m. Dotted line is $\frac{1}{5}{\Gamma }_{\mathbf{k}=0}$ for $d=10$ $\mu$m with the angular dependence of the three-magnon coupling omitted, $V_{0;\mathbf{q},-\mathbf{q}}^{\left(3\right)}\Rightarrow V_0$.

Figure 4

Same as in Fig. 3, but for $T=300$ K.