Parallel-Pumped Spin-Wave Instability Threshold Characteristics in Polycrystalline Yttrium Iron Garnet Excited by the Varied Rising-Edge Microwave Pulses

The parallel-pumped spin-wave instability (SWI) threshold power,
$P_{\mathrm {th}}$
, of polycrystalline yttrium iron garnet (YIG) excited by microwave pulses with the varied rising-edge time was investigated theoretically and experimentally. The SWI threshold model associated with the rising-edge time
$t_{r}$
is developed in terms of the attributes of half-frequency spin waves in the applied static fields
$H_{\mathrm {ext}}$
. The results manifest a significant increase in microwave-excited SWI threshold power level when the rising-edge time
$t_{r}$
is shortened from 600 to 100 ns at the X-band. In addition, the rising-edge microwave pulses with different time scale distinctly present different threshold responses under the left-wing field region of the butterfly curves. The SWI thresholds associated with the spin-wave initial amplitude grow with increasing
$H_{\mathrm {ext}}$
when
$t_{r}$
is smaller than the spin-wave relaxation time (
$t_{r}~ \boldsymbol {\le }~200$
ns), while SWI thresholds are more sensitive to the
$k$
-dependent spin-wave linewidth, which decreases with the increasing
$H_{\mathrm {ext}}$
as
$t_{r}$
exceeds the spin-wave relaxation time (
$t_{r} ~ \boldsymbol {\ge }~400$
ns). The calculated responses of the SWI threshold are in close agreement with the measurements.